[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 - - 1 1 1 1 1 - - - - - - - - 1 1 - - 1 1 1 1 - - - - 1 1 - - 1 1 1 1]
[1 - - 1 1 1 1 - - 1 - 1 1 1 - 1 - - 1 1 - 1 - 1 - - - 1 - 1 - 1 - 1 - -]
[1 - - 1 1 1 1 - 1 - 1 - 1 1 1 - - - 1 1 1 - 1 - - - 1 - 1 - 1 - 1 - - -]
[1 1 1 - - 1 1 - - 1 - - - 1 - - - 1 - 1 - 1 1 1 - 1 1 1 1 - 1 - - - - 1]
[1 1 1 - - 1 1 - 1 - - - 1 - - - 1 - 1 - 1 - 1 1 1 - 1 1 - 1 - 1 - - 1 -]
[1 1 1 1 - - 1 - - - 1 - 1 - 1 1 - 1 - - - 1 1 - 1 - - - 1 1 1 1 - 1 - -]
[1 1 1 - 1 1 - - - - - 1 - 1 1 1 1 - - - 1 - - 1 - 1 - - 1 1 1 1 1 - - -]
[1 1 1 1 - - 1 - - 1 1 1 - - - 1 - - 1 - 1 - - 1 - - 1 - - - 1 - 1 1 1 1]
[1 1 1 - 1 1 - - 1 - 1 1 - - 1 - - - - 1 - 1 1 - - - - 1 - - - 1 1 1 1 1]
[1 - - 1 - 1 - - 1 1 - - - - 1 - - 1 - 1 - - - 1 1 1 1 - - 1 1 1 1 1 1 -]
[1 - - - 1 - 1 - 1 1 - - - - - 1 1 - 1 - - - 1 - 1 1 - 1 1 - 1 1 1 1 - 1]
[1 - - - 1 - 1 - 1 - - 1 1 - 1 1 - 1 - - 1 1 - - - 1 1 1 - 1 1 - - - 1 1]
[1 - - 1 - 1 - - - 1 1 - - 1 1 1 1 - - - 1 1 - - 1 - 1 1 1 - - 1 - - 1 1]
[1 1 1 1 1 - - - - 1 - - 1 - 1 - 1 1 1 1 1 - - - - 1 - 1 1 - - - - 1 1 -]
[1 1 1 1 1 - - - 1 - - - - 1 - 1 1 1 1 1 - 1 - - 1 - 1 - - 1 - - 1 - - 1]
[1 - - - - - - - - - 1 1 1 - - 1 1 1 1 1 - 1 1 1 - 1 1 - 1 - - 1 1 - 1 -]
[1 - - - - - - - - - 1 1 - 1 1 - 1 1 1 1 1 - 1 1 1 - - 1 - 1 1 - - 1 - 1]
[1 1 - - - - 1 1 1 1 - 1 - 1 1 1 1 - - 1 - - 1 - - - 1 - 1 1 - - - 1 1 -]
[1 1 - - - 1 - 1 1 1 1 - 1 - 1 1 - 1 1 - - - - 1 - - - 1 1 1 - - 1 - - 1]
[1 1 - - - 1 1 - 1 1 1 1 1 1 - - 1 1 - - 1 1 - - 1 1 - - - - - - 1 1 - -]
[1 - 1 1 1 - - - 1 1 1 1 1 1 - - - - - - - - 1 1 1 1 - - 1 1 - - - - 1 1]
[1 - 1 1 - 1 1 1 - - - 1 - 1 1 1 - 1 1 - - - 1 - 1 1 - 1 - - - - 1 - 1 -]
[1 - 1 - 1 1 1 1 - - 1 - 1 - 1 1 1 - - 1 - - - 1 1 1 1 - - - - - - 1 - 1]
[1 - 1 1 - 1 - 1 1 1 - 1 1 - - 1 1 1 - 1 1 - 1 - - - - - - - 1 1 - - - 1]
[1 - 1 - 1 - 1 1 1 1 1 - - 1 1 - 1 1 1 - - 1 - 1 - - - - - - 1 1 - - 1 -]
[1 - 1 - 1 - 1 1 - 1 1 1 - - - - - 1 - 1 1 - - - 1 - 1 1 1 1 - 1 1 - - -]
[1 - 1 1 - 1 - 1 1 - 1 1 - - - - 1 - 1 - - 1 - - - 1 1 1 1 1 1 - - 1 - -]
[1 1 - - 1 1 - 1 - - - 1 1 1 - - - 1 1 - - - - - 1 - 1 - 1 - 1 1 - 1 1 1]
[1 1 - 1 - - 1 1 - - 1 - 1 1 - - 1 - - 1 - - - - - 1 - 1 - 1 1 1 1 - 1 1]
[1 1 - - 1 1 - 1 - 1 1 - - - - 1 - - 1 1 1 1 1 - 1 1 - - - 1 1 - - - 1 -]
[1 1 - 1 - - 1 1 1 - - 1 - - 1 - - - 1 1 1 1 - 1 1 1 - - 1 - - 1 - - - 1]
[1 1 - 1 1 - - 1 1 - 1 - - 1 - 1 - 1 - - 1 - 1 1 - 1 1 1 - - - 1 - 1 - -]
[1 1 - 1 1 - - 1 - 1 - 1 1 - 1 - 1 - - - - 1 1 1 1 - 1 1 - - 1 - 1 - - -]
[1 - 1 - - - - 1 1 - - - 1 1 - 1 - - - 1 1 1 - 1 1 - - 1 1 - 1 - 1 1 1 -]
[1 - 1 - - - - 1 - 1 - - 1 1 1 - - - 1 - 1 1 1 - - 1 1 - - 1 - 1 1 1 - 1]

Permutation group acting on a set of cardinality 72
Order = 144 = 2^4 * 3^2
    (1, 3, 37, 39)(2, 25, 38, 61)(4, 33, 40, 69)(5, 36, 41, 72)(6, 58, 42,
        22)(7, 26, 43, 62)(8, 16, 44, 52)(9, 63, 45, 27)(10, 55, 46, 19)(11, 53,
        47, 17)(12, 30, 48, 66)(13, 68, 49, 32)(14, 24, 50, 60)(15, 31, 51,
        67)(18, 64, 54, 28)(20, 34, 56, 70)(21, 65, 57, 29)(23, 71, 59, 35)
    (1, 2, 37, 38)(3, 62, 39, 26)(4, 61, 40, 25)(5, 29, 41, 65)(6, 30, 42,
        66)(7, 34, 43, 70)(8, 33, 44, 69)(9, 31, 45, 67)(10, 32, 46, 68)(11, 72,
        47, 36)(12, 71, 48, 35)(13, 64, 49, 28)(14, 63, 50, 27)(15, 20, 51,
        56)(16, 19, 52, 55)(17, 60, 53, 24)(18, 59, 54, 23)(21, 58, 57, 22)
    (3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(23,
        24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(39, 40)(41, 42)(43,
        44)(45, 46)(47, 48)(49, 50)(51, 52)(53, 54)(55, 56)(59, 60)(61, 62)(63,
        64)(65, 66)(67, 68)(69, 70)(71, 72)
Automorphism group has centre of order: 2
Number of regular subgroups: 4
Number of regular subgroups containing zeta: 4
Number of centrally regular subgroups: 4
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 4> <72, 4>
<36, 4> <72, 4>
<36, 4> <72, 4>
<36, 5> <72, 11>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 - - - - - 1 - - 1 - - 1 - - 1 1 - - - 1 1 - 1 1 - 1 1 1 1 1 - 1 1 - 1]
[1 1 - 1 1 1 1 - 1 1 1 - 1 - 1 1 - - 1 1 1 - - 1 - - - - - - 1 - 1 - - -]
[1 - 1 1 1 1 1 1 - 1 - 1 1 1 - - 1 - 1 1 - 1 - - 1 - - - - 1 - - - 1 - -]
[1 1 1 - - - - - - 1 1 1 1 1 1 1 1 1 - - 1 1 1 1 1 1 - - - - - - - - - -]
[1 1 1 - - 1 - - 1 - - 1 1 - 1 - 1 - 1 - 1 1 - - - - 1 1 - 1 - 1 1 - 1 -]
[1 1 1 1 - - - 1 - 1 - - - 1 1 1 - - 1 - 1 - 1 - - - - 1 1 1 1 - - 1 1 -]
[1 1 1 - 1 - 1 - - - 1 - 1 1 - - - 1 1 - - 1 1 - - - 1 - 1 - 1 1 1 1 - -]
[1 - - - 1 1 - - 1 - - - - 1 1 1 1 - 1 - - 1 - 1 1 1 - - 1 - 1 1 - 1 1 -]
[1 - 1 - 1 - 1 - 1 1 1 1 - - 1 - 1 - - 1 - 1 1 - - - - 1 1 - 1 - - - 1 1]
[1 1 - - - 1 - 1 1 1 1 1 - 1 - 1 - - - 1 1 1 - - - - 1 - 1 - - 1 - 1 - 1]
[1 1 - 1 - - - 1 1 - - - 1 1 1 - 1 1 - 1 - 1 - - - 1 - 1 - - 1 - 1 1 - 1]
[1 - 1 - - 1 1 - 1 - - - 1 1 1 1 - 1 - 1 - - 1 1 - - 1 - - 1 - - - 1 1 1]
[1 - - 1 - 1 - - 1 1 1 1 - - - - - 1 1 - - 1 1 1 - 1 1 1 - 1 1 - - 1 - -]
[1 1 1 - - - 1 1 1 - - - - - - - - - 1 1 1 1 1 1 1 1 - - - 1 1 1 - - - 1]
[1 - - 1 - - - - - - 1 1 1 1 - - 1 1 1 1 1 - - 1 - - - - 1 1 1 1 - - 1 1]
[1 1 - 1 1 - 1 1 1 - - 1 1 - - - 1 - - - 1 - 1 1 - 1 1 - 1 - - - - 1 1 -]
[1 - 1 1 - 1 1 1 1 - 1 - - 1 - - - 1 - - 1 1 - 1 1 - - 1 1 - - - 1 - 1 -]
[1 - 1 1 - 1 - - - - 1 - - - 1 - 1 - 1 1 1 - 1 - 1 1 1 - 1 - - - 1 1 - 1]
[1 1 - 1 1 - - - - - - 1 - 1 - 1 - - 1 1 - 1 1 1 1 - 1 1 - - - - 1 - 1 1]
[1 - - 1 - - 1 1 1 - 1 1 - 1 1 1 1 - - - - - 1 - 1 - 1 - - 1 1 1 1 - - -]
[1 - 1 - - - - 1 1 1 - 1 1 - - 1 - 1 1 1 - - - - 1 1 1 - 1 - 1 - 1 - 1 -]
[1 1 - - - - 1 1 - 1 1 - - - 1 - 1 1 1 1 - - - 1 1 - 1 1 - - - 1 - 1 1 -]
[1 - - 1 1 1 - 1 - 1 - - 1 - 1 - - 1 - - 1 1 1 - 1 - 1 - - - 1 1 - - 1 1]
[1 - - - 1 - - - 1 1 1 - 1 1 - - - - - 1 1 - 1 - 1 1 - 1 - 1 - 1 1 1 1 -]
[1 - 1 1 1 - 1 - 1 1 - - - 1 - 1 1 1 1 - 1 - - - - 1 1 1 - - - 1 - - - 1]
[1 1 - - 1 1 - 1 1 - 1 - 1 - - 1 1 1 1 - - - 1 - 1 - - 1 1 1 - - - - - 1]
[1 - 1 1 1 - - 1 - - 1 - 1 - 1 1 - - - 1 - 1 - 1 - 1 1 1 1 1 - 1 - - - -]
[1 - - - 1 - 1 1 - - 1 1 - - 1 1 - 1 1 - 1 1 - - - 1 - - - 1 - - 1 1 1 1]
[1 1 - - 1 1 1 - - - - 1 - 1 1 - - 1 - 1 1 - - - 1 1 1 1 1 1 1 - - - - -]
[1 1 1 1 - 1 1 - - - 1 1 1 - - 1 - - - - - - - - 1 1 - 1 - - 1 1 - 1 1 1]
[1 1 1 1 1 - - - 1 1 - 1 - - 1 - - 1 - - - - - 1 1 - - - 1 1 - 1 1 1 - 1]
[1 1 1 - 1 1 - 1 - 1 1 - - 1 - - 1 - - - - - - 1 - 1 1 - - 1 1 - 1 - 1 1]
[1 - 1 - 1 1 - 1 - - - 1 - - - 1 1 1 - 1 1 - 1 1 - - - 1 - - 1 1 1 1 - -]
[1 - - - - 1 1 1 - 1 - 1 1 1 1 - - - 1 - - - 1 1 - 1 - 1 1 - - 1 1 - - 1]
[1 1 - 1 - 1 1 - - 1 - - - - - 1 1 1 - 1 - 1 1 - - 1 - - 1 1 - 1 1 - 1 -]

Permutation group acting on a set of cardinality 72
Order = 216 = 2^3 * 3^3
    (1, 52, 57, 41, 17, 19, 15, 18, 20)(2, 49, 58, 34, 32, 62, 6, 30, 9)(3, 64,
        61, 35, 50, 11, 44, 67, 60)(4, 69, 10, 72, 29, 23, 43, 12, 27)(5, 53,
        55, 51, 54, 56, 37, 16, 21)(7, 48, 63, 40, 33, 46, 36, 65, 59)(8, 31,
        24, 39, 28, 25, 71, 14, 47)(13, 22, 70, 68, 26, 42, 66, 45, 38)
    (1, 2, 37, 38)(3, 40, 39, 4)(5, 70, 41, 34)(6, 51, 42, 15)(7, 8, 43, 44)(9,
        60, 45, 24)(10, 57, 46, 21)(11, 26, 47, 62)(12, 30, 48, 66)(13, 69, 49,
        33)(14, 53, 50, 17)(16, 64, 52, 28)(18, 31, 54, 67)(19, 59, 55, 23)(20,
        63, 56, 27)(22, 25, 58, 61)(29, 32, 65, 68)(35, 36, 71, 72)
    (2, 39, 40)(3, 4, 38)(6, 8, 7)(9, 47, 46)(10, 45, 11)(12, 13, 50)(14, 48,
        49)(16, 53, 54)(17, 18, 52)(19, 57, 20)(21, 56, 55)(22, 60, 23)(24, 59,
        58)(25, 63, 62)(26, 61, 27)(28, 65, 30)(29, 66, 64)(31, 33, 32)(34, 71,
        36)(35, 72, 70)(42, 44, 43)(67, 69, 68)
Automorphism group has centre of order: 6
Number of regular subgroups: 3
Number of regular subgroups containing zeta: 3
Number of centrally regular subgroups: 3
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 3> <72, 3>
<36, 3> <72, 3>
<36, 5> <72, 11>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 - 1 1 1 1 1 1 - - 1 1 - - - 1 - 1 - - 1 - 1 - - - - - - 1 - 1 1 1 -]
[1 - 1 1 1 1 1 1 1 1 1 - - - - - - 1 - 1 - - - - 1 - 1 1 - - - 1 - 1 1 -]
[1 - - - - - - - - 1 1 1 1 - - - 1 1 1 1 - 1 - 1 1 - 1 1 - - 1 1 1 - - 1]
[1 - 1 1 - - 1 1 1 1 - 1 1 1 - 1 - 1 - - - 1 1 1 - - - 1 1 - - - - - - 1]
[1 1 - 1 1 - - 1 1 - 1 - 1 1 1 - - - 1 1 - - 1 - - 1 1 1 - - 1 - - - - 1]
[1 - - - 1 - 1 - - - - - 1 1 - 1 - 1 1 1 - 1 1 - - 1 - 1 - 1 - 1 1 1 1 -]
[1 - - 1 - - - 1 - - - 1 - - 1 - 1 1 - 1 1 - 1 1 - 1 - 1 1 - 1 1 - 1 1 -]
[1 1 - - 1 1 1 1 - 1 - 1 - 1 1 - 1 1 - - - - 1 - 1 1 - - - - - 1 1 - - 1]
[1 - 1 1 1 1 1 - - - 1 1 1 - 1 - - - - 1 1 1 - 1 - 1 - - - 1 - 1 - - - 1]
[1 - - 1 - 1 1 - 1 1 - - 1 - 1 1 1 1 - - 1 - - - - 1 1 1 - 1 1 - 1 - - -]
[1 - - 1 - 1 1 - 1 - 1 1 - 1 - 1 - - 1 1 1 - 1 - 1 - - - 1 - 1 1 1 - - -]
[1 - 1 - - 1 - - 1 - 1 1 - 1 - - 1 - - - 1 1 1 - - 1 1 1 - - - - 1 1 1 1]
[1 - 1 - - 1 - - 1 1 - - 1 - 1 1 - - 1 - - - 1 1 1 1 - - - - 1 1 - 1 1 1]
[1 1 - 1 - - 1 - - - 1 1 - 1 - 1 - 1 - - - - - 1 1 1 1 - - 1 1 - - 1 1 1]
[1 1 - 1 - - 1 - - 1 - - 1 - 1 - - - - 1 1 1 1 - 1 - 1 - 1 - - - 1 1 1 1]
[1 1 1 1 - 1 - - - 1 - 1 1 1 - - 1 - 1 1 - - - - 1 1 - 1 1 1 - - - - 1 -]
[1 1 1 - 1 - - - 1 1 1 1 - - 1 1 - 1 - 1 - 1 - - - 1 - - 1 - 1 - 1 - 1 -]
[1 1 1 - - - 1 1 - - 1 - 1 1 1 1 1 - - - 1 1 - - 1 - - 1 - - 1 1 - - 1 -]
[1 1 1 1 1 - - - - 1 - 1 - 1 1 1 - - 1 - 1 - - 1 - - 1 1 - - - 1 1 1 - -]
[1 1 1 - - 1 - 1 - 1 1 - 1 1 - - - 1 - 1 1 - 1 1 - - - - - 1 1 - 1 1 - -]
[1 1 1 - - - 1 - 1 - 1 1 1 - 1 - 1 1 1 - - - 1 - - - 1 - 1 1 - 1 - 1 - -]
[1 1 1 - 1 1 1 - - - - - - - - - - 1 1 - 1 1 1 1 1 1 1 1 1 - 1 - - - - -]
[1 1 1 1 - - - 1 1 - - - - - - 1 1 - - 1 - 1 1 1 1 1 1 - - 1 - 1 1 - - -]
[1 1 - 1 1 1 - - - 1 1 - - - - 1 1 - - - - 1 1 - - - - 1 1 1 1 1 - 1 - 1]
[1 - 1 1 - 1 - 1 - - - - - 1 1 - - 1 1 - - 1 - - - - 1 - 1 1 1 1 1 - 1 1]
[1 - - - - 1 1 1 - 1 1 - - 1 1 1 1 - 1 1 - 1 - 1 - 1 1 - 1 - - - - 1 - -]
[1 1 - - - - 1 1 1 1 1 - - - - - - - 1 - 1 - - 1 - 1 - 1 1 1 - 1 1 - 1 1]
[1 - - 1 1 - - - 1 1 1 - - 1 1 - 1 1 1 - 1 1 1 1 1 - - - - 1 - - - - 1 -]
[1 - 1 - 1 - 1 - 1 - - - - 1 1 - 1 - - 1 - - - 1 1 - - 1 1 1 1 - 1 1 - 1]
[1 1 - - 1 1 - - 1 - - - 1 1 - 1 1 1 - 1 1 - - 1 - - 1 - 1 - - 1 - - 1 1]
[1 - - - 1 - - 1 1 1 - 1 1 1 - - - - - - 1 1 - - 1 1 1 - 1 1 1 1 - 1 - -]
[1 - 1 - 1 - 1 1 - 1 - 1 - - - 1 1 - 1 1 1 - 1 - - - 1 - - 1 1 - - - 1 1]
[1 - 1 1 1 - - 1 - - 1 - 1 - - 1 1 1 1 - 1 - - - 1 1 - - 1 - - - 1 1 - 1]
[1 1 - - - 1 - 1 1 - - 1 - - 1 1 - 1 1 1 1 1 - - 1 - - 1 - 1 - - - 1 - 1]
[1 - - - 1 1 - 1 - - 1 1 1 - 1 1 - - - - - - 1 1 1 - 1 1 1 1 - - 1 - 1 -]

Permutation group acting on a set of cardinality 72
Order = 432 = 2^4 * 3^3
    (1, 5, 36, 15, 31, 42)(2, 11, 71, 66, 23, 65)(3, 56, 60, 22, 32, 13)(4, 25,
        70, 7, 69, 57)(6, 37, 41, 72, 51, 67)(8, 18)(9, 16, 63, 26, 50, 17)(10,
    19, 48, 46, 55, 12)(14, 53, 45, 52, 27, 62)(20, 24, 58, 68, 49, 39)(21,
        40, 61, 34, 43, 33)(28, 64)(29, 38, 47, 35, 30, 59)(44, 54)
    (2, 3, 40)(4, 38, 39)(5, 43, 6)(7, 42, 41)(8, 45, 46)(9, 10, 44)(11, 51,
        49)(12, 52, 50)(13, 47, 15)(14, 48, 16)(17, 18, 19)(20, 22, 21)(25, 30,
        65)(26, 63, 28)(27, 64, 62)(29, 61, 66)(31, 33, 68)(32, 67, 69)(34, 72,
        35)(36, 71, 70)(53, 54, 55)(56, 58, 57)
    (5, 10)(6, 9)(7, 8)(11, 12)(13, 14)(15, 16)(17, 22)(18, 21)(19, 20)(23,
        24)(25, 28)(26, 30)(27, 29)(31, 35)(32, 36)(33, 34)(41, 46)(42, 45)(43,
        44)(47, 48)(49, 50)(51, 52)(53, 58)(54, 57)(55, 56)(59, 60)(61, 64)(62,
        66)(63, 65)(67, 71)(68, 72)(69, 70)
Automorphism group has centre of order: 2
Number of regular subgroups: 3
Number of regular subgroups containing zeta: 3
Number of centrally regular subgroups: 3
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 5> <72, 11>
<36, 3> <72, 3>
<36, 4> <72, 4>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 - - 1 1 1 - - 1 - 1 1 1 - - - - - 1 1 - - 1 - 1 - - 1 1 - 1 - 1 1 - 1]
[1 1 - 1 1 - 1 - 1 1 1 - - 1 - 1 - - 1 - 1 - - - - - 1 1 - 1 1 - 1 - 1 -]
[1 1 1 - - 1 1 1 - - 1 - 1 - - 1 - 1 1 1 1 - - - 1 1 - - - - 1 1 1 - - -]
[1 - - 1 1 - 1 1 - - 1 - 1 - 1 - - 1 - 1 - - 1 1 - 1 1 - - 1 1 - - 1 1 -]
[1 - 1 - - - - 1 - 1 1 1 - 1 - - 1 1 1 - - - 1 - 1 1 1 1 - 1 1 - - - - 1]
[1 - 1 - - 1 1 1 - 1 1 - 1 1 1 1 - - 1 - - 1 1 - - - - 1 1 - - - - 1 1 -]
[1 1 1 - - - - - - - 1 - 1 - - - 1 1 - - 1 1 - 1 - - 1 1 1 - 1 - 1 1 1 1]
[1 1 1 - - 1 - - 1 - - 1 - 1 1 - - 1 1 1 - - - 1 - 1 - 1 - 1 - - 1 1 1 -]
[1 1 - 1 1 1 - 1 - 1 - - - - 1 - - 1 1 - - 1 - 1 1 - - 1 - - 1 1 - - 1 1]
[1 - 1 1 - 1 - - 1 - 1 - - - - - - - 1 - 1 1 1 1 1 1 1 - 1 1 - 1 - - 1 -]
[1 1 1 - 1 - 1 - - - - 1 1 1 1 - - - - - 1 - 1 1 1 - - 1 1 1 1 1 - - - -]
[1 1 1 - 1 1 1 - 1 1 - - 1 - - - 1 - - 1 - - 1 - - 1 1 1 - - - 1 - - 1 1]
[1 1 - 1 - - 1 1 - - - - - - 1 - 1 - 1 1 1 1 1 - - 1 - 1 1 1 - - 1 - - 1]
[1 - 1 1 - - - 1 1 1 - - 1 1 1 - 1 - 1 1 - - - 1 - - 1 - 1 - 1 1 1 - - -]
[1 - 1 - 1 - - - - 1 1 1 - - 1 1 - - - 1 - 1 - - - 1 - - 1 1 1 1 1 - 1 1]
[1 - 1 1 - - 1 - 1 - - 1 - - 1 1 1 1 1 - 1 - 1 - - - - - - - 1 1 - 1 1 1]
[1 - - 1 - 1 - - - - - 1 1 1 1 1 1 - - 1 1 1 - - 1 1 1 1 - - 1 - - - 1 -]
[1 - - - 1 1 1 - 1 - - - 1 1 - 1 1 1 1 - - 1 - 1 - 1 - - 1 1 1 - - - - 1]
[1 1 - - 1 1 - - - 1 1 1 - - 1 1 1 1 1 1 1 - 1 1 - - 1 - 1 - - - - - - -]
[1 - - - 1 - - - - 1 - - 1 1 - - 1 1 1 1 1 1 1 - 1 - - - - 1 - 1 1 1 1 -]
[1 1 - 1 - 1 1 - - 1 1 1 - 1 - - 1 - - - - 1 1 1 - 1 - - - - 1 1 1 1 - -]
[1 - - - 1 - 1 1 - - - 1 - - - 1 1 - 1 - - - - 1 1 1 1 1 1 - - 1 1 1 1 -]
[1 1 - - 1 - - 1 1 - 1 1 1 1 1 - - - 1 - 1 1 - - - 1 1 - - - - 1 - 1 - 1]
[1 1 1 1 - - 1 - - 1 - 1 1 - - 1 - - 1 1 - 1 - 1 1 - 1 - - 1 - - - 1 - 1]
[1 1 - 1 - 1 - 1 - - - 1 1 1 - 1 - 1 - - - - 1 - - - 1 - 1 1 - 1 1 - 1 1]
[1 1 - 1 - - - - 1 1 1 - 1 - 1 1 1 1 - - - - - - 1 1 - 1 1 1 - 1 - 1 - -]
[1 1 1 - 1 1 - 1 1 - - - - - 1 1 1 - - - - 1 1 - 1 - 1 - - 1 1 - 1 1 - -]
[1 - 1 1 1 1 - 1 - - 1 - - 1 - 1 1 - - 1 1 - - 1 - - - 1 - 1 - 1 - 1 - 1]
[1 1 - - - - - 1 1 1 - - - 1 - 1 - - - 1 1 - 1 1 1 1 - - 1 - 1 - - 1 1 1]
[1 - - - - 1 1 1 1 1 1 1 1 - 1 - 1 - - - 1 - - 1 1 - - - - 1 - - 1 - 1 1]
[1 1 1 1 1 - 1 1 1 - 1 1 - 1 - - 1 1 - 1 - 1 - - 1 - - - 1 - - - - - 1 -]
[1 - 1 1 1 - - 1 1 1 - 1 1 - - 1 - 1 - - 1 1 1 1 - 1 - 1 - - - - 1 - - -]
[1 - - - - 1 1 1 1 1 - 1 - - - - - 1 - 1 1 1 - - - - 1 1 1 1 1 1 - 1 - -]
[1 - - - - - 1 - 1 - 1 - - 1 1 1 - 1 - 1 - 1 1 1 1 - 1 1 - - - 1 1 - - 1]
[1 - 1 1 1 1 1 - - 1 - - - 1 1 - - 1 - - 1 - - - 1 1 1 - 1 - - - 1 1 - 1]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 62, 38, 34, 52, 13, 37, 26, 2, 70, 16, 49)(3, 5, 40, 21, 46, 69, 39, 41,
        4, 57, 10, 33)(6, 9, 48, 61, 35, 59, 42, 45, 12, 25, 71, 23)(7, 18, 63,
        64, 44, 67, 43, 54, 27, 28, 8, 31)(11, 36, 32, 58, 56, 29, 47, 72, 68,
        22, 20, 65)(14, 51, 17, 19, 30, 60, 50, 15, 53, 55, 66, 24)
    (1, 3, 68, 51, 7, 45, 37, 39, 32, 15, 43, 9)(2, 46, 56, 60, 27, 23, 38, 10,
        20, 24, 63, 59)(4, 11, 55, 44, 61, 16, 40, 47, 19, 8, 25, 52)(5, 13, 48,
        31, 53, 72, 41, 49, 12, 67, 17, 36)(6, 18, 50, 22, 69, 62, 42, 54, 14,
        58, 33, 26)(21, 34, 35, 28, 66, 29, 57, 70, 71, 64, 30, 65)
Automorphism group has centre of order: 2
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 10> <72, 24>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 - - 1 1 1 1 - 1 1 - 1 1 - 1 1 - 1 - 1 1 1 - 1 - 1 - - - - - - - - 1 -]
[1 - - 1 1 - 1 1 - - 1 1 1 1 - - - 1 - - - - 1 1 - - 1 1 - - - 1 1 1 1 -]
[1 - - 1 1 - - - 1 1 - - - - - - 1 1 - - 1 1 1 - 1 - 1 1 1 1 - - - 1 1 1]
[1 1 1 - - - 1 - 1 - 1 - 1 1 - - 1 1 - - 1 1 - - 1 1 - - - - 1 - 1 1 1 -]
[1 1 1 - 1 - 1 - 1 1 1 - 1 - - 1 1 - - - - - - 1 - 1 1 1 1 - - 1 - - - 1]
[1 1 1 - 1 - - 1 - - - 1 - - 1 - 1 1 - 1 1 - 1 - - 1 1 - - - 1 1 - - 1 1]
[1 1 1 - 1 1 - - 1 1 - 1 - 1 - 1 - - - - 1 - 1 1 - - 1 - - 1 1 - 1 1 - -]
[1 - - 1 - - - 1 1 1 1 1 - - - - 1 - 1 - 1 1 1 1 - 1 - - 1 - 1 1 1 - - -]
[1 - - 1 - 1 1 - - - - - - 1 - 1 1 - - 1 1 - - - - 1 1 1 1 1 1 1 1 - 1 -]
[1 - - - 1 1 - 1 1 - - - 1 - - 1 - - - 1 - 1 1 - 1 1 - 1 - - 1 1 1 1 - 1]
[1 1 1 1 - 1 - 1 - 1 - - 1 - - 1 - 1 1 - - - 1 - 1 1 1 - 1 - - - 1 - 1 -]
[1 - - - 1 - - 1 - - - - 1 1 1 1 1 1 1 - 1 - - 1 - 1 - - 1 1 - - 1 1 - 1]
[1 - - - 1 - 1 1 - 1 1 1 - 1 - 1 - - 1 - - 1 - - 1 1 1 - - 1 1 - - - 1 1]
[1 1 1 1 - 1 1 1 - - - 1 - - - - - 1 - - - 1 - 1 - 1 - 1 1 1 1 - - 1 - 1]
[1 1 1 1 1 - - - 1 - - 1 1 1 - - - - 1 1 - 1 - - - - - - 1 1 - 1 1 - 1 1]
[1 1 1 1 1 - 1 1 - - - - - 1 - 1 1 - 1 1 1 1 1 1 1 - - 1 - - - - - - - -]
[1 - - - - 1 1 - 1 - - 1 1 1 - - 1 1 1 1 - - 1 1 1 - 1 - 1 - 1 - - - - 1]
[1 - 1 - - - - - - - - 1 1 - 1 1 - - 1 - 1 1 - 1 1 - 1 1 1 - 1 1 - 1 1 -]
[1 1 - 1 1 1 1 - - 1 - - - - 1 - 1 - 1 - - - - 1 1 - - - - - 1 1 1 1 1 1]
[1 - 1 - - 1 1 1 1 1 - - - 1 1 - - 1 1 - 1 1 - - - - 1 1 - - - 1 1 - - 1]
[1 1 - - - 1 - 1 1 - 1 - - - - 1 1 1 1 1 - 1 - 1 - - 1 - - 1 - 1 - 1 1 -]
[1 1 - - - - 1 - - 1 - 1 1 - 1 - 1 - 1 1 - 1 1 - - 1 1 1 - 1 - - 1 1 - -]
[1 - 1 1 1 - - - 1 - 1 - - - 1 - - 1 1 1 - - - 1 1 1 1 1 - 1 1 - 1 - - -]
[1 1 - - - - - - - 1 1 - - 1 1 1 - 1 - 1 - 1 1 1 - - - 1 1 - 1 - 1 - 1 1]
[1 - 1 - - - 1 1 1 1 - - - 1 1 - - - - 1 - - 1 1 1 1 - - 1 1 - 1 - 1 1 -]
[1 - 1 1 1 1 - 1 - 1 1 - 1 1 1 - 1 - - 1 - 1 - - - - 1 - 1 - 1 - - 1 - -]
[1 - 1 - - 1 - 1 - 1 1 1 1 - - - 1 - - 1 1 - - 1 1 - - 1 - 1 - - 1 - 1 1]
[1 1 - 1 - - - 1 1 1 - 1 1 1 1 1 1 1 - - - - - - 1 - - 1 - 1 1 1 - - - -]
[1 - 1 1 - 1 - - 1 - 1 1 - 1 1 1 1 - 1 - - - 1 - - 1 - 1 - - - - - 1 1 1]
[1 - 1 1 - - 1 - - 1 1 - 1 - - 1 - 1 1 1 1 - 1 - - - - - - 1 1 1 - 1 - 1]
[1 1 - - 1 1 - - - 1 1 1 - 1 - - - 1 1 1 1 - - - 1 1 - 1 1 - - 1 - 1 - -]
[1 1 - - 1 1 1 1 1 - 1 - 1 - 1 - - - 1 - 1 - 1 - - - - 1 1 1 1 - - - 1 -]
[1 1 - 1 - 1 - - - - 1 - 1 1 1 - - - - - 1 1 1 1 1 1 1 - - 1 - 1 - - - 1]
[1 - 1 - 1 1 1 - - - 1 1 - - 1 1 1 1 - - - 1 1 - 1 - - - 1 1 - 1 1 - - -]
[1 1 - 1 - - 1 1 1 - 1 1 - - 1 1 - - - 1 1 - - - 1 - 1 - 1 - - - 1 1 - 1]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 45, 37, 9)(2, 71, 38, 35)(3, 40, 39, 4)(5, 53, 41, 17)(6, 62, 42, 26)(7,
        31, 43, 67)(8, 23, 44, 59)(10, 13, 46, 49)(11, 68, 47, 32)(12, 58, 48,
        22)(14, 28, 50, 64)(15, 16, 51, 52)(18, 66, 54, 30)(19, 57, 55, 21)(20,
        29, 56, 65)(24, 34, 60, 70)(25, 33, 61, 69)(27, 72, 63, 36)
    (1, 3, 66, 50, 67, 16, 37, 39, 30, 14, 31, 52)(2, 25, 65, 21, 72, 8, 38, 61,
        29, 57, 36, 44)(4, 41, 51, 49, 64, 22, 40, 5, 15, 13, 28, 58)(6, 35, 47,
        63, 24, 20, 42, 71, 11, 27, 60, 56)(7, 19, 54, 33, 45, 59, 43, 55, 18,
        69, 9, 23)(10, 32, 17, 62, 48, 70, 46, 68, 53, 26, 12, 34)
Automorphism group has centre of order: 2
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 10> <72, 24>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 - - - 1 1 1 1 - 1 - 1 - 1 - 1 - 1 - - 1 - - 1 - - - 1 - - 1 1 1 -]
[1 - - 1 1 - - 1 1 1 1 1 - - 1 - 1 1 - - 1 - 1 - - - - 1 1 - 1 - - 1 1 -]
[1 - - 1 1 1 1 - 1 - - 1 1 - - 1 1 - - - - - 1 1 - 1 1 1 - 1 - - - - 1 1]
[1 - - 1 1 1 1 1 - - - - - 1 1 1 1 - 1 1 1 1 1 - - 1 - - - - 1 - 1 - - -]
[1 1 1 - - 1 - 1 - - - 1 1 - - - 1 - 1 - 1 - - - - 1 1 - 1 - 1 - 1 1 1 1]
[1 1 1 - - - 1 - - 1 1 1 - - 1 - 1 - - - 1 1 1 1 - 1 1 - - 1 1 1 - - - -]
[1 - - 1 - - 1 - - - 1 1 1 1 1 1 - - 1 1 1 - - - - - 1 - 1 1 - 1 - 1 1 -]
[1 - - 1 - 1 - - 1 1 1 1 - - - - - 1 1 1 1 1 - 1 1 1 1 - - - - - 1 - 1 -]
[1 1 1 - 1 1 - - 1 - 1 - - 1 1 1 - - 1 - - - 1 1 1 - 1 - - - 1 - - 1 1 -]
[1 1 1 1 - - 1 1 1 - 1 - 1 1 - - - - - 1 1 1 - 1 - - - 1 - - 1 - - - 1 1]
[1 1 1 1 - 1 - - - - 1 - 1 - - 1 1 1 - 1 1 - 1 - 1 1 - 1 - - - 1 - 1 - -]
[1 - - - 1 1 1 - - 1 1 - - 1 - - - - - - 1 - - - 1 1 - 1 - 1 1 1 1 1 1 1]
[1 - - - - 1 1 1 - - 1 1 1 1 1 - - 1 - - - 1 1 1 1 1 - - 1 - - - - 1 - 1]
[1 - - - - - - 1 1 - - 1 1 - - 1 - - 1 - 1 1 1 1 1 - - 1 - 1 1 1 1 1 - -]
[1 - - - - 1 - 1 1 1 1 - 1 1 - - 1 1 1 1 - - 1 - - - 1 - - 1 1 1 - - - 1]
[1 1 1 1 1 1 - - - 1 1 1 1 1 - - - - 1 - - 1 1 - - - - 1 1 1 - - 1 - - -]
[1 1 1 1 1 1 1 1 1 - - 1 - - 1 - - 1 1 - 1 - - - 1 - - - - 1 - 1 - - - 1]
[1 1 - 1 1 - - 1 - 1 - - 1 1 - 1 - 1 - - 1 - - 1 1 1 1 - 1 1 1 - - - - -]
[1 - 1 - - 1 - 1 - 1 - - - - 1 1 - - - 1 1 1 1 - 1 - 1 1 1 1 - - - - 1 1]
[1 - 1 1 1 - - 1 1 1 1 - 1 - 1 1 - - - - - 1 - - - 1 1 - - - - 1 1 1 - 1]
[1 1 - - - 1 1 - 1 1 - - 1 - 1 1 - 1 1 - - 1 - - - 1 - 1 1 - 1 1 - - 1 -]
[1 - 1 1 1 - - - - - - - - - - - - 1 1 1 - 1 1 1 - 1 - - 1 1 1 1 - 1 1 1]
[1 - 1 - - - - - 1 - 1 - - 1 1 1 1 1 1 - 1 - - 1 - 1 - 1 1 1 - - 1 - - 1]
[1 1 - 1 - - 1 1 - 1 1 - - - - 1 1 - 1 - - - 1 1 1 - - - 1 - - 1 1 - 1 1]
[1 1 - - 1 - 1 1 1 - 1 - - - - - 1 - 1 1 - 1 - - 1 1 1 1 1 1 - - - 1 - -]
[1 - 1 - 1 1 1 1 - - 1 1 - - - 1 - 1 - 1 - - - 1 - - 1 1 1 - 1 1 1 - - -]
[1 1 - - 1 - 1 - - 1 - - 1 - 1 - - 1 1 1 1 - 1 1 - - 1 1 - - - - 1 1 - 1]
[1 - 1 - 1 - - 1 - 1 - 1 1 1 1 - 1 - 1 1 - - - 1 1 1 - 1 - - - 1 - - 1 -]
[1 1 - - 1 1 - - 1 1 - 1 - 1 - 1 1 - - 1 1 1 - 1 - - - - 1 - - 1 - 1 - 1]
[1 1 - 1 - 1 - 1 - - - - - 1 1 - 1 1 - - - 1 - 1 - - 1 1 - 1 - 1 1 1 1 -]
[1 - 1 1 - - 1 - - 1 - 1 - 1 - 1 1 1 1 - - 1 - - 1 - 1 1 - - 1 - - 1 - 1]
[1 1 - - 1 - - - - - 1 1 1 - 1 1 1 1 - 1 - 1 - - 1 - - - - 1 1 - 1 - 1 1]
[1 - 1 1 - 1 1 - 1 1 - - 1 - 1 - 1 - - 1 - - - 1 1 - - - 1 1 1 - 1 1 - -]
[1 - 1 - 1 - 1 - 1 - - - 1 1 - - 1 1 - - 1 1 1 - 1 - 1 - 1 - - 1 1 - 1 -]
[1 1 - 1 - - - - 1 - - 1 - 1 1 - - - - 1 - - 1 - 1 1 1 1 1 - 1 1 1 - - 1]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 52, 37, 16)(2, 42, 38, 6)(3, 5, 39, 41)(4, 55, 40, 19)(7, 46, 43, 10)(8,
        57, 44, 21)(9, 18, 45, 54)(11, 53, 47, 17)(12, 35, 48, 71)(13, 69, 49,
        33)(14, 72, 50, 36)(15, 22, 51, 58)(20, 32, 56, 68)(23, 26, 59, 62)(24,
        28, 60, 64)(25, 65, 61, 29)(27, 67, 63, 31)(30, 34, 66, 70)
    (1, 50, 37, 14)(2, 33, 38, 69)(3, 45, 39, 9)(4, 48, 40, 12)(5, 68, 41,
        32)(6, 10, 42, 46)(7, 13, 43, 49)(8, 27, 44, 63)(11, 28, 47, 64)(15, 19,
        51, 55)(16, 26, 52, 62)(17, 61, 53, 25)(18, 56, 54, 20)(21, 70, 57,
        34)(22, 35, 58, 71)(23, 72, 59, 36)(24, 29, 60, 65)(30, 67, 66, 31)
    (1, 3, 47, 37, 39, 11)(2, 71, 57, 38, 35, 21)(4, 63, 10, 40, 27, 46)(5, 17,
    16, 41, 53, 52)(6, 48, 8, 42, 12, 44)(7, 19, 67, 43, 55, 31)(9, 28, 50,
        45, 64, 14)(13, 51, 66, 49, 15, 30)(18, 60, 36, 54, 24, 72)(20, 29, 59,
        56, 65, 23)(22, 34, 69, 58, 70, 33)(25, 62, 68, 61, 26, 32)
    (1, 2, 37, 38)(3, 21, 39, 57)(4, 61, 40, 25)(5, 44, 41, 8)(6, 16, 42, 52)(7,
        59, 43, 23)(9, 70, 45, 34)(10, 62, 46, 26)(11, 71, 47, 35)(12, 53, 48,
    17)(13, 72, 49, 36)(14, 33, 50, 69)(15, 60, 51, 24)(18, 66, 54, 30)(19,
        29, 55, 65)(20, 31, 56, 67)(22, 28, 58, 64)(27, 32, 63, 68)
Automorphism group has centre of order: 2
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 10> <72, 24>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 - 1 - - - - 1 - 1 1 - 1 - - 1 - - - - 1 - 1 1 1 1 1 1 1 1 - 1 1 - - -]
[1 1 1 - - - - 1 - - - 1 1 1 1 1 1 - - 1 - 1 - - - 1 1 1 1 - 1 - - - 1 -]
[1 - - 1 1 - - 1 - - 1 1 1 1 - 1 - 1 1 1 1 - 1 - - - - 1 - - - - 1 - 1 1]
[1 1 - 1 1 - 1 - - - - - 1 - 1 - 1 - - - - - 1 - 1 - - 1 1 1 1 1 1 - 1 1]
[1 - - 1 1 1 - - - 1 1 1 - 1 1 1 1 - - - - 1 1 1 - - 1 - - 1 1 - 1 - - -]
[1 - - 1 1 1 - 1 - 1 1 - 1 - - - 1 1 1 - - 1 - - 1 1 - 1 1 - 1 - - 1 - -]
[1 1 1 - - 1 1 - 1 1 1 1 1 - - - - 1 1 - - - 1 - - - 1 - 1 - 1 - 1 - 1 -]
[1 1 - 1 1 1 - - 1 - 1 - 1 - - 1 - - - 1 - - - 1 - 1 1 - 1 1 - - - 1 1 1]
[1 - 1 - - - - 1 1 1 1 - - - 1 - 1 1 - 1 - - - 1 - - - 1 - 1 1 - 1 1 1 1]
[1 - 1 - 1 - 1 - - - - - 1 1 - 1 1 1 1 - - - - 1 - 1 1 - - - 1 1 1 1 - 1]
[1 1 - - 1 - - - - 1 - 1 - - - 1 - 1 - 1 1 1 - 1 1 - - - 1 - 1 1 1 1 1 -]
[1 - - - 1 - 1 1 1 - 1 1 - - 1 1 1 1 1 1 - - - - 1 - 1 - 1 1 - 1 - - - -]
[1 1 1 1 - - - - - - 1 - - 1 1 - - 1 1 1 - 1 1 - - 1 - - 1 1 - 1 1 1 - -]
[1 1 - 1 - - 1 1 - 1 1 - 1 - 1 - - - 1 1 1 1 - 1 - - 1 - - - 1 1 - - - 1]
[1 - 1 1 - 1 1 - 1 - 1 1 - - - 1 - - - 1 - 1 - - 1 1 - 1 - - 1 1 1 - - 1]
[1 1 - 1 - 1 - 1 1 - - 1 1 1 1 - - 1 - - - - - 1 1 - 1 1 - - - 1 1 1 - -]
[1 1 1 - 1 - - - 1 - 1 1 1 - 1 - 1 1 - - 1 1 1 1 1 1 - - - - - - - - - 1]
[1 - - 1 - - 1 1 1 - 1 1 - 1 - - 1 - - - 1 - 1 1 - 1 - - 1 - 1 1 - 1 1 -]
[1 - 1 - 1 1 1 1 - - 1 - - 1 1 - - - - - 1 1 - - 1 - 1 - 1 - - - 1 1 1 1]
[1 - 1 1 - 1 - - - - - 1 - - - - 1 1 1 - 1 1 - 1 - - 1 1 1 1 - 1 - - 1 1]
[1 1 - - 1 - 1 1 1 1 - 1 - 1 - - - - 1 - - 1 - 1 - 1 - 1 1 1 - - 1 - - 1]
[1 - - - 1 1 - - 1 1 - - - 1 1 - - 1 - 1 1 - 1 - - 1 1 1 1 - 1 1 - - - 1]
[1 1 1 1 - 1 1 1 - 1 - - - 1 - 1 1 1 - 1 - - 1 1 1 - - - 1 - - - - - - 1]
[1 1 1 - 1 1 1 - - 1 1 1 1 1 - - 1 - - 1 1 - - - - - - 1 - 1 - 1 - 1 - -]
[1 - - 1 - - 1 - 1 1 - - 1 1 - - 1 1 - 1 1 1 - - 1 1 1 - - 1 - - 1 - 1 -]
[1 - 1 - 1 1 - 1 1 - - - 1 1 - - - - 1 1 - 1 1 1 1 - - - - 1 1 1 - - 1 -]
[1 - 1 1 - - - - 1 1 - 1 1 1 1 1 - - 1 - 1 - - - 1 - - - 1 1 1 - - 1 - 1]
[1 - 1 1 1 - 1 - - 1 - 1 - - 1 - - - 1 1 - - 1 1 1 1 1 1 - - - - - 1 1 -]
[1 - - - - 1 1 - 1 - - - 1 - 1 1 1 - 1 1 1 1 1 1 - - - 1 1 - - - 1 1 - -]
[1 1 - - - - - - 1 1 1 - - 1 - 1 1 - 1 - - 1 1 - 1 - 1 1 - - - 1 - 1 1 1]
[1 1 1 1 1 1 - 1 1 1 - - - - 1 1 1 - 1 - 1 - - - - 1 - - - - - 1 1 - 1 -]
[1 1 - - - 1 1 - - - 1 - - 1 1 1 - 1 1 - 1 - - 1 1 1 - 1 - 1 1 - - - 1 -]
[1 - - - - 1 1 1 - 1 - 1 1 - 1 1 - 1 - - - 1 1 - - 1 - - - 1 - 1 - 1 1 1]
[1 1 1 1 1 - 1 1 1 - - - - - - 1 - 1 - - 1 1 1 - - - 1 1 - 1 1 - - 1 - -]
[1 1 - - - 1 - 1 - - - 1 - - - - 1 - 1 1 1 - 1 - 1 1 1 - - 1 1 - 1 1 - 1]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 66, 5, 23, 47, 62, 37, 30, 41, 59, 11, 26)(2, 31, 32, 57, 17, 54, 38,
        67, 68, 21, 53, 18)(3, 29, 12, 25, 63, 33, 39, 65, 48, 61, 27, 69)(4, 6,
        49, 70, 19, 7, 40, 42, 13, 34, 55, 43)(8, 52, 9, 50, 64, 51, 44, 16, 45,
    14, 28, 15)(10, 22, 24, 56, 36, 71, 46, 58, 60, 20, 72, 35)
    (1, 3, 37, 39)(2, 28, 38, 64)(4, 32, 40, 68)(5, 51, 41, 15)(6, 11, 42,
        47)(7, 36, 43, 72)(8, 35, 44, 71)(9, 26, 45, 62)(10, 27, 46, 63)(12, 67,
        48, 31)(13, 22, 49, 58)(14, 24, 50, 60)(16, 21, 52, 57)(17, 69, 53,
        33)(18, 34, 54, 70)(19, 30, 55, 66)(20, 29, 56, 65)(23, 61, 59, 25)
Automorphism group has centre of order: 6
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 12> <72, 26>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 - 1 1 - 1 1 - 1 1 - - - - 1 - 1 1 - - 1 1 - 1 1 - 1 - - - 1 1 1 - - -]
[1 1 - - 1 1 1 1 - 1 - - 1 1 - - 1 - - - 1 - 1 - - - 1 - 1 - 1 - 1 - 1 1]
[1 1 - - - 1 1 - 1 - - 1 1 - - 1 - 1 - - - - 1 1 1 1 1 1 - - - 1 - - 1 1]
[1 - 1 1 1 1 1 - - - - 1 - 1 - - - 1 1 - 1 - 1 - - 1 - 1 1 1 - 1 1 - - -]
[1 1 - - 1 1 - - - - 1 - 1 - - - 1 1 1 1 1 - - 1 1 - - - - 1 - 1 1 1 1 -]
[1 - 1 1 1 1 1 1 1 - 1 - 1 - 1 - - - 1 1 - - 1 1 1 - - - 1 - - - - - - 1]
[1 - 1 1 - 1 1 - 1 1 1 - 1 1 - 1 1 - - 1 - - - - - 1 - 1 - - - - 1 1 1 -]
[1 1 - - - 1 1 - - - 1 1 - - 1 1 1 - 1 1 - 1 - - - 1 - - 1 - 1 1 1 - - 1]
[1 - 1 1 1 - - 1 - - 1 1 - 1 - 1 - 1 - 1 - - - 1 - - 1 - - - 1 1 1 - 1 1]
[1 1 1 - 1 - 1 - 1 - 1 - - 1 1 - - - 1 - 1 1 - - - - 1 1 - - - 1 - 1 1 1]
[1 - - 1 1 - - - - - 1 - 1 - 1 1 1 - - - 1 - 1 1 - 1 1 1 1 - 1 1 - 1 - -]
[1 1 - 1 1 1 - - - 1 - 1 - 1 1 1 - - - 1 1 1 - 1 1 - - 1 1 - - - - - 1 -]
[1 - 1 - 1 1 - - 1 1 - 1 1 - - 1 - - - 1 1 1 1 - - - - - - 1 1 1 - 1 - 1]
[1 - 1 - - 1 - 1 - 1 1 1 - - - 1 1 1 1 - 1 - - - 1 - 1 1 1 - - - - 1 - 1]
[1 1 1 - 1 - - - 1 1 1 1 - - 1 - - 1 - - - - 1 - 1 1 - - 1 - 1 - 1 1 1 -]
[1 1 - 1 1 1 1 1 - 1 1 - - - - - - 1 - - - 1 - 1 - 1 - 1 - 1 1 - - 1 - 1]
[1 1 - 1 1 - - - 1 1 - - - - 1 1 1 1 1 1 - - 1 - - - 1 1 - 1 - - 1 - - 1]
[1 - 1 - 1 1 - 1 - - - - 1 - 1 1 - - 1 - - 1 - - 1 1 1 1 - 1 1 - 1 - 1 -]
[1 - - 1 1 - 1 1 - 1 - 1 - - - - 1 - 1 1 - 1 1 - 1 1 1 - - - - 1 - 1 1 -]
[1 1 1 - - - 1 - - 1 1 - - 1 - 1 - - 1 1 1 - 1 1 1 1 1 - - 1 1 - - - - -]
[1 1 1 - - - 1 1 - 1 - 1 1 - 1 - - - - 1 - - - 1 - - 1 1 1 1 - 1 1 1 - -]
[1 - - 1 - - - - 1 1 1 1 1 - - - - - 1 - 1 1 - 1 - 1 1 - 1 1 - - 1 - 1 1]
[1 1 - 1 - 1 - 1 1 - 1 - - 1 - 1 - - - - - 1 1 - 1 - 1 - 1 1 - 1 1 1 - -]
[1 1 - 1 - 1 - 1 1 - - 1 1 1 1 - - 1 1 1 1 - - - - 1 1 - - - 1 - - 1 - -]
[1 - 1 - - 1 - - - - - - - 1 1 - 1 1 - 1 - 1 1 1 - 1 1 - 1 1 - - - 1 1 1]
[1 - - 1 - - 1 - - 1 - - 1 1 1 1 - 1 1 - - - - - 1 - - - 1 1 1 1 - 1 1 1]
[1 1 1 - 1 - - 1 1 1 - - 1 1 - 1 1 1 1 - - 1 - 1 - 1 - - 1 - - 1 - - - -]
[1 - - - 1 - 1 - 1 - 1 1 1 1 - - 1 1 - 1 - 1 - - 1 - 1 1 1 1 1 - - - - -]
[1 1 1 1 - - - 1 1 - - - - - - - 1 - - 1 1 - - - 1 1 - 1 1 1 1 1 - - 1 1]
[1 - - - 1 - 1 1 1 - - 1 - 1 1 1 1 - - - 1 - - 1 1 1 - - - 1 - - 1 1 - 1]
[1 1 1 1 - - 1 1 - - 1 1 1 - 1 1 1 1 - - 1 1 1 - - - - - - 1 - - - - 1 -]
[1 - - - - - - 1 - 1 1 - 1 1 1 - - 1 - 1 1 1 1 - 1 1 - 1 - - - 1 1 - - 1]
[1 - - - - 1 - 1 1 1 1 1 - 1 1 - 1 - 1 - - - 1 1 - - - 1 - 1 1 1 - - 1 -]
[1 1 1 1 - - - - - - - 1 1 1 - - 1 - 1 - - 1 1 1 1 - - 1 - - 1 - 1 1 - 1]
[1 - - - - - 1 1 1 - - - - - - 1 - 1 1 1 1 1 1 1 - - - 1 1 - 1 - 1 1 1 -]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 55, 37, 19)(2, 68, 38, 32)(3, 40, 39, 4)(5, 16, 41, 52)(6, 15, 42,
        51)(7, 23, 43, 59)(8, 46, 44, 10)(9, 22, 45, 58)(11, 34, 47, 70)(12, 21,
        48, 57)(13, 61, 49, 25)(14, 71, 50, 35)(17, 67, 53, 31)(18, 66, 54,
        30)(20, 72, 56, 36)(24, 27, 60, 63)(26, 28, 62, 64)(29, 33, 65, 69)
    (1, 3, 44, 70, 72, 66, 37, 39, 8, 34, 36, 30)(2, 33, 57, 16, 25, 15, 38, 69,
        21, 52, 61, 51)(4, 19, 54, 56, 11, 10, 40, 55, 18, 20, 47, 46)(5, 48,
        29, 32, 42, 13, 41, 12, 65, 68, 6, 49)(7, 28, 24, 22, 50, 67, 43, 64,
        60, 58, 14, 31)(9, 63, 26, 59, 53, 35, 45, 27, 62, 23, 17, 71)
    (1, 2, 62)(3, 33, 23)(4, 7, 29)(5, 47, 14)(6, 18, 60)(8, 21, 53)(9, 72,
        25)(10, 67, 12)(11, 50, 41)(13, 56, 22)(15, 63, 66)(16, 71, 70)(17, 44,
        57)(19, 28, 32)(20, 58, 49)(24, 42, 54)(26, 37, 38)(27, 30, 51)(31, 48,
        46)(34, 52, 35)(36, 61, 45)(39, 69, 59)(40, 43, 65)(55, 64, 68)
Automorphism group has centre of order: 2
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 13> <72, 31>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 1 1 1 1 1 1 - - - - - - - - 1 1 1 1 1 1 1 1 1 - - - - - - - - - -]
[1 - - 1 1 - - - - 1 1 - 1 - - 1 1 1 1 1 1 1 1 - - - 1 1 - - - - - - 1 1]
[1 1 1 - - - - - - 1 1 1 - 1 1 - - 1 1 1 1 - - 1 1 - - - 1 1 - - - - 1 1]
[1 1 - - - 1 1 - - 1 - 1 1 1 - - - 1 - - - 1 1 - 1 1 - 1 - - 1 1 - - 1 1]
[1 - 1 - - 1 - 1 - - 1 1 - - 1 1 - - 1 - - 1 1 1 - 1 1 - - - 1 - 1 - 1 1]
[1 1 1 - - - 1 1 - 1 - 1 - - 1 - 1 - - 1 1 1 1 - - - 1 1 - 1 - 1 1 - - -]
[1 1 1 1 1 - - - - 1 1 - - 1 - - 1 1 - - - 1 - 1 - 1 1 - 1 - 1 1 1 - - -]
[1 - - - 1 1 1 1 - 1 - 1 1 - - 1 - 1 1 - 1 - - 1 - - 1 - 1 1 1 1 - - - -]
[1 1 - - 1 1 - - 1 - 1 1 1 1 - - - - 1 1 - - 1 - - 1 1 1 1 1 - - 1 - - -]
[1 - 1 1 - 1 - - 1 - 1 - - 1 1 1 - 1 - - 1 - 1 - 1 - 1 1 - 1 1 1 - - - -]
[1 1 - 1 - 1 - 1 - 1 1 - 1 - 1 - - - 1 - 1 1 - - 1 - - 1 1 - 1 - 1 1 - -]
[1 - - 1 - 1 1 - 1 - - - 1 1 1 - - - - 1 1 1 - 1 - - 1 - 1 - - 1 1 - 1 1]
[1 1 - - 1 - - 1 1 - 1 - 1 - - - 1 - - - 1 - 1 1 1 - - - - 1 1 1 1 - 1 1]
[1 - 1 1 1 1 - 1 - 1 - - - - - 1 - - - 1 - - - - 1 1 - 1 1 1 - 1 1 - 1 1]
[1 1 - 1 - - 1 1 1 - - - - - 1 - 1 1 1 - - - - - - 1 1 1 1 1 1 - - - 1 1]
[1 - - - - - - 1 1 - 1 1 1 - 1 1 1 1 - 1 - 1 - 1 1 1 - 1 1 - - 1 - - - -]
[1 - - 1 - - 1 - - 1 - - 1 1 1 1 1 - 1 1 - - 1 1 1 1 - - - 1 1 - 1 - - -]
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - - - - - - - - - 1 -]
[1 1 - - 1 1 - - - - - - - 1 1 1 1 - 1 - 1 1 - 1 - 1 - 1 - 1 - 1 - 1 1 -]
[1 - - - 1 1 - - 1 1 - 1 - - 1 - 1 1 - 1 1 - - - 1 1 1 - - - 1 - 1 1 1 -]
[1 - 1 1 - - - 1 - - - 1 1 1 - - 1 - 1 - 1 - 1 - 1 1 1 - 1 - - 1 - 1 1 -]
[1 - - - - - 1 1 1 1 1 - - 1 - 1 - 1 - - 1 1 1 - - 1 - - 1 1 - - 1 1 1 -]
[1 - 1 - 1 - 1 - 1 - - 1 - 1 - 1 1 - 1 - 1 1 - - 1 - - 1 1 - 1 - 1 - - 1]
[1 - 1 - 1 - 1 - 1 1 1 - 1 - 1 - - - 1 - - 1 - - 1 1 1 - - 1 - 1 - 1 - 1]
[1 1 1 - - - - 1 1 1 - - 1 1 - 1 - - - 1 1 - - 1 - 1 1 1 - - 1 - - 1 - 1]
[1 - - 1 1 - - 1 1 1 - 1 - 1 1 - - 1 1 - - - 1 1 - - - 1 - - - 1 1 1 - 1]
[1 1 - 1 1 - 1 - - - 1 1 - - 1 1 - - - 1 1 - 1 - - 1 - - 1 - 1 1 - 1 - 1]
[1 1 - - - 1 1 1 - - 1 - - 1 - 1 1 1 1 1 - - - - 1 - 1 - - - - 1 1 1 - 1]
[1 - 1 - 1 1 - 1 - - - - 1 1 1 - 1 1 - 1 - 1 1 - - - - - 1 1 1 - - 1 - 1]
[1 1 - 1 - 1 - - 1 1 - 1 - - - 1 1 - - - - 1 1 1 1 - 1 - 1 1 - - - 1 - 1]
[1 - 1 1 - 1 1 - - - 1 1 1 - - - 1 1 - - 1 - - 1 - 1 - 1 - 1 - - 1 1 - 1]
[1 - 1 - - 1 1 - 1 1 1 - - - - - 1 - 1 1 - - 1 1 - - - 1 1 - 1 1 - 1 1 -]
[1 1 1 1 - - - - 1 - - 1 1 - - 1 - 1 1 1 - 1 - - - - - - - 1 1 1 1 1 1 -]
[1 - - 1 1 - 1 1 - - 1 1 - 1 - - - - - 1 - 1 - 1 1 - 1 1 - 1 1 - - 1 1 -]
[1 1 1 - 1 - 1 - - - - - 1 - 1 1 - 1 - - - - 1 1 1 - 1 1 1 - - - 1 1 1 -]

Permutation group acting on a set of cardinality 72
Order = 19584 = 2^7 * 3^2 * 17
    (1, 2, 37, 38)(3, 55, 39, 19)(4, 28, 40, 64)(5, 21, 41, 57)(6, 65, 42,
        29)(7, 59, 43, 23)(8, 33, 44, 69)(9, 58, 45, 22)(10, 36, 46, 72)(11, 31,
        47, 67)(12, 56, 48, 20)(13, 32, 49, 68)(14, 71, 50, 35)(15, 63, 51,
        27)(16, 66, 52, 30)(17, 62, 53, 26)(18, 34, 54, 70)(24, 25, 60, 61)
    (2, 39, 7, 18)(3, 43, 54, 38)(4, 45, 6, 14)(5, 46, 53, 13)(8, 12, 11, 52)(9,
        42, 50, 40)(10, 17, 49, 41)(16, 44, 48, 47)(19, 62, 33, 66)(20, 68, 65,
        61)(21, 22, 64, 34)(23, 35, 63, 67)(25, 56, 32, 29)(26, 69, 30, 55)(27,
        31, 59, 71)(28, 70, 57, 58)
    (3, 43, 53, 15, 54, 6, 46, 47, 13, 48, 44, 45, 14, 5, 4, 16)(7, 17, 51, 18,
        42, 10, 11, 49, 12, 8, 9, 50, 41, 40, 52, 39)(19, 30, 64, 57, 35, 58,
        33, 56, 68, 31, 36, 29, 34, 27, 62, 59)(20, 32, 67, 72, 65, 70, 63, 26,
        23, 55, 66, 28, 21, 71, 22, 69)(24, 60)(25, 61)
Automorphism group has centre of order: 2
Number of regular subgroups: 4
Number of regular subgroups containing zeta: 4
Number of centrally regular subgroups: 4
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 4> <72, 4>
<36, 5> <72, 11>
<36, 4> <72, 4>
<36, 4> <72, 4>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 - - - 1 - 1 - 1 - - - 1 - 1 1 1 - 1 - - - 1 1 1 - 1 1 1 - 1 - - -]
[1 1 1 - - - - 1 - 1 - 1 - - - 1 1 1 - 1 - 1 - - 1 1 - 1 1 1 - 1 - 1 - -]
[1 - - 1 1 1 - - - - - - - - 1 1 - - - - 1 1 - - 1 1 - - 1 1 1 1 1 1 1 1]
[1 1 1 - 1 - - - - 1 1 1 - 1 1 1 - - - 1 - - 1 1 - 1 - - 1 - 1 - 1 - - 1]
[1 1 1 - - 1 - - 1 - 1 1 1 - 1 1 - - 1 - - - 1 1 1 - - - - 1 - 1 - 1 1 -]
[1 1 1 - - 1 - 1 1 - - 1 1 1 - - - - - 1 1 1 - - - 1 1 - - 1 - - 1 - 1 1]
[1 1 1 - 1 - 1 - - 1 1 - 1 1 - - - - 1 - 1 1 - - 1 - - 1 1 - - - - 1 1 1]
[1 - - - 1 1 - - 1 1 - 1 - 1 - 1 1 1 1 - 1 - 1 - - - 1 - 1 1 - - - 1 - 1]
[1 - - - 1 1 - - 1 1 1 - 1 - 1 - 1 1 - 1 - 1 - 1 - - - 1 1 1 - - 1 - 1 -]
[1 - - - - 1 1 1 - - 1 1 1 1 1 - 1 - - - 1 - 1 - - 1 - 1 1 - - 1 1 1 - -]
[1 - - - 1 - 1 1 - - 1 1 1 1 - 1 - 1 - - - 1 - 1 1 - 1 - - 1 1 - 1 1 - -]
[1 1 1 - 1 1 1 - - - - - 1 - 1 - 1 1 - 1 - 1 1 - - - 1 - - - 1 1 - 1 - 1]
[1 1 1 - 1 1 - 1 - - - - - 1 - 1 1 1 1 - 1 - - 1 - - - 1 - - 1 1 1 - 1 -]
[1 - - - - 1 1 - - - - 1 1 - - 1 1 - 1 1 - - - 1 1 1 1 1 1 - 1 - - - 1 1]
[1 - - - 1 - - 1 - - 1 - - 1 1 - - 1 1 1 - - 1 - 1 1 1 1 - 1 - 1 - - 1 1]
[1 - - - - - 1 - 1 1 - 1 - 1 1 - - 1 1 1 1 1 - 1 - 1 - - - - 1 1 - 1 1 -]
[1 - - - - - - 1 1 1 1 - 1 - - 1 1 - 1 1 1 1 1 - 1 - - - - - 1 1 1 - - 1]
[1 - 1 1 1 1 1 1 1 - 1 1 - - - - - 1 - 1 1 - - 1 1 - - - 1 - - 1 - - - 1]
[1 - 1 1 1 1 1 1 - 1 1 1 - - - - 1 - 1 - - 1 1 - - 1 - - - 1 1 - - - 1 -]
[1 - 1 1 1 - 1 - - 1 - 1 1 - 1 1 - - 1 1 1 - - - - - 1 1 - 1 - 1 1 - - -]
[1 - 1 1 - 1 - 1 1 - 1 - - 1 1 1 - - 1 1 - 1 - - - - 1 1 1 - 1 - - 1 - -]
[1 1 - 1 - - - 1 - - - 1 1 - 1 - - 1 1 - 1 1 1 1 - - - 1 1 1 1 - - - - 1]
[1 1 - 1 - - 1 - - - 1 - - 1 - 1 1 - - 1 1 1 1 1 - - 1 - 1 1 - 1 - - 1 -]
[1 - 1 1 1 - - - 1 - - - 1 1 - - 1 - - 1 1 - 1 1 1 1 - 1 - 1 1 - - 1 - -]
[1 - 1 1 - 1 - - - 1 - - 1 1 - - - 1 1 - - 1 1 1 1 1 1 - 1 - - 1 1 - - -]
[1 1 - 1 1 - - - 1 - 1 1 - - - - 1 - 1 - - 1 - 1 - 1 1 1 - - - 1 1 1 - 1]
[1 1 - 1 - 1 - - - 1 1 1 - - - - - 1 - 1 1 - 1 - 1 - 1 1 - - 1 - 1 1 1 -]
[1 - 1 1 - - - 1 - 1 1 - 1 - 1 1 1 1 - - 1 - - 1 - 1 1 - - - - - - 1 1 1]
[1 - 1 1 - - 1 - 1 - - 1 - 1 1 1 1 1 - - - 1 1 - 1 - - 1 - - - - 1 - 1 1]
[1 1 - 1 1 - - 1 1 1 - 1 1 1 1 - 1 - - - - - - - 1 - 1 - 1 - 1 1 - - 1 -]
[1 1 - 1 - 1 1 - 1 1 1 - 1 1 - 1 - 1 - - - - - - - 1 - 1 - 1 1 1 - - - 1]
[1 1 - - 1 1 1 1 1 1 - - - - 1 1 - - - - 1 1 1 1 1 1 1 1 - - - - - - - -]
[1 1 - 1 1 - 1 1 1 - - - 1 - - 1 - 1 1 1 - - 1 - - 1 - - 1 - - - 1 1 1 -]
[1 1 - 1 - 1 1 1 - 1 - - - 1 1 - 1 - 1 1 - - - 1 1 - - - - 1 - - 1 1 - 1]
[1 - 1 - - - 1 1 1 1 - - - - - - - - - - - - 1 1 - - 1 1 1 1 1 1 1 1 1 1]

Permutation group acting on a set of cardinality 72
Order = 144 = 2^4 * 3^2
    (1, 61, 37, 25)(2, 58, 38, 22)(3, 69, 39, 33)(4, 17, 40, 53)(5, 12, 41,
        48)(6, 14, 42, 50)(7, 28, 43, 64)(8, 26, 44, 62)(9, 47, 45, 11)(10, 57,
        46, 21)(13, 67, 49, 31)(15, 19, 51, 55)(16, 71, 52, 35)(18, 32, 54,
        68)(20, 30, 56, 66)(23, 63, 59, 27)(24, 29, 60, 65)(34, 72, 70, 36)
    (1, 2, 37, 38)(3, 7, 39, 43)(4, 35, 40, 71)(5, 19, 41, 55)(6, 23, 42, 59)(8,
        45, 44, 9)(10, 60, 46, 24)(11, 66, 47, 30)(12, 28, 48, 64)(13, 65, 49,
        29)(14, 16, 50, 52)(15, 17, 51, 53)(18, 36, 54, 72)(20, 68, 56, 32)(21,
        25, 57, 61)(22, 27, 58, 63)(26, 69, 62, 33)(31, 70, 67, 34)
    (2, 3)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21,
        22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(34, 35)(38, 39)(41, 42)(43,
        44)(45, 46)(47, 48)(49, 50)(51, 52)(53, 54)(55, 56)(57, 58)(59, 60)(61,
        62)(63, 64)(65, 66)(67, 68)(70, 71)
Automorphism group has centre of order: 2
Number of regular subgroups: 4
Number of regular subgroups containing zeta: 4
Number of centrally regular subgroups: 4
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 4> <72, 4>
<36, 4> <72, 4>
<36, 4> <72, 4>
<36, 5> <72, 11>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 - 1 - - - - 1 1 - 1 - - 1 - - 1 - - 1 1 1 1 1 - 1 - - 1 - - 1 1 1 -]
[1 - 1 1 - - - - 1 - 1 - - 1 - - 1 - 1 - 1 1 1 - 1 1 - 1 - - - 1 1 - 1 1]
[1 - - - 1 1 1 1 1 - - 1 - 1 1 - 1 1 1 - - - - - 1 - 1 1 - 1 - 1 - - 1 -]
[1 1 1 - - 1 1 1 1 - 1 - 1 - 1 - - 1 - 1 1 - - - - 1 - - - 1 - - 1 - 1 1]
[1 1 1 - 1 1 - 1 1 1 - - - 1 - 1 - - 1 1 - - 1 - 1 - - - - - 1 - 1 1 1 -]
[1 1 1 - 1 - 1 1 - 1 1 1 - - - - 1 1 1 - - 1 - 1 - - - - - - - 1 1 1 - 1]
[1 1 - 1 - 1 - - - - 1 1 1 1 1 - 1 - 1 1 1 - - 1 - - - - - - 1 1 - 1 1 -]
[1 - 1 1 - - 1 - - 1 - 1 1 1 - 1 1 1 - 1 - 1 - - 1 - - - - 1 1 - - - 1 1]
[1 - - - - 1 1 1 - 1 1 - - - - - 1 - - 1 1 1 - 1 1 - 1 1 1 - 1 - 1 - 1 -]
[1 1 1 - 1 1 1 - - - - 1 1 1 - - - - - - 1 1 1 - - - 1 1 1 - - - - 1 1 1]
[1 - - - 1 - - 1 1 - - 1 1 - - - - - 1 1 1 1 - 1 1 1 - 1 - 1 1 - - 1 - 1]
[1 1 - 1 1 - 1 - 1 1 - - 1 - 1 1 1 - 1 - 1 - - - - - 1 1 - - 1 - 1 - - 1]
[1 - 1 1 1 1 - - 1 - 1 1 - - 1 1 1 - - 1 - 1 - - - - - 1 1 1 - - 1 1 - -]
[1 1 - - - - 1 1 - 1 - - - 1 1 1 1 - - 1 1 1 1 - - 1 - 1 - 1 - 1 - 1 - -]
[1 - - 1 1 - 1 - 1 1 - - 1 1 - - - 1 - 1 - - - 1 - 1 - 1 1 - - 1 1 1 1 -]
[1 - 1 - 1 - - 1 1 - - - 1 - 1 1 1 1 - - 1 1 1 1 - - - - 1 - 1 1 - - 1 -]
[1 - 1 1 - - 1 1 - - - 1 - - - 1 - - 1 - 1 - - - - 1 1 - 1 1 1 1 1 1 1 -]
[1 - - - - 1 1 - 1 1 1 1 1 - - 1 1 1 1 - 1 - 1 - 1 1 - - 1 - - - - 1 - -]
[1 1 - 1 - 1 - 1 - - - - 1 - - - 1 1 - - - - 1 - 1 - - 1 1 1 1 1 1 1 - 1]
[1 - - 1 - - 1 1 1 - 1 - - 1 1 - - 1 1 1 - 1 1 - - - 1 - 1 - 1 - - 1 - 1]
[1 - 1 - 1 - 1 - - - 1 - 1 1 1 - 1 - - - - - 1 1 1 1 1 - - 1 1 - 1 1 - -]
[1 1 - - - 1 1 - 1 - - 1 - 1 1 1 - - - - - 1 - 1 1 1 - - 1 - 1 1 1 - - 1]
[1 1 1 1 - - 1 1 1 - 1 1 1 - - 1 - - - 1 - - 1 1 1 - 1 1 - - - 1 - - - -]
[1 1 1 1 1 - - 1 - 1 1 1 - 1 1 - - 1 - - 1 - - - 1 1 - 1 1 - 1 - - - - -]
[1 1 1 1 - 1 - 1 1 1 - - 1 1 - - 1 - 1 - - 1 - 1 - 1 1 - 1 1 - - - - - -]
[1 - - - - - - 1 - 1 1 1 1 1 1 1 - - 1 - - - 1 1 - - - 1 1 1 - - 1 - 1 1]
[1 - 1 1 1 1 1 - - 1 - - - - 1 - - - 1 1 1 - 1 1 1 - - - 1 1 - 1 - - - 1]
[1 1 - 1 1 1 1 - - - 1 - - - - 1 - 1 1 - - 1 1 1 - 1 - 1 - 1 1 - - - 1 -]
[1 1 - - 1 - - - 1 1 1 1 - - - - 1 - - 1 - - 1 - - 1 1 - 1 1 1 1 - - 1 1]
[1 - 1 - - 1 - - 1 1 1 - - 1 - 1 - 1 - - 1 - - 1 - - 1 1 - 1 1 1 - 1 - 1]
[1 - - 1 1 1 - 1 - - - 1 - 1 - 1 1 1 - 1 1 - 1 1 - 1 1 - - - - - 1 - - 1]
[1 1 - - 1 - - - - - 1 - 1 1 - 1 - 1 1 1 1 1 - - 1 - 1 - 1 1 - 1 1 - - -]
[1 - - 1 1 1 - 1 - 1 1 - 1 - 1 1 - - - - - 1 - - 1 1 1 - - - - 1 - 1 1 1]
[1 - 1 - - 1 - - - 1 - 1 1 - 1 - - 1 1 1 - 1 1 - - 1 1 1 - - 1 1 1 - - -]
[1 1 1 - - - - - - - - - - - 1 1 1 1 1 1 - - - 1 1 1 1 1 1 - - - - 1 1 1]

Permutation group acting on a set of cardinality 72
Order = 216 = 2^3 * 3^3
    (1, 67, 19, 72, 32, 54, 47, 66, 56)(2, 45, 13, 7, 69, 27, 21, 53, 24)(3, 16,
        65, 6, 10, 25, 59, 71, 14)(4, 70, 62, 41, 15, 12, 22, 8, 28)(5, 51, 48,
        58, 44, 64, 40, 34, 26)(9, 49, 43, 33, 63, 57, 17, 60, 38)(11, 30, 20,
        37, 31, 55, 36, 68, 18)(23, 35, 50, 39, 52, 29, 42, 46, 61)
    (1, 42, 57, 37, 6, 21)(2, 72, 23, 38, 36, 59)(3, 7, 47, 39, 43, 11)(4, 5,
        22, 40, 41, 58)(8, 51, 70, 44, 15, 34)(9, 30, 10, 45, 66, 46)(12,
        48)(13, 19, 29, 49, 55, 65)(14, 24, 56, 50, 60, 20)(16, 53, 32, 52, 17,
        68)(18, 25, 27, 54, 61, 63)(26, 62)(28, 64)(31, 71, 69, 67, 35, 33)
    (2, 3, 40)(4, 38, 39)(5, 7, 6)(8, 9, 46)(10, 44, 45)(12, 49, 50)(13, 14,
        48)(15, 17, 52)(16, 51, 53)(18, 55, 20)(19, 56, 54)(21, 59, 58)(22, 57,
        23)(24, 25, 26)(27, 65, 64)(28, 63, 29)(30, 31, 68)(32, 66, 67)(33, 35,
        70)(34, 69, 71)(41, 43, 42)(60, 61, 62)
Automorphism group has centre of order: 6
Number of regular subgroups: 3
Number of regular subgroups containing zeta: 3
Number of centrally regular subgroups: 3
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 5> <72, 11>
<36, 3> <72, 3>
<36, 3> <72, 3>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 - - - - - - - - 1 1 1 - - - 1 1 1 - - 1 1 - - 1 1 1 1 1 1 1 - - -]
[1 1 1 - - - - - - 1 1 - - - 1 1 1 - - - 1 1 - - 1 1 - 1 1 1 1 1 1 - - -]
[1 - - 1 - 1 - 1 1 1 1 1 - 1 - 1 - 1 - 1 1 - - - - - - - 1 1 1 - 1 - - 1]
[1 - 1 1 - 1 - - - 1 - 1 - - - 1 - 1 - - - 1 1 1 1 1 1 - - 1 1 - - 1 1 -]
[1 1 - - - - - 1 1 - 1 - - 1 - - - - - 1 1 1 1 1 1 1 1 - 1 - - - 1 1 1 -]
[1 1 - 1 1 - - - - 1 1 - - - - 1 1 1 1 1 - 1 1 1 - - - 1 1 - - - - 1 - 1]
[1 - 1 - 1 - - 1 - - - 1 1 - - 1 1 - 1 1 1 - 1 - 1 1 - - 1 1 - - - - 1 1]
[1 - - - 1 1 1 1 - 1 1 1 - - 1 - - - 1 - - - 1 1 1 - - - 1 1 - 1 1 1 - -]
[1 1 - - - 1 1 - - - - 1 - 1 - 1 1 1 1 - 1 1 - 1 1 - - - - - - 1 1 - 1 1]
[1 - 1 - - - 1 - 1 1 - - - - 1 - 1 1 1 1 1 - 1 - 1 - 1 - - - 1 - 1 1 - 1]
[1 - - 1 1 - 1 - 1 1 - 1 1 1 - - 1 - - - - 1 1 - 1 - - 1 1 - 1 - 1 - 1 -]
[1 1 1 1 - 1 - 1 1 - - 1 - 1 1 - 1 - 1 - 1 1 1 - - - - 1 - 1 - - - 1 - -]
[1 1 1 1 1 1 1 - - - 1 1 1 - - 1 - - - 1 1 - - - 1 - 1 1 - - - - 1 1 - -]
[1 1 1 - 1 - 1 1 1 1 - - 1 1 - 1 1 1 - - - - - 1 - 1 - - - 1 - - 1 1 - -]
[1 1 1 - 1 - 1 1 1 - 1 1 - - 1 1 - 1 1 - - 1 - - - - 1 - 1 - 1 - - - 1 -]
[1 1 1 1 - 1 - 1 1 1 1 - 1 - - - 1 - 1 1 - - - 1 1 - - - - - 1 1 - - 1 -]
[1 1 1 1 1 1 1 - - 1 - - - 1 1 - - 1 - 1 1 - 1 - - 1 - - 1 - - 1 - - 1 -]
[1 1 - - 1 1 1 1 - 1 - - - 1 - - - - 1 1 - 1 - - 1 1 1 1 - 1 1 - - - - 1]
[1 - 1 1 1 - - 1 1 - - 1 - - 1 - - 1 - 1 - 1 - 1 1 1 - 1 - - - 1 1 - - 1]
[1 - 1 - - 1 1 1 1 1 - - 1 - - 1 - - - - 1 1 1 1 - - 1 1 1 - - 1 - - - 1]
[1 - - - 1 - - 1 - 1 - 1 - 1 1 1 1 - - 1 1 - - 1 - - 1 1 - - 1 1 - 1 1 -]
[1 1 - 1 1 - 1 - 1 - 1 1 - - - - 1 - - - 1 - 1 1 - 1 1 - - 1 1 1 - - - 1]
[1 - - - - - 1 - 1 1 1 1 1 - - - - 1 1 1 1 1 - - - 1 - 1 - 1 - 1 - 1 1 -]
[1 - - 1 1 1 - 1 - - - - 1 - - - 1 1 1 - 1 1 - - - 1 1 - 1 - 1 1 1 1 - -]
[1 1 - - - 1 - 1 - 1 1 1 1 - 1 - 1 1 - - - - 1 - - 1 1 1 - - - - 1 - 1 1]
[1 - 1 1 1 - - - - 1 1 - 1 1 1 - - - 1 - 1 1 - 1 - - 1 - - 1 - - 1 - 1 1]
[1 1 - 1 - - - - 1 1 - 1 1 1 1 1 - - 1 - - - - - 1 1 1 - 1 - - 1 - 1 - 1]
[1 - - 1 - 1 1 - 1 - - - - - 1 1 1 - 1 1 - - - 1 - 1 1 1 1 1 - - 1 - 1 -]
[1 - 1 - - 1 1 - - - 1 1 1 1 1 - 1 - - 1 - 1 - 1 - 1 - - 1 - 1 - - 1 - 1]
[1 - - 1 - - 1 1 - - 1 - 1 1 1 1 1 1 - 1 - 1 1 - 1 - 1 - - 1 - 1 - - - -]
[1 - 1 - 1 1 - - 1 - 1 - - 1 - - 1 1 - - - - - - 1 - 1 1 1 1 - 1 - 1 1 1]
[1 - 1 1 - - 1 1 - - 1 - - 1 - 1 - - 1 - - - 1 - - 1 - 1 - - 1 1 1 1 1 1]
[1 1 - 1 - - 1 1 - - - - 1 - 1 - - 1 - - 1 - - 1 1 - - 1 1 1 1 - - 1 1 1]
[1 - - - 1 1 - - 1 - 1 - 1 1 1 1 - 1 1 - 1 - 1 1 1 1 - 1 - - 1 - - - - -]
[1 1 - - 1 1 - - 1 - - - 1 - 1 1 - - - 1 - 1 1 - - - - - - 1 1 1 1 1 1 1]

Permutation group acting on a set of cardinality 72
Order = 432 = 2^4 * 3^3
    (1, 48, 29, 31, 27, 43)(2, 13, 5, 36, 66, 50)(3, 19, 61, 32, 42, 56)(4, 15,
        64, 47, 62, 58)(6, 20, 39, 55, 25, 68)(7, 37, 12, 65, 67, 63)(8, 52)(9,
        54, 34, 23, 57, 71)(10, 33, 17)(11, 26, 22, 40, 51, 28)(14, 38, 49, 41,
        72, 30)(16, 44)(18, 70, 59, 21, 35, 45)(46, 69, 53)
    (2, 3)(7, 10)(8, 11)(9, 12)(13, 17)(14, 18)(15, 16)(19, 23)(20, 21)(22,
        24)(25, 29)(26, 28)(27, 30)(31, 35)(32, 33)(34, 36)(38, 39)(43, 46)(44,
        47)(45, 48)(49, 53)(50, 54)(51, 52)(55, 59)(56, 57)(58, 60)(61, 65)(62,
        64)(63, 66)(67, 71)(68, 69)(70, 72)
    (4, 41, 42)(5, 6, 40)(7, 48, 11)(8, 10, 45)(9, 44, 46)(12, 47, 43)(13, 15,
    14)(16, 18, 17)(19, 58, 20)(21, 23, 60)(22, 56, 55)(24, 57, 59)(25, 63,
        62)(26, 61, 27)(28, 65, 30)(29, 66, 64)(31, 68, 72)(32, 36, 67)(33, 34,
        71)(35, 69, 70)(49, 51, 50)(52, 54, 53)
Automorphism group has centre of order: 2
Number of regular subgroups: 3
Number of regular subgroups containing zeta: 3
Number of centrally regular subgroups: 3
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 5> <72, 11>
<36, 3> <72, 3>
<36, 4> <72, 4>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 1 1 - 1 1 - - 1 1 1 - - - 1 - 1 - 1 1 - 1 - 1 - 1 - - - 1 - - - -]
[1 1 1 1 1 1 - - 1 - - - 1 - 1 - 1 1 - 1 - - - 1 1 - 1 1 - - - - 1 - - 1]
[1 1 1 1 1 1 - - - 1 1 - - - 1 - - - 1 1 - 1 - - - - - - 1 - 1 1 1 1 1 -]
[1 1 1 1 1 - 1 - - - 1 1 - 1 1 - - - - - 1 - 1 - 1 - 1 - 1 1 1 - - - - 1]
[1 - - - - - 1 - - 1 1 - 1 - 1 - 1 1 - - - 1 1 1 1 - - 1 1 1 1 1 1 - - -]
[1 1 1 1 - - - - 1 1 1 - - 1 - 1 1 1 1 - - - 1 - 1 1 - 1 - - 1 - - 1 - -]
[1 - 1 1 1 - 1 1 - 1 - - - 1 - 1 - 1 - 1 - 1 - - - 1 1 1 1 1 - - 1 - - -]
[1 - 1 - - 1 - - - - - 1 1 1 - - - 1 1 1 1 - 1 - - 1 - 1 1 - 1 1 1 - - 1]
[1 - - 1 - - 1 - 1 1 1 1 1 1 - - 1 - - 1 - - - - - - 1 1 1 - - 1 - 1 1 1]
[1 - - - 1 - - 1 1 - 1 - - 1 1 1 1 - 1 - - - - 1 - 1 1 - 1 - 1 1 1 - - 1]
[1 - - 1 - - - - - 1 - 1 - 1 1 - 1 - 1 1 1 1 - 1 1 1 - - - 1 - - 1 1 - 1]
[1 - - 1 - 1 1 1 - - 1 - - 1 1 - - 1 1 - 1 - 1 1 - - 1 1 - - - - 1 1 1 -]
[1 1 - - - 1 1 - - - 1 - 1 1 - 1 1 - - 1 1 1 - - 1 1 1 - - - 1 - 1 - 1 -]
[1 - 1 - - 1 1 1 1 - 1 1 - - 1 - 1 1 1 1 - - - - 1 1 - - 1 1 - - - - 1 -]
[1 1 - - - 1 - 1 - 1 1 1 - - - 1 - - 1 1 - 1 1 1 1 - 1 1 1 - - - - - - 1]
[1 - - - 1 - 1 - 1 - - 1 - - 1 1 - 1 1 1 1 1 - - 1 - 1 1 - - 1 1 - 1 - -]
[1 - 1 - - 1 - 1 1 1 1 - 1 - 1 - - - - - 1 1 - - - 1 1 1 - 1 1 - - 1 - 1]
[1 - 1 - 1 - - - - - 1 1 1 - - 1 1 1 1 - - 1 1 - - - 1 - - 1 - - 1 1 1 1]
[1 - - 1 1 - - 1 - 1 1 - 1 - 1 1 - 1 - 1 1 - 1 - 1 1 - - - - - 1 - - 1 1]
[1 1 - 1 - 1 1 - 1 1 - 1 1 - 1 1 - - 1 - - - 1 - - 1 1 - - 1 - 1 1 - - -]
[1 1 - - 1 - 1 1 1 1 - - - - - - 1 - 1 1 1 - 1 - - - - 1 - 1 1 - 1 - 1 1]
[1 1 1 - - - 1 1 - 1 - 1 - - - - - 1 - - - - - 1 1 1 1 - - - 1 1 1 1 1 1]
[1 1 - 1 - - - 1 1 - 1 1 1 - - 1 - 1 - 1 1 - - 1 - - - - 1 1 1 - 1 1 - -]
[1 - 1 1 - 1 1 1 1 - - - - - - 1 1 - - - 1 1 1 - 1 - - - 1 - - 1 1 1 - 1]
[1 - - 1 1 1 - - 1 1 - 1 - - - - 1 1 - - 1 1 1 1 - 1 1 - 1 - 1 - - - 1 -]
[1 - - 1 1 1 1 - - - - - 1 - - 1 - - 1 - - - - 1 1 1 - 1 1 1 1 - - 1 1 1]
[1 1 1 - - - - - - - - - - - 1 1 1 - - 1 1 - 1 1 - 1 1 1 1 1 - 1 - 1 1 -]
[1 - 1 - 1 1 - - 1 1 1 1 - 1 - 1 - - - - 1 - - 1 1 - - 1 - 1 - 1 1 - 1 -]
[1 1 - - 1 1 1 - 1 - 1 - - 1 - - - 1 - 1 - 1 1 1 - 1 - - - 1 - 1 - 1 - 1]
[1 1 - 1 - 1 - 1 - - - 1 - 1 1 1 1 1 - - - 1 - - - - - 1 - 1 1 1 - - 1 1]
[1 - 1 - 1 1 1 1 - 1 - 1 1 1 1 1 1 - - 1 - - 1 1 - - - - - - 1 - - 1 - -]
[1 - 1 1 - - - 1 1 - - - 1 1 - - - - 1 1 - 1 1 1 1 - 1 - - 1 1 1 - - 1 -]
[1 1 - - 1 - - 1 1 - - 1 1 1 1 - - - - - - 1 1 - 1 1 - 1 1 - - - 1 1 1 -]
[1 1 - - 1 1 - 1 - 1 - - 1 1 - - 1 1 1 - 1 - - - 1 - 1 - 1 1 - 1 - 1 - -]
[1 1 1 - - - 1 - 1 1 - - 1 1 1 1 - 1 1 - 1 1 - 1 - - - - 1 - - - - - 1 1]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 63, 39, 58, 55, 49, 37, 27, 3, 22, 19, 13)(2, 56, 28, 69, 32, 4, 38, 20,
        64, 33, 68, 40)(5, 29, 54, 48, 57, 31, 41, 65, 18, 12, 21, 67)(6, 53,
        30, 62, 60, 70, 42, 17, 66, 26, 24, 34)(7, 11, 51, 44, 61, 35, 43, 47,
    15, 8, 25, 71)(9, 72, 59, 10, 52, 50, 45, 36, 23, 46, 16, 14)
    (1, 53, 37, 17)(2, 9, 38, 45)(3, 70, 39, 34)(4, 36, 40, 72)(5, 71, 41,
        35)(6, 27, 42, 63)(7, 31, 43, 67)(8, 18, 44, 54)(10, 69, 46, 33)(11, 57,
        47, 21)(12, 51, 48, 15)(13, 30, 49, 66)(14, 20, 50, 56)(16, 64, 52,
        28)(19, 62, 55, 26)(22, 60, 58, 24)(23, 68, 59, 32)(25, 65, 61, 29)
    (1, 2, 61)(3, 64, 7)(4, 22, 35)(5, 60, 36)(6, 10, 18)(8, 33, 63)(9, 53,
        29)(11, 56, 49)(12, 23, 26)(13, 47, 20)(14, 57, 66)(15, 55, 32)(16, 34,
        67)(17, 65, 45)(19, 68, 51)(21, 30, 50)(24, 72, 41)(25, 37, 38)(27, 44,
        69)(28, 43, 39)(31, 52, 70)(40, 58, 71)(42, 46, 54)(48, 59, 62)
Automorphism group has centre of order: 2
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 10> <72, 24>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 - 1 - - - 1 1 - 1 - - 1 - 1 - 1 - - - 1 - - 1 1 1 - 1 1 1 - - 1 1 1 -]
[1 1 1 - - - - - 1 - - - 1 - - - 1 - 1 1 - 1 1 - 1 1 1 1 - - - 1 1 1 - 1]
[1 - 1 1 1 1 1 - - - 1 - - - - 1 1 - 1 1 1 1 - - 1 1 1 - 1 1 - - - - - -]
[1 - 1 - - - 1 - 1 1 1 - - 1 1 1 - 1 1 - - 1 - - - 1 1 - - - 1 - 1 1 1 -]
[1 - 1 - - - - 1 - - 1 1 1 1 - 1 - 1 - 1 - 1 - - 1 - - - 1 1 - 1 1 - 1 1]
[1 - - 1 1 1 - - - - 1 1 1 - 1 - - - 1 - - - - - 1 - 1 1 1 - 1 - 1 1 1 1]
[1 1 - - - - 1 - 1 1 - 1 1 - 1 1 - 1 1 - 1 - 1 - 1 - 1 - 1 1 - - - - - 1]
[1 - - 1 1 1 1 - 1 - - - 1 1 1 1 - - - - - 1 1 1 1 - - - - 1 - 1 1 1 - -]
[1 1 1 1 1 - - - - 1 1 - 1 - - - - 1 - - - - 1 1 1 1 1 - - 1 1 1 - - 1 -]
[1 1 - - - 1 - - - - - 1 - - 1 1 1 1 - 1 - - - 1 - 1 1 - 1 1 1 1 1 1 - -]
[1 1 1 1 - 1 - - 1 - - - 1 1 1 1 - - - 1 1 - - - - 1 - 1 - 1 1 - - - 1 1]
[1 1 1 - 1 1 1 1 1 - - 1 - - 1 - - 1 - 1 - 1 - 1 1 - 1 1 - - - - - - 1 -]
[1 - 1 1 - 1 - - - 1 - - - - 1 1 1 1 1 - - 1 1 1 - - - 1 1 - - 1 - - 1 1]
[1 1 - 1 - 1 - 1 1 1 1 - 1 1 - - 1 1 - - - 1 - - - - 1 1 1 1 - - - 1 - -]
[1 1 1 - 1 1 - 1 - 1 1 1 - 1 1 1 1 - - - - - 1 - 1 1 - - - - - - - 1 - 1]
[1 - - 1 1 - - 1 1 1 - - - - 1 - - 1 - 1 1 1 - - 1 1 - - 1 - 1 1 - 1 - 1]
[1 1 - 1 - - - 1 - 1 1 - - 1 1 1 - - 1 1 1 - - 1 1 - 1 1 - - - 1 1 - - -]
[1 1 - - - 1 1 - - - 1 - - 1 - - - 1 - - 1 1 1 1 1 1 - 1 1 - 1 - 1 - - 1]
[1 - 1 1 - 1 1 1 - - - 1 1 1 - - - 1 1 - 1 - - 1 - 1 1 - - - - 1 - 1 - 1]
[1 - 1 1 - - - 1 1 - 1 1 - - 1 - 1 - - - 1 1 1 1 - - 1 - - 1 1 - 1 - - 1]
[1 1 - 1 - - 1 - - 1 - 1 - 1 - - 1 - 1 1 - 1 - 1 1 - - - - 1 1 - - 1 1 1]
[1 - 1 - 1 - - - - 1 - 1 1 1 - 1 - - - 1 1 1 1 1 - - 1 1 1 - 1 - - 1 - -]
[1 - - 1 1 - 1 - 1 1 1 1 1 - - 1 1 1 - 1 - - - 1 - 1 - 1 - - - - 1 - - 1]
[1 1 - - 1 1 1 1 - 1 - - 1 - - 1 1 - - - 1 1 - - - - 1 - - - 1 1 1 - 1 1]
[1 - 1 - 1 1 - - 1 1 - 1 - 1 - - 1 1 1 - 1 - - - 1 - - 1 - 1 1 1 1 - - -]
[1 1 1 1 1 - 1 1 - - - - 1 1 1 - 1 1 1 1 - - 1 - - - - - 1 - 1 - 1 - - -]
[1 - - - 1 - 1 - - - 1 - - 1 1 - 1 1 - 1 1 - 1 - - - 1 1 - 1 - 1 - 1 1 1]
[1 - - - - 1 - 1 1 - 1 - 1 - - 1 1 1 1 1 1 - 1 1 1 - - - - - 1 - - 1 1 -]
[1 1 1 - 1 - 1 1 1 - 1 - - - - 1 - - 1 - - - - 1 - - - 1 1 1 1 1 - 1 - 1]
[1 - - - 1 1 - 1 1 1 - - - 1 - - - - 1 1 - - 1 1 - 1 1 - 1 1 - - 1 - 1 1]
[1 1 1 1 - 1 1 - 1 1 1 1 - - - - - - - 1 1 - 1 - - - - - 1 - - 1 1 1 1 -]
[1 - - 1 - - 1 1 1 - - 1 - 1 - 1 1 - - - - - 1 - 1 1 1 1 1 - 1 1 - - 1 -]
[1 1 - - 1 - - - 1 - 1 1 1 1 1 - 1 - 1 - 1 1 - 1 - 1 - - 1 - - 1 - - 1 -]
[1 - - - - 1 1 1 - 1 1 1 1 - 1 - - - 1 1 - 1 1 - - 1 - 1 - 1 1 1 - - - -]
[1 1 - 1 1 - - 1 - - - 1 - - - 1 - 1 1 - 1 1 1 - - 1 - 1 - 1 - - 1 1 1 -]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 3, 28, 8, 27, 15, 37, 39, 64, 44, 63, 51)(2, 57, 72, 62, 10, 17, 38, 21,
        36, 26, 46, 53)(4, 55, 71, 61, 11, 65, 40, 19, 35, 25, 47, 29)(5, 67,
        69, 42, 34, 59, 41, 31, 33, 6, 70, 23)(7, 56, 13, 50, 52, 68, 43, 20,
        49, 14, 16, 32)(9, 12, 60, 22, 66, 18, 45, 48, 24, 58, 30, 54)
    (1, 2, 37, 38)(3, 65, 39, 29)(4, 66, 40, 30)(5, 16, 41, 52)(6, 48, 42,
    12)(7, 34, 43, 70)(8, 61, 44, 25)(9, 47, 45, 11)(10, 28, 46, 64)(13, 69,
        49, 33)(14, 57, 50, 21)(15, 55, 51, 19)(17, 32, 53, 68)(18, 59, 54,
        23)(20, 62, 56, 26)(22, 31, 58, 67)(24, 71, 60, 35)(27, 36, 63, 72)
Automorphism group has centre of order: 2
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 10> <72, 24>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 - - 1 - 1 1 1 - - - 1 - - - 1 - - 1 - 1 1 1 - - 1 1 - - 1 - - 1 1]
[1 1 1 - - 1 1 - 1 - - 1 1 1 - 1 1 - - - - - - - 1 - 1 - - - 1 - 1 1 1 1]
[1 1 1 - - - - 1 - - - 1 - - 1 1 1 1 1 - 1 1 - 1 - - 1 1 - - - 1 1 1 - -]
[1 1 1 - - 1 1 - - - 1 - 1 - - - - 1 1 1 1 - 1 - - 1 1 1 - 1 - - 1 - - 1]
[1 - - 1 - - - 1 - - 1 - 1 - - - - 1 1 - - - - 1 1 1 1 - 1 - 1 1 1 1 1 1]
[1 - - 1 - 1 1 1 - - - - 1 1 1 1 1 - 1 - 1 - 1 - 1 - - - 1 1 - 1 1 - - -]
[1 - - 1 - - 1 - - 1 - 1 1 1 - - 1 1 1 - - 1 1 1 - - - 1 - 1 - - - 1 1 1]
[1 - - 1 - - - 1 - 1 1 1 - 1 - 1 - - - 1 1 1 1 - 1 - 1 1 - - 1 - 1 - - 1]
[1 - - 1 - 1 1 - 1 - - - - 1 1 - - - - 1 1 1 - 1 - 1 1 1 1 - - - 1 1 1 -]
[1 1 1 1 - - 1 - 1 1 1 - - 1 - 1 - - 1 - - 1 - 1 1 1 1 - - 1 - 1 - - - -]
[1 1 1 1 - - - - - - 1 1 1 1 1 - 1 - - 1 1 - 1 1 - 1 - - - - 1 1 - - 1 -]
[1 1 1 1 - - - 1 1 - - - 1 - 1 1 - - - - - 1 1 - - 1 - 1 1 1 1 - - 1 - 1]
[1 1 1 1 - 1 - - - 1 - 1 - - 1 - - 1 1 1 - 1 - - 1 - - - 1 1 1 - 1 - 1 -]
[1 - - - 1 1 - - 1 - - 1 1 1 1 - - 1 1 - - 1 1 - 1 1 1 1 - - 1 1 - - - -]
[1 - - - - - - - 1 1 - 1 1 - 1 1 1 1 - 1 1 - - 1 1 1 1 - 1 1 - - - - - 1]
[1 - - - - 1 1 1 1 - 1 1 - - 1 1 - - 1 1 - - - 1 - - - 1 - 1 1 1 - - 1 1]
[1 - - - - 1 - - 1 1 1 - - - - 1 1 1 - - 1 1 1 - - 1 - - - 1 1 1 1 1 1 -]
[1 - 1 1 1 - 1 - 1 1 - 1 - - - - 1 - 1 - 1 - - - - 1 - 1 1 - 1 1 1 - - 1]
[1 - 1 1 1 1 - 1 1 1 - 1 1 - - - - - - 1 - - 1 1 - - 1 - - 1 - 1 1 1 - -]
[1 1 - 1 1 - 1 1 1 - - 1 - - - 1 - 1 1 1 1 - 1 - 1 1 - - - - - - - 1 1 -]
[1 - 1 1 1 1 1 - - 1 1 - 1 - 1 1 - 1 - - 1 - - 1 1 - - 1 - - 1 - - 1 - -]
[1 - 1 - - - 1 1 1 1 1 - - 1 1 - 1 1 1 1 - - 1 - - - 1 - 1 - 1 - - 1 - -]
[1 1 - 1 1 1 1 - - - - - - - - 1 1 1 - 1 - 1 1 1 - - 1 - 1 - 1 1 - - - 1]
[1 1 - 1 1 1 - 1 1 1 1 - 1 - 1 - 1 - 1 - 1 1 - - - - 1 - - - - - - - 1 1]
[1 - 1 1 1 1 - 1 - - 1 1 - 1 - 1 1 1 - - - - - - - 1 1 1 1 1 - - - - 1 -]
[1 1 - 1 1 - - - 1 - 1 - - 1 1 - 1 1 - 1 - - - - 1 - - 1 - 1 - 1 1 1 - 1]
[1 1 - - - 1 1 1 - 1 1 1 1 - - - 1 - - 1 - 1 - - 1 1 - 1 1 - - 1 - 1 - -]
[1 - 1 - 1 - 1 1 - 1 - - 1 1 1 1 - 1 - 1 - 1 - - - 1 - - - - - 1 1 - 1 1]
[1 1 - - 1 - 1 1 1 - 1 1 1 1 - - - 1 - - 1 1 - 1 - - - - 1 1 1 - 1 - - -]
[1 - 1 - 1 1 - 1 - - - - - 1 - - 1 - 1 1 1 1 - 1 1 1 - - - 1 1 - - 1 - 1]
[1 1 - - 1 1 - - - 1 1 1 - 1 1 1 - - 1 - - - 1 1 - 1 - - 1 - - - 1 1 - 1]
[1 1 - - 1 - - - - 1 - - 1 1 - 1 - - 1 1 1 - - - - - 1 1 1 1 1 1 - 1 1 -]
[1 - 1 - 1 - 1 - - - 1 1 - - 1 - - - - - 1 1 1 - 1 - 1 - 1 1 - 1 - 1 1 1]
[1 - 1 - 1 - - - 1 - 1 - 1 - - 1 1 - 1 1 - 1 1 1 1 - - 1 1 - - - 1 - 1 -]
[1 1 - - 1 - 1 1 - 1 - - - - 1 - 1 - - - - - 1 1 1 1 1 1 - 1 1 - 1 - 1 -]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 40, 37, 4)(2, 5, 38, 41)(3, 33, 39, 69)(6, 24, 42, 60)(7, 9, 43, 45)(8,
    10, 44, 46)(11, 20, 47, 56)(12, 55, 48, 19)(13, 16, 49, 52)(14, 68, 50,
        32)(15, 21, 51, 57)(17, 66, 53, 30)(18, 23, 54, 59)(22, 28, 58, 64)(25,
        27, 61, 63)(26, 29, 62, 65)(31, 72, 67, 36)(34, 35, 70, 71)
    (1, 3, 48, 57, 50, 17, 37, 39, 12, 21, 14, 53)(2, 60, 10, 25, 56, 35, 38,
        24, 46, 61, 20, 71)(4, 66, 32, 15, 19, 33, 40, 30, 68, 51, 55, 69)(5,
        34, 47, 63, 8, 42, 41, 70, 11, 27, 44, 6)(7, 67, 54, 62, 49, 64, 43, 31,
    18, 26, 13, 28)(9, 58, 16, 29, 23, 72, 45, 22, 52, 65, 59, 36)
    (1, 2, 36)(3, 23, 61)(4, 67, 41)(5, 40, 31)(6, 13, 66)(7, 15, 34)(8, 55,
        28)(9, 35, 21)(10, 58, 48)(11, 32, 62)(12, 46, 22)(14, 20, 65)(16, 24,
        53)(17, 52, 60)(18, 69, 27)(19, 64, 44)(25, 39, 59)(26, 47, 68)(29, 50,
        56)(30, 42, 49)(33, 63, 54)(37, 38, 72)(43, 51, 70)(45, 71, 57)
Automorphism group has centre of order: 2
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 10> <72, 24>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 - - 1 1 1 - 1 - 1 - - - 1 1 - - 1 1 1 - - - - 1 - - 1 - 1 - 1 - 1 1]
[1 1 - - 1 1 - - - - - - 1 1 - 1 1 - - - 1 1 1 - - - 1 1 1 - - 1 1 1 - 1]
[1 - 1 1 - 1 - 1 - - 1 - 1 - - - - - 1 1 1 - - 1 - - 1 1 1 1 - 1 - - 1 1]
[1 1 - - 1 - - 1 - - 1 - 1 1 1 - 1 1 1 - - 1 - 1 - 1 1 - - - 1 1 - - 1 -]
[1 1 - - 1 1 1 1 1 1 - 1 - 1 - - - - - - - - - 1 - - - 1 1 1 1 1 - 1 1 -]
[1 1 1 1 - - - 1 1 - - 1 1 1 1 1 - - 1 - 1 - 1 1 - - - - - - - - 1 1 1 -]
[1 1 1 1 - 1 1 - - 1 - - - - - - 1 1 1 - 1 - - - 1 - 1 - - - 1 1 1 1 1 -]
[1 - - - 1 1 - - 1 1 - 1 1 - 1 - - 1 1 - 1 1 - 1 1 - 1 - 1 1 - - 1 - - -]
[1 - - - 1 - - - - 1 1 1 - 1 - 1 - - 1 1 1 - 1 - 1 1 1 - - 1 - 1 - 1 1 -]
[1 - 1 1 1 - - - 1 1 1 - - - 1 1 - - - 1 - 1 - 1 - - 1 1 - - 1 1 1 1 - -]
[1 - 1 1 1 1 1 1 - 1 - - - 1 1 - - - - - - 1 1 - - 1 1 - - 1 - - 1 - 1 1]
[1 - 1 1 1 1 - 1 - - 1 1 - 1 - 1 - 1 1 - - 1 - - 1 - - - 1 - 1 - - 1 - 1]
[1 1 - - - 1 1 1 - - 1 1 - - - 1 - 1 - 1 - 1 1 1 1 - 1 1 - - - - 1 - 1 -]
[1 - - - - - 1 1 - 1 - - 1 1 - - - - 1 1 1 1 - 1 1 1 - 1 - - 1 - 1 1 - 1]
[1 - - - - - 1 1 - 1 1 - - - 1 1 1 1 1 - - - 1 1 - - - - 1 1 - 1 1 1 - 1]
[1 1 1 1 1 - 1 - - - - - 1 1 - 1 - 1 - 1 - - - 1 1 1 - - 1 1 - 1 1 - - -]
[1 1 1 1 1 - 1 - - 1 1 1 - - - - 1 - 1 - 1 1 1 1 - 1 - 1 1 - - - - - - -]
[1 - - 1 - 1 1 - 1 - 1 1 1 1 - - 1 - 1 1 - 1 1 - - - - - - 1 1 1 1 - - -]
[1 - 1 - - 1 1 - 1 - - 1 - 1 1 1 1 - 1 - - - - 1 1 1 1 1 - - - 1 - - - 1]
[1 1 - 1 1 - - 1 1 - - 1 - - - - 1 1 1 1 - - - - - 1 1 1 - 1 - - 1 1 - 1]
[1 - 1 - - 1 - - - 1 1 1 1 1 1 - 1 1 - 1 - - - - - 1 - 1 1 - - - 1 1 1 -]
[1 - - 1 - 1 - 1 1 1 - - - 1 - 1 1 1 - 1 1 - 1 1 - 1 1 - 1 - 1 - - - - -]
[1 1 1 - 1 1 - 1 - 1 - - 1 - 1 1 1 - 1 1 - - 1 - 1 - - 1 - 1 1 - - - - -]
[1 - - 1 - - - 1 - - - 1 - - 1 1 1 - - - 1 1 - - 1 1 - 1 1 1 1 1 1 - 1 -]
[1 - 1 - - - 1 - 1 - - - 1 - - 1 - 1 1 - - 1 1 - - 1 1 1 1 1 1 - - 1 1 -]
[1 1 - 1 - - 1 - - 1 1 1 1 1 1 1 - 1 - - 1 - - - - - 1 1 - 1 1 - - - - 1]
[1 - - 1 1 1 1 1 1 - 1 - 1 - 1 - - 1 - - 1 - 1 - 1 1 - 1 - - - 1 - 1 - -]
[1 1 - 1 - - - - 1 1 - - - 1 1 - - 1 1 1 - 1 1 - 1 - - 1 1 - - 1 - - 1 1]
[1 - - 1 1 - 1 - - - - 1 1 - 1 - 1 - - 1 - - 1 1 1 - 1 - 1 - 1 - - 1 1 1]
[1 1 1 - - - 1 1 1 - 1 - - 1 1 - 1 - - 1 1 1 - - 1 - 1 - 1 1 - - - 1 - -]
[1 - 1 - 1 - 1 1 1 1 - 1 1 - - 1 1 1 - 1 1 1 - - - - - - - - - 1 - - 1 1]
[1 1 - 1 - 1 - - 1 1 1 - 1 - - 1 1 - - - - 1 - 1 1 1 - - - 1 - - - 1 1 1]
[1 1 1 - - 1 - - - - - 1 - - 1 - - 1 - 1 1 1 1 1 - 1 - - - 1 1 1 - 1 - 1]
[1 1 1 - - - - 1 1 1 1 1 1 - - - - - - - - - 1 - 1 1 1 - 1 - 1 1 1 - - 1]
[1 - 1 - 1 - - - 1 - 1 - - 1 - - 1 1 - - 1 - 1 1 1 - - 1 - 1 1 - 1 - 1 1]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 53, 37, 17)(2, 48, 38, 12)(3, 65, 39, 29)(4, 55, 40, 19)(5, 23, 41,
        59)(6, 8, 42, 44)(7, 62, 43, 26)(9, 56, 45, 20)(10, 52, 46, 16)(11, 27,
        47, 63)(13, 34, 49, 70)(14, 18, 50, 54)(15, 66, 51, 30)(21, 36, 57,
        72)(22, 28, 58, 64)(24, 25, 60, 61)(31, 71, 67, 35)(32, 69, 68, 33)
    (1, 3, 37, 39)(2, 24, 38, 60)(4, 43, 40, 7)(5, 67, 41, 31)(6, 34, 42, 70)(8,
        68, 44, 32)(9, 15, 45, 51)(10, 71, 46, 35)(11, 30, 47, 66)(12, 72, 48,
        36)(13, 69, 49, 33)(14, 62, 50, 26)(16, 59, 52, 23)(17, 64, 53, 28)(18,
        55, 54, 19)(20, 27, 56, 63)(21, 25, 57, 61)(22, 65, 58, 29)
    (1, 2, 37, 38)(3, 13, 39, 49)(4, 17, 40, 53)(5, 24, 41, 60)(6, 56, 42,
        20)(7, 45, 43, 9)(8, 28, 44, 64)(10, 36, 46, 72)(11, 18, 47, 54)(12, 15,
        48, 51)(14, 29, 50, 65)(16, 62, 52, 26)(19, 67, 55, 31)(21, 22, 57,
        58)(23, 34, 59, 70)(25, 63, 61, 27)(30, 33, 66, 69)(32, 71, 68, 35)
Automorphism group has centre of order: 2
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 10> <72, 24>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 - - - - 1 1 - 1 - 1 1 - 1 1 1 - - - 1 - 1 - 1 - 1 1 - 1 - - 1 - 1 1 -]
[1 1 1 1 - - - - 1 1 1 - - - - - 1 - - 1 - 1 1 1 - 1 - 1 1 1 1 1 - - - -]
[1 - - - 1 - 1 - - 1 1 1 - - 1 - 1 1 - 1 - - 1 - 1 - 1 1 1 - 1 - - - 1 1]
[1 1 1 1 1 1 - - - - 1 - - 1 - 1 - 1 - 1 - - - - - 1 1 1 - 1 - - 1 - 1 1]
[1 - - - 1 1 - 1 1 1 1 1 - - - 1 1 - 1 1 1 - - - - - - - 1 1 - 1 1 - - 1]
[1 - - - 1 - - - 1 - - - 1 - 1 1 - 1 1 - - - - 1 1 1 - 1 1 1 1 1 1 - 1 -]
[1 1 1 1 1 - 1 1 1 - - 1 - - 1 1 1 - - - - - 1 - 1 1 1 - - - - 1 1 - - -]
[1 - - - 1 - - - 1 - 1 - 1 1 1 - 1 - - - 1 1 1 - - 1 1 - - 1 1 - 1 1 - 1]
[1 - - 1 - 1 - 1 1 1 - - 1 1 1 - 1 1 - 1 - - - - 1 1 - 1 - - - 1 - 1 - 1]
[1 1 1 - - - 1 1 - - - - - 1 1 1 1 - - - 1 - - - - - - 1 1 1 1 1 - 1 1 1]
[1 - - 1 1 1 1 1 - - - - - 1 - 1 1 1 1 - - 1 1 1 - 1 - - 1 - 1 - - - - 1]
[1 1 1 - - 1 - - 1 1 - - - - 1 1 - 1 1 - - 1 1 - 1 - 1 - 1 1 - - - 1 - 1]
[1 1 1 - 1 1 1 - - 1 - - 1 - 1 - - - 1 1 1 - - 1 - 1 1 - - - 1 1 - - - 1]
[1 - - 1 1 1 1 - - 1 - - - 1 - - - - - - 1 - 1 1 1 - 1 1 1 1 - 1 1 1 - -]
[1 - - 1 - - 1 1 - - 1 - 1 - 1 1 - 1 1 1 1 1 1 - - - 1 1 - 1 - 1 - - - -]
[1 1 1 - 1 1 - 1 1 - 1 1 1 1 1 - - 1 - - 1 - 1 1 - - - 1 1 - - - - - - -]
[1 1 1 - 1 - 1 - - - 1 - 1 1 - - 1 1 1 1 - 1 - - 1 - - - 1 - - 1 1 1 - -]
[1 - 1 - - - - 1 - 1 - 1 1 1 - - - - 1 - - 1 1 - - 1 1 1 1 - - 1 1 - 1 1]
[1 1 - 1 - 1 1 - 1 - 1 1 1 1 - - - - 1 - - - 1 - 1 - - - - 1 1 1 - - 1 1]
[1 - 1 - - 1 1 - 1 - - - 1 - - 1 1 - - 1 1 1 1 1 1 - - 1 - - - - 1 - 1 1]
[1 1 - 1 - 1 1 - - 1 - 1 1 - 1 - 1 1 - - 1 1 - - - 1 - - 1 1 - - 1 - 1 -]
[1 - 1 - - - 1 1 1 1 1 - - 1 - - 1 1 1 - 1 - - 1 1 1 1 - - 1 - - - - 1 -]
[1 1 - 1 1 - - 1 1 1 - - 1 1 - 1 - - - 1 1 1 - - 1 - 1 - 1 - 1 - - - 1 -]
[1 1 - 1 1 - 1 1 1 1 1 - - - 1 - - - 1 - - 1 - 1 - - - 1 - - - - 1 1 1 1]
[1 - 1 - 1 1 1 1 - 1 1 1 1 - - 1 - - - - - 1 - - 1 1 - 1 - 1 1 - - 1 - -]
[1 1 - 1 - - - - - - 1 1 1 - - 1 1 - 1 - 1 - - 1 1 1 1 1 1 - - - - 1 - 1]
[1 1 - - - 1 - 1 - - - 1 - 1 1 - 1 - 1 1 - 1 - 1 1 - 1 1 - 1 1 - 1 - - -]
[1 - 1 1 - 1 - 1 - - 1 - - - 1 - - - 1 1 1 - 1 - 1 1 - - 1 - 1 - 1 1 1 -]
[1 1 - - 1 - - 1 - - - 1 - - - - - 1 - 1 1 1 1 1 1 1 - - - 1 - 1 - 1 1 1]
[1 - 1 1 1 1 - - 1 - - 1 - - - - 1 1 1 - 1 1 - - - - 1 1 - - 1 1 - 1 1 -]
[1 - 1 1 - - - - - 1 1 1 - 1 1 1 - 1 - - 1 1 - 1 1 - - - - - 1 1 1 - - 1]
[1 1 - - - 1 - 1 - 1 1 - 1 - - 1 1 1 - - - - 1 1 - - 1 - - - 1 1 1 1 1 -]
[1 1 - - - - 1 - 1 1 - 1 - 1 - 1 - 1 1 1 1 - 1 - - 1 - 1 - - 1 - 1 1 - -]
[1 - 1 1 1 - - - - 1 - 1 1 1 1 1 1 - 1 1 - - 1 1 - - - - - 1 - - - 1 1 -]
[1 - 1 1 - - 1 1 1 - - 1 1 - - - - 1 - 1 - - - 1 - - 1 - 1 1 1 - 1 1 - 1]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 71, 34, 37, 35, 70)(2, 22, 43, 38, 58, 7)(3, 67, 66, 39, 31, 30)(4, 63,
        72, 40, 27, 36)(5, 32, 52, 41, 68, 16)(6, 49, 19, 42, 13, 55)(8, 10, 54,
        44, 46, 18)(9, 33, 56, 45, 69, 20)(11, 26, 48, 47, 62, 12)(14, 61, 23,
        50, 25, 59)(15, 64, 53, 51, 28, 17)(21, 24, 65, 57, 60, 29)
    (1, 3, 8)(2, 15, 47)(4, 67, 26)(5, 21, 72)(6, 59, 69)(7, 16, 54)(9, 30,
        29)(10, 20, 64)(11, 38, 51)(12, 34, 19)(13, 60, 22)(14, 35, 68)(17, 61,
        27)(18, 43, 52)(23, 33, 42)(24, 58, 49)(25, 63, 53)(28, 46, 56)(31, 62,
        40)(32, 50, 71)(36, 41, 57)(37, 39, 44)(45, 66, 65)(48, 70, 55)
Automorphism group has centre of order: 6
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 11> <72, 25>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 - - - 1 1 1 1 1 - - 1 - - - 1 - 1 1 1 1 1 - - - 1 - 1 1 - - 1 - - 1 -]
[1 - - - 1 1 1 - - 1 1 - 1 1 1 1 - - 1 - 1 - - - 1 - 1 1 - 1 - - 1 - 1 -]
[1 - 1 1 - - - - - - 1 - - - 1 1 - 1 - 1 - 1 - 1 - 1 1 1 1 1 - - 1 1 1 -]
[1 - 1 1 - - - 1 1 - 1 - 1 1 - 1 1 1 1 - - - 1 - 1 - 1 - 1 - - 1 - - 1 -]
[1 - 1 1 - 1 - 1 - - - 1 1 1 1 1 - - - - 1 - 1 - - 1 - 1 - - 1 - - 1 1 1]
[1 - 1 - - 1 1 1 1 - 1 1 - - 1 - - - 1 - - 1 1 1 1 1 1 - - 1 - - - - - 1]
[1 - 1 - 1 1 - 1 - 1 - - - 1 1 - 1 1 - 1 1 - 1 1 1 1 - - 1 - - - 1 - - -]
[1 - 1 - - 1 1 - - - 1 1 1 - - - 1 - - 1 1 - - 1 - - 1 - 1 - 1 1 1 - 1 1]
[1 - - 1 - 1 - - - 1 1 1 1 1 - - - 1 1 1 1 1 1 1 - - - - - 1 - 1 - 1 - -]
[1 1 - 1 - - 1 1 1 - 1 - - 1 - - - - 1 1 1 - - 1 1 1 - - - - 1 - 1 1 1 -]
[1 - - 1 - - 1 1 - 1 - 1 - - 1 1 1 - - 1 - 1 1 - 1 - - - - 1 1 1 1 - 1 -]
[1 1 1 - 1 1 - - 1 1 - - - - 1 1 - - 1 1 - - 1 1 - - 1 - - - 1 1 - 1 1 -]
[1 - 1 - 1 - 1 1 - 1 1 - 1 - - 1 1 1 1 1 - - - - - 1 - - - 1 1 - - 1 - 1]
[1 - - 1 1 - - 1 1 - - - 1 - 1 - - 1 - 1 1 - - 1 1 - 1 1 - 1 1 1 - - - 1]
[1 1 1 - 1 - 1 1 - - - - - 1 - - - 1 - - 1 1 1 - - - 1 - - 1 - 1 1 1 1 1]
[1 - 1 1 1 - - - 1 1 - 1 - 1 - - 1 - 1 - - - - 1 - 1 - 1 - 1 - 1 1 - 1 1]
[1 - - - 1 1 - - 1 - 1 - - 1 - - 1 - - 1 - 1 1 - 1 - - 1 1 1 1 - - 1 1 1]
[1 1 - - 1 - 1 - - - 1 1 1 - 1 - 1 1 - - - - 1 1 1 1 - 1 - - - 1 - 1 1 -]
[1 1 1 1 1 - - - - 1 1 1 - - 1 - - 1 1 - 1 1 - - 1 - - - 1 - 1 - - - 1 1]
[1 1 1 - - - 1 - 1 - - 1 1 1 1 - - 1 1 1 - - 1 - - - - 1 1 1 1 - 1 - - -]
[1 1 - - - 1 - 1 - - 1 - - 1 1 1 1 1 1 - - 1 - 1 - - - 1 - - 1 1 1 - - 1]
[1 1 1 1 - 1 1 1 1 1 1 - - - 1 - 1 - - - 1 - - - - - - 1 1 1 - 1 - 1 - -]
[1 - - 1 - 1 1 - - 1 - - - - - - - 1 1 - - - 1 - 1 1 1 1 1 - 1 1 1 1 - 1]
[1 1 1 1 1 1 - 1 - - - 1 1 - - - 1 - 1 1 - 1 - - 1 - 1 1 - - - - 1 1 - -]
[1 - - 1 1 - 1 - 1 - - - 1 - 1 1 1 - 1 - 1 1 1 1 - - - - 1 - - - 1 1 - 1]
[1 1 - 1 - 1 1 - 1 1 - - 1 1 1 - 1 1 - 1 - 1 - - - 1 1 - - - - - - - 1 1]
[1 1 - 1 1 - 1 1 - 1 1 1 - 1 - 1 - - - 1 - - 1 1 - - 1 1 1 - - - - - - 1]
[1 1 - 1 1 1 - - 1 - 1 1 - - - 1 1 1 - - 1 - 1 - - 1 1 - - 1 1 - 1 - - -]
[1 - 1 - - - 1 - 1 1 - 1 - 1 - 1 1 1 - - 1 1 - 1 1 - 1 1 - - 1 - - 1 - -]
[1 - - - 1 - - 1 1 1 1 1 1 1 1 - - - - - - 1 - - - 1 1 - 1 - 1 1 1 1 - -]
[1 1 - - - 1 - 1 1 1 - 1 1 - - 1 - 1 - - - - - 1 1 - - - 1 1 - - 1 1 1 1]
[1 1 - - - - - 1 - 1 - - 1 - - - 1 - 1 - 1 1 1 1 - 1 1 1 1 1 1 - - - 1 -]
[1 1 1 - - - - - 1 1 1 - 1 - - 1 - - - 1 1 1 1 - 1 1 - 1 - - - 1 1 - - 1]
[1 1 1 1 1 1 1 - - - - - 1 1 - 1 - - - - - 1 - 1 1 1 - - 1 1 1 1 - - - -]
[1 1 - - - - - - - - - 1 - 1 1 1 1 - 1 1 1 - - - 1 1 1 - 1 1 - 1 - 1 - 1]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 60, 57)(2, 26, 63)(3, 43, 29)(4, 70, 49)(5, 18, 9)(6, 47, 48)(7, 65,
        39)(8, 53, 59)(10, 32, 25)(11, 12, 42)(13, 40, 34)(14, 20, 67)(15, 55,
        35)(16, 30, 28)(17, 23, 44)(19, 71, 51)(21, 37, 24)(22, 72, 33)(27, 38,
        62)(31, 50, 56)(36, 69, 58)(41, 54, 45)(46, 68, 61)(52, 66, 64)
    (1, 3, 52, 25, 23, 49, 37, 39, 16, 61, 59, 13)(2, 22, 48, 41, 15, 31, 38,
        58, 12, 5, 51, 67)(4, 14, 7, 72, 46, 54, 40, 50, 43, 36, 10, 18)(6, 44,
        55, 24, 62, 30, 42, 8, 19, 60, 26, 66)(9, 28, 20, 53, 33, 57, 45, 64,
        56, 17, 69, 21)(11, 29, 71, 32, 63, 70, 47, 65, 35, 68, 27, 34)
Automorphism group has centre of order: 6
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 11> <72, 25>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 1 1 1 - - - - - - - - 1 1 1 1 - - - - 1 1 - - - - - 1 1 1 1 1 - 1]
[1 - - - - 1 1 - 1 - - 1 - 1 1 - 1 - - - 1 - 1 1 1 - 1 1 - 1 - 1 - 1 1 -]
[1 - - - - 1 - 1 - 1 - - 1 1 - 1 - 1 - - - 1 1 1 - 1 1 - 1 1 - - 1 1 1 -]
[1 - - - - - - - 1 1 1 - - 1 1 1 1 1 - 1 1 1 1 1 1 1 - - - - 1 - - - - 1]
[1 1 1 1 1 - - - 1 1 1 1 1 - - - - - - 1 - - 1 1 1 1 1 - - 1 - - - 1 - -]
[1 1 1 1 1 - 1 1 1 1 - - - 1 1 1 - - - - 1 1 - - - - 1 - - - 1 - - 1 1 -]
[1 1 1 1 1 1 - - - - - - - 1 - - 1 1 - 1 1 1 - - 1 1 - 1 1 1 - - - - 1 -]
[1 - - 1 - - 1 - - - 1 1 - - - 1 - 1 - 1 - 1 - - - 1 1 1 - 1 1 1 - 1 1 1]
[1 - - - 1 - - 1 - - 1 - 1 - 1 - 1 - - 1 1 - - - 1 - 1 - 1 1 1 - 1 1 1 1]
[1 1 1 - - - 1 1 - - - 1 1 - - - 1 1 1 1 1 1 1 1 - - - - - - - - - 1 1 1]
[1 1 1 - - 1 1 1 1 1 1 - - - - - 1 1 - - - - - - 1 1 1 - - - - 1 1 - 1 1]
[1 - - 1 1 - - - 1 1 - 1 1 1 - - 1 1 1 - 1 1 - - - - 1 - - 1 - 1 1 - - 1]
[1 - - 1 1 1 1 1 - - 1 1 1 1 1 1 1 1 1 - - - - - 1 1 - - - - - - - 1 - -]
[1 - - 1 1 1 1 1 - - - - - - - - - - 1 1 1 1 1 1 1 1 1 - - - 1 1 1 - - -]
[1 1 1 - - - 1 - - - 1 1 - 1 1 - - 1 1 - - 1 1 - 1 - 1 - 1 1 1 - 1 - - -]
[1 1 1 - - - - 1 - - 1 - 1 1 - 1 1 - 1 - 1 - - 1 - 1 1 1 - 1 1 1 - - - -]
[1 - - 1 1 - 1 1 1 1 1 - - - - - 1 1 1 - - - 1 1 - - - 1 1 1 1 - - - 1 -]
[1 1 - - - 1 - 1 1 1 - 1 - - - 1 1 - 1 1 - 1 - - 1 - - 1 - 1 1 - 1 1 - -]
[1 - 1 - - 1 1 - 1 1 - - 1 - 1 - - 1 1 1 1 - - - - 1 - - 1 1 1 1 - 1 - -]
[1 - 1 - 1 1 - - - 1 1 - 1 1 - - - - 1 - - 1 1 - 1 - - 1 - - 1 1 - 1 1 1]
[1 1 - 1 - 1 - - 1 - 1 1 - 1 - - - - 1 - 1 - - 1 - 1 - - 1 - 1 - 1 1 1 1]
[1 1 - - 1 1 1 1 - 1 1 1 - 1 - 1 - - - 1 1 - 1 - - - - - 1 1 - 1 - - - 1]
[1 - 1 1 - 1 1 1 1 - 1 - 1 1 1 - - - - 1 - 1 - 1 - - - 1 - 1 - - 1 - - 1]
[1 1 - 1 - 1 - - 1 - 1 - 1 - 1 1 1 - 1 1 - 1 1 - - - 1 - 1 - - 1 - - 1 -]
[1 - 1 - 1 1 - - - 1 1 1 - - 1 1 - 1 1 1 1 - - 1 - - 1 1 - - - - 1 - 1 -]
[1 - 1 1 - - 1 - - 1 - 1 1 1 - 1 1 - - 1 - - - 1 1 - - - 1 - 1 1 1 - 1 -]
[1 1 - - 1 - - 1 1 - - 1 1 1 1 - - 1 - 1 - - 1 - - 1 - 1 - - 1 1 1 - 1 -]
[1 1 - 1 - - 1 - - 1 - - 1 - 1 1 - - 1 - 1 - 1 - 1 1 - 1 - 1 - - 1 - 1 1]
[1 - 1 - 1 - - 1 1 - - 1 - - 1 1 - - 1 - - 1 - 1 1 1 - - 1 1 - 1 - - 1 1]
[1 - 1 1 - - - 1 - 1 1 1 - - 1 - 1 - - - 1 1 1 - - 1 - 1 1 - - 1 1 1 - -]
[1 1 - - 1 - 1 - 1 - 1 - 1 - - 1 - 1 - - 1 1 - 1 1 - - 1 1 - - 1 1 1 - -]
[1 1 - - 1 1 1 - - 1 - 1 1 - 1 - 1 - - - - 1 - 1 - 1 1 1 1 - 1 - - - - 1]
[1 - 1 1 - 1 - 1 1 - - 1 1 - - 1 - 1 - - 1 - 1 - 1 - 1 1 1 - 1 - - - - 1]
[1 - 1 - 1 - 1 - 1 - - - - 1 - 1 1 - 1 1 - - 1 - - 1 1 1 1 - - - 1 1 - 1]
[1 1 - 1 - - - 1 - 1 - - - 1 1 - - 1 1 1 - - - 1 1 - 1 1 1 - - 1 - 1 - 1]

Permutation group acting on a set of cardinality 72
Order = 144 = 2^4 * 3^2
    (1, 3, 37, 39)(2, 65, 38, 29)(4, 10, 40, 46)(5, 9, 41, 45)(6, 24, 42, 60)(7,
        22, 43, 58)(8, 67, 44, 31)(11, 55, 47, 19)(12, 17, 48, 53)(13, 25, 49,
        61)(14, 63, 50, 27)(15, 72, 51, 36)(16, 56, 52, 20)(18, 34, 54, 70)(21,
        28, 57, 64)(23, 32, 59, 68)(26, 35, 62, 71)(30, 69, 66, 33)
    (1, 2, 37, 38)(3, 72, 39, 36)(4, 71, 40, 35)(5, 13, 41, 49)(6, 12, 42,
        48)(7, 47, 43, 11)(8, 18, 44, 54)(9, 34, 45, 70)(10, 33, 46, 69)(14, 51,
        50, 15)(16, 64, 52, 28)(17, 63, 53, 27)(19, 31, 55, 67)(20, 32, 56,
        68)(21, 62, 57, 26)(22, 61, 58, 25)(23, 30, 59, 66)(24, 29, 60, 65)
    (3, 4)(9, 10)(16, 17)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31,
        32)(33, 34)(35, 36)(39, 40)(45, 46)(52, 53)(55, 56)(57, 58)(59, 60)(61,
        62)(63, 64)(65, 66)(67, 68)(69, 70)(71, 72)
Automorphism group has centre of order: 2
Number of regular subgroups: 4
Number of regular subgroups containing zeta: 4
Number of centrally regular subgroups: 4
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 10> <72, 24>
<36, 13> <72, 31>
<36, 12> <72, 26>
<36, 10> <72, 24>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 - - 1 1 - 1 - 1 1 - - - 1 1 - - 1 - 1 1 1 - - 1 1 - 1 - 1 1 - - - - 1]
[1 1 1 - - 1 1 1 - - - 1 - - - 1 - 1 1 - - 1 - - - 1 - 1 - 1 1 1 - - 1 1]
[1 1 1 - - - - - - 1 - - - 1 1 1 1 - 1 - 1 1 1 1 1 - 1 1 - 1 - - - - 1 -]
[1 1 1 - - 1 1 - 1 - - - 1 1 1 - - 1 - - 1 1 - - - - 1 1 1 - - 1 1 1 - -]
[1 1 1 - - - - 1 - 1 1 - 1 1 1 1 - - - 1 - - - 1 - 1 - 1 - - 1 - 1 1 - 1]
[1 - - 1 1 - - 1 - - - 1 1 1 1 - - 1 1 - - - - 1 - - 1 1 1 1 - - - 1 1 1]
[1 1 1 1 - 1 - - 1 - 1 1 - 1 - - - 1 1 1 1 - - 1 1 - - - - - 1 - - 1 1 -]
[1 1 1 - 1 - 1 1 1 1 - 1 - 1 - - 1 - - - - - - - 1 - 1 - 1 - 1 - 1 - 1 1]
[1 - - - 1 1 - 1 - - - 1 - 1 - 1 - - - 1 1 - 1 - 1 - 1 1 - 1 1 1 1 1 - -]
[1 - - 1 - 1 1 - - 1 - - - 1 - 1 1 - 1 1 - 1 - 1 - - 1 - 1 - 1 1 - 1 - 1]
[1 - - 1 - 1 1 - - 1 1 1 1 1 - 1 1 1 - - 1 - 1 - - - - 1 - - - - 1 - 1 1]
[1 - - - 1 - 1 - 1 1 1 1 - - 1 - - - 1 - - 1 1 1 - - - 1 - - 1 1 1 1 1 -]
[1 - - - - 1 - 1 1 1 1 - - 1 - - 1 1 1 - - - - 1 1 1 - 1 1 1 - 1 1 - - -]
[1 1 1 1 1 1 1 1 1 1 - - 1 - - - 1 - 1 1 - - 1 - - - - 1 - 1 - - - 1 - -]
[1 - - - - 1 - 1 1 - 1 - 1 - 1 - 1 - 1 1 1 1 - - - - 1 - - 1 1 - 1 - 1 1]
[1 - - - - - 1 1 1 - - 1 1 - - 1 1 - - 1 1 1 - 1 1 1 - 1 1 - - - - 1 1 -]
[1 1 1 1 1 - - - - - 1 1 - - - - 1 - - 1 1 1 - 1 - - - 1 1 1 - 1 1 - - 1]
[1 - 1 1 1 - - 1 1 1 1 1 1 1 - 1 - - 1 - 1 1 - - - 1 1 - - - - 1 - - - -]
[1 - 1 1 1 1 1 - - - 1 - - - 1 1 - - 1 1 - - - - 1 1 1 1 1 - - - 1 - 1 -]
[1 1 - - - - 1 - 1 - 1 1 1 1 1 1 - - 1 1 - - 1 - 1 - - - 1 1 - 1 - - - 1]
[1 1 - - 1 1 1 - - 1 1 - 1 - - - - - - - 1 - - 1 1 1 1 - - 1 - 1 - 1 1 1]
[1 - 1 1 - 1 - - 1 - - 1 1 - 1 - 1 - - - - - 1 1 1 1 1 1 - - 1 1 - - - 1]
[1 1 - 1 - - - - 1 1 - 1 - - 1 1 1 1 - 1 - - - - - 1 1 - - 1 - 1 1 1 1 -]
[1 - 1 - 1 1 - - - 1 1 1 1 - 1 1 1 1 - - - 1 - - 1 - - - 1 1 1 - - 1 - -]
[1 - 1 1 - - 1 1 1 - 1 - - - - 1 - 1 - - - 1 1 1 1 - 1 - - 1 - - 1 1 - 1]
[1 1 - 1 - - - 1 - 1 1 - 1 - - - - 1 - 1 - 1 1 - 1 - 1 1 1 - 1 1 - - 1 -]
[1 1 - 1 - 1 - 1 - 1 - 1 - - 1 - - - 1 - 1 1 1 - 1 1 - - 1 - - - 1 1 - 1]
[1 - 1 - 1 1 - 1 1 1 - - - - 1 1 - 1 - 1 1 - 1 1 - - - - 1 - - 1 - - 1 1]
[1 1 - - 1 - - - 1 - 1 - - - - 1 1 1 1 - 1 - 1 - - 1 1 1 1 - 1 - - 1 - 1]
[1 1 - - 1 1 1 1 - - 1 1 - 1 1 - 1 1 - 1 - 1 1 1 - 1 1 - - - - - - - - -]
[1 - 1 1 - - 1 1 - - 1 - - 1 1 - 1 - - - 1 - 1 - - 1 - - 1 1 1 1 - 1 1 -]
[1 - 1 - 1 - - - - - - - 1 1 - - 1 1 1 1 - 1 1 - 1 1 - - - - - 1 1 1 1 1]
[1 - 1 - - - 1 - - 1 - 1 1 - - - - 1 1 1 1 - 1 1 - 1 1 - 1 1 1 - 1 - - -]
[1 1 - 1 1 1 - - 1 - - - 1 1 - 1 - - - - - 1 1 1 - 1 - - 1 1 1 - 1 - 1 -]
[1 1 - 1 1 - 1 1 - - - - 1 - 1 1 1 1 1 - 1 - - 1 1 - - - - - 1 1 1 - - -]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 3, 67, 34, 19, 30, 37, 39, 31, 70, 55, 66)(2, 5, 62, 35, 47, 63, 38, 41,
        26, 71, 11, 27)(4, 15, 33, 65, 52, 36, 40, 51, 69, 29, 16, 72)(6, 28,
    12, 24, 25, 20, 42, 64, 48, 60, 61, 56)(7, 49, 46, 14, 9, 21, 43, 13,
    10, 50, 45, 57)(8, 59, 18, 58, 68, 17, 44, 23, 54, 22, 32, 53)
    (1, 2, 9, 68, 36, 28, 37, 38, 45, 32, 72, 64)(3, 6, 69, 53, 14, 35, 39, 42,
        33, 17, 50, 71)(4, 58, 13, 41, 66, 61, 40, 22, 49, 5, 30, 25)(7, 8, 15,
        60, 67, 62, 43, 44, 51, 24, 31, 26)(10, 54, 29, 20, 55, 11, 46, 18, 65,
        56, 19, 47)(12, 16, 59, 21, 63, 70, 48, 52, 23, 57, 27, 34)
Automorphism group has centre of order: 6
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 12> <72, 26>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 - - 1 1 - - - 1 1 - 1 - - 1 1 1 1 - - - 1 1 - - 1 - - 1 1 - 1 1 - 1 -]
[1 1 1 - - 1 - - 1 1 1 1 - 1 - - - - - - 1 - - - 1 - - 1 1 1 1 1 1 - 1 -]
[1 - - 1 1 - 1 1 1 1 1 - 1 - 1 - - - 1 1 1 - - - - - 1 - - 1 1 - 1 - 1 -]
[1 1 1 - - 1 1 1 1 - - - 1 1 1 1 1 - 1 - - - - - - 1 - - - - - 1 1 - 1 1]
[1 - - 1 1 1 1 - - 1 1 1 - 1 1 1 1 - - - - - - - 1 1 1 1 - - 1 - - - - 1]
[1 - - 1 - 1 - - 1 - 1 - 1 1 - 1 - - 1 - - 1 1 1 - 1 - 1 - 1 1 - 1 1 - -]
[1 - - 1 - - 1 1 1 - - 1 - 1 1 - - - - 1 1 - 1 1 1 1 - 1 - - - 1 - 1 1 -]
[1 1 1 - 1 - - 1 1 - - 1 - 1 1 1 - 1 - 1 - 1 - - - - 1 1 - - 1 - 1 1 - -]
[1 - - 1 - 1 - 1 - - - 1 1 - - 1 1 1 - 1 1 - - - 1 - - - - 1 1 1 1 1 - 1]
[1 1 1 1 - 1 1 - 1 1 1 - 1 - 1 1 - 1 - 1 - - 1 - 1 - - - 1 - - - - 1 - -]
[1 - - - 1 1 - 1 - 1 - - - 1 1 - - 1 1 - - - 1 1 1 - - - 1 - 1 - 1 1 1 1]
[1 - - - 1 1 1 - 1 - - - - - - 1 - - 1 1 - 1 - - 1 - 1 1 1 1 - 1 - 1 1 1]
[1 - - - 1 1 1 - - - 1 - 1 1 1 - 1 1 - 1 1 1 - 1 - - - 1 1 - - 1 1 - - -]
[1 1 1 1 1 - - - - - 1 - - - 1 1 1 - 1 - 1 1 - 1 1 - - - - - 1 1 - 1 1 -]
[1 1 1 1 1 1 1 1 - 1 - - - - - - 1 - - - - - 1 1 - - 1 1 - 1 - 1 1 1 - -]
[1 1 1 1 1 - - - - - - 1 1 - 1 - - - 1 1 - - - 1 1 1 - 1 1 1 - - 1 - - 1]
[1 1 1 1 1 1 1 - - - - - - 1 - - - 1 - 1 1 1 1 - - 1 - - - 1 1 - - - 1 1]
[1 1 - 1 1 1 - 1 1 - - 1 1 1 - - 1 - 1 - 1 1 1 - 1 - 1 - 1 - - - - - - -]
[1 1 - - - 1 - - - 1 1 1 - - 1 - - - 1 1 1 1 1 - - 1 1 - - - - 1 1 1 - 1]
[1 1 - - - 1 - 1 - 1 - - 1 - 1 1 - 1 - - 1 1 - 1 1 1 1 1 - 1 - - - - 1 -]
[1 - 1 - - 1 1 - 1 - - 1 - - 1 - 1 1 1 - 1 - - 1 - 1 1 - 1 1 1 - - 1 - -]
[1 - 1 - - - - - 1 1 - - 1 1 1 - 1 - - 1 - 1 1 1 1 - 1 - - 1 1 1 - - - 1]
[1 1 - - - - 1 - - - 1 1 - 1 - 1 1 1 1 1 - - 1 1 1 - 1 - - 1 - - 1 - 1 -]
[1 - 1 - - - 1 1 - 1 - - - - - 1 1 - 1 1 1 1 1 - 1 1 - 1 1 - 1 - 1 - - -]
[1 1 - - - - 1 1 - - 1 1 1 - 1 - 1 - - - - 1 1 - - - - 1 1 1 1 - - 1 1 1]
[1 - 1 1 - - - 1 - - 1 - - 1 1 1 - 1 1 - 1 - 1 - - - 1 1 1 1 - 1 - - - 1]
[1 1 - 1 - - 1 1 1 - 1 - - - - - - 1 - - - 1 - 1 1 1 1 - 1 - 1 1 1 - - 1]
[1 1 - 1 - - - - - 1 - - 1 1 - - 1 1 1 1 - - - - - 1 1 1 1 - 1 1 - 1 1 -]
[1 1 - - 1 - 1 - 1 1 - 1 1 - - 1 - 1 1 - 1 - 1 1 - - - 1 - - 1 1 - - - 1]
[1 - 1 1 - - 1 - - 1 - 1 1 1 - 1 - - - - 1 1 - 1 - - 1 - 1 - - - 1 1 1 1]
[1 - 1 - 1 1 - 1 - - 1 1 1 - - 1 - - - 1 - - 1 1 - 1 1 - 1 - 1 1 - - 1 -]
[1 1 - - 1 - - 1 1 1 1 - - 1 - 1 1 - - 1 1 - - 1 - 1 - - 1 1 - - - 1 - 1]
[1 - 1 - 1 - 1 1 - 1 1 1 1 1 - - - 1 1 - - 1 - - 1 1 - - - 1 - 1 - 1 - -]
[1 - 1 1 - 1 - 1 1 1 1 1 - - - - 1 1 1 1 - 1 - 1 - - - 1 - - - - - - 1 1]
[1 - 1 - 1 - - - 1 - 1 - 1 - - - 1 1 - - 1 - 1 - 1 1 1 1 - - - - 1 1 1 1]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 49, 31, 57, 42, 59, 37, 13, 67, 21, 6, 23)(2, 33, 40, 65, 20, 53, 38,
        69, 4, 29, 56, 17)(3, 5, 16, 47, 32, 10, 39, 41, 52, 11, 68, 46)(7, 48,
        28, 26, 45, 8, 43, 12, 64, 62, 9, 44)(14, 35, 24, 22, 63, 61, 50, 71,
        60, 58, 27, 25)(15, 54, 72, 34, 66, 55, 51, 18, 36, 70, 30, 19)
    (1, 3, 18)(2, 28, 58)(4, 9, 61)(5, 21, 15)(6, 68, 55)(7, 71, 56)(8, 17,
        63)(10, 49, 66)(11, 59, 36)(12, 33, 50)(13, 30, 46)(14, 48, 69)(16, 70,
        31)(19, 42, 32)(20, 43, 35)(22, 38, 64)(23, 72, 47)(24, 26, 29)(25, 40,
        45)(27, 44, 53)(34, 67, 52)(37, 39, 54)(41, 57, 51)(60, 62, 65)
    (1, 2, 37, 38)(3, 61, 39, 25)(4, 31, 40, 67)(5, 14, 41, 50)(6, 56, 42,
        20)(7, 18, 43, 54)(8, 51, 44, 15)(9, 55, 45, 19)(10, 63, 46, 27)(11, 60,
        47, 24)(12, 36, 48, 72)(13, 33, 49, 69)(16, 71, 52, 35)(17, 23, 53,
        59)(21, 65, 57, 29)(22, 32, 58, 68)(26, 66, 62, 30)(28, 70, 64, 34)
Automorphism group has centre of order: 6
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 12> <72, 26>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - - - - - - - - - - 1 1 1]
[1 1 1 - - - - - - - - - 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - 1 1 1]
[1 1 1 - - 1 1 - - - - 1 - - - - - - 1 - - - 1 1 - - 1 1 1 - 1 1 1 1 1 1]
[1 1 1 - 1 - - - - 1 1 - - - - 1 - - - 1 1 - - - 1 1 - 1 1 1 - - 1 1 1 1]
[1 1 1 1 - - - 1 1 - - - - - - - 1 1 - - - 1 - - 1 1 1 - - 1 1 1 - 1 1 1]
[1 1 1 1 1 - - 1 1 1 1 - - - - - 1 1 1 - - 1 1 1 - - - 1 1 - - - 1 - - -]
[1 1 1 - 1 1 1 - - 1 1 1 - - - 1 1 1 - 1 1 1 - - - - 1 - - - 1 1 - - - -]
[1 1 1 1 - 1 1 1 1 - - 1 - - - 1 - - 1 1 1 - 1 1 1 1 - - - 1 - - - - - -]
[1 1 - 1 1 1 1 - - - - - 1 1 - 1 1 1 1 - - - - - 1 1 1 1 1 - - - - 1 - -]
[1 1 - 1 1 - 1 - 1 - - - 1 - 1 1 - 1 - - 1 - - 1 - - - 1 - 1 1 1 1 - 1 -]
[1 1 - 1 1 1 - - - 1 - - - 1 1 - 1 - 1 1 - - 1 - 1 - - - - 1 1 1 1 - - 1]
[1 1 - - 1 - 1 - 1 - 1 - - 1 1 - - - - - 1 1 1 1 1 1 1 - 1 - - 1 - - - 1]
[1 1 - 1 - 1 - 1 - 1 - - 1 - 1 - - - - 1 1 1 1 - - 1 1 1 1 - 1 - - - 1 -]
[1 1 - - - - 1 - 1 - 1 1 1 1 - - 1 - - 1 - 1 1 - - 1 - 1 - 1 1 - 1 1 - -]
[1 1 - - - 1 - 1 - 1 - 1 1 1 - - - 1 - - 1 1 - 1 1 - - - 1 1 - 1 1 1 - -]
[1 1 - - - - - 1 - 1 1 1 - 1 1 1 - 1 1 - - - - 1 - 1 1 1 - 1 1 - - - - 1]
[1 1 - - - - - 1 1 - 1 1 1 - 1 1 1 - 1 1 - - - - 1 - 1 - 1 - - 1 1 - 1 -]
[1 - 1 - 1 1 - 1 - - 1 - 1 - 1 1 1 - - - - - 1 1 - 1 - - 1 1 1 1 - 1 - -]
[1 - 1 1 - - 1 1 - - 1 - 1 1 - - - 1 1 1 1 - - - - 1 - - 1 - 1 1 1 - - 1]
[1 - - 1 - 1 - - 1 - 1 1 - - 1 - 1 1 - 1 1 - - 1 1 - - 1 1 - 1 - - 1 - 1]
[1 - 1 - 1 1 - 1 1 - - - 1 1 - 1 - - - 1 - 1 - 1 1 - 1 1 - - 1 - 1 - - 1]
[1 - 1 1 - - 1 - - 1 1 - 1 - 1 - - - 1 1 - 1 - 1 1 - 1 1 - 1 - 1 - 1 - -]
[1 - - - 1 - 1 1 - 1 - 1 1 - - - 1 1 - 1 - - 1 1 1 1 - 1 - - - 1 - - 1 1]
[1 - - 1 1 - - 1 - - 1 1 - 1 - 1 - - 1 - 1 1 1 - 1 - - 1 - - 1 1 - 1 1 -]
[1 - 1 - - 1 1 1 - - 1 - - 1 1 - 1 1 - - 1 - 1 - 1 - 1 1 - 1 - - 1 - 1 -]
[1 - - - - 1 1 1 1 1 - - - - 1 1 1 - 1 - 1 1 - - - 1 - 1 - - - 1 1 1 - 1]
[1 - - - - 1 1 - 1 1 1 - 1 - - 1 - 1 1 - - 1 1 - 1 - - - 1 1 1 - - - 1 1]
[1 - - 1 - 1 - - 1 1 1 - - 1 - 1 - 1 - 1 - - 1 1 - 1 1 - - - - 1 1 1 1 -]
[1 - 1 - 1 1 - - 1 - - 1 - 1 1 - - 1 1 1 - 1 - - - 1 - 1 1 1 - 1 - - 1 -]
[1 - 1 1 - - 1 - - 1 - 1 - 1 1 1 1 - - - - 1 - 1 1 1 - - 1 - 1 - 1 - 1 -]
[1 - - - 1 - 1 1 1 1 - - - 1 - - 1 - 1 1 1 - - 1 - - 1 - 1 1 1 - - 1 1 -]
[1 - - 1 1 1 - - - - 1 1 1 - - - 1 - 1 - 1 1 - 1 - 1 1 - - 1 - - 1 - 1 1]
[1 - - 1 1 - 1 1 - - - 1 - - 1 1 - 1 - 1 - 1 1 - - - 1 - 1 1 - - 1 1 - 1]
[1 - 1 - 1 - - - 1 1 - 1 1 - 1 - - 1 1 - 1 - 1 - 1 1 1 - - - 1 - 1 1 - -]
[1 - 1 1 - - - - 1 1 - 1 1 1 - 1 1 - - - 1 - 1 - - - 1 1 1 1 - 1 - - - 1]

Permutation group acting on a set of cardinality 72
Order = 1944 = 2^3 * 3^5
    (10, 16, 15)(11, 14, 18)(12, 17, 13)(19, 35, 23)(20, 22, 36)(21, 34, 27)(24,
        28, 33)(25, 32, 29)(26, 30, 31)(46, 52, 51)(47, 50, 54)(48, 53, 49)(55,
        71, 59)(56, 58, 72)(57, 70, 63)(60, 64, 69)(61, 68, 65)(62, 66, 67)
    (10, 30, 65)(11, 22, 64)(12, 35, 57)(13, 19, 63)(14, 36, 69)(15, 26, 68)(16,
        31, 61)(17, 23, 70)(18, 20, 60)(21, 48, 71)(24, 54, 56)(25, 52, 67)(27,
        49, 55)(28, 47, 58)(29, 46, 66)(32, 51, 62)(33, 50, 72)(34, 53, 59)
    (1, 10, 37, 46)(2, 65, 38, 29)(3, 30, 39, 66)(4, 25, 40, 61)(5, 67, 41,
        31)(6, 52, 42, 16)(7, 15, 43, 51)(8, 68, 44, 32)(9, 26, 45, 62)(11, 34,
        47, 70)(12, 60, 48, 24)(13, 20, 49, 56)(14, 59, 50, 23)(17, 18, 53,
        54)(19, 36, 55, 72)(21, 28, 57, 64)(22, 27, 58, 63)(33, 35, 69, 71)
    (4, 6, 5)(7, 8, 9)(10, 64, 35, 15, 60, 19, 16, 69, 23)(11, 63, 30, 18, 70,
        26, 14, 57, 31)(12, 65, 36, 13, 68, 22, 17, 61, 20)(21, 67, 47, 27, 66,
        54, 34, 62, 50)(24, 55, 52, 33, 59, 46, 28, 71, 51)(25, 56, 48, 29, 72,
        49, 32, 58, 53)(40, 42, 41)(43, 44, 45)
Automorphism group has centre of order: 6
Number of regular subgroups: 3
Number of regular subgroups containing zeta: 3
Number of centrally regular subgroups: 2
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 10> <72, 24>
<36, 12> <72, 26>
<36, 11> <72, 25>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 - - - - - 1 - - - - - 1 1 1 1 1 1 1 - 1 1 1 1 1 - - - - - - 1 1 1 - 1]
[1 1 1 1 1 - 1 1 - - - 1 - - - - 1 1 1 - 1 - 1 - 1 - - 1 - 1 1 - - - - 1]
[1 1 1 1 - 1 - - - 1 - - - 1 1 - - - 1 1 1 - 1 1 1 - 1 1 1 - - - - 1 - -]
[1 - - - 1 - - 1 - 1 1 1 1 1 - - - - 1 1 1 1 1 - - - - 1 1 1 - 1 1 - - -]
[1 1 1 1 1 1 1 1 - 1 1 1 1 - 1 - - 1 - - - - - 1 - - - - - - - 1 1 1 - -]
[1 1 1 1 - - - - - - 1 1 1 - - 1 1 - 1 - - 1 1 - - - 1 - 1 - 1 1 - 1 1 -]
[1 - - - - 1 1 - - - 1 1 - 1 - - 1 1 - 1 1 - - 1 - - 1 1 - 1 1 1 - 1 1 -]
[1 - - - 1 1 - 1 - - - 1 1 1 1 1 - 1 1 - - - - - 1 1 1 - 1 1 1 - - 1 - -]
[1 - 1 - 1 1 - 1 - 1 - - - - - 1 1 1 - 1 - 1 1 - - 1 1 1 - - - 1 - 1 - 1]
[1 - 1 1 1 - - - 1 - 1 - - 1 1 - - 1 - - - 1 - - 1 - - 1 1 1 - 1 - 1 1 1]
[1 1 1 - - 1 1 - 1 1 1 - 1 1 - 1 1 - 1 - - - - - 1 1 - 1 - 1 - 1 - - - -]
[1 - 1 1 - - 1 1 - 1 - - 1 1 - - 1 - - - 1 - - - - 1 1 - 1 1 - - 1 1 1 1]
[1 - 1 - - - 1 1 - 1 1 - - - 1 1 - 1 1 - 1 1 - 1 - 1 - 1 1 - 1 - - - 1 -]
[1 1 - 1 - - - 1 - - 1 - - 1 1 1 - - - - - - 1 1 - 1 1 1 - 1 1 1 1 - - 1]
[1 - 1 - - 1 1 - - - - 1 1 - 1 - - - - 1 - - 1 - 1 1 - 1 1 - 1 1 1 - 1 1]
[1 - - 1 1 1 - - 1 - 1 - 1 - 1 - 1 1 1 - 1 - 1 - - 1 1 1 - - - - 1 - 1 -]
[1 - - 1 1 - - - 1 1 - 1 - - - 1 1 - - - 1 - - 1 1 1 - 1 1 - 1 1 1 1 - -]
[1 1 - - - - - 1 1 1 1 - 1 - 1 - 1 1 - 1 1 - - - 1 - 1 - 1 - 1 1 - - - 1]
[1 - - 1 - - 1 1 1 - 1 1 1 - - - - - 1 1 - 1 - 1 1 1 1 1 - - - - - 1 - 1]
[1 - 1 1 - - - - 1 1 - 1 1 1 1 - 1 1 - 1 - 1 1 1 - 1 - - - 1 1 - - - - -]
[1 1 - 1 - 1 - 1 - - - - - - - - 1 1 1 1 - 1 - 1 1 1 - - 1 1 - 1 1 - 1 -]
[1 1 1 - - 1 - - 1 - - 1 1 - - 1 - 1 - - 1 1 - 1 - - 1 1 1 1 - - 1 - - 1]
[1 1 - - 1 - 1 - 1 1 - 1 - 1 - - - 1 1 - - - 1 1 - 1 1 - 1 - - 1 - - 1 1]
[1 1 1 - 1 - 1 - 1 - - - - - 1 - - - 1 1 1 1 - - - 1 1 - - 1 1 1 1 1 - -]
[1 - 1 - 1 1 1 1 1 - 1 - - 1 - - 1 - - - - 1 1 1 1 - 1 - 1 - 1 - 1 - - -]
[1 1 - - - 1 - 1 1 1 - 1 - 1 1 - 1 - 1 - - 1 - - - - - 1 - - 1 - 1 1 1 1]
[1 - 1 1 1 1 - 1 1 - - - 1 1 - 1 - - 1 1 1 - - 1 - - - - - - 1 1 - - 1 1]
[1 - - 1 - 1 1 1 1 1 - 1 - - 1 1 - - - - 1 1 1 - 1 - 1 - - 1 - 1 - - 1 -]
[1 1 - - 1 1 - - - 1 1 - 1 - - - - - - - 1 1 1 1 1 1 - - - 1 1 - - 1 1 1]
[1 1 - 1 1 1 1 - - - 1 1 - 1 1 1 1 - - 1 1 1 - - - 1 - - 1 - - - - - - 1]
[1 - - 1 - 1 1 - 1 1 1 - - - - 1 - 1 1 1 - - 1 - - - - - 1 1 1 - 1 1 - 1]
[1 1 1 - - - - 1 1 - 1 1 - 1 - 1 - 1 - 1 1 - 1 - 1 1 - - - - - - 1 1 1 -]
[1 1 - - 1 - 1 1 1 - - - 1 - 1 1 1 - - 1 - - 1 1 - - - 1 1 1 - - - 1 1 -]
[1 1 - 1 1 - 1 - - 1 - - 1 1 - 1 - 1 - 1 - 1 - - 1 - 1 1 - - 1 - 1 - 1 -]
[1 - 1 - 1 - - - - 1 1 1 - - 1 1 1 - 1 1 - - - 1 1 - 1 - - 1 - - 1 - 1 1]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 3, 11, 25, 51, 4, 37, 39, 47, 61, 15, 40)(2, 29, 57, 53, 43, 36, 38, 65,
        21, 17, 7, 72)(5, 58, 67, 24, 12, 59, 41, 22, 31, 60, 48, 23)(6, 16, 64,
    18, 66, 20, 42, 52, 28, 54, 30, 56)(8, 35, 33, 27, 62, 34, 44, 71, 69,
        63, 26, 70)(9, 10, 13, 50, 55, 68, 45, 46, 49, 14, 19, 32)
    (1, 2, 8, 49, 31, 6, 37, 38, 44, 13, 67, 42)(3, 52, 24, 50, 71, 65, 39, 16,
        60, 14, 35, 29)(4, 56, 22, 46, 70, 72, 40, 20, 58, 10, 34, 36)(5, 66,
    15, 7, 26, 45, 41, 30, 51, 43, 62, 9)(11, 57, 33, 19, 48, 64, 47, 21,
        69, 55, 12, 28)(17, 61, 18, 23, 32, 27, 53, 25, 54, 59, 68, 63)
Automorphism group has centre of order: 6
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 12> <72, 26>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - - - - 1 1 1 - - - - - -]
[1 1 1 1 1 1 - - - - - - 1 1 1 - - - - - - - - - 1 1 1 - - - 1 1 1 1 1 1]
[1 1 1 1 - - 1 1 - - - - 1 - - 1 1 1 1 - - 1 - - 1 1 - 1 1 - 1 1 - - - -]
[1 - 1 - 1 1 1 1 - - - - - 1 - 1 - 1 - 1 1 - 1 - 1 - 1 1 1 - - - 1 - 1 -]
[1 - 1 - - - - - 1 1 1 1 1 1 - 1 - 1 - - - 1 1 - 1 - - - - 1 1 1 1 - 1 -]
[1 - 1 1 1 - - - 1 1 - - - - 1 1 1 1 - 1 - - - 1 - 1 1 1 - 1 - 1 - - 1 -]
[1 - - - 1 - 1 1 - - 1 1 1 - 1 - - 1 - 1 - 1 - 1 - 1 - - 1 - - 1 1 1 1 -]
[1 1 1 - - 1 - - - - 1 1 - - 1 1 - 1 1 - 1 - - 1 - 1 1 - 1 1 1 - 1 - - -]
[1 1 - 1 1 - - - - - 1 1 - 1 - - 1 1 1 1 - - 1 - 1 - 1 - 1 1 - 1 - 1 - -]
[1 1 - - - - 1 1 1 1 - - - 1 1 - - 1 1 - - - 1 1 - - 1 1 - - 1 1 1 1 - -]
[1 1 - - 1 1 - - 1 1 - - 1 - - - - 1 1 1 1 1 - - 1 1 - 1 - 1 - - 1 1 - -]
[1 1 1 - - - - - - 1 1 - - 1 1 1 - - - 1 1 1 - 1 1 - - 1 1 - - 1 - 1 - 1]
[1 1 - 1 - - - - 1 - - 1 - 1 1 - 1 - - 1 1 1 1 - - 1 - 1 1 - 1 - 1 - 1 -]
[1 - 1 - - 1 - - 1 - - 1 1 - 1 - 1 1 1 - - - 1 1 1 - - 1 1 - - - - 1 1 1]
[1 - 1 - - 1 1 1 1 - - 1 - - 1 - 1 - - 1 1 1 - - 1 - 1 - - 1 1 1 - 1 - -]
[1 1 - 1 - - 1 1 1 - - 1 - 1 - 1 - 1 - - 1 - - 1 1 1 - - - 1 - - - 1 1 1]
[1 1 1 - - - 1 1 - 1 1 - - - 1 - 1 - 1 1 - - 1 - 1 1 - - - 1 - - 1 - 1 1]
[1 - - - 1 1 1 - 1 1 1 - - 1 - - 1 - 1 - 1 - - 1 1 1 - - 1 - 1 1 - - 1 -]
[1 - 1 1 - - 1 - - - 1 - 1 1 - - 1 - 1 - 1 1 - 1 - - 1 1 - 1 - - 1 1 1 -]
[1 1 - - 1 - 1 - 1 - - - 1 - 1 1 - - 1 - 1 1 1 - - - 1 - 1 1 - 1 - - 1 1]
[1 1 - - - 1 - 1 - 1 - - 1 1 - - 1 1 - 1 - 1 - 1 - - 1 - 1 1 1 - - - 1 1]
[1 - - 1 1 - - 1 - 1 - - 1 - 1 1 1 - - - 1 - 1 1 1 - - - 1 1 1 - 1 1 - -]
[1 - - 1 1 - - 1 - 1 1 1 - - 1 - - 1 1 - 1 1 - - 1 - 1 1 - - 1 - - - 1 1]
[1 - 1 - 1 - - 1 1 1 - 1 - 1 - 1 1 - 1 - - 1 - - - 1 1 - 1 - - - 1 1 - 1]
[1 - 1 - 1 - - 1 - - - 1 1 1 - - - - 1 1 1 - 1 1 - 1 - 1 - 1 1 1 - - - 1]
[1 1 - - 1 - 1 - 1 - 1 1 1 - - 1 1 - - 1 - - - 1 1 - 1 1 - - 1 - 1 - - 1]
[1 1 - - - 1 - 1 - 1 1 1 1 - - 1 1 - - - 1 - 1 - - 1 1 1 - - - 1 - 1 1 -]
[1 - 1 1 - - 1 - 1 1 1 - 1 - - - - 1 - 1 1 - 1 - - 1 1 - 1 - 1 - - 1 - 1]
[1 - - - 1 1 1 - - - 1 - - 1 1 1 1 1 - - - 1 1 - - 1 - 1 - 1 1 - - 1 - 1]
[1 - - 1 - 1 - 1 1 - 1 - 1 1 1 1 1 1 1 1 1 - - - - - - - - - - 1 1 - - 1]
[1 - - 1 - 1 - 1 1 - 1 - - - - - - - - - - 1 1 1 1 1 1 1 1 1 - 1 1 - - 1]
[1 - - 1 - 1 1 - - 1 - 1 1 1 1 1 - - 1 1 - 1 1 1 1 1 1 - - - - - - - - -]
[1 - - 1 - 1 1 - - 1 - 1 - - - 1 - - 1 1 - - - - - - - 1 1 1 1 1 1 1 1 1]
[1 1 1 1 1 1 - 1 1 - 1 - - - - 1 - - 1 1 - 1 1 1 - - - - - - 1 - - 1 1 -]
[1 1 1 1 1 1 1 - - 1 - 1 - - - - 1 1 - - 1 1 1 1 - - - - - - - 1 1 - - 1]

Permutation group acting on a set of cardinality 72
Order = 1296 = 2^4 * 3^4
    (5, 42)(6, 41)(7, 44)(8, 43)(9, 10)(13, 14)(15, 52)(16, 51)(17, 18)(19,
        56)(20, 55)(21, 22)(23, 60)(24, 59)(25, 62)(26, 61)(27, 28)(29, 66)(30,
        65)(31, 68)(32, 67)(33, 70)(34, 69)(35, 36)(45, 46)(49, 50)(53, 54)(57,
        58)(63, 64)(71, 72)
    (1, 53, 11, 66, 68, 21, 6, 25, 35, 55, 8, 56)(2, 26, 40, 58, 36, 52, 43, 27,
        70, 60, 46, 59)(3, 28, 12, 15, 69, 29, 9, 54, 67, 49, 5, 14)(4, 22, 72,
    16, 7, 63, 34, 24, 10, 23, 38, 62)(13, 41, 50, 39, 64, 48, 51, 33, 65,
        45, 18, 31)(17, 47, 30, 32, 57, 42, 61, 71, 19, 44, 20, 37)
    (4, 12, 47)(5, 7, 10, 42, 44, 9)(6, 8, 45, 41, 43, 46)(11, 40, 48)(13, 30,
        64, 14, 65, 63)(15, 26, 23, 52, 61, 60)(16, 25, 24, 51, 62, 59)(17, 56,
        57, 18, 19, 58)(20, 21, 54, 55, 22, 53)(27, 49, 66, 28, 50, 29)(31,
        68)(32, 67)(33, 70)(34, 69)(35, 36)(71, 72)
    (4, 7, 10)(5, 12, 9)(6, 8, 11)(13, 26, 21)(14, 20, 23)(15, 30, 22)(16, 19,
        28)(17, 29, 24)(18, 25, 27)(40, 43, 46)(41, 48, 45)(42, 44, 47)(49, 62,
        57)(50, 56, 59)(51, 66, 58)(52, 55, 64)(53, 65, 60)(54, 61, 63)
Automorphism group has centre of order: 6
Number of regular subgroups: 6
Number of regular subgroups containing zeta: 6
Number of centrally regular subgroups: 3
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 9> <72, 45>
<36, 10> <72, 21>
<36, 10> <72, 20>
<36, 12> <72, 29>
<36, 8> <72, 36>
<36, 12> <72, 27>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 - - 1 1 1 1 - 1 1 1 - - 1 - 1 - 1 - - 1 - - 1 1 1 1 - - - 1 - - - - 1]
[1 1 1 - - - - - 1 1 1 - 1 1 1 1 - 1 - - 1 1 1 - - - - - 1 - 1 - 1 - 1 -]
[1 1 1 - - - 1 1 1 - - - 1 - - - 1 - 1 - 1 - 1 1 1 - 1 - - - 1 1 1 - - 1]
[1 1 1 - 1 - - 1 - 1 1 1 - - - - - - - - 1 1 1 - 1 1 - 1 - 1 1 - - 1 - 1]
[1 - - - 1 1 1 - - 1 1 1 1 - 1 - - - 1 - 1 1 - - 1 - 1 - 1 1 - 1 1 - - -]
[1 - - - - 1 1 - - 1 - 1 1 - 1 1 1 - 1 1 1 - 1 - - 1 - 1 - - 1 - - - 1 1]
[1 - - 1 - - 1 1 - 1 - 1 1 1 - - - 1 - - - 1 1 1 1 - - 1 1 - - 1 - - 1 1]
[1 1 1 1 - 1 - - - 1 - 1 - 1 1 - - - 1 - - - - 1 - 1 - - 1 - 1 1 1 1 - 1]
[1 - - 1 - - 1 1 1 1 - - - - 1 - - 1 1 1 1 1 1 1 - 1 - - - 1 - - 1 1 - -]
[1 - - 1 - 1 - 1 - 1 1 - 1 1 - 1 1 - - 1 - - 1 - 1 - - - - 1 1 1 1 1 - -]
[1 1 1 - - 1 1 1 - 1 - 1 - - - 1 1 1 - 1 - 1 - 1 - - 1 - 1 1 1 - - - - -]
[1 1 1 - - 1 1 - 1 - - 1 1 1 - - - 1 - 1 1 - - - 1 1 - - - 1 - 1 - 1 1 -]
[1 - - - - 1 - 1 1 - 1 - - 1 - - 1 - 1 - 1 1 - 1 - 1 - 1 1 1 1 1 - - 1 -]
[1 - - - 1 - - - 1 - - 1 1 1 1 - 1 - - 1 - 1 1 1 1 1 1 - 1 - 1 - - 1 - -]
[1 1 1 1 1 - 1 - - 1 1 - - 1 - - 1 - 1 1 - 1 1 - - 1 1 - - - - 1 - - 1 -]
[1 - - - 1 - - 1 - - - 1 - 1 - 1 - 1 1 1 1 1 - - - - 1 - - - 1 1 1 1 1 1]
[1 1 1 1 1 1 - 1 - - - - 1 1 1 1 - - 1 1 1 1 - 1 1 - - 1 - - - - - - - -]
[1 - 1 1 1 1 - 1 1 - 1 1 - - 1 - 1 1 - 1 1 - 1 - - - - - 1 - - 1 - - - 1]
[1 1 - - 1 - - - 1 1 1 1 1 1 - - 1 1 1 1 - - - 1 - - - 1 - 1 - - 1 - - 1]
[1 1 - - - - 1 - - - 1 - - 1 1 1 - - - 1 1 - 1 1 - - 1 1 1 1 - 1 - 1 - 1]
[1 - 1 - 1 1 1 - - - 1 - - - - - - 1 1 1 - - 1 1 1 - - 1 1 - 1 - 1 1 1 -]
[1 - 1 1 1 - 1 - 1 - - - 1 - - 1 - - - 1 - 1 - - - 1 - 1 1 1 1 1 1 - - 1]
[1 1 - 1 - - - 1 - - 1 - 1 - 1 - - 1 1 1 - - - - 1 1 1 - 1 1 1 - - - 1 1]
[1 - 1 - 1 - 1 1 1 1 - - - 1 1 1 1 - 1 - - - - - 1 - - - 1 1 - - - 1 1 1]
[1 1 - 1 - 1 - - 1 1 - - - - - - 1 - - 1 1 1 - - 1 - 1 1 1 - - - 1 1 1 1]
[1 1 - - 1 1 - - - - - - - - 1 1 1 1 - - - 1 1 1 1 1 - - - 1 - 1 1 - 1 1]
[1 - 1 1 - 1 - - 1 - 1 1 1 - - 1 - - 1 - - 1 1 1 - - 1 - - 1 - - - 1 1 1]
[1 - 1 1 1 - - - - 1 - - 1 - 1 - 1 1 - - 1 - - 1 - - 1 1 - 1 1 1 - 1 1 -]
[1 1 - - 1 1 - 1 1 1 - - 1 - - 1 - 1 1 - - - 1 - - 1 1 1 1 - - 1 - 1 - -]
[1 1 - 1 - - 1 - 1 - 1 1 - - 1 1 1 1 1 - - 1 - - 1 - - 1 - - 1 1 - 1 - -]
[1 - 1 - - 1 1 1 - - 1 - 1 1 1 - 1 1 - - - 1 - - - 1 1 1 - - - - 1 1 - 1]
[1 1 - 1 1 - 1 1 - - 1 1 1 - - 1 1 - - - 1 - - 1 - 1 - - 1 - - - 1 1 1 -]
[1 - 1 1 - - - - - - - 1 - 1 - 1 1 1 1 - 1 - 1 - 1 1 1 1 1 1 - - 1 - - -]
[1 1 - 1 1 1 1 1 1 - - 1 - 1 1 - - - - - - - 1 - - - 1 1 - 1 1 - 1 - 1 -]
[1 - 1 - - - - 1 1 1 1 1 - - 1 1 - - - 1 - - - 1 1 1 1 1 - - - 1 1 - 1 -]

Permutation group acting on a set of cardinality 72
Order = 72 = 2^3 * 3^2
    (1, 54, 24, 37, 18, 60)(2, 11, 67, 38, 47, 31)(3, 68, 29, 39, 32, 65)(4, 46,
        50, 40, 10, 14)(5, 13, 61, 41, 49, 25)(6, 43, 15, 42, 7, 51)(8, 45, 70,
        44, 9, 34)(12, 20, 72, 48, 56, 36)(16, 28, 57, 52, 64, 21)(17, 30, 55,
        53, 66, 19)(22, 33, 71, 58, 69, 35)(23, 63, 62, 59, 27, 26)
    (1, 63, 17, 43, 34, 13, 37, 27, 53, 7, 70, 49)(2, 14, 39, 21, 20, 22, 38,
        50, 3, 57, 56, 58)(4, 32, 16, 72, 33, 47, 40, 68, 52, 36, 69, 11)(5, 24,
        59, 55, 42, 45, 41, 60, 23, 19, 6, 9)(8, 61, 18, 26, 66, 51, 44, 25, 54,
        62, 30, 15)(10, 29, 64, 12, 35, 67, 46, 65, 28, 48, 71, 31)
    (1, 3, 37, 39)(2, 17, 38, 53)(4, 23, 40, 59)(5, 16, 41, 52)(6, 33, 42,
        69)(7, 58, 43, 22)(8, 12, 44, 48)(9, 72, 45, 36)(10, 62, 46, 26)(11, 19,
        47, 55)(13, 21, 49, 57)(14, 63, 50, 27)(15, 35, 51, 71)(18, 29, 54,
        65)(20, 70, 56, 34)(24, 32, 60, 68)(25, 28, 61, 64)(30, 67, 66, 31)
Automorphism group has centre of order: 2
Number of regular subgroups: 1
Number of regular subgroups containing zeta: 1
Number of centrally regular subgroups: 1
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 13> <72, 31>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 1 1 1 - - 1 1 1 1 1 1 - - - - - - - - - - 1 1 1 1 1 - - - 1 - - -]
[1 1 1 - 1 - 1 1 - - 1 - 1 - 1 1 - - - - 1 - 1 - 1 - - 1 1 1 1 - - 1 - -]
[1 1 - 1 - 1 1 1 - - - 1 - 1 1 1 - - - - - 1 - 1 - 1 - 1 1 1 - 1 - - 1 -]
[1 1 - - - - - - 1 1 - 1 - 1 1 1 - 1 - 1 1 - 1 - 1 - - 1 - - - 1 1 1 1 -]
[1 1 - - - - - - 1 1 1 - 1 - 1 1 1 - 1 - - 1 - 1 - 1 - - 1 - 1 - 1 1 1 -]
[1 1 1 - 1 - 1 1 1 1 - - - - - - - 1 - 1 - 1 - 1 - 1 1 1 - - 1 1 - 1 - -]
[1 1 - 1 - 1 1 1 1 1 - - - - - - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 1 - - 1 -]
[1 1 1 1 1 1 - - - - - - - - 1 1 1 1 1 1 - - - - 1 1 - - - 1 1 1 1 - - -]
[1 - 1 1 - - 1 1 1 1 - - 1 1 1 1 1 1 - - - - 1 1 - - 1 - - 1 - - 1 - - -]
[1 - 1 1 - - - - - - - - 1 1 - - 1 1 - - - - 1 1 1 1 - 1 1 - 1 1 - 1 1 1]
[1 - 1 - 1 1 1 - 1 - 1 1 - 1 1 - 1 - 1 1 - - 1 1 - - - 1 - - 1 - - - 1 -]
[1 - - 1 1 1 - 1 - 1 1 1 1 - - 1 - 1 1 1 - - 1 1 - - - - 1 - - 1 - 1 - -]
[1 - - - - 1 1 - 1 - 1 - - - 1 - - - - 1 - - 1 1 1 1 1 - 1 1 - 1 1 1 - 1]
[1 - - - 1 - - 1 - 1 - 1 - - - 1 - - 1 - - - 1 1 1 1 1 1 - 1 1 - 1 - 1 1]
[1 1 1 - - 1 - 1 - 1 1 - - 1 - 1 1 - - 1 1 1 1 1 1 1 - - - - - - - - - 1]
[1 1 - 1 1 - 1 - 1 - - 1 1 - 1 - - 1 1 - 1 1 1 1 1 1 - - - - - - - - - 1]
[1 - 1 1 - 1 - 1 1 1 - 1 1 - 1 - - - - 1 1 - - - - 1 - - - 1 1 - - 1 1 1]
[1 - 1 1 1 - 1 - 1 1 1 - - 1 - 1 - - 1 - - 1 - - 1 - - - - 1 - 1 - 1 1 1]
[1 - - 1 - - 1 - - 1 1 1 1 - - - 1 - - 1 1 1 - 1 1 - - 1 - 1 1 1 1 - - -]
[1 - 1 - - - - 1 1 - 1 1 - 1 - - - 1 1 - 1 1 1 - - 1 - - 1 1 1 1 1 - - -]
[1 - - - 1 1 - - 1 - - - 1 1 - 1 - 1 - 1 1 1 - 1 1 - 1 - 1 1 1 - - - 1 -]
[1 - - - 1 1 - - - 1 - - 1 1 1 - 1 - 1 - 1 1 1 - - 1 1 1 - 1 - 1 - 1 - -]
[1 1 - 1 1 - - 1 1 - - - - 1 - - 1 - 1 1 1 - - 1 - - - 1 1 1 - - 1 1 - 1]
[1 1 1 - - 1 1 - - 1 - - 1 - - - - 1 1 1 - 1 1 - - - - 1 1 1 - - 1 - 1 1]
[1 - - - 1 1 1 1 1 - 1 - 1 - - 1 1 1 - - 1 - - - - 1 - 1 - - - 1 1 - 1 1]
[1 - - - 1 1 1 1 - 1 - 1 - 1 1 - 1 1 - - - 1 - - 1 - - - 1 - 1 - 1 1 - 1]
[1 - 1 - - - - 1 1 - - 1 1 - 1 1 1 - 1 1 - 1 - - 1 - 1 1 1 - - 1 - - - 1]
[1 - - 1 - - 1 - - 1 1 - - 1 1 1 - 1 1 1 1 - - - - 1 1 1 1 - 1 - - - - 1]
[1 1 - 1 1 - - 1 - - 1 - 1 1 1 - - - - 1 - 1 1 - - - 1 - - - 1 1 1 - 1 1]
[1 1 1 - - 1 1 - - - - 1 1 1 - 1 - - 1 - 1 - - 1 - - 1 - - - 1 1 1 1 - 1]
[1 - 1 1 1 - 1 - - - - 1 - - - 1 1 - - 1 1 1 1 - - 1 1 - 1 - - - 1 1 1 -]
[1 - 1 1 - 1 - 1 - - 1 - - - 1 - - 1 1 - 1 1 - 1 1 - 1 1 - - - - 1 1 1 -]
[1 1 - 1 - 1 - - 1 - 1 1 - - - 1 1 1 - - - 1 1 - - - 1 1 - 1 1 - - 1 - 1]
[1 1 1 - 1 - - - - 1 1 1 - - 1 - 1 1 - - 1 - - 1 - - 1 - 1 1 - 1 - - 1 1]
[1 1 - - - - 1 1 - - 1 1 1 1 - - 1 1 1 1 - - - - 1 1 1 - - 1 - - - 1 1 -]

Permutation group acting on a set of cardinality 72
Order = 1152 = 2^7 * 3^2
    (1, 62, 49, 57)(2, 28, 5, 30)(3, 55, 36, 61)(4, 63, 42, 70)(6, 34, 40,
        27)(7, 22, 43, 58)(8, 33, 9, 56)(10, 65, 52, 59)(11, 18, 50, 32)(12, 24,
        53, 71)(13, 21, 37, 26)(14, 68, 47, 54)(15, 67, 51, 31)(16, 23, 46,
        29)(17, 35, 48, 60)(19, 72, 25, 39)(20, 44, 69, 45)(38, 64, 41, 66)
    (2, 3, 9, 7)(4, 42, 8, 41)(5, 40, 6, 44)(10, 13, 47, 51)(11, 15, 46, 49)(12,
    17, 50, 16)(14, 52, 48, 53)(18, 26, 57, 59)(19, 30, 56, 25)(20, 61, 55,
        66)(21, 23, 54, 62)(22, 69, 63, 28)(24, 65, 31, 32)(27, 64, 58, 33)(29,
        67, 68, 60)(34, 70)(36, 72)(38, 39, 45, 43)
    (3, 4)(5, 6)(7, 8)(12, 13)(14, 15)(16, 17)(18, 19)(20, 21)(22, 23)(24,
        25)(26, 27)(28, 29)(30, 31)(32, 33)(34, 35)(39, 40)(41, 42)(43, 44)(48,
        49)(50, 51)(52, 53)(54, 55)(56, 57)(58, 59)(60, 61)(62, 63)(64, 65)(66,
        67)(68, 69)(70, 71)
Automorphism group has centre of order: 2
Number of regular subgroups: 5
Number of regular subgroups containing zeta: 4
Number of centrally regular subgroups: 4
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 13> <72, 34>
<36, 14> <72, 36>
<36, 13> <72, 32>
<36, 6> <72, 29>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 - - 1 - 1 - - - - - 1 1 1 1 - 1 - 1 - 1 - 1 1 1 - 1 1 - 1 - 1 - - 1 -]
[1 - - - 1 - 1 - - - - 1 1 1 1 - - 1 - 1 - 1 1 1 - 1 1 - 1 - 1 1 - - - 1]
[1 - - - - - 1 - 1 - 1 - 1 - - - 1 1 - 1 1 - - - 1 - 1 - 1 1 1 1 1 1 1 -]
[1 - - - - 1 - 1 - 1 - 1 - - - - 1 1 1 - - 1 - - - 1 1 1 - 1 1 1 1 1 - 1]
[1 1 1 1 1 1 1 - - - - 1 1 - - 1 - - 1 1 - - - - 1 1 1 - - 1 1 - 1 - - -]
[1 1 1 1 1 1 1 - - 1 1 - - - - - 1 1 - - 1 1 1 1 - - 1 - - - - 1 1 - - -]
[1 1 1 - - 1 1 1 - 1 - - 1 1 - - - - - 1 1 - 1 - - 1 - - - 1 - 1 - 1 1 1]
[1 1 1 - - 1 1 - 1 - 1 1 - - 1 - - - 1 - - 1 - 1 1 - - - - - 1 1 - 1 1 1]
[1 1 1 1 1 - - - - - - - - - - - 1 1 - - - - 1 1 1 1 - 1 1 1 1 - - 1 1 1]
[1 - - - 1 1 1 1 - 1 1 - - 1 - 1 1 - - 1 - - - 1 1 - 1 1 - - 1 - - - 1 1]
[1 - - 1 - 1 1 - 1 1 1 - - - 1 1 - 1 1 - - - 1 - - 1 1 - 1 1 - - - - 1 1]
[1 1 1 - - - - 1 1 1 1 1 1 - - 1 - - - - - - 1 1 - - 1 1 1 1 1 1 - - - -]
[1 - - 1 1 - - 1 1 - - - - - - 1 - - 1 1 1 1 1 1 - - - - - 1 1 1 1 - 1 1]
[1 1 1 1 - - - 1 - - 1 1 - 1 1 - 1 - - 1 - 1 - - - - 1 - 1 1 - - 1 - 1 1]
[1 1 1 - 1 - - - 1 1 - - 1 1 1 - - 1 1 - 1 - - - - - 1 1 - - 1 - 1 - 1 1]
[1 - - 1 1 - 1 - 1 1 1 1 1 1 - - - - - - - 1 1 - 1 - - 1 - 1 - - 1 1 - 1]
[1 - - 1 1 1 - 1 - 1 1 1 1 - 1 - - - - - 1 - - 1 - 1 - - 1 - 1 - 1 1 1 -]
[1 1 - - - - - 1 - - 1 - 1 1 - 1 - 1 1 - - 1 1 1 1 1 1 - - - - - 1 1 1 -]
[1 - 1 - - - - - 1 1 - 1 - - 1 1 1 - - 1 1 - 1 1 1 1 1 - - - - - 1 1 - 1]
[1 1 - - 1 - - - - 1 1 1 - - 1 1 - 1 - 1 1 1 - - 1 1 - 1 - 1 - 1 - - 1 -]
[1 - 1 1 - - - - - 1 1 - 1 1 - 1 1 - 1 - 1 1 - - 1 1 - - 1 - 1 1 - - - 1]
[1 1 - 1 1 1 - 1 1 - - 1 - 1 - 1 - 1 - - 1 - - - 1 - 1 - 1 - - 1 - 1 - 1]
[1 - 1 1 1 - 1 1 1 - - - 1 - 1 1 1 - - - - 1 - - - 1 1 1 - - - 1 - 1 1 -]
[1 - 1 1 - 1 - 1 1 - 1 - - 1 1 - - 1 - 1 - - 1 - 1 1 - 1 - - 1 1 1 - - -]
[1 1 - - 1 - 1 1 1 1 - - - 1 1 - 1 - 1 - - - - 1 1 1 - - 1 1 - 1 1 - - -]
[1 1 - 1 - - 1 1 1 - 1 1 1 - - - 1 1 1 1 1 - - 1 - 1 - 1 - - - - - - - 1]
[1 - 1 - 1 1 - 1 1 1 - 1 1 - - - 1 1 1 1 - 1 1 - 1 - - - 1 - - - - - 1 -]
[1 1 - - 1 1 - - - - 1 - 1 - 1 1 1 - 1 1 - - 1 - - - - 1 1 - - 1 1 1 - 1]
[1 - 1 1 - - 1 - - 1 - 1 - 1 - 1 - 1 1 1 - - - 1 - - - 1 1 - - 1 1 1 1 -]
[1 1 - - - 1 1 - 1 - - 1 - 1 - 1 1 - - - 1 1 1 - - 1 - 1 1 - 1 - 1 - 1 -]
[1 - 1 - - 1 1 1 - - - - 1 - 1 1 - 1 - - 1 1 - 1 1 - - 1 1 1 - - 1 - - 1]
[1 - 1 - 1 1 - - 1 - 1 - - 1 - - - - 1 1 1 1 - 1 - 1 1 1 1 1 - - - 1 - -]
[1 1 - 1 - - 1 1 - 1 - - - - 1 - - - 1 1 1 1 1 - 1 - 1 1 1 - 1 - - 1 - -]
[1 1 - 1 - 1 - - 1 1 - - 1 1 1 1 1 1 - 1 - 1 - 1 - - - - - 1 1 - - 1 - -]
[1 - 1 - 1 - 1 1 - - 1 1 - 1 1 1 1 1 1 - 1 - 1 - - - - - - 1 1 - - 1 - -]

Permutation group acting on a set of cardinality 72
Order = 144 = 2^4 * 3^2
    (1, 2, 50, 60, 46, 30, 42, 34, 7, 44, 49, 52)(3, 64, 59, 67, 29, 71, 33, 47,
        45, 4, 51, 58)(5, 17, 57, 20, 63, 62, 68, 54, 72, 55, 48, 25)(6, 70, 43,
        8, 13, 16, 37, 38, 14, 24, 10, 66)(9, 40, 15, 22, 39, 28, 23, 31, 65,
        35, 69, 11)(12, 61, 41, 53, 21, 56, 27, 26, 32, 18, 36, 19)
    (2, 3)(4, 5)(8, 9)(11, 12)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25,
        26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(38, 39)(40, 41)(44, 45)(47,
        48)(51, 52)(53, 54)(55, 56)(57, 58)(59, 60)(61, 62)(63, 64)(65, 66)(67,
        68)(69, 70)(71, 72)
Automorphism group has centre of order: 12
Number of regular subgroups: 2
Number of regular subgroups containing zeta: 2
Number of centrally regular subgroups: 2
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 6> <72, 29>
<36, 14> <72, 36>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 - - - - 1 - 1 1 1 1 - - - 1 1 - - 1 1 1 1 - - 1 - - 1 - - 1 - 1 - 1]
[1 1 - - - 1 - 1 1 - 1 - 1 - - 1 1 1 - - - 1 1 1 1 - - 1 - - 1 - - - 1 1]
[1 1 - - 1 - - 1 - 1 - 1 1 - - 1 1 - 1 - 1 - - 1 1 1 1 - - 1 - - - 1 1 -]
[1 - 1 1 1 - 1 1 - - - - 1 - - 1 1 1 1 - 1 - - - - 1 - 1 1 - 1 1 - - - 1]
[1 - 1 1 1 1 - - 1 - 1 - - - - 1 1 1 - 1 - - - 1 1 - 1 - 1 1 - 1 - 1 - -]
[1 - 1 1 - 1 1 - - 1 - 1 - - - 1 1 - 1 1 - 1 1 - - - 1 1 - 1 1 - - - 1 -]
[1 - 1 1 - - 1 1 - 1 - 1 1 - - - - 1 - - - 1 1 1 1 - - - 1 - - 1 1 1 1 -]
[1 - 1 1 1 - - 1 1 - 1 - 1 - - - - - - 1 1 1 1 - - 1 1 - - 1 - - 1 - 1 1]
[1 - 1 1 - 1 - - 1 1 1 1 - - - - - - 1 - 1 - - 1 1 1 - 1 - - 1 - 1 1 - 1]
[1 1 - 1 - - - - 1 1 - - 1 - 1 1 - - - - - - 1 - 1 1 1 1 1 1 1 1 1 - - -]
[1 1 1 - - - - 1 - - 1 1 - 1 - - 1 - - - 1 1 - 1 - - 1 1 1 1 1 1 1 - - -]
[1 1 - 1 - - - 1 - - 1 1 - - 1 1 - 1 1 1 - - - - - - 1 1 - - - 1 1 1 1 1]
[1 1 1 - - - - - 1 1 - - 1 1 - - 1 1 1 1 - - - - - - - - 1 1 1 - 1 1 1 1]
[1 - - 1 - - 1 - - - 1 1 1 1 1 - 1 - - 1 - - - 1 1 1 - - - 1 1 1 - - 1 1]
[1 - 1 - - - 1 1 1 1 - - - 1 1 1 - - - 1 1 - - 1 1 - 1 1 1 - - - - - 1 1]
[1 - 1 - - 1 - - 1 - - 1 1 1 1 1 - 1 - - 1 1 - - - 1 1 - - - 1 1 - 1 1 -]
[1 - 1 - 1 - - - - 1 1 - 1 1 1 1 - - 1 - - 1 1 1 - - - 1 - 1 - 1 - 1 - 1]
[1 - - 1 1 - - 1 1 - - 1 - 1 1 - 1 - 1 - - 1 1 - 1 - 1 - 1 - 1 - - 1 - 1]
[1 - - 1 - 1 - 1 - 1 1 - - 1 1 - 1 1 - - 1 - 1 - - 1 - 1 1 1 - - - 1 1 -]
[1 1 - 1 1 1 - - - 1 - 1 1 1 - - - 1 - 1 - 1 - 1 - 1 1 1 1 - - - - - - 1]
[1 1 - 1 1 - 1 - 1 1 1 - - 1 - - - 1 1 - 1 - 1 1 - - 1 - - - 1 1 - - 1 -]
[1 1 - 1 - 1 1 1 1 - - - 1 1 - - - - 1 1 1 1 - - 1 - - 1 - 1 - 1 - 1 - -]
[1 1 1 - 1 - 1 - 1 - 1 1 - - 1 - - 1 1 - - 1 - - 1 1 - 1 1 1 - - - - 1 -]
[1 1 1 - - 1 1 1 - - 1 - 1 - 1 - - - 1 1 - - 1 1 - 1 1 - 1 - 1 - - 1 - -]
[1 1 1 - 1 1 - 1 - 1 - 1 - - 1 - - 1 - 1 1 - 1 - 1 - - - - 1 1 1 - - - 1]
[1 1 - 1 1 1 1 - - - - - - - 1 1 - - - - 1 1 - 1 - - - - 1 1 1 - 1 1 1 1]
[1 1 1 - 1 1 1 - - - - - - 1 - - 1 - - - - - 1 - 1 1 1 1 - - - 1 1 1 1 1]
[1 1 1 1 - - - - - - - - - 1 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - 1 - - -]
[1 - - - - 1 1 1 1 1 - - - - 1 - 1 1 1 - - 1 - 1 - 1 1 - - 1 - 1 1 - - 1]
[1 - - - 1 1 - 1 - 1 1 - - 1 - 1 - - 1 1 - 1 - - 1 1 - - 1 - 1 1 1 - 1 -]
[1 - - - 1 - 1 1 1 - - 1 - 1 - 1 - 1 - 1 - - 1 1 - 1 - 1 - 1 1 - 1 1 - -]
[1 - - - 1 1 - - 1 - - 1 1 - 1 - 1 - 1 1 1 - 1 1 - - - 1 1 - - 1 1 - 1 -]
[1 - - - 1 - 1 - - 1 1 - 1 - 1 - 1 1 - 1 1 1 - - 1 - 1 1 - - 1 - 1 1 - -]
[1 - - - - 1 1 - - - 1 1 1 1 - 1 - 1 1 - 1 - 1 - 1 - 1 - 1 1 - - 1 - - 1]
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - - - - - - - 1 - - -]

Permutation group acting on a set of cardinality 72
Order = 432 = 2^4 * 3^3
    (1, 11, 29, 27, 36, 13)(2, 60, 42, 16, 10, 68)(3, 61, 41, 17, 9, 71)(4, 62,
        43, 18, 8, 67)(5, 53, 45, 35, 39, 25)(6, 52, 46, 32, 38, 24)(7, 54, 44,
        31, 40, 26)(12, 50, 28, 48, 14, 64)(15, 22, 70, 51, 58, 34)(19, 21, 69,
        55, 57, 33)(20, 23, 66, 56, 59, 30)(37, 47, 65, 63, 72, 49)
    (1, 2, 5)(3, 42, 8)(4, 72, 45)(6, 44, 39)(7, 10, 65)(9, 40, 36)(11, 59, 54,
    12, 61, 55)(13, 69, 24, 14, 67, 22)(15, 35, 28, 16, 30, 27)(17, 70, 62,
        20, 68, 57)(18, 48, 25, 19, 47, 23)(21, 53, 34, 26, 56, 32)(29, 43,
        46)(31, 58, 49, 33, 60, 50)(37, 38, 41)(51, 71, 64, 52, 66, 63)
    (2, 3, 4)(5, 7, 6)(8, 10, 9)(15, 20, 19)(16, 17, 18)(21, 22, 23)(24, 25,
        26)(30, 33, 34)(31, 32, 35)(38, 39, 40)(41, 43, 42)(44, 46, 45)(51, 56,
        55)(52, 53, 54)(57, 58, 59)(60, 61, 62)(66, 69, 70)(67, 68, 71)
    (11, 12)(13, 14)(15, 16)(17, 20)(18, 19)(21, 26)(22, 24)(23, 25)(27, 28)(30,
        35)(31, 33)(32, 34)(47, 48)(49, 50)(51, 52)(53, 56)(54, 55)(57, 62)(58,
        60)(59, 61)(63, 64)(66, 71)(67, 69)(68, 70)
Automorphism group has centre of order: 6
Number of regular subgroups: 7
Number of regular subgroups containing zeta: 7
Number of centrally regular subgroups: 3
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 14> <72, 38>
<36, 11> <72, 25>
<36, 11> <72, 25>
<36, 11> <72, 25>
<36, 11> <72, 25>
<36, 11> <72, 25>
<36, 12> <72, 26>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 - - - - - - - - 1 1 1 - - - - - - 1 1 1 - 1 1 1 1 1 1 - - - 1 1 1]
[1 1 1 - - - 1 1 1 1 1 1 1 1 - - - - - - 1 1 1 1 - - - - - - 1 1 1 - - -]
[1 1 - 1 1 - - - 1 - - - - - 1 1 - 1 - - 1 1 1 1 1 1 - 1 - - 1 1 - 1 - -]
[1 - 1 - 1 1 - - - - 1 - - - - 1 1 - - 1 1 1 1 1 1 - 1 - - 1 - 1 1 - 1 -]
[1 - - - 1 - 1 1 1 - 1 1 1 1 - 1 - 1 - 1 - - - - 1 - - 1 - 1 - 1 - 1 1 -]
[1 - 1 - - - - - 1 - - 1 1 - 1 - 1 1 1 1 - 1 - 1 - - 1 1 - - 1 1 - - 1 1]
[1 - - 1 1 1 1 1 1 1 - 1 - - - - 1 - - - 1 1 - - 1 - 1 1 1 - 1 - - - 1 -]
[1 1 - - - - - - - 1 - 1 - 1 - 1 1 1 1 1 1 - - 1 1 - - - 1 - 1 - 1 1 1 -]
[1 - 1 - - - 1 1 - 1 1 - - - 1 1 - 1 1 - 1 1 - - 1 - 1 1 - - - - 1 1 - 1]
[1 1 - - - - 1 1 1 - 1 - - - 1 - 1 - 1 1 1 - 1 - 1 1 - - 1 - - 1 - - 1 1]
[1 - - 1 1 1 - - - - 1 1 1 1 1 - - - 1 - 1 - - 1 1 - - 1 1 - - 1 1 - - 1]
[1 1 - - 1 1 1 1 - - - 1 1 - 1 1 - - 1 1 - 1 1 1 - - 1 - 1 - - - - 1 - -]
[1 - 1 1 - 1 1 1 - - - - 1 1 - 1 1 1 1 - 1 - 1 1 - 1 - 1 - - - - - - 1 -]
[1 - - - - 1 - - 1 1 1 - 1 - - 1 - - 1 - - - 1 - - 1 1 1 1 - 1 1 1 1 1 -]
[1 - 1 1 1 - - - 1 1 1 - 1 1 1 - 1 1 - 1 1 - 1 - - - 1 - 1 - - - - 1 - -]
[1 - - 1 - - 1 1 - - - - 1 - - - 1 1 - - - - 1 1 1 - 1 - 1 1 1 1 1 1 - 1]
[1 1 - 1 - 1 - - 1 1 1 1 1 - - 1 1 1 1 - - 1 1 - 1 - - - - 1 - - - - - 1]
[1 1 - - 1 1 - 1 - 1 - - - 1 - - - 1 1 1 1 - 1 - - - 1 1 - 1 1 1 - - - 1]
[1 - 1 1 - 1 - 1 1 - - 1 - - - - - 1 1 1 1 1 - - - 1 - - 1 1 - 1 1 1 - -]
[1 - - - - 1 1 - 1 1 - 1 - 1 1 1 1 - - - 1 - - 1 - 1 1 - - 1 - 1 - 1 - 1]
[1 - - 1 - - - 1 1 1 - - - 1 1 1 - - - 1 - 1 1 1 - - - 1 1 1 - - 1 - 1 1]
[1 - 1 1 1 - 1 - 1 - - 1 - 1 - 1 - - 1 1 - - 1 - 1 1 1 - - - 1 - 1 - - 1]
[1 1 - 1 - 1 1 - - 1 - - 1 1 1 - - 1 - 1 - 1 - - 1 1 1 - - - - 1 1 - 1 -]
[1 1 1 1 - 1 1 - - - 1 - - 1 - 1 1 - - 1 - 1 - - - - - 1 1 - 1 1 - 1 - 1]
[1 1 1 1 1 - 1 - - 1 - 1 - - 1 - 1 - 1 - - - 1 - - - - 1 - 1 - 1 1 1 1 -]
[1 1 1 - 1 1 1 - 1 - - - 1 - 1 1 - 1 - - 1 - - - - - - - 1 1 1 - 1 - 1 1]
[1 1 - - 1 - 1 - 1 - 1 - - 1 - - 1 1 1 - - 1 - 1 - 1 1 1 1 1 - - 1 - - -]
[1 - 1 - - 1 1 - - 1 1 1 - - 1 - - 1 - 1 - - 1 1 1 1 - 1 1 1 1 - - - - -]
[1 - - - 1 1 - 1 - - 1 1 - 1 1 - 1 1 - - - 1 1 - - 1 - - - - 1 - 1 1 1 1]
[1 1 1 - 1 1 - 1 1 1 - - 1 - - - 1 - - 1 - - - 1 1 1 - 1 - - - - 1 1 - 1]
[1 1 1 1 - 1 - 1 1 - 1 - - 1 1 - - - 1 - - - - 1 1 - 1 - - 1 1 - - 1 1 -]
[1 1 1 1 1 - - 1 - 1 1 1 - - - 1 - 1 - - - - - 1 - 1 1 - 1 - - 1 - - 1 1]
[1 - 1 - 1 - - 1 - 1 - - 1 1 1 1 1 - 1 - - 1 - - 1 1 - - 1 1 1 1 - - - -]
[1 - - 1 1 - 1 - - 1 1 - 1 - - - - - 1 1 1 1 - 1 - 1 - - - 1 1 - - 1 1 1]
[1 1 - 1 - - - 1 - - 1 1 1 - 1 1 1 - - 1 1 - - - - 1 1 1 - 1 1 - 1 - - -]

Permutation group acting on a set of cardinality 72
Order = 216 = 2^3 * 3^3
    (1, 4, 11)(2, 21, 71)(3, 24, 61)(5, 12, 64)(6, 51, 68)(7, 56, 14)(8, 59,
        63)(9, 54, 72)(10, 67, 17)(13, 30, 22)(15, 32, 42)(16, 26, 29)(18, 36,
        45)(19, 34, 69)(20, 50, 43)(23, 27, 44)(25, 39, 60)(28, 41, 48)(31, 53,
        46)(33, 55, 70)(35, 38, 57)(37, 40, 47)(49, 66, 58)(52, 62, 65)
    (4, 5, 42)(6, 40, 41)(7, 44, 9)(8, 45, 43)(10, 48, 11)(12, 47, 46)(13, 14,
        51)(15, 49, 50)(16, 53, 18)(17, 54, 52)(19, 20, 57)(21, 55, 56)(22, 60,
        59)(23, 58, 24)(25, 26, 27)(28, 29, 66)(30, 64, 65)(31, 32, 33)(34, 71,
        36)(35, 72, 70)(61, 62, 63)(67, 68, 69)
Automorphism group has centre of order: 6
Number of regular subgroups: 3
Number of regular subgroups containing zeta: 3
Number of centrally regular subgroups: 3
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 11> <72, 25>
<36, 14> <72, 38>
<36, 11> <72, 25>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - 1 1 - - - - - - 1 - - -]
[1 1 1 - - - 1 1 - 1 1 - 1 1 - 1 1 - 1 1 - 1 1 - - - 1 - - 1 - - - 1 - -]
[1 1 1 - - - 1 - - 1 - - - 1 - - - 1 - - 1 - - 1 1 1 1 1 - 1 1 - 1 1 1 -]
[1 1 1 - - - 1 - 1 1 - 1 - 1 1 1 - 1 - 1 1 1 - 1 - - - - 1 - - 1 - - - 1]
[1 1 1 - - - - - 1 - - 1 - - 1 - 1 - 1 - - - 1 - 1 1 1 - 1 1 - 1 1 1 - 1]
[1 1 1 - - - - 1 1 - 1 1 1 - 1 - 1 1 1 - 1 - 1 1 - - - 1 - - 1 - - - 1 -]
[1 1 1 - - - - 1 - - 1 - 1 - - 1 - - - 1 - 1 - - 1 1 - 1 1 - 1 1 1 - 1 1]
[1 1 1 1 1 1 - - - - - - - - - 1 1 1 1 1 1 1 1 1 1 1 - - - - - - 1 - - -]
[1 - - - - 1 1 - 1 - 1 - 1 - 1 - 1 1 - 1 - 1 - 1 - 1 1 1 1 1 - - 1 - - -]
[1 1 - 1 - 1 - - 1 1 1 - 1 - - - 1 - - 1 1 - - 1 1 - - - - 1 - 1 - 1 1 1]
[1 - 1 - 1 1 1 - - - 1 1 - - 1 - - 1 1 1 - 1 - - 1 - - - - 1 1 - - 1 1 1]
[1 - - 1 - - - 1 1 1 - 1 - 1 - - 1 1 1 1 - 1 - - 1 - - 1 - 1 1 1 1 - - -]
[1 1 - 1 1 - - 1 - - - 1 - 1 1 - 1 - - 1 - 1 - 1 - 1 1 1 - - - - - 1 1 1]
[1 - 1 1 - 1 - - 1 1 - - 1 1 - - - 1 1 - - 1 1 - - 1 - 1 1 - - - - 1 1 1]
[1 1 - 1 1 - 1 - 1 - - - 1 - 1 1 - - 1 - 1 1 - - - 1 - 1 - 1 1 1 - 1 - -]
[1 - 1 1 - 1 1 1 - - - - - 1 1 - 1 - - 1 1 - 1 - - 1 - - 1 1 1 1 - - 1 -]
[1 - - 1 - - 1 - - 1 1 1 - - 1 1 1 - - - 1 1 1 - 1 - - 1 1 - - - 1 1 1 -]
[1 1 - 1 - 1 1 1 - - - 1 1 - - - - 1 - - - 1 1 1 1 - 1 - 1 - 1 1 - 1 - -]
[1 - 1 - 1 1 - 1 1 1 - - - - 1 1 - - - - - 1 1 1 1 - 1 1 - 1 - 1 - - 1 -]
[1 - - - - 1 - 1 - 1 - 1 1 - 1 1 - 1 1 1 1 - - - - 1 1 - - - - 1 1 1 1 -]
[1 - 1 - 1 1 - - 1 - - 1 1 1 - 1 1 - - 1 1 - - - 1 - 1 1 1 - 1 - - 1 - -]
[1 1 - 1 - 1 - 1 - - 1 - - 1 1 1 - 1 1 - 1 - - - 1 - 1 1 1 1 - - - - - 1]
[1 - - - - 1 - 1 1 - 1 1 - 1 - 1 - - - - 1 1 1 1 - 1 - - - 1 1 - 1 1 - 1]
[1 - - 1 - - 1 - 1 - - - 1 1 1 1 - - 1 1 - - 1 1 1 - 1 - - - 1 - 1 - 1 1]
[1 - 1 1 - 1 1 - - 1 1 1 - - - 1 1 - 1 - - - - 1 - 1 1 1 - - 1 1 - - - 1]
[1 1 - 1 1 - - - 1 1 1 1 - - - 1 - 1 - 1 - - 1 - - 1 1 - 1 1 1 - - - 1 -]
[1 1 - - 1 1 1 - - - - 1 1 1 - 1 1 1 - - - - 1 - - - - 1 - 1 - 1 1 - 1 1]
[1 - - - 1 - 1 1 - 1 - 1 1 - - - - - 1 1 1 - 1 1 1 1 - 1 1 1 - - - - - 1]
[1 - 1 1 1 - - 1 - 1 - - 1 - 1 1 1 1 - - - - - 1 - - - - 1 1 1 - 1 1 - 1]
[1 1 - - 1 1 1 1 1 1 - - - - - - 1 - 1 - 1 1 - - - - 1 - 1 - 1 - 1 - 1 1]
[1 - - - 1 - - - - 1 1 - 1 1 1 - 1 1 - - 1 1 1 - 1 1 1 - - - 1 1 - - - 1]
[1 - 1 1 1 - 1 1 1 - 1 - - - - - - 1 - 1 1 - 1 - - - 1 1 - - - 1 1 1 - 1]
[1 1 - - 1 1 - - - 1 1 - - 1 1 - - - 1 1 - - 1 1 - - - 1 1 - 1 1 1 1 - -]
[1 - - - 1 - 1 1 1 - 1 - - 1 - 1 1 1 1 - - - - 1 1 1 - - 1 - - 1 - 1 1 -]
[1 - 1 1 1 - - - - - 1 1 1 1 - - - - 1 - 1 1 - 1 - - 1 - 1 1 - 1 1 - 1 -]

Permutation group acting on a set of cardinality 72
Order = 1728 = 2^6 * 3^3
    (1, 10, 71, 42, 70, 65)(2, 67, 27, 44, 21, 22)(3, 24, 16, 5, 64, 12)(4, 26,
        50, 45, 17, 56)(6, 34, 29, 37, 46, 35)(7, 51, 68)(8, 57, 58, 38, 31,
        63)(9, 53, 20, 40, 62, 14)(11, 30, 33, 23, 54, 49)(13, 47, 66, 69, 59,
    18)(15, 32, 43)(25, 72)(28, 48, 39, 60, 52, 41)(36, 61)
    (2, 3, 40)(4, 38, 39)(5, 9, 44)(8, 41, 45)(10, 61, 29)(11, 52, 21)(12, 31,
        59)(13, 22, 26)(14, 28, 18)(15, 55, 68)(16, 57, 47)(17, 69, 27)(19, 32,
        51)(20, 60, 66)(23, 48, 67)(24, 30, 56)(25, 65, 46)(33, 63, 53)(34, 72,
        71)(35, 70, 36)(49, 58, 62)(50, 64, 54)
    (3, 5, 7)(4, 6, 8)(10, 48, 47)(11, 46, 12)(13, 51, 50)(14, 49, 15)(16, 54,
    17)(18, 53, 52)(19, 57, 20)(21, 56, 55)(22, 23, 60)(24, 58, 59)(25, 62,
        63)(26, 27, 61)(28, 65, 30)(29, 66, 64)(31, 68, 33)(32, 69, 67)(34, 71,
        36)(35, 72, 70)(39, 41, 43)(40, 42, 44)
Automorphism group has centre of order: 2
Number of regular subgroups: 5
Number of regular subgroups containing zeta: 3
Number of centrally regular subgroups: 3
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 14> <72, 38>
<36, 13> <72, 31>
<36, 11> <72, 25>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 1 1 1 1 1 1 - - - - - - - - - - - - - - - - - - 1 1 1 1 1 1 1 1 1]
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - 1 1 1 - - - - - - - - -]
[1 1 1 1 1 - - - - 1 1 - - - - 1 1 1 1 1 - - - - 1 1 - 1 1 1 1 - - - - -]
[1 - 1 1 1 1 - - - - - 1 - 1 - 1 - - - - 1 1 1 1 1 1 - 1 - 1 - 1 - 1 - -]
[1 - - - - 1 - 1 1 1 1 1 - 1 - 1 - 1 1 1 - - - - - - 1 1 - 1 - 1 - 1 - 1]
[1 - 1 - 1 1 - - 1 - - - 1 - 1 - 1 1 1 1 - - - 1 1 1 - - - - - 1 - 1 1 1]
[1 - 1 - - 1 - - 1 1 1 - 1 - 1 - 1 - - - 1 1 - 1 - - 1 1 1 1 1 1 - - - -]
[1 - 1 - 1 1 - - - - - 1 1 1 1 1 - 1 1 - - - 1 - - - 1 1 1 - 1 - 1 - 1 -]
[1 - 1 - - 1 - 1 1 1 1 - - - - 1 - - 1 - 1 1 1 - 1 1 - - - - 1 - 1 - 1 1]
[1 - 1 1 1 - - - - 1 1 1 - 1 - - 1 - - 1 1 - - 1 - - 1 - - - 1 - 1 1 1 1]
[1 - - - - 1 1 1 1 - - 1 - 1 - - 1 1 - 1 1 - - 1 1 1 - 1 1 - 1 - 1 - - -]
[1 1 - - - 1 1 - - 1 1 1 1 - - 1 1 - - - - - 1 1 1 - - 1 1 - - - - 1 1 1]
[1 1 - - 1 - - 1 1 - - 1 1 - - 1 1 1 - - 1 1 - - 1 - 1 - - 1 1 - - 1 1 -]
[1 - - - 1 - 1 - 1 1 1 - - 1 1 1 - 1 - - - 1 - 1 - 1 - - 1 1 - - 1 1 1 -]
[1 - 1 1 - - 1 - 1 - - 1 1 - - 1 - - 1 1 - 1 - 1 1 - 1 - 1 1 - - 1 - - 1]
[1 1 - 1 - 1 - - 1 - - - - 1 1 1 1 - - 1 - 1 1 - - 1 1 - 1 - 1 - - 1 - 1]
[1 1 1 - - - 1 1 - - - - - 1 1 1 1 - 1 - 1 - - 1 - 1 1 1 - 1 - - - - 1 1]
[1 - - 1 - - 1 - 1 1 - 1 1 - 1 - - - 1 1 1 - 1 - - 1 - 1 - 1 1 - - 1 1 -]
[1 - - 1 1 - 1 - 1 1 - - - - 1 1 1 1 - - 1 - 1 - 1 - 1 1 - - - 1 1 - - 1]
[1 1 - 1 - 1 1 - - - 1 - 1 - - 1 - 1 1 - 1 - - 1 - 1 1 - - - 1 1 1 1 - -]
[1 1 1 - - 1 1 - - 1 - 1 - - - - 1 1 - 1 - 1 1 - - 1 1 - - 1 - 1 1 - 1 -]
[1 - 1 - 1 - 1 1 - - 1 - 1 - - - - 1 - 1 1 1 1 - - 1 1 1 1 - - - - 1 - 1]
[1 - 1 - - - 1 1 - - 1 - 1 1 1 1 1 - - 1 - - 1 - 1 - - - - 1 1 1 1 1 - -]
[1 1 - - 1 - 1 - 1 - 1 - - 1 - - - - 1 1 - 1 1 1 1 - 1 1 - - 1 1 - - 1 -]
[1 1 - - 1 1 - 1 - 1 - - - - 1 - - - 1 1 1 - 1 1 1 - 1 - 1 1 - - 1 1 - -]
[1 1 1 - - - 1 - - 1 - 1 - 1 1 - - 1 1 - 1 1 - - 1 - - - 1 - 1 1 - 1 - 1]
[1 1 - 1 - 1 - - - - 1 - 1 1 1 - - 1 - 1 1 1 - - 1 - - 1 - 1 - - 1 - 1 1]
[1 1 - - 1 - - - 1 - 1 1 1 1 - - 1 - 1 - 1 - 1 - - 1 - - 1 1 - 1 1 - - 1]
[1 1 - - 1 - - 1 - 1 - 1 1 - 1 1 - - - 1 - 1 - 1 - 1 - 1 - - 1 1 1 - - 1]
[1 - - 1 1 1 1 1 - - 1 1 - - 1 - 1 1 1 - - 1 1 1 - - - - - 1 1 - - - - 1]
[1 - - 1 - - - 1 - - 1 1 - - 1 - 1 - 1 - - 1 - - 1 1 1 1 1 - - 1 1 1 1 -]
[1 - - 1 - - - 1 - 1 - - 1 1 - - - 1 - - - - 1 1 1 1 1 - 1 1 1 1 - - 1 1]
[1 - - 1 1 1 1 1 - 1 - - 1 1 - 1 1 - 1 1 1 1 - - - - - - 1 - - 1 - - 1 -]
[1 1 1 1 - - - 1 1 - 1 1 - - 1 1 - 1 - 1 1 - 1 1 - - - - 1 - - 1 - - 1 -]
[1 1 1 1 - - - 1 1 1 - - 1 1 - - 1 1 1 - - 1 1 1 - - - 1 - - - - 1 1 - -]

Permutation group acting on a set of cardinality 72
Order = 3888 = 2^4 * 3^5
    (5, 42)(6, 41)(7, 44)(8, 43)(9, 46)(10, 45)(11, 48)(12, 47)(15, 52)(16,
        51)(17, 18)(19, 56)(20, 55)(21, 22)(23, 60)(24, 59)(25, 26)(27, 28)(29,
        30)(31, 68)(32, 67)(33, 70)(34, 69)(35, 36)(53, 54)(57, 58)(61, 62)(63,
        64)(65, 66)(71, 72)
    (1, 4)(2, 13)(3, 14)(5, 20)(6, 19)(9, 32)(10, 31)(11, 24)(12, 23)(15,
        33)(16, 34)(17, 35)(18, 36)(27, 29)(28, 30)(37, 40)(38, 49)(39, 50)(41,
        56)(42, 55)(45, 68)(46, 67)(47, 60)(48, 59)(51, 69)(52, 70)(53, 71)(54,
        72)(63, 65)(64, 66)
    (1, 2, 3, 37, 38, 39)(4, 8, 10, 48, 45, 41)(5, 40, 44, 46, 12, 9)(6, 47)(7,
        43)(11, 42)(13, 21, 53, 63, 54, 23)(14, 62, 51, 56, 16, 29)(15, 20, 52,
        65, 50, 26)(17, 27, 18, 59, 49, 57)(19, 66)(22, 58)(24, 64)(25, 61)(28,
        60)(30, 55)(31, 70, 69, 72, 35, 32)(33, 36, 71, 68, 67, 34)
    (4, 14, 49)(5, 25, 63, 42, 26, 64)(6, 62, 28, 41, 61, 27)(7, 20, 60, 44, 55,
        23)(8, 19, 59, 43, 56, 24)(9, 15, 54, 46, 52, 53)(10, 16, 17, 45, 51,
    18)(11, 29, 58, 48, 30, 57)(12, 66, 21, 47, 65, 22)(13, 40, 50)(31,
        68)(32, 67)(33, 70)(34, 69)(35, 36)(71, 72)
    (4, 23, 16, 12, 17, 26)(5, 18, 20, 10, 21, 14)(6, 28, 30, 11, 24, 19)(7, 22,
        25)(8, 13, 29, 9, 27, 15)(31, 36)(32, 33)(34, 35)(40, 59, 52, 48, 53,
        62)(41, 54, 56, 46, 57, 50)(42, 64, 66, 47, 60, 55)(43, 58, 61)(44, 49,
        65, 45, 63, 51)(67, 72)(68, 69)(70, 71)
Automorphism group has centre of order: 6
Number of regular subgroups: 10
Number of regular subgroups containing zeta: 5
Number of centrally regular subgroups: 3
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 9> <72, 45>
<36, 10> <72, 46>
<36, 11> <72, 47>
<36, 8> <72, 36>
<36, 12> <72, 48>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 1 1 1 1 1 1 - - - 1 1 1 1 1 1 1 1 1 - - - - - - - - - - - - - - -]
[1 1 1 1 1 1 1 1 1 - - - - - - - - - - - - 1 1 1 1 1 1 1 1 1 - - - - - -]
[1 - 1 - 1 1 - 1 1 1 1 1 1 - - - 1 - 1 - - 1 1 - - 1 - - - - 1 - 1 - 1 -]
[1 - 1 - - 1 - - - - - - 1 - 1 1 1 - 1 - 1 - - 1 1 - 1 1 1 1 1 - 1 - 1 -]
[1 - 1 - - 1 - - - - - - 1 1 - - 1 1 1 1 - 1 1 1 - 1 1 - 1 - - 1 - 1 - 1]
[1 - 1 - 1 1 - 1 1 1 1 1 - - 1 1 - - - - 1 - - 1 - - 1 - 1 - - 1 - 1 - 1]
[1 1 1 1 - 1 1 - - 1 1 1 - 1 - - - 1 - 1 - - - 1 - - 1 - 1 - 1 - 1 - 1 -]
[1 1 1 1 - 1 1 - - 1 1 1 1 - - - 1 - 1 - - - - - 1 - - 1 - 1 - 1 - 1 - 1]
[1 1 1 1 1 - - - - 1 - - 1 1 1 1 - - - - - 1 1 1 1 - - - - - 1 1 1 1 - -]
[1 - - 1 1 - 1 - - 1 - 1 1 1 - 1 1 - - - 1 1 - - - 1 1 - 1 1 - - - 1 1 -]
[1 - - 1 - - 1 1 1 - 1 - - - - 1 1 - 1 1 - 1 - 1 1 - 1 - - - 1 1 - 1 1 -]
[1 1 - 1 - - - - 1 1 1 - 1 - 1 1 1 - - 1 - - 1 - - 1 1 1 1 - 1 - - - - 1]
[1 1 1 - - - - 1 - 1 1 - - 1 1 1 - 1 1 - - 1 - - - 1 1 1 - 1 - 1 - - 1 -]
[1 - - 1 1 1 - - - 1 1 - - - 1 - 1 1 - 1 1 - 1 1 1 1 - - - 1 - 1 - - 1 -]
[1 - - 1 - 1 - 1 1 - - 1 1 1 1 - - - - 1 - - 1 - - - 1 1 - 1 - 1 1 1 1 -]
[1 - 1 1 - - - - 1 1 - 1 - - - 1 - 1 1 1 1 1 1 - 1 - 1 - - 1 - - 1 - - 1]
[1 - - - 1 1 1 - 1 - 1 - 1 1 - 1 - 1 - - - - - - 1 1 1 - - 1 1 1 1 - - 1]
[1 1 - - 1 1 1 - - - - 1 - - 1 1 - - 1 1 - 1 1 - - - - - 1 1 1 1 - - 1 1]
[1 1 - - - - - 1 1 1 - 1 1 1 - - - - 1 1 1 - - 1 1 1 - - 1 1 1 1 - - - -]
[1 - - - 1 - 1 1 - 1 1 - 1 - - 1 - 1 1 1 - - 1 1 - - - 1 1 1 - - 1 1 - -]
[1 - 1 1 - - 1 1 - - - 1 1 - - 1 - 1 - - 1 - 1 1 - 1 - 1 - - 1 1 - - 1 1]
[1 1 - 1 - 1 - 1 - - 1 - - 1 - 1 - - 1 - 1 - 1 - 1 1 - - 1 - - - 1 1 1 1]
[1 1 1 - - - 1 - 1 - 1 - 1 - 1 - - - - 1 1 1 - 1 - 1 - - - 1 - - 1 1 1 1]
[1 - 1 1 1 - - 1 - - 1 - - 1 - - 1 - - 1 1 1 - - - - - 1 1 1 1 1 1 - - 1]
[1 - - - - 1 1 1 - 1 - 1 - 1 1 1 1 - - 1 - 1 - 1 1 1 - 1 - - - - 1 - - 1]
[1 1 1 - 1 - - - 1 - - 1 - - - 1 1 1 - 1 - - - - 1 1 - 1 1 - - 1 1 1 1 -]
[1 1 - 1 1 - - 1 - - - 1 - - 1 - 1 1 1 - - - - 1 - 1 1 - - 1 1 - 1 1 - 1]
[1 - 1 - - - 1 1 1 1 - - - 1 1 - 1 1 - - - - 1 - 1 - - - 1 1 1 - - 1 1 1]
[1 - 1 - 1 - 1 - - - 1 1 - 1 1 - - - 1 1 1 - 1 - 1 1 1 1 - - 1 - - 1 - -]
[1 - - 1 1 - - - 1 - 1 1 1 1 1 - - 1 1 - - 1 - 1 1 - - 1 1 - - - - - 1 1]
[1 - - 1 - 1 1 - 1 1 - - - - 1 - - 1 1 - 1 1 - - - 1 - 1 1 - 1 1 1 1 - -]
[1 1 - - 1 - 1 - 1 1 - - - 1 - - 1 - 1 - 1 - 1 1 - - 1 1 - - - 1 1 - 1 1]
[1 1 - - 1 1 - 1 - 1 - - 1 - - - - 1 - 1 1 1 - - 1 - 1 1 - - 1 - - 1 1 1]
[1 1 - - - - 1 1 - - 1 1 1 - 1 - 1 1 - - 1 1 1 - 1 - 1 - 1 - - 1 1 - - -]
[1 1 - - - 1 - - 1 - 1 1 - 1 - 1 1 1 - - 1 1 1 1 - - - 1 - 1 1 - - 1 - -]

Permutation group acting on a set of cardinality 72
Order = 31104 = 2^7 * 3^5
    (1, 10, 62, 25, 44, 57, 33, 16)(2, 68, 17, 11, 4, 55, 30, 13)(3, 31, 48, 54,
        42, 58, 36, 63)(5, 24, 51, 29, 43, 56, 28, 34)(6, 22, 72, 27, 39, 67,
    12, 18)(7, 20, 64, 70, 41, 60, 15, 65)(8, 21, 69, 52, 37, 46, 26, 61)(9,
        59, 14, 35)(19, 66, 49, 38, 32, 53, 47, 40)(23, 50, 71, 45)
    (2, 4)(3, 7)(5, 6)(10, 26, 24, 15, 22, 36)(11, 35, 13)(12, 31, 28, 20, 33,
        21)(14, 32, 30, 23, 17, 19)(16, 27, 34, 29, 18, 25)(38, 40)(39, 43)(41,
        42)(46, 62, 60, 51, 58, 72)(47, 71, 49)(48, 67, 64, 56, 69, 57)(50, 68,
        66, 59, 53, 55)(52, 63, 70, 65, 54, 61)
    (4, 42, 8)(5, 45, 43)(6, 44, 40)(7, 41, 9)(10, 49, 12)(11, 30, 21)(13, 48,
        46)(14, 60, 70)(15, 59, 35)(16, 62, 67)(17, 68, 63)(18, 33, 19)(20, 65,
        64)(22, 25, 72)(23, 71, 51)(24, 34, 50)(26, 31, 52)(27, 53, 32)(28, 56,
        29)(36, 58, 61)(47, 66, 57)(54, 69, 55)
    (10, 67, 32)(11, 54, 61)(12, 62, 53)(13, 52, 63)(14, 64, 15)(16, 27, 49)(17,
        48, 26)(18, 25, 47)(19, 22, 57)(20, 59, 60)(21, 55, 58)(23, 24, 56)(28,
        51, 50)(29, 71, 34)(30, 69, 36)(31, 68, 46)(33, 72, 66)(35, 70, 65)
    (4, 9)(5, 6)(7, 8)(10, 16, 24, 34, 22, 18)(11, 31, 13, 20, 35, 21)(12, 33,
        28)(14, 26, 30, 15, 17, 36)(19, 25, 32, 27, 23, 29)(40, 45)(41, 42)(43,
        44)(46, 52, 60, 70, 58, 54)(47, 67, 49, 56, 71, 57)(48, 69, 64)(50, 62,
        66, 51, 53, 72)(55, 61, 68, 63, 59, 65)
    (10, 24, 22)(11, 13, 35)(12, 28, 33)(14, 30, 17)(15, 36, 26)(16, 34, 18)(19,
        32, 23)(20, 21, 31)(25, 27, 29)(46, 60, 58)(47, 49, 71)(48, 64, 69)(50,
        66, 53)(51, 72, 62)(52, 70, 54)(55, 68, 59)(56, 57, 67)(61, 63, 65)
Automorphism group has centre of order: 2
Number of regular subgroups: 25
Number of regular subgroups containing zeta: 12
Number of centrally regular subgroups: 12
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 9> <72, 45>
<36, 10> <72, 21>
<36, 10> <72, 46>
<36, 7> <72, 34>
<36, 8> <72, 36>
<36, 9> <72, 45>
<36, 10> <72, 24>
<36, 10> <72, 20>
<36, 12> <72, 48>
<36, 12> <72, 29>
<36, 12> <72, 26>
<36, 12> <72, 27>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - 1 1 - - - - - - 1 - - -]
[1 1 1 - - - 1 1 - 1 1 1 1 - - 1 1 - 1 1 1 1 - - - - 1 1 - - - - - 1 - -]
[1 1 1 - - - - 1 1 1 - - 1 1 1 1 - 1 - 1 1 - 1 1 - - - - 1 - 1 - - - - 1]
[1 1 1 - - - 1 - 1 - 1 1 - 1 1 - 1 1 1 - - 1 1 1 - - - - - 1 - 1 - - 1 -]
[1 1 1 - - - - - 1 - - - - 1 1 1 - - - 1 1 - - - 1 1 1 1 - 1 - 1 1 1 1 -]
[1 1 1 - - - 1 - - - 1 1 - - - - - 1 - - - - 1 1 1 1 1 1 1 - 1 - 1 1 - 1]
[1 1 1 - - - - 1 - 1 - - 1 - - - 1 - 1 - - 1 - - 1 1 - - 1 1 1 1 1 - 1 1]
[1 1 1 1 1 1 - - - - - - - - - 1 1 1 1 1 1 1 1 1 1 1 - - - - - - 1 - - -]
[1 - 1 1 1 - - - - 1 1 - 1 1 - 1 1 - - - - - 1 1 1 - - 1 - 1 - - - 1 1 1]
[1 - - 1 - - 1 1 1 1 - - - 1 - 1 - - 1 - - 1 1 1 - 1 1 1 1 1 - - 1 - - -]
[1 1 - 1 - 1 - - - 1 - 1 - 1 1 1 - 1 1 - - 1 - - 1 - 1 - 1 - - - - 1 1 1]
[1 - - - - 1 - - 1 1 1 1 1 - - 1 1 1 - 1 - - - 1 1 - 1 - 1 1 - 1 1 - - -]
[1 - 1 1 - 1 - 1 1 - 1 1 - - - - - - - 1 1 1 - 1 - 1 - - 1 1 - - - 1 1 1]
[1 1 - - 1 1 1 - 1 1 - - 1 - - - - - 1 1 - - 1 1 - 1 1 - - - - 1 - 1 1 1]
[1 1 - 1 - 1 1 - 1 - - - 1 - 1 - 1 - 1 - 1 - - 1 1 - - 1 1 1 1 - - 1 - -]
[1 - 1 1 1 - 1 1 - - - - 1 - 1 - - 1 - 1 - 1 1 - 1 - 1 - 1 1 - 1 - 1 - -]
[1 1 - 1 - 1 - 1 1 - 1 - - 1 - - 1 - - 1 - 1 1 - 1 - 1 1 - - 1 1 - - - 1]
[1 - - 1 - - - 1 - - 1 - 1 1 1 - 1 1 1 - 1 - - 1 - 1 1 - - - - 1 1 1 - 1]
[1 - - 1 - - - - 1 1 - 1 1 - 1 - 1 1 - 1 - 1 1 - - 1 - 1 - - 1 - 1 1 1 -]
[1 - 1 1 1 - - 1 1 1 - 1 - - - - - 1 1 - 1 - - 1 1 - 1 1 - - 1 1 - - 1 -]
[1 1 - - 1 1 - 1 - 1 1 - - - 1 1 - 1 - - - 1 - 1 - 1 - 1 - 1 1 1 - 1 - -]
[1 - - - - 1 1 1 - 1 1 - - - 1 - - 1 1 1 1 - 1 - 1 - - 1 - 1 - - 1 - 1 1]
[1 1 - - 1 1 - 1 - - - 1 1 1 - - 1 1 - - 1 - 1 - - 1 1 1 1 1 - - - - 1 -]
[1 - 1 1 - 1 1 - - 1 1 - - - 1 1 1 - - - 1 - 1 - - 1 1 - 1 - 1 1 - - 1 -]
[1 - 1 1 - 1 1 - - - - 1 1 1 - 1 - 1 1 1 - - - - - 1 - 1 - 1 1 1 - - - 1]
[1 - - - - 1 1 1 - - - 1 1 1 - 1 - - - - 1 1 1 1 1 - - - - - 1 1 1 1 1 -]
[1 1 - 1 1 - 1 1 - - - 1 - - 1 1 1 - - 1 - - - 1 - - - 1 1 - - 1 1 - 1 1]
[1 1 - 1 1 - 1 - 1 - 1 - 1 - - 1 - 1 - - 1 1 - - - - 1 - - 1 1 - 1 - 1 1]
[1 - - - 1 - 1 - - 1 - 1 - 1 1 - 1 - - 1 1 1 - 1 1 1 1 - - 1 1 - - - - 1]
[1 - - - 1 - - - 1 - 1 1 1 - 1 1 - - 1 - 1 1 1 - 1 1 - 1 1 - - 1 - - - 1]
[1 - 1 - 1 1 - 1 1 - - 1 - - 1 1 1 - 1 - - - 1 - - - 1 - - 1 1 - 1 1 - 1]
[1 - 1 - 1 1 1 - 1 1 - - - 1 - - 1 1 - - 1 1 - - - - - 1 1 - - 1 1 1 - 1]
[1 1 - 1 1 - - - - 1 1 1 - 1 - - - - 1 1 1 - 1 - - - - - 1 1 1 1 1 1 - -]
[1 - 1 - 1 1 - - - - 1 - 1 1 1 - - - 1 1 - 1 - 1 - - 1 1 1 - 1 - 1 - 1 -]
[1 - - - 1 - 1 1 1 - 1 - - 1 - 1 1 1 1 1 - - - - 1 1 - - 1 - 1 - - 1 1 -]

Permutation group acting on a set of cardinality 72
Order = 3456 = 2^7 * 3^3
    (1, 10, 71, 38, 36, 12)(2, 72, 48, 37, 46, 35)(3, 22, 54, 6, 60, 32)(4, 67,
        69, 7, 53, 16)(5, 21, 23, 8, 30, 63)(9, 15, 13, 45, 51, 49)(11, 34)(14,
        50)(17, 52, 40, 31, 33, 43)(18, 42, 24, 68, 39, 58)(19, 25, 64, 29, 62,
        56)(20, 55, 61, 28, 65, 26)(27, 41, 57, 59, 44, 66)(47, 70)
    (2, 3, 4, 9, 44, 42)(5, 43)(6, 38, 39, 40, 45, 8)(7, 41)(10, 28, 54, 15, 29,
        27)(11, 59, 30, 50, 16, 31)(12, 53, 62, 49, 58, 20)(13, 22, 56, 48, 17,
        26)(14, 52, 67, 47, 23, 66)(18, 51, 65, 63, 46, 64)(19, 32, 60, 61, 33,
        57)(21, 55, 68, 24, 25, 69)(34, 71, 72)(35, 36, 70)
    (3, 44)(4, 43)(5, 42)(6, 41)(7, 40)(8, 39)(10, 12)(13, 51)(15, 49)(16,
    17)(18, 21)(19, 20)(22, 59)(23, 58)(24, 63)(25, 26)(27, 60)(28, 29)(30,
        68)(31, 69)(32, 66)(33, 67)(35, 72)(36, 71)(46, 48)(52, 53)(54, 57)(55,
        56)(61, 62)(64, 65)
    (3, 42)(4, 44)(5, 43)(6, 39)(7, 41)(8, 40)(10, 47)(11, 46)(14, 15)(16,
    18)(17, 56)(19, 57)(20, 53)(21, 55)(22, 26)(23, 27)(24, 25)(28, 67)(29,
        66)(30, 65)(31, 64)(32, 33)(34, 72)(36, 70)(50, 51)(52, 54)(58, 62)(59,
        63)(60, 61)(68, 69)
Automorphism group has centre of order: 2
Number of regular subgroups: 14
Number of regular subgroups containing zeta: 4
Number of centrally regular subgroups: 4
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 14> <72, 50>
<36, 13> <72, 49>
<36, 11> <72, 47>
<36, 6> <72, 29>


[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 1 1 1 1 - 1 - 1 - - - 1 - - 1 1 - - - - - - - 1 1 - 1 1 1 - - 1 -]
[1 1 1 1 1 1 1 - - 1 - 1 - - - 1 - - - 1 1 - - - 1 - - - 1 1 - 1 1 - - 1]
[1 1 1 1 1 1 1 1 - - - - 1 1 - - 1 - - - - 1 - - - 1 - 1 1 - 1 - 1 1 - -]
[1 - 1 - 1 - - - - - - 1 - - 1 - 1 - - - - 1 1 1 1 - 1 1 1 - 1 1 1 - 1 1]
[1 - - 1 - - 1 - - - 1 - - 1 - - - - - 1 1 - 1 1 - 1 1 - 1 1 1 1 1 1 1 -]
[1 1 - - - 1 - - - - - - 1 - - 1 - 1 1 - - - 1 1 1 1 - 1 - 1 1 1 1 1 - 1]
[1 1 1 - - - - - - 1 1 - 1 1 1 - - 1 - 1 1 1 - - - - - 1 - - - 1 1 1 1 1]
[1 - - - 1 - 1 - 1 - - 1 1 1 - 1 1 1 1 1 - - - - - - - - 1 - 1 1 - 1 1 1]
[1 - - 1 - 1 - 1 - - 1 1 - - 1 1 1 - 1 - 1 1 - - - - - - - 1 1 - 1 1 1 1]
[1 - - 1 - - 1 - - 1 1 1 - 1 - 1 1 1 1 - - 1 - - 1 1 1 1 - - - 1 1 - - -]
[1 1 - - - 1 - - 1 - 1 - 1 - 1 1 1 - - 1 1 1 - - 1 1 1 - 1 - 1 1 - - - -]
[1 - 1 - 1 - - 1 - - - 1 1 1 1 - - 1 1 1 1 - - - 1 1 1 - - 1 1 - 1 - - -]
[1 - 1 - - 1 - 1 1 - 1 - - 1 - 1 1 1 - 1 - - 1 - - - 1 1 1 1 - - 1 - - 1]
[1 1 - 1 - - - - 1 1 - 1 1 - 1 - 1 - 1 1 - - - 1 - - 1 1 1 1 - - 1 1 - -]
[1 1 - - 1 - - 1 1 - 1 1 - 1 - - - - 1 - 1 1 - 1 - 1 - 1 1 1 - 1 - - - 1]
[1 - 1 - - - 1 1 - 1 - - 1 - 1 1 1 - 1 - 1 - 1 - - 1 - 1 1 1 - 1 - - 1 -]
[1 - - 1 1 - - 1 - 1 1 - 1 - - 1 - 1 - 1 - 1 - 1 1 - - 1 1 1 1 - - - 1 -]
[1 - - - - 1 1 - 1 1 - 1 - 1 1 - - 1 - - 1 1 1 - 1 - - 1 1 1 1 - - 1 - -]
[1 1 1 - 1 - 1 - - - 1 1 - - 1 1 1 1 - 1 - 1 1 1 - 1 - - - 1 - - - 1 - -]
[1 - - 1 1 1 1 - - - 1 - 1 1 1 - 1 - 1 1 1 - 1 1 1 - - 1 - - - - - - - 1]
[1 1 1 1 - 1 - - - - - 1 1 1 - 1 - 1 1 - 1 1 1 1 - - 1 - 1 - - - - - 1 -]
[1 - 1 - - 1 1 1 1 1 1 1 1 - - - - - 1 1 - 1 1 1 - - - - - - 1 1 1 - - -]
[1 1 - 1 1 - - 1 1 1 - - - 1 1 1 1 1 - - 1 - 1 1 - - - - - - 1 1 1 - - -]
[1 - - - 1 1 1 - 1 1 - - 1 1 1 1 - - - - - 1 - 1 - 1 1 - - 1 - - 1 - 1 1]
[1 1 1 1 - - - - 1 1 1 1 1 1 - - 1 - - - - - 1 - 1 1 - - - 1 1 - - - 1 1]
[1 1 1 - - - 1 1 - 1 1 - - 1 1 1 - - 1 - - - - 1 1 - 1 - 1 - 1 - - 1 - 1]
[1 1 - - 1 - 1 1 1 - 1 1 1 - - 1 - - - - 1 - 1 - 1 - 1 1 - - - - 1 1 1 -]
[1 - 1 1 - 1 - 1 1 - - 1 - 1 1 1 - - - 1 - - - 1 1 1 - 1 - - - 1 - 1 1 -]
[1 - - 1 1 1 - 1 - 1 1 1 1 - 1 - - 1 - - - - 1 - - 1 1 - 1 - - 1 - 1 - 1]
[1 - 1 1 - - 1 1 1 - - - 1 - - - 1 1 - - 1 1 - 1 1 - 1 - - 1 - 1 - 1 - 1]
[1 1 - - 1 1 - 1 - 1 - - - 1 - - 1 - 1 1 - 1 1 - 1 - 1 - - 1 - 1 - 1 1 -]
[1 1 - - - 1 1 1 - 1 - 1 - - - - 1 1 - 1 1 - - 1 - 1 1 1 - - 1 - - - 1 1]
[1 - 1 1 1 - - - 1 1 - - - - - 1 - - 1 1 1 1 1 - - 1 1 1 - - 1 - - 1 - 1]
[1 1 - 1 - - 1 1 1 - - - - - 1 - - 1 1 1 - 1 1 - 1 1 - - 1 - - - 1 - 1 1]
[1 - 1 - 1 1 - - 1 1 1 - - - - - 1 1 1 - 1 - - 1 1 1 - - 1 - - - 1 1 1 -]

Permutation group acting on a set of cardinality 72
Order = 432 = 2^4 * 3^3
    (1, 2, 43, 12, 22, 9)(3, 10, 66, 54, 72, 64)(4, 8, 63, 53, 71, 61)(5, 26,
        57, 34, 60, 19)(6, 29, 56, 31, 59, 16)(7, 48, 58, 45, 37, 38)(11, 50,
        68, 13, 51, 69)(14, 32, 49, 15, 33, 47)(17, 35, 25, 40, 44, 27)(18, 36,
        28, 39, 46, 30)(20, 67, 23, 52, 42, 65)(21, 70, 24, 55, 41, 62)
    (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11,
        47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20,
        56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29,
        65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)
    (2, 3)(6, 7)(8, 9)(11, 12)(14, 18)(15, 19)(16, 17)(21, 22)(23, 24)(25,
        26)(27, 28)(29, 30)(31, 32)(33, 35)(34, 36)(38, 39)(42, 43)(44, 45)(47,
        48)(50, 54)(51, 55)(52, 53)(57, 58)(59, 60)(61, 62)(63, 64)(65, 66)(67,
        68)(69, 71)(70, 72)
    (3, 4)(5, 6)(8, 10)(11, 13)(14, 15)(16, 19)(17, 18)(20, 21)(23, 24)(25,
        28)(26, 29)(27, 30)(31, 34)(32, 33)(35, 36)(39, 40)(41, 42)(44, 46)(47,
        49)(50, 51)(52, 55)(53, 54)(56, 57)(59, 60)(61, 64)(62, 65)(63, 66)(67,
        70)(68, 69)(71, 72)
Automorphism group has centre of order: 2
Number of regular subgroups: 5
Number of regular subgroups containing zeta: 3
Number of centrally regular subgroups: 3
Matrix is cocyclic over \Expanded matrix is group developed over:
<36, 14> <72, 50>
<36, 11> <72, 47>
<36, 6> <72, 29>