[ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[ 1 1 1 1 1 1 1 1 - - - - - - - -]
[ 1 1 1 1 - - - - 1 1 1 1 - - - -]
[ 1 1 1 1 - - - - - - - - 1 1 1 1]
[ 1 1 - - 1 1 - - 1 1 - - 1 1 - -]
[ 1 1 - - 1 1 - - - - 1 1 - - 1 1]
[ 1 1 - - - - 1 1 1 1 - - - - 1 1]
[ 1 1 - - - - 1 1 - - 1 1 1 1 - -]
[ 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 -]
[ 1 - 1 - 1 - 1 - - 1 - 1 - 1 - 1]
[ 1 - 1 - - 1 - 1 1 - 1 - - 1 - 1]
[ 1 - 1 - - 1 - 1 - 1 - 1 1 - 1 -]
[ 1 - - 1 1 - - 1 1 - - 1 1 - - 1]
[ 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 32
Order = 10321920 = 2^15 * 3^2 * 5 * 7
  (1, 2)(7, 8)(11, 12)(13, 14)(17, 18)(23, 24)(27, 28)(29, 30)
  (2, 3)(6, 7)(10, 11)(14, 15)(18, 19)(22, 23)(26, 27)(30, 31)
  (9, 26)(10, 25)(11, 28)(12, 27)(13, 30)(14, 29)(15, 32)(16, 31)
  (3, 9, 5)(4, 10, 6)(7, 11, 13)(8, 12, 14)(19, 25, 21)(20, 26, 22)(23, 27, 
    29)(24, 28, 30)
  (5, 9)(6, 10)(7, 11)(8, 12)(21, 25)(22, 26)(23, 27)(24, 28)
  (9, 13)(10, 14)(11, 15)(12, 16)(25, 29)(26, 30)(27, 31)(28, 32)
  (9, 11)(10, 12)(13, 15)(14, 16)(25, 27)(26, 28)(29, 31)(30, 32)
  (9, 12)(10, 11)(13, 16)(14, 15)(25, 28)(26, 27)(29, 32)(30, 31)
Automorphism group has centre of order: 2
Number of regular subgroups: 159
Number of regular subgroups containing zeta: 113
Matrix is cocyclic over /Expanded matrix is group developed over:
<16, 14> <32, 51>
<16, 14> <32, 45>
<16, 14> <32, 47>
<16, 10> <32, 45>
<16, 14> <32, 49>
<16, 14> <32, 47>
<16, 14> <32, 46>
<16, 2> <32, 21>
<16, 2> <32, 2>
<16, 12> <32, 23>
<16, 10> <32, 23>
<16, 10> <32, 21>
<16, 10> <32, 22>
<16, 11> <32, 46>
<16, 11> <32, 23>
<16, 12> <32, 47>
<16, 14> <32, 48>
<16, 14> <32, 49>
<16, 2> <32, 2>
<16, 2> <32, 21>
<16, 14> <32, 50>
<16, 11> <32, 23>
<16, 11> <32, 22>
<16, 11> <32, 22>
<16, 11> <32, 46>
<16, 10> <32, 24>
<16, 14> <32, 48>
<16, 3> <32, 22>
<16, 3> <32, 22>
<16, 3> <32, 2>
<16, 3> <32, 2>
<16, 12> <32, 23>
<16, 10> <32, 22>
<16, 10> <32, 45>
<16, 10> <32, 21>
<16, 10> <32, 23>
<16, 2> <32, 21>
<16, 2> <32, 2>
<16, 11> <32, 22>
<16, 10> <32, 26>
<16, 11> <32, 30>
<16, 11> <32, 28>
<16, 11> <32, 31>
<16, 11> <32, 29>
<16, 11> <32, 35>
<16, 12> <32, 29>
<16, 4> <32, 23>
<16, 4> <32, 2>
<16, 4> <32, 2>
<16, 4> <32, 23>
<16, 10> <32, 36>
<16, 10> <32, 37>
<16, 3> <32, 22>
<16, 3> <32, 2>
<16, 11> <32, 27>
<16, 13> <32, 28>
<16, 13> <32, 24>
<16, 13> <32, 29>
<16, 13> <32, 48>
<16, 11> <32, 28>
<16, 4> <32, 23>
<16, 4> <32, 2>
<16, 3> <32, 2>
<16, 3> <32, 22>
<16, 13> <32, 30>
<16, 13> <32, 33>
<16, 13> <32, 33>
<16, 13> <32, 26>
<16, 13> <32, 32>
<16, 13> <32, 32>
<16, 13> <32, 29>
<16, 13> <32, 25>
<16, 13> <32, 24>
<16, 13> <32, 32>
<16, 3> <32, 6>
<16, 6> <32, 5>
<16, 6> <32, 37>
<16, 11> <32, 28>
<16, 11> <32, 30>
<16, 11> <32, 23>
<16, 11> <32, 30>
<16, 11> <32, 25>
<16, 11> <32, 29>
<16, 11> <32, 35>
<16, 11> <32, 29>
<16, 5> <32, 5>
<16, 5> <32, 36>
<16, 3> <32, 5>
<16, 11> <32, 29>
<16, 11> <32, 25>
<16, 10> <32, 25>
<16, 11> <32, 43>
<16, 11> <32, 44>
<16, 11> <32, 40>
<16, 11> <32, 41>
<16, 11> <32, 43>
<16, 11> <32, 40>
<16, 11> <32, 44>
<16, 11> <32, 41>
<16, 10> <32, 38>
<16, 3> <32, 11>
<16, 3> <32, 10>
<16, 11> <32, 42>
<16, 11> <32, 44>
<16, 11> <32, 41>
<16, 11> <32, 44>
<16, 11> <32, 42>
<16, 3> <32, 11>
<16, 3> <32, 10>
<16, 8> <32, 40>
<16, 8> <32, 10>
<16, 9> <32, 41>
<16, 9> <32, 10>


[ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[ 1 1 1 1 1 1 1 1 - - - - - - - -]
[ 1 1 1 1 - - - - 1 1 1 1 - - - -]
[ 1 1 1 1 - - - - - - - - 1 1 1 1]
[ 1 1 - - 1 1 - - 1 1 - - 1 1 - -]
[ 1 1 - - 1 1 - - - - 1 1 - - 1 1]
[ 1 1 - - - - 1 1 1 1 - - - - 1 1]
[ 1 1 - - - - 1 1 - - 1 1 1 1 - -]
[ 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 -]
[ 1 - 1 - 1 - - 1 - 1 - 1 - 1 1 -]
[ 1 - 1 - - 1 1 - - 1 1 - - 1 - 1]
[ 1 - 1 - - 1 - 1 1 - - 1 1 - - 1]
[ 1 - - 1 1 - 1 - 1 - - 1 - 1 - 1]
[ 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 32
Order = 86016 = 2^12 * 3 * 7
  (1, 9)(2, 15, 5, 10, 7, 12)(3, 11, 8, 14, 6, 16)(4, 13)(17, 25)(18, 31, 21, 
    26, 23, 28)(19, 27, 24, 30, 22, 32)(20, 29)
  (2, 3, 4)(5, 6, 8)(10, 11, 12)(13, 16, 15)(18, 19, 20)(21, 22, 24)(26, 27, 
    28)(29, 32, 31)
  (3, 4)(5, 22)(6, 21)(7, 23)(8, 24)(10, 11)(13, 32)(14, 30)(15, 31)(16, 
    29)(19, 20)(26, 27)
  (9, 27)(10, 28)(11, 25)(12, 26)(13, 31)(14, 32)(15, 29)(16, 30)
  (3, 6, 7)(4, 5, 8)(10, 13, 11)(12, 14, 15)(19, 22, 23)(20, 21, 24)(26, 29, 
    27)(28, 30, 31)
  (9, 14)(10, 13)(11, 16)(12, 15)(25, 30)(26, 29)(27, 32)(28, 31)
  (9, 13)(10, 14)(11, 15)(12, 16)(25, 29)(26, 30)(27, 31)(28, 32)
  (9, 15)(10, 16)(11, 13)(12, 14)(25, 31)(26, 32)(27, 29)(28, 30)
Order of automorphism group: 86016
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:
<16, 7> <32, 20>


[ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[ 1 1 1 1 1 1 1 1 - - - - - - - -]
[ 1 1 1 1 - - - - 1 1 1 1 - - - -]
[ 1 1 - - 1 1 - - 1 1 - - 1 1 - -]
[ 1 1 - - - 1 1 - 1 - - 1 - - 1 1]
[ 1 1 - - 1 - - 1 - 1 1 - - - 1 1]
[ 1 1 - - - - 1 1 - - 1 1 1 1 - -]
[ 1 - - 1 - - 1 1 1 1 - - 1 - - 1]
[ 1 - - 1 1 1 - - - - 1 1 1 - - 1]
[ 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 -]
[ 1 - 1 - 1 - - 1 1 - - 1 - 1 - 1]
[ 1 - 1 - - 1 1 - - 1 1 - - 1 - 1]
[ 1 - 1 - - 1 - 1 - 1 - 1 1 - 1 -]
[ 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 32
Order = 86016 = 2^12 * 3 * 7
  (1, 2)(3, 16)(4, 5, 7, 6)(8, 11, 9, 12)(10, 15)(13, 14)(17, 18)(19, 32)(20, 
    21, 23, 22)(24, 27, 25, 28)(26, 31)(29, 30)
  (2, 8, 7)(3, 9, 4)(5, 14, 10)(6, 15, 13)(18, 24, 23)(19, 25, 20)(21, 30, 
    26)(22, 31, 29)
  (3, 19)(4, 8, 31, 13, 27, 21)(5, 20, 24, 15, 29, 11)(6, 7, 25, 30, 26, 
    28)(9, 14, 10, 12, 22, 23)(16, 32)
  (8, 25)(9, 24)(10, 29)(11, 28)(12, 27)(13, 26)(14, 31)(15, 30)
  (4, 11, 14)(5, 13, 8)(6, 10, 9)(7, 12, 15)(20, 27, 30)(21, 29, 24)(22, 26, 
    25)(23, 28, 31)
  (5, 6)(10, 13)(11, 12)(14, 15)(21, 22)(26, 29)(27, 28)(30, 31)
Order of automorphism group: 86016
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:
<16, 7> <32, 20>


[ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[ 1 1 1 1 1 1 1 1 - - - - - - - -]
[ 1 1 1 1 - - - - 1 1 1 1 - - - -]
[ 1 1 - - 1 1 - - 1 1 - - 1 1 - -]
[ 1 1 - - - 1 1 - - 1 1 - - - 1 1]
[ 1 1 - - 1 - - 1 1 - - 1 - - 1 1]
[ 1 1 - - - - 1 1 - - 1 1 1 1 - -]
[ 1 - - 1 - - 1 1 1 1 - - 1 - - 1]
[ 1 - - 1 1 1 - - - - 1 1 1 - - 1]
[ 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 -]
[ 1 - 1 - - 1 - 1 - 1 - 1 1 - 1 -]
[ 1 - - 1 1 - - 1 - 1 1 - - 1 1 -]
[ 1 - - 1 - 1 1 - 1 - - 1 - 1 1 -]
[ 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 32
Order = 294912 = 2^15 * 3^2
  (1, 2)(3, 14)(10, 15)(11, 16)(17, 18)(19, 30)(26, 31)(27, 32)
  (2, 8, 7)(3, 9, 4)(5, 12, 10, 6, 13, 11)(15, 16)(18, 24, 23)(19, 25, 20)(21,
    28, 26, 22, 29, 27)(31, 32)
  (8, 25)(9, 24)(10, 27)(11, 26)(12, 29)(13, 28)(15, 32)(16, 31)
  (3, 11, 10)(4, 7, 12)(5, 8, 9)(14, 16, 15)(19, 27, 26)(20, 23, 28)(21, 24, 
    25)(30, 32, 31)
  (4, 9)(5, 12)(6, 13)(7, 8)(10, 11)(15, 16)(20, 25)(21, 28)(22, 29)(23, 
    24)(26, 27)(31, 32)
  (4, 5, 7, 6)(8, 12, 9, 13)(10, 11)(15, 16)(20, 21, 23, 22)(24, 28, 25, 
    29)(26, 27)(31, 32)
  (5, 6)(10, 11)(12, 13)(15, 16)(21, 22)(26, 27)(28, 29)(31, 32)
Order of automorphism group: 294912
Automorphism group has centre of order: 2
Number of regular subgroups: 3
Number of regular subgroups containing zeta: 2
Number of centrally regular subgroups: 2
Matrix is cocyclic over /Expanded matrix is group developed over:
<16, 5> <32, 36>
<16, 7> <32, 14>


[ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[ 1 - - - - - - - - 1 1 1 1 1 1 1]
[ 1 1 1 1 1 - - - - 1 1 1 - - - -]
[ 1 1 1 - - 1 1 - - 1 - - 1 1 - -]
[ 1 1 - 1 - 1 - 1 - - - 1 1 - 1 -]
[ 1 - 1 - 1 - 1 - 1 - - 1 1 - 1 -]
[ 1 - 1 1 - 1 - - 1 - 1 - - 1 1 -]
[ 1 1 - - 1 - 1 1 - - 1 - - 1 1 -]
[ 1 - - 1 1 - - 1 1 1 - - 1 1 - -]
[ 1 - - - - 1 1 1 1 1 1 1 - - - -]
[ 1 1 1 - - - - 1 1 - - 1 - 1 - 1]
[ 1 - 1 - 1 1 - 1 - - 1 - 1 - - 1]
[ 1 1 - 1 - - 1 - 1 - 1 - 1 - - 1]
[ 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 32
Order = 49152 = 2^14 * 3
  (1, 3)(2, 10)(4, 15)(5, 13)(6, 12)(7, 11)(8, 14)(9, 16)(17, 19)(18, 26)(20, 
    31)(21, 29)(22, 28)(23, 27)(24, 30)(25, 32)
  (2, 18)(3, 10, 19, 26)(4, 6, 25, 5)(7, 23)(9, 21, 20, 22)(11, 14, 27, 
    30)(12, 32, 29, 31)(13, 15, 28, 16)
  (5, 21)(6, 22)(7, 23)(8, 24)(11, 30)(12, 28)(13, 29)(14, 27)(15, 16)(31, 32)
  (3, 5, 4)(6, 9, 10)(11, 13, 16)(12, 15, 14)(19, 21, 20)(22, 25, 26)(27, 29, 
    32)(28, 31, 30)
  (4, 8, 5)(6, 9, 7)(11, 16, 13)(12, 14, 15)(20, 24, 21)(22, 25, 23)(27, 32, 
    29)(28, 30, 31)
  (5, 6)(7, 8)(12, 13)(15, 16)(21, 22)(23, 24)(28, 29)(31, 32)
Order of automorphism group: 49152
Automorphism group has centre of order: 2
Number of regular subgroups: 50
Number of regular subgroups containing zeta: 48
Number of centrally regular subgroups: 48
Matrix is cocyclic over /Expanded matrix is group developed over:
<16, 11> <32, 34>
<16, 11> <32, 35>
<16, 14> <32, 48>
<16, 14> <32, 47>
<16, 12> <32, 32>
<16, 11> <32, 31>
<16, 12> <32, 35>
<16, 13> <32, 26>
<16, 12> <32, 26>
<16, 10> <32, 26>
<16, 12> <32, 47>
<16, 13> <32, 48>
<16, 10> <32, 25>
<16, 2> <32, 3>
<16, 2> <32, 4>
<16, 11> <32, 35>
<16, 11> <32, 31>
<16, 13> <32, 26>
<16, 13> <32, 25>
<16, 13> <32, 32>
<16, 13> <32, 31>
<16, 12> <32, 26>
<16, 11> <32, 25>
<16, 10> <32, 21>
<16, 10> <32, 24>
<16, 10> <32, 26>
<16, 11> <32, 29>
<16, 13> <32, 24>
<16, 4> <32, 12>
<16, 13> <32, 33>
<16, 12> <32, 35>
<16, 5> <32, 3>
<16, 6> <32, 4>
<16, 5> <32, 12>
<16, 6> <32, 12>
<16, 13> <32, 31>
<16, 13> <32, 29>
<16, 12> <32, 29>
<16, 3> <32, 8>
<16, 3> <32, 7>
<16, 8> <32, 10>
<16, 7> <32, 9>
<16, 8> <32, 13>
<16, 7> <32, 14>
<16, 10> <32, 37>
<16, 4> <32, 15>
<16, 11> <32, 44>
<16, 11> <32, 41>