[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - - - - - - 1] [1 1 1 1 1 1 - - - - - - - 1 1 1 1 1 1 1 - - - - - - - 1] [1 - - 1 - - - 1 1 1 1 - - 1 1 - 1 1 - - 1 1 - - 1 - - 1] [1 1 - 1 1 - 1 - - - 1 - 1 1 - - 1 - - 1 - 1 1 - 1 - 1 -] [1 - 1 1 - 1 1 - - - 1 1 - - 1 - - 1 - 1 - 1 - 1 1 1 - -] [1 - - 1 1 1 - - - 1 1 - 1 - - 1 - 1 1 - 1 1 1 - - 1 - -] [1 - 1 - - - 1 1 - 1 1 - - 1 - 1 - - 1 1 - 1 - - - 1 1 1] [1 1 - - - - 1 - 1 1 - - 1 - 1 1 - 1 - 1 - - 1 - 1 1 - 1] [1 1 - - 1 1 - 1 1 - - 1 - 1 - 1 - - - 1 1 1 - - 1 1 - -] [1 - 1 1 1 - - - 1 1 - - 1 1 1 - - - - 1 1 - - 1 - 1 1 -] [1 - - - 1 - 1 - 1 - - 1 1 1 - - 1 1 1 - - 1 - 1 - 1 - 1] [1 1 1 - 1 - - 1 - 1 - 1 - - 1 - 1 1 - - - 1 1 - - 1 1 -] [1 1 1 - - 1 - - 1 1 1 - - 1 - - 1 - 1 - - - 1 1 1 1 - -] [1 1 1 1 - - - 1 1 - - - 1 - - 1 - 1 1 - - 1 - 1 1 - 1 -] [1 - 1 - - 1 1 - - 1 - 1 1 1 - 1 1 1 - - 1 - - - 1 - 1 -] [1 1 - 1 - - 1 - 1 - 1 1 - - 1 1 1 - 1 - 1 - - - - 1 1 -] [1 - - 1 - 1 - - 1 1 - 1 - - - 1 1 - - 1 - 1 1 1 - - 1 1] [1 - - - 1 1 1 1 1 - 1 - - 1 1 1 - 1 - - - - 1 1 - - 1 -] [1 - 1 - 1 - - - 1 - 1 1 - - - - - 1 1 1 1 - 1 - 1 - 1 1] [1 1 - - - 1 - 1 - - 1 - 1 - - - 1 1 - 1 1 - - 1 - 1 1 1] [1 - 1 - - 1 1 1 1 - - - 1 - 1 - 1 - 1 1 1 1 1 - - - - -] [1 1 - 1 - - 1 1 - 1 - 1 - 1 - - - 1 1 1 1 - 1 1 - - - -] [1 - - 1 - 1 - 1 - - - 1 1 1 1 - - - 1 - - - 1 - 1 1 1 1] [1 1 1 - - - - - - - 1 1 1 1 1 1 - - - - 1 1 1 1 - - - 1] [1 - - - 1 - - 1 - 1 1 1 1 - 1 1 1 - 1 1 - - - 1 1 - - -] [1 - 1 1 1 - 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 56 Order = 58968 = 2^3 * 3^4 * 7 * 13 (4, 33, 34)(5, 6, 32)(7, 37, 36)(8, 35, 9)(10, 11, 40)(12, 38, 39)(13, 15, 14)(16, 46, 17)(18, 45, 44)(19, 49, 48)(20, 47, 21)(22, 52, 23)(24, 51, 50)(26, 56, 55)(27, 54, 28)(41, 43, 42) (1, 2, 29, 30)(3, 24, 19, 26, 18, 50, 31, 52, 47, 54, 46, 22)(4, 15, 55, 21, 38, 7, 32, 43, 27, 49, 10, 35)(5, 44, 28, 14, 53, 41, 33, 16, 56, 42, 25, 13)(6, 9, 12, 48, 23, 45, 34, 37, 40, 20, 51, 17)(8, 39, 36, 11) (2, 3, 4)(5, 23, 7)(6, 17, 15)(8, 28, 12)(9, 20, 25)(10, 16, 26)(13, 19, 14)(18, 27, 24)(30, 31, 32)(33, 51, 35)(34, 45, 43)(36, 56, 40)(37, 48, 53)(38, 44, 54)(41, 47, 42)(46, 55, 52) (3, 20, 44)(4, 54, 25)(5, 11, 52)(6, 56, 40)(7, 49, 46)(8, 41, 47)(12, 34, 28)(13, 19, 36)(14, 17, 15)(16, 31, 48)(18, 35, 21)(22, 55, 23)(24, 33, 39)(26, 53, 32)(27, 51, 50)(42, 45, 43) Automorphism group has centre of order: 2 Number of regular subgroups: 1 Number of regular subgroups containing zeta: 1 Matrix is cocyclic over /Expanded matrix is group developed over: <28, 3> <56, 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] Permutation group acting on a set of cardinality 56 Order = 8736 = 2^5 * 3 * 7 * 13 (1, 2, 29, 30)(3, 49, 31, 21)(4, 45, 32, 17)(5, 48, 33, 20)(6, 46, 34, 18)(7, 47, 35, 19)(8, 44, 36, 16)(9, 22, 37, 50)(10, 23, 38, 51)(11, 24, 39, 52)(12, 27, 40, 55)(13, 25, 41, 53)(14, 26, 42, 54)(15, 28, 43, 56) (2, 3)(4, 5)(6, 37)(7, 38)(8, 40)(9, 34)(10, 35)(12, 36)(13, 14)(16, 52)(17, 20)(18, 53)(19, 54)(21, 56)(22, 23)(24, 44)(25, 46)(26, 47)(28, 49)(30, 31)(32, 33)(41, 42)(45, 48)(50, 51) (3, 41, 8, 38)(4, 42, 7, 39)(5, 40, 6, 37)(9, 33, 12, 34)(10, 31, 13, 36)(11, 32, 14, 35)(15, 43)(16, 25, 21, 23)(17, 24, 19, 26)(18, 27, 20, 22)(28, 56)(44, 53, 49, 51)(45, 52, 47, 54)(46, 55, 48, 50) (3, 6, 7)(4, 8, 5)(9, 11, 13)(10, 12, 14)(16, 17, 20)(18, 21, 19)(22, 25, 24)(23, 26, 27)(31, 34, 35)(32, 36, 33)(37, 39, 41)(38, 40, 42)(44, 45, 48)(46, 49, 47)(50, 53, 52)(51, 54, 55) Automorphism group has centre of order: 2 Number of regular subgroups: 4 Number of regular subgroups containing zeta: 4 Matrix is cocyclic over /Expanded matrix is group developed over: <28, 3> <56, 3> <28, 4> <56, 10> <28, 3> <56, 3> <28, 3> <56, 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] Permutation group acting on a set of cardinality 56 Order = 336 = 2^4 * 3 * 7 (1, 48, 43, 34, 12, 8)(2, 9, 22, 41, 52, 53)(3, 49, 26, 47, 14, 44)(4, 23, 38, 56, 33, 17)(5, 45, 32, 51, 10, 28)(6, 40, 36, 29, 20, 15)(7, 27, 11, 35, 55, 39)(13, 24, 25, 30, 37, 50)(16, 31, 21, 54, 19, 42)(18, 46) (1, 2, 29, 30)(3, 4, 31, 32)(5, 12, 33, 40)(6, 13, 34, 41)(7, 46, 35, 18)(8, 44, 36, 16)(9, 49, 37, 21)(10, 50, 38, 22)(11, 27, 39, 55)(14, 24, 42, 52)(15, 54, 43, 26)(17, 53, 45, 25)(19, 28, 47, 56)(20, 51, 48, 23) (2, 3, 4)(5, 47, 49, 7, 17, 50)(6, 20, 46, 36, 43, 12)(8, 15, 40, 34, 48, 18)(9, 11, 44, 10, 42, 41)(13, 37, 39, 16, 38, 14)(19, 21, 35, 45, 22, 33)(23, 55, 53, 54, 24, 56)(25, 26, 52, 28, 51, 27)(30, 31, 32) (5, 7)(6, 36)(8, 34)(9, 10)(11, 42)(12, 46)(13, 16)(14, 39)(15, 48)(17, 47)(18, 40)(19, 45)(20, 43)(21, 22)(23, 54)(24, 55)(25, 28)(26, 51)(27, 52)(33, 35)(37, 38)(41, 44)(49, 50)(53, 56) Automorphism group has centre of order: 2 Number of regular subgroups: 2 Number of regular subgroups containing zeta: 2 Matrix is cocyclic over /Expanded matrix is group developed over: <28, 4> <56, 10> <28, 3> <56, 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 - -] Permutation group acting on a set of cardinality 56 Order = 336 = 2^4 * 3 * 7 (1, 2, 29, 30)(3, 11, 31, 39)(4, 41, 32, 13)(5, 53, 33, 25)(6, 35, 34, 7)(8, 23, 36, 51)(9, 17, 37, 45)(10, 21, 38, 49)(12, 54, 40, 26)(14, 47, 42, 19)(15, 22, 43, 50)(16, 55, 44, 27)(18, 52, 46, 24)(20, 28, 48, 56) (2, 34, 4, 33, 3, 7)(5, 31, 35, 30, 6, 32)(8, 13, 11, 40, 10, 9)(12, 38, 37, 36, 41, 39)(14, 44, 17, 43, 46, 19)(15, 18, 47, 42, 16, 45)(20, 22, 49)(21, 48, 50)(23, 55, 52, 56, 26, 25)(24, 28, 54, 53, 51, 27) Automorphism group has centre of order: 2 Number of regular subgroups: 2 Number of regular subgroups containing zeta: 2 Matrix is cocyclic over /Expanded matrix is group developed over: <28, 4> <56, 10> <28, 3> <56, 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 - - - -] Permutation group acting on a set of cardinality 56 Order = 56 = 2^3 * 7 (1, 3, 33, 36, 22, 54, 19, 34, 4, 38, 44, 42, 51, 11, 29, 31, 5, 8, 50, 26, 47, 6, 32, 10, 16, 14, 23, 39)(2, 15, 40, 21, 13, 48, 52, 56, 37, 55, 25, 18, 35, 45, 30, 43, 12, 49, 41, 20, 24, 28, 9, 27, 53, 46, 7, 17) (1, 2, 29, 30)(3, 17, 31, 45)(4, 24, 32, 52)(5, 35, 33, 7)(6, 56, 34, 28)(8, 18, 36, 46)(9, 47, 37, 19)(10, 48, 38, 20)(11, 43, 39, 15)(12, 23, 40, 51)(13, 44, 41, 16)(14, 21, 42, 49)(22, 53, 50, 25)(26, 55, 54, 27) Automorphism group has centre of order: 2 Number of regular subgroups: 1 Number of regular subgroups containing zeta: 1 Matrix is cocyclic over /Expanded matrix is group developed over: <28, 3> <56, 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] Permutation group acting on a set of cardinality 56 Order = 56 = 2^3 * 7 (1, 52, 34, 49, 35, 53, 19, 56, 26, 41, 43, 33, 11, 42, 29, 24, 6, 21, 7, 25, 47, 28, 54, 13, 15, 5, 39, 14)(2, 44, 17, 51, 31, 10, 37, 55, 40, 22, 4, 46, 48, 36, 30, 16, 45, 23, 3, 38, 9, 27, 12, 50, 32, 18, 20, 8) (1, 3, 29, 31)(2, 35, 30, 7)(4, 54, 32, 26)(5, 27, 33, 55)(6, 17, 34, 45)(8, 53, 36, 25)(9, 11, 37, 39)(10, 14, 38, 42)(12, 43, 40, 15)(13, 50, 41, 22)(16, 21, 44, 49)(18, 56, 46, 28)(19, 48, 47, 20)(23, 24, 51, 52) Automorphism group has centre of order: 2 Number of regular subgroups: 1 Number of regular subgroups containing zeta: 1 Matrix is cocyclic over /Expanded matrix is group developed over: <28, 3> <56, 3>