[ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - - - -] [ 1 1 1 1 1 1 - - - - - - 1 1 1 1 1 1 - - - - - -] [ 1 1 1 1 1 1 - - - - - - - - - - - - 1 1 1 1 1 1] [ 1 1 1 - - - 1 1 1 - - - 1 1 1 - - - 1 1 1 - - -] [ 1 1 1 - - - 1 1 1 - - - - - - 1 1 1 - - - 1 1 1] [ 1 1 - 1 - - 1 - - 1 1 - 1 1 - 1 - - 1 - - 1 1 -] [ 1 1 - - 1 - - 1 - 1 - 1 1 - 1 - 1 - 1 - - 1 - 1] [ 1 1 - - - 1 - - 1 - 1 1 - 1 1 - - 1 1 - - - 1 1] [ 1 - - - 1 1 1 1 - - 1 - 1 - - 1 - 1 1 1 - - - 1] [ 1 - 1 1 - - - 1 - - 1 1 1 - 1 - - 1 - 1 - 1 1 -] [ 1 - 1 - - 1 1 - - 1 - 1 1 1 - - 1 - - 1 - - 1 1] [ 1 - - 1 - 1 - 1 1 1 - - - - 1 1 1 - 1 1 - - 1 -] [ 1 - - 1 1 - 1 - 1 - - 1 - 1 - - 1 1 1 1 - 1 - -] [ 1 - 1 - 1 - - - 1 1 1 - - 1 1 1 - - - 1 - 1 - 1] [ 1 1 - 1 - - 1 - - 1 1 - - - 1 - 1 1 - 1 1 - - 1] [ 1 1 - - - 1 - - 1 - 1 1 1 - - 1 1 - - 1 1 1 - -] [ 1 1 - - 1 - - 1 - 1 - 1 - 1 - 1 - 1 - 1 1 - 1 -] [ 1 - - - 1 1 1 1 - - 1 - - 1 1 - 1 - - - 1 1 1 -] [ 1 - 1 1 - - - 1 - - 1 1 - 1 - 1 1 - 1 - 1 - - 1] [ 1 - 1 - - 1 1 - - 1 - 1 - - 1 1 - 1 1 - 1 1 - -] [ 1 - - 1 - 1 - 1 1 1 - - 1 1 - - - 1 - - 1 1 - 1] [ 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 48 Order = 760320 = 2^9 * 3^3 * 5 * 11 (8, 9)(10, 35)(11, 34)(12, 37)(13, 36)(14, 39)(15, 38)(17, 18)(19, 44)(20, 43)(21, 46)(22, 45)(23, 48)(24, 47)(32, 33)(41, 42) (7, 9, 8)(10, 14, 13)(11, 12, 15)(16, 17, 18)(19, 23, 22)(20, 21, 24)(31, 33, 32)(34, 38, 37)(35, 36, 39)(40, 41, 42)(43, 47, 46)(44, 45, 48) (7, 12)(8, 15)(9, 11)(10, 14)(16, 21)(17, 20)(18, 24)(19, 23)(31, 36)(32, 39)(33, 35)(34, 38)(40, 45)(41, 44)(42, 48)(43, 47) (1, 3, 25, 27)(2, 28, 26, 4)(5, 8, 29, 32)(6, 42, 30, 18)(7, 41, 31, 17)(9, 40, 33, 16)(10, 19, 34, 43)(11, 20, 35, 44)(12, 21, 36, 45)(13, 24, 37, 48)(14, 23, 38, 47)(15, 22, 39, 46) (2, 26)(3, 27)(5, 17, 16, 18)(6, 33, 7, 32)(8, 30, 9, 31)(12, 15, 14, 13)(19, 43)(20, 44)(21, 48, 23, 46)(22, 45, 24, 47)(29, 41, 40, 42)(36, 39, 38, 37) (5, 17, 16, 18)(6, 9, 7, 8)(10, 34)(11, 35)(12, 39, 14, 37)(13, 36, 15, 38)(19, 43)(20, 44)(21, 48, 23, 46)(22, 45, 24, 47)(29, 41, 40, 42)(30, 33, 31, 32) (3, 10)(4, 19)(8, 12)(9, 14)(13, 15)(17, 23)(18, 21)(22, 24)(27, 34)(28, 43)(32, 36)(33, 38)(37, 39)(41, 47)(42, 45)(46, 48) Automorphism group has centre of order: 2 Number of regular subgroups: 13 Number of regular subgroups containing zeta: 13 Matrix is cocyclic over /Expanded matrix is group developed over: <24, 15> <48, 47> <24, 14> <48, 41> <24, 13> <48, 33> <24, 14> <48, 34> <24, 14> <48, 40> <24, 14> <48, 40> <24, 14> <48, 37> <24, 14> <48, 34> <24, 15> <48, 46> <24, 14> <48, 40> <24, 14> <48, 39> <24, 14> <48, 40> <24, 14> <48, 34> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - - - -] [ 1 1 1 1 1 1 - - - - - - 1 1 1 1 1 1 - - - - - -] [ 1 1 1 1 1 1 - - - - - - - - - - - - 1 1 1 1 1 1] [ 1 1 1 - - - 1 1 1 - - - 1 1 1 - - - 1 1 1 - - -] [ 1 1 1 - - - 1 1 1 - - - - - - 1 1 1 - - - 1 1 1] [ 1 1 - 1 - - 1 - - 1 1 - 1 1 - 1 - - 1 - - 1 1 -] [ 1 1 - - 1 - - - 1 - 1 1 - 1 1 1 - - - - 1 - 1 1] [ 1 1 - - - 1 - 1 - 1 - 1 - 1 1 - - 1 1 - - 1 - 1] [ 1 - - 1 1 - 1 1 - - - 1 1 - - 1 - 1 1 - 1 - - 1] [ 1 - - - 1 1 1 - 1 1 - - - 1 - 1 - 1 - 1 1 1 - -] [ 1 - - 1 - 1 - 1 1 - 1 - - - 1 1 1 - 1 - 1 1 - -] [ 1 - 1 - - 1 1 - - - 1 1 1 - 1 - - 1 - - 1 1 1 -] [ 1 - 1 1 - - - - 1 1 - 1 1 - 1 1 - - - 1 - 1 - 1] [ 1 - 1 - 1 - - 1 - 1 1 - 1 1 - - 1 - - - 1 1 - 1] [ 1 1 - 1 - - 1 - - 1 1 - - - 1 - 1 1 - 1 1 - - 1] [ 1 1 - - - 1 - 1 - 1 - 1 1 - - 1 1 - - 1 1 - 1 -] [ 1 1 - - 1 - - - 1 - 1 1 1 - - - 1 1 1 1 - 1 - -] [ 1 - - - 1 1 1 - 1 1 - - 1 - 1 - 1 - 1 - - - 1 1] [ 1 - - 1 - 1 - 1 1 - 1 - 1 1 - - - 1 - 1 - - 1 1] [ 1 - 1 - - 1 1 - - - 1 1 - 1 - 1 1 - 1 1 - - - 1] [ 1 - 1 1 - - - - 1 1 - 1 - 1 - - 1 1 1 - 1 - 1 -] [ 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 48 Order = 5280 = 2^5 * 3 * 5 * 11 (1, 3, 22, 24, 17, 13, 43, 47, 6, 7, 44, 8, 25, 27, 46, 48, 41, 37, 19, 23, 30, 31, 20, 32)(2, 28, 14, 34, 9, 45, 35, 15, 5, 40, 36, 42, 26, 4, 38, 10, 33, 21, 11, 39, 29, 16, 12, 18) (1, 2)(3, 4)(5, 6)(7, 16)(8, 18)(9, 17)(10, 24)(11, 19)(12, 20)(13, 21)(14, 22)(15, 23)(25, 26)(27, 28)(29, 30)(31, 40)(32, 42)(33, 41)(34, 48)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47) (2, 26)(3, 46)(4, 14)(5, 36)(6, 20)(7, 47)(8, 19)(9, 10)(11, 42)(12, 29)(13, 37)(15, 16)(17, 48)(18, 35)(22, 27)(23, 31)(24, 41)(28, 38)(30, 44)(32, 43)(33, 34)(39, 40) (3, 47, 31, 24, 6)(4, 39, 40, 10, 5)(7, 48, 30, 27, 23)(8, 46, 13, 43, 20)(11, 36, 42, 14, 45)(12, 18, 38, 21, 35)(15, 16, 34, 29, 28)(19, 44, 32, 22, 37) (5, 14, 10, 11, 9)(6, 22, 24, 19, 17)(7, 23, 20, 8, 13)(12, 18, 21, 16, 15)(29, 38, 34, 35, 33)(30, 46, 48, 43, 41)(31, 47, 44, 32, 37)(36, 42, 45, 40, 39) Automorphism group has centre of order: 2 Number of regular subgroups: 3 Number of regular subgroups containing zeta: 3 Matrix is cocyclic over /Expanded matrix is group developed over: <24, 6> <48, 8> <24, 6> <48, 8> <24, 12> <48, 28> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - - - -] [ 1 1 1 1 1 1 - - - - - - 1 1 1 1 1 1 - - - - - -] [ 1 1 1 1 1 1 - - - - - - - - - - - - 1 1 1 1 1 1] [ 1 1 1 - - - 1 1 1 - - - 1 1 1 - - - 1 1 1 - - -] [ 1 1 1 - - - 1 1 1 - - - - - - 1 1 1 - - - 1 1 1] [ 1 1 - 1 - - 1 - - 1 1 - 1 1 - 1 - - 1 - - 1 1 -] [ 1 1 - - 1 - - - 1 - 1 1 - 1 1 1 - - - - 1 - 1 1] [ 1 1 - - - 1 - 1 - 1 - 1 - 1 1 - - 1 1 - - 1 - 1] [ 1 - - 1 1 - 1 1 - - - 1 1 - - 1 - 1 1 - 1 - - 1] [ 1 - - - 1 1 1 - 1 1 - - - - 1 1 1 - 1 - 1 1 - -] [ 1 - - 1 - 1 - 1 1 - 1 - - 1 - 1 - 1 - 1 1 1 - -] [ 1 - 1 - - 1 1 - - - 1 1 1 1 - - 1 - - - 1 1 - 1] [ 1 - 1 1 - - - - 1 1 - 1 1 - 1 1 - - - 1 - 1 - 1] [ 1 - 1 - 1 - - 1 - 1 1 - 1 - 1 - - 1 - - 1 1 1 -] [ 1 1 - 1 - - 1 - - 1 1 - - - 1 - 1 1 - 1 1 - - 1] [ 1 1 - - - 1 - 1 - 1 - 1 1 - - 1 1 - - 1 1 - 1 -] [ 1 1 - - 1 - - - 1 - 1 1 1 - - - 1 1 1 1 - 1 - -] [ 1 - - - 1 1 1 - 1 1 - - 1 1 - - - 1 - 1 - - 1 1] [ 1 - - 1 - 1 - 1 1 - 1 - 1 - 1 - 1 - 1 - - - 1 1] [ 1 - 1 - - 1 1 - - - 1 1 - - 1 1 - 1 1 1 - - 1 -] [ 1 - 1 1 - - - - 1 1 - 1 - 1 - - 1 1 1 - 1 - 1 -] [ 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 48 Order = 576 = 2^6 * 3^2 (1, 3, 31, 19, 25, 27, 7, 43)(2, 28, 40, 35, 26, 4, 16, 11)(5, 18, 39, 34, 29, 42, 15, 10)(6, 32, 47, 24, 30, 8, 23, 48)(9, 45, 20, 46, 33, 21, 44, 22)(12, 14, 41, 37, 36, 38, 17, 13) (1, 2)(3, 4)(5, 6)(7, 16)(8, 18)(9, 17)(10, 24)(11, 19)(12, 20)(13, 21)(14, 22)(15, 23)(25, 26)(27, 28)(29, 30)(31, 40)(32, 42)(33, 41)(34, 48)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47) (2, 26)(3, 19)(4, 35)(5, 29)(7, 31)(8, 48)(10, 18)(11, 28)(13, 38)(14, 37)(17, 41)(20, 44)(21, 22)(23, 47)(24, 32)(27, 43)(34, 42)(45, 46) (3, 46, 29, 21, 43, 44)(4, 38, 30, 13, 35, 36)(5, 45, 19, 20, 27, 22)(6, 37, 11, 12, 28, 14)(7, 10, 42)(8, 40, 48)(9, 15)(16, 24, 32)(17, 23)(18, 31, 34)(33, 39)(41, 47) Automorphism group has centre of order: 2 Number of regular subgroups: 9 Number of regular subgroups containing zeta: 9 Matrix is cocyclic over /Expanded matrix is group developed over: <24, 10> <48, 27> <24, 10> <48, 27> <24, 6> <48, 8> <24, 8> <48, 18> <24, 6> <48, 8> <24, 8> <48, 18> <24, 8> <48, 18> <24, 8> <48, 18> <24, 12> <48, 28> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - - - -] [ 1 1 1 1 1 1 - - - - - - 1 1 1 1 1 1 - - - - - -] [ 1 1 1 1 1 1 - - - - - - - - - - - - 1 1 1 1 1 1] [ 1 1 1 - - - 1 1 1 - - - 1 1 1 - - - 1 1 1 - - -] [ 1 1 1 - - - 1 1 1 - - - - - - 1 1 1 - - - 1 1 1] [ 1 1 - 1 - - 1 - - 1 1 - 1 1 - 1 - - 1 - - 1 1 -] [ 1 1 - - 1 - - - 1 - 1 1 - 1 1 1 - - - - 1 - 1 1] [ 1 1 - - - 1 - 1 - 1 - 1 - 1 1 - - 1 1 - - 1 - 1] [ 1 - - 1 1 - 1 1 - - - 1 1 - - 1 - 1 1 - 1 - - 1] [ 1 - - - 1 1 1 - 1 1 - - - - 1 1 1 - 1 - 1 1 - -] [ 1 - - 1 - 1 - 1 1 - 1 - - 1 - 1 - 1 - 1 1 1 - -] [ 1 - 1 - - 1 1 - - - 1 1 1 1 - - 1 - - - 1 1 - 1] [ 1 - 1 1 - - - - 1 1 - 1 1 - 1 - - 1 - - 1 1 1 -] [ 1 - 1 - 1 - - 1 - 1 1 - 1 - 1 1 - - - 1 - 1 - 1] [ 1 1 - 1 - - 1 - - 1 1 - - - 1 - 1 1 - 1 1 - - 1] [ 1 1 - - - 1 - 1 - 1 - 1 1 - - 1 1 - - 1 1 - 1 -] [ 1 1 - - 1 - - - 1 - 1 1 1 - - - 1 1 1 1 - 1 - -] [ 1 - - - 1 1 1 - 1 1 - - 1 1 - - - 1 - 1 - - 1 1] [ 1 - - 1 - 1 - 1 1 - 1 - 1 - 1 - 1 - 1 - - - 1 1] [ 1 - 1 - - 1 1 - - - 1 1 - - 1 1 - 1 1 1 - - 1 -] [ 1 - 1 1 - - - - 1 1 - 1 - 1 - 1 1 - 1 1 - - - 1] [ 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 48 Order = 480 = 2^5 * 3 * 5 (1, 3, 48, 43, 12, 14)(2, 28, 34, 11, 20, 46)(4, 10, 35, 44, 22, 26)(5, 47, 9, 13, 7, 18)(6, 15, 17, 45, 16, 32)(8, 30, 39, 41, 21, 40)(19, 36, 38, 25, 27, 24)(23, 33, 37, 31, 42, 29) (2, 26)(3, 38)(4, 22)(6, 30)(7, 9)(8, 39)(10, 20)(12, 48)(13, 37)(14, 27)(15, 32)(16, 41)(17, 40)(18, 23)(19, 43)(24, 36)(28, 46)(31, 33)(34, 44)(42, 47) (3, 39, 8, 38, 5)(4, 47, 18, 46, 6)(7, 9, 34, 45, 44)(10, 21, 20, 31, 33)(12, 40, 41, 24, 13)(14, 29, 27, 15, 32)(16, 17, 48, 37, 36)(22, 30, 28, 23, 42) 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: <24, 13> <48, 32> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - - - -] [ 1 1 1 1 1 1 - - - - - - 1 1 1 1 1 1 - - - - - -] [ 1 1 1 1 1 1 - - - - - - - - - - - - 1 1 1 1 1 1] [ 1 1 1 - - - 1 1 1 - - - 1 1 1 - - - 1 1 1 - - -] [ 1 1 1 - - - 1 1 1 - - - - - - 1 1 1 - - - 1 1 1] [ 1 1 - 1 - - 1 - - 1 1 - 1 1 - 1 - - 1 - - 1 1 -] [ 1 1 - - 1 - - - 1 - 1 1 - 1 1 1 - - - - 1 - 1 1] [ 1 1 - - - 1 - 1 - 1 - 1 - 1 1 - - 1 1 - - 1 - 1] [ 1 - - 1 1 - 1 1 - - - 1 1 - - 1 - 1 1 - 1 - - 1] [ 1 - - - 1 1 1 - 1 1 - - - - 1 1 1 - 1 - 1 1 - -] [ 1 - - 1 - 1 - 1 1 - 1 - - 1 - 1 - 1 - 1 1 1 - -] [ 1 - 1 - - 1 1 - - - 1 1 1 - 1 1 - - - 1 - 1 - 1] [ 1 - 1 1 - - - - 1 1 - 1 1 1 - - 1 - - - 1 1 - 1] [ 1 - 1 - 1 - - 1 - 1 1 - 1 - 1 - - 1 - - 1 1 1 -] [ 1 1 - 1 - - 1 - - 1 1 - - - 1 - 1 1 - 1 1 - - 1] [ 1 1 - - - 1 - 1 - 1 - 1 1 - - 1 1 - - 1 1 - 1 -] [ 1 1 - - 1 - - - 1 - 1 1 1 - - - 1 1 1 1 - 1 - -] [ 1 - - - 1 1 1 - 1 1 - - 1 1 - - - 1 - 1 - - 1 1] [ 1 - - 1 - 1 - 1 1 - 1 - 1 - 1 - 1 - 1 - - - 1 1] [ 1 - 1 - - 1 1 - - - 1 1 - 1 - - 1 1 1 - 1 - 1 -] [ 1 - 1 1 - - - - 1 1 - 1 - - 1 1 - 1 1 1 - - 1 -] [ 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 48 Order = 1536 = 2^9 * 3 (5, 41)(6, 33)(7, 37)(8, 24)(9, 30)(10, 18)(12, 46)(13, 31)(14, 44)(16, 45)(17, 29)(20, 38)(21, 40)(22, 36)(32, 48)(34, 42) (1, 3, 25, 27)(2, 28, 26, 4)(5, 6, 29, 30)(7, 40, 31, 16)(8, 20, 32, 44)(9, 41, 33, 17)(10, 22, 34, 46)(11, 23, 35, 47)(12, 18, 36, 42)(13, 45, 37, 21)(14, 24, 38, 48)(15, 19, 39, 43) (2, 26)(4, 28)(5, 31)(6, 16)(7, 29)(8, 32)(9, 21)(11, 35)(13, 41)(14, 38)(17, 37)(20, 44)(23, 47)(24, 48)(30, 40)(33, 45) (3, 21, 19, 9)(4, 13, 11, 17)(5, 32, 7, 48)(6, 42, 16, 34)(8, 31, 24, 29)(10, 30, 18, 40)(14, 38)(15, 39)(22, 46)(23, 47)(27, 45, 43, 33)(28, 37, 35, 41) 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: <24, 14> <48, 34> <24, 14> <48, 40> <24, 14> <48, 34> <24, 14> <48, 39> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - - - -] [ 1 1 1 1 1 1 - - - - - - 1 1 1 1 1 1 - - - - - -] [ 1 1 1 1 - - 1 1 - - - - 1 1 - - - - 1 1 1 1 - -] [ 1 - - - 1 - 1 1 - - 1 1 1 1 1 - - 1 - - - 1 1 -] [ 1 1 - 1 1 - - - - 1 - 1 - - 1 1 - - - 1 1 1 1 -] [ 1 - 1 1 1 - - - 1 - 1 - 1 - 1 - - - 1 1 - - 1 1] [ 1 1 1 - - 1 - 1 1 - - - - - 1 - - 1 - - 1 1 1 1] [ 1 1 - - - - 1 1 1 1 - - 1 - 1 1 1 - 1 - - - 1 -] [ 1 1 - - 1 1 1 - - - 1 - - 1 - 1 - - 1 - 1 - 1 1] [ 1 - 1 - 1 1 1 - - 1 - - - - - - 1 1 1 1 - 1 1 -] [ 1 - 1 - - - 1 - 1 1 1 - - 1 1 1 - 1 - 1 1 - - -] [ 1 1 1 - - - - - - 1 1 1 - 1 1 - 1 - 1 - - 1 - 1] [ 1 1 - 1 - - 1 - 1 - - 1 - 1 - - 1 1 - 1 - - 1 1] [ 1 - 1 1 - - - 1 - - 1 1 - - - 1 1 1 1 - 1 - 1 -] [ 1 - - - 1 1 - 1 1 - - 1 - 1 1 - 1 - 1 1 1 - - -] [ 1 - - 1 - 1 1 1 - - 1 - - - 1 1 1 - - 1 - 1 - 1] [ 1 - - 1 - 1 - - 1 1 1 - 1 1 - - 1 - - - 1 1 1 -] [ 1 1 - - - 1 - - 1 - 1 1 1 - - 1 - 1 1 1 - 1 - -] [ 1 - 1 - 1 - 1 - 1 - - 1 1 - - 1 1 - - - 1 1 - 1] [ 1 1 - - 1 - - 1 - 1 1 - 1 - - - 1 1 - 1 1 - - 1] [ 1 - 1 - - 1 - 1 - 1 - 1 1 1 - 1 - - - 1 - - 1 1] [ 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 48 Order = 12144 = 2^4 * 3 * 11 * 23 (1, 2, 25, 26)(3, 42, 27, 18)(4, 29, 28, 5)(6, 23, 30, 47)(7, 12, 31, 36)(8, 17, 32, 41)(9, 20, 33, 44)(10, 19, 34, 43)(11, 24, 35, 48)(13, 46, 37, 22)(14, 21, 38, 45)(15, 16, 39, 40) (2, 27, 16, 14, 6, 11, 10, 43, 46, 31, 29, 13, 44, 24, 45, 33, 17, 8, 28, 42, 12, 15, 47)(3, 40, 38, 30, 35, 34, 19, 22, 7, 5, 37, 20, 48, 21, 9, 41, 32, 4, 18, 36, 39, 23, 26) (3, 48, 22, 20, 4, 30, 34, 7, 40, 38, 41)(5, 9, 37, 35, 18, 32, 21, 39, 36, 19, 23)(6, 10, 31, 16, 14, 17, 27, 24, 46, 44, 28)(8, 45, 15, 12, 43, 47, 29, 33, 13, 11, 42) Automorphism group has centre of order: 2 Number of regular subgroups: 3 Number of regular subgroups containing zeta: 3 Matrix is cocyclic over /Expanded matrix is group developed over: <24, 12> <48, 28> <24, 6> <48, 8> <24, 12> <48, 28> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 1 1 1 1 1 1 1 1 1 1 1 - - - - - - - - - - - -] [ 1 1 1 1 1 1 - - - - - - 1 1 1 1 1 1 - - - - - -] [ 1 - - - 1 1 - - 1 1 1 - - - - 1 1 1 - - - 1 1 1] [ 1 - - 1 1 - 1 1 1 - - - 1 - 1 - - 1 - 1 - - 1 1] [ 1 1 - - - 1 1 1 - 1 - - - 1 1 - - 1 - - 1 1 - 1] [ 1 1 1 - - - 1 - 1 - 1 - 1 - - - 1 1 - 1 1 1 - -] [ 1 - 1 1 - - - 1 - 1 1 - - 1 - 1 - 1 - 1 1 - 1 -] [ 1 - - 1 - 1 1 - - - 1 1 1 1 - - 1 - - - 1 - 1 1] [ 1 - 1 - 1 - 1 - - 1 - 1 - 1 1 - 1 - - 1 - 1 1 -] [ 1 1 - - 1 - - 1 - - 1 1 1 1 - 1 - - - 1 - 1 - 1] [ 1 - 1 - - 1 - 1 1 - - 1 1 - 1 1 - - - - 1 1 1 -] [ 1 1 - 1 - - - - 1 1 - 1 - - 1 1 1 - - 1 1 - - 1] [ 1 - - - - - 1 1 1 1 1 - 1 1 1 1 1 - 1 - - - - -] [ 1 1 1 1 - - - 1 - - 1 - - - 1 - 1 - 1 - - 1 1 1] [ 1 - 1 1 - 1 1 - - 1 - - 1 - - 1 - - 1 1 - 1 - 1] [ 1 1 - 1 1 - 1 - 1 - - - - 1 - 1 - - 1 - 1 1 1 -] [ 1 - 1 - 1 1 - 1 1 - - - - 1 - - 1 - 1 1 1 - - 1] [ 1 1 - - 1 1 - - - 1 1 - 1 - 1 - - - 1 1 1 - 1 -] [ 1 - 1 - 1 - 1 - - - 1 1 - - 1 1 - 1 1 - 1 - - 1] [ 1 1 - - - 1 1 1 - - - 1 - - - 1 1 1 1 1 - - 1 -] [ 1 - - 1 1 - - 1 - 1 - 1 1 - - - 1 1 1 - 1 1 - -] [ 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 48 Order = 5280 = 2^5 * 3 * 5 * 11 (1, 2)(3, 16)(4, 21)(5, 20)(6, 19)(7, 22)(8, 15)(9, 18)(10, 17)(11, 14)(12, 23)(13, 24)(25, 26)(27, 40)(28, 45)(29, 44)(30, 43)(31, 46)(32, 39)(33, 42)(34, 41)(35, 38)(36, 47)(37, 48) (2, 3, 8, 12, 7)(4, 6, 5, 11, 9)(14, 19, 23, 21, 22)(15, 16, 20, 18, 24)(26, 27, 32, 36, 31)(28, 30, 29, 35, 33)(38, 43, 47, 45, 46)(39, 40, 44, 42, 48) (2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37) (3, 30, 8, 28, 35)(4, 11, 27, 6, 32)(5, 9, 31, 36, 34)(7, 12, 10, 29, 33)(14, 21, 39, 19, 40)(15, 43, 16, 38, 45)(17, 23, 22, 42, 44)(18, 20, 41, 47, 46) Automorphism group has centre of order: 2 Number of regular subgroups: 3 Number of regular subgroups containing zeta: 3 Matrix is cocyclic over /Expanded matrix is group developed over: <24, 6> <48, 8> <24, 6> <48, 8> <24, 12> <48, 28> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 1 1 1 1 1 1 1 1 1 - - - - - - 1 1 - - - - - -] [ 1 - 1 - 1 - 1 - 1 1 1 1 - 1 1 - - - - 1 - - 1 -] [ 1 - 1 - 1 - - 1 - - - 1 - - - 1 1 1 1 1 - 1 1 -] [ 1 - 1 - 1 1 - 1 - 1 - 1 1 1 - 1 - - - - 1 - - 1] [ 1 - 1 - - - 1 - - 1 1 - - 1 - - 1 1 1 - 1 1 - 1] [ 1 - - 1 1 - - - 1 - - - 1 1 - - 1 1 - 1 1 - 1 1] [ 1 - - 1 1 - 1 1 1 - 1 - 1 1 - 1 - - 1 - - 1 - -] [ 1 1 1 1 - - - - - - 1 1 1 1 1 1 1 1 - - - - - -] [ 1 1 1 1 1 - - - 1 - - 1 - - 1 - - - 1 - 1 1 - 1] [ 1 1 1 1 - 1 - - - 1 - - 1 1 - - - - 1 1 - 1 1 -] [ 1 1 1 1 - - 1 1 - - 1 - - - - 1 - - - 1 1 - 1 1] [ 1 1 - - 1 1 1 - - - 1 1 1 - - - 1 - 1 1 1 - - -] [ 1 1 - - - 1 1 - 1 - - 1 - 1 - 1 - 1 - - 1 1 1 -] [ 1 1 - - 1 - 1 - - 1 - - 1 - 1 1 - 1 - 1 - 1 - 1] [ 1 1 - - - - - 1 1 1 1 1 1 - - - - 1 1 - - - 1 1] [ 1 - - 1 1 1 - - - 1 1 - - - 1 1 - 1 1 - 1 - 1 -] [ 1 - - 1 - - 1 1 - 1 - 1 1 - 1 - 1 - - - 1 1 1 -] [ 1 - 1 - - 1 1 - 1 - - - 1 - 1 1 1 - 1 - - - 1 1] [ 1 - 1 - - 1 - 1 1 - 1 - 1 - 1 - - 1 - 1 1 1 - -] [ 1 - - 1 - 1 - - 1 1 1 1 - - - 1 1 - - 1 - 1 - 1] [ 1 - - 1 - 1 1 1 - - - 1 - 1 1 - - 1 1 1 - - - 1] [ 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 48 Order = 1536 = 2^9 * 3 (1, 2, 25, 26)(3, 42, 27, 18)(4, 41, 28, 17)(5, 21, 29, 45)(6, 22, 30, 46)(7, 11, 31, 35)(8, 34, 32, 10)(9, 36, 33, 12)(13, 16, 37, 40)(14, 19, 38, 43)(15, 44, 39, 20)(23, 24, 47, 48) (2, 3, 31, 5, 9, 30, 8, 28)(4, 26, 27, 7, 29, 33, 6, 32)(10, 35, 34, 11)(12, 36)(13, 17, 20, 22, 23, 45, 43, 42)(14, 15, 38, 39)(16, 40)(18, 37, 41, 44, 46, 47, 21, 19) (3, 30)(4, 29)(5, 28)(6, 27)(13, 37)(14, 38)(15, 39)(16, 40)(17, 21)(18, 22)(19, 43)(20, 44)(23, 47)(24, 48)(41, 45)(42, 46) (3, 5)(4, 6)(7, 32)(8, 31)(10, 11)(13, 37)(14, 39)(15, 38)(16, 40)(17, 46)(18, 45)(19, 20)(21, 42)(22, 41)(23, 47)(24, 48)(27, 29)(28, 30)(34, 35)(43, 44) 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: <24, 15> <48, 47> <24, 14> <48, 34> <24, 14> <48, 34> <24, 14> <48, 34> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 1 1 1 1 1 1 1 1 1 - - - - - - 1 1 - - - - - -] [ 1 - - - - - 1 1 - 1 - - 1 - - 1 1 1 - 1 1 - 1 1] [ 1 - 1 1 1 1 - - - 1 1 1 1 - - 1 - - - 1 1 - - -] [ 1 1 - - - 1 1 1 1 - - 1 1 1 1 - - - - 1 1 - - -] [ 1 1 - - 1 - 1 1 - 1 1 - 1 1 - 1 - - 1 - - 1 - -] [ 1 1 1 1 - - 1 1 - - 1 1 - - 1 1 - - - - - - 1 1] [ 1 1 - 1 1 - - 1 - - - 1 - - - - 1 - 1 1 1 1 1 -] [ 1 1 1 - - 1 1 - - - 1 - - - - - - 1 1 1 1 1 - 1] [ 1 1 1 1 - - - - - - - - 1 1 1 1 1 1 - - 1 1 - -] [ 1 1 - - 1 1 - - - - 1 1 1 1 - - 1 1 - - - - 1 1] [ 1 - 1 - - - - 1 - 1 1 1 - 1 1 - 1 1 1 1 - - - -] [ 1 - 1 - 1 1 - 1 - 1 - - - 1 1 - - - - - 1 1 1 1] [ 1 1 1 1 - - - - 1 1 - - 1 1 - - - - 1 1 - - 1 1] [ 1 1 - - - 1 - - 1 1 1 - - - 1 1 1 - - 1 - 1 1 -] [ 1 1 - - 1 - - - 1 1 - 1 - - 1 1 - 1 1 - 1 - - 1] [ 1 - - 1 - - 1 - 1 1 1 1 - 1 - - 1 - - - 1 1 - 1] [ 1 - - 1 1 1 1 - - - - - - 1 1 1 1 - 1 1 - - - 1] [ 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 -] [ 1 - 1 - - 1 - 1 1 - - 1 1 - - 1 1 - 1 - - 1 - 1] [ 1 - - 1 - 1 - 1 1 - 1 - - 1 - 1 - 1 1 - 1 - 1 -] [ 1 - - 1 - 1 1 - - 1 - 1 1 - 1 - - 1 1 - - 1 1 -] [ 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 48 Order = 96 = 2^5 * 3 (1, 41, 23, 18, 25, 17, 47, 42)(2, 33, 24, 32, 26, 9, 48, 8)(3, 44, 28, 38, 27, 20, 4, 14)(5, 46, 6, 34, 29, 22, 30, 10)(7, 39, 45, 40, 31, 15, 21, 16)(11, 12, 19, 37, 35, 36, 43, 13) (1, 3, 25, 27)(2, 36, 26, 12)(4, 47, 28, 23)(5, 11, 29, 35)(6, 43, 30, 19)(7, 17, 31, 41)(8, 46, 32, 22)(9, 34, 33, 10)(13, 24, 37, 48)(14, 39, 38, 15)(16, 20, 40, 44)(18, 21, 42, 45) (1, 2, 25, 26)(3, 36, 27, 12)(4, 37, 28, 13)(5, 17, 29, 41)(6, 42, 30, 18)(7, 11, 31, 35)(8, 40, 32, 16)(9, 39, 33, 15)(10, 14, 34, 38)(19, 21, 43, 45)(20, 46, 44, 22)(23, 24, 47, 48) (3, 28)(4, 27)(5, 6)(8, 9)(12, 37)(13, 36)(15, 16)(17, 42)(18, 41)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(29, 30)(32, 33)(39, 40) 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: <24, 5> <48, 4> <24, 6> <48, 8> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 1 1 1 1 1 1 1 - - - - - - - - - - - - 1 1 1 1] [ 1 1 1 - 1 1 1 - - 1 1 - 1 - - 1 - 1 - 1 - - - -] [ 1 - 1 1 1 - 1 1 - 1 1 1 - - 1 - 1 - 1 - - - - -] [ 1 - - - 1 - - - - 1 1 - 1 - 1 - 1 - - 1 1 1 1 1] [ 1 1 - 1 1 1 - 1 1 - - - 1 1 1 - 1 - - 1 - - - -] [ 1 1 1 1 - - - - 1 1 1 1 1 1 - - - - - - 1 1 - -] [ 1 1 1 1 - - - - 1 1 - - - - 1 1 1 1 - - - - 1 1] [ 1 1 1 - - - - 1 - - - 1 1 - 1 - - 1 1 1 - 1 1 -] [ 1 - 1 1 - 1 - - - - - 1 1 - - 1 1 - 1 1 1 - - 1] [ 1 - - - - 1 1 1 1 1 - 1 1 - 1 1 - - - - - 1 - 1] [ 1 1 - 1 - - 1 - - - 1 - - 1 1 1 - - 1 1 - 1 - 1] [ 1 - - 1 1 - - 1 1 1 - - - - - 1 - 1 1 1 1 1 - -] [ 1 - - 1 1 - - 1 - - 1 1 1 1 - 1 - 1 - - - - 1 1] [ 1 - 1 - - 1 - 1 1 1 1 - - 1 - - - - 1 1 - - 1 1] [ 1 - 1 - - 1 - 1 - - 1 - - 1 1 1 1 1 - - 1 1 - -] [ 1 1 - - 1 1 - - 1 - 1 1 - - 1 1 - - 1 - 1 - 1 -] [ 1 1 - - 1 1 - - - 1 - 1 - 1 - - 1 1 1 - - 1 - 1] [ 1 1 - - - - 1 1 - 1 - 1 - 1 - 1 1 - - 1 1 - 1 -] [ 1 - - 1 - 1 1 - 1 - 1 1 - - - - 1 1 - 1 - 1 1 -] [ 1 1 - - - - 1 1 1 - 1 - 1 - - - 1 1 1 - 1 - - 1] [ 1 - - 1 - 1 1 - - 1 - - 1 1 1 - - 1 1 - 1 - 1 -] [ 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 48 Order = 96 = 2^5 * 3 (1, 3, 48, 21, 9, 40, 25, 27, 24, 45, 33, 16)(2, 5, 23, 19, 10, 15, 26, 29, 47, 43, 34, 39)(4, 41, 44, 11, 32, 14, 28, 17, 20, 35, 8, 38)(6, 42, 22, 12, 31, 37, 30, 18, 46, 36, 7, 13) (1, 2, 25, 26)(3, 39, 27, 15)(4, 31, 28, 7)(5, 40, 29, 16)(6, 8, 30, 32)(9, 47, 33, 23)(10, 48, 34, 24)(11, 42, 35, 18)(12, 17, 36, 41)(13, 38, 37, 14)(19, 21, 43, 45)(20, 46, 44, 22) (3, 4)(5, 30)(6, 29)(7, 15)(8, 16)(11, 35)(12, 36)(13, 37)(14, 38)(17, 41)(18, 42)(19, 46)(20, 45)(21, 44)(22, 43)(27, 28)(31, 39)(32, 40) 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: <24, 8> <48, 18> <24, 6> <48, 8> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 1 1 1 1 1 - - 1 1 1 1 1 1 - - - - - - - - - -] [ 1 - - - - - 1 - 1 1 1 1 1 - 1 1 - 1 - 1 1 - - -] [ 1 - 1 1 1 1 1 - - - - - 1 - - - - 1 - 1 1 - 1 1] [ 1 1 - - - - - - 1 1 - - 1 1 - - 1 1 1 1 - - 1 1] [ 1 1 - - 1 1 1 1 1 1 - - - - - 1 - - - 1 - 1 - 1] [ 1 1 1 1 - - 1 1 1 - - - 1 - 1 1 1 - - - - - 1 -] [ 1 1 1 - - 1 1 1 - 1 1 - - - - - 1 1 1 - 1 - - -] [ 1 1 - 1 1 - 1 1 - - - 1 - 1 1 - - 1 1 1 - - - -] [ 1 1 - - - - 1 1 - - 1 1 1 1 - - - - - - 1 1 1 1] [ 1 1 1 1 - - - - - 1 - 1 - - - 1 - - 1 1 1 1 1 -] [ 1 1 - - 1 1 - - 1 - - 1 - - 1 - 1 1 - - 1 1 1 -] [ 1 1 - 1 - 1 - - - - 1 - - 1 1 1 1 - - 1 1 - - 1] [ 1 1 1 - 1 - - - - - 1 - 1 - 1 1 - 1 1 - - 1 - 1] [ 1 - - - 1 1 - 1 - - 1 1 1 - - 1 1 - 1 1 - - 1 -] [ 1 - - 1 - 1 - 1 1 - - - 1 1 - 1 - 1 1 - 1 1 - -] [ 1 - 1 1 - - - 1 1 - 1 1 - - - - 1 1 - 1 - 1 - 1] [ 1 - 1 - 1 - - 1 - 1 - - 1 1 1 - 1 - - 1 1 1 - -] [ 1 - - 1 1 - - 1 1 1 1 - - - 1 - - - 1 - 1 - 1 1] [ 1 - - 1 1 - 1 - - 1 1 - - 1 - 1 1 1 - - - 1 1 -] [ 1 - 1 - - 1 1 - 1 - 1 - - 1 1 - - - 1 1 - 1 1 -] [ 1 - - 1 - 1 1 - - 1 - 1 1 - 1 - 1 - 1 - - 1 - 1] [ 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 48 Order = 96 = 2^5 * 3 (1, 33, 47, 42, 46, 32, 25, 9, 23, 18, 22, 8)(2, 15, 40, 41, 29, 10, 26, 39, 16, 17, 5, 34)(3, 12, 28, 24, 35, 19, 27, 36, 4, 48, 11, 43)(6, 13, 20, 38, 31, 21, 30, 37, 44, 14, 7, 45) (1, 3, 16, 37, 25, 27, 40, 13)(2, 38, 22, 28, 26, 14, 46, 4)(5, 21, 23, 35, 29, 45, 47, 11)(6, 17, 19, 33, 30, 41, 43, 9)(7, 34, 24, 42, 31, 10, 48, 18)(8, 44, 15, 12, 32, 20, 39, 36) (2, 29)(3, 28)(4, 27)(5, 26)(6, 7)(8, 9)(11, 35)(12, 36)(13, 38)(14, 37)(15, 17)(19, 24)(20, 44)(21, 45)(22, 47)(23, 46)(30, 31)(32, 33)(39, 41)(43, 48) 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: <24, 8> <48, 18> <24, 6> <48, 8> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 1 - 1 1 1 1 - 1 1 1 - - 1 - 1 - - - - 1 - - -] [ 1 1 1 - 1 1 - 1 1 1 - 1 1 - 1 - - - - - - 1 - -] [ 1 1 - - - - 1 1 1 1 1 1 - - - - - - 1 1 - - 1 1] [ 1 1 - - - - 1 1 - - - - 1 1 1 1 - - 1 1 1 1 - -] [ 1 - 1 - - - - - 1 1 1 - 1 1 1 1 - 1 - 1 - - - 1] [ 1 - 1 - 1 1 1 1 - - 1 - - - - - - 1 - 1 1 1 - 1] [ 1 1 1 1 - - - - - - 1 1 - - 1 1 - - - - 1 1 1 1] [ 1 1 - - 1 1 - - - - 1 1 - - 1 1 1 1 1 1 - - - -] [ 1 - - 1 - - 1 1 1 - 1 1 - 1 1 - 1 1 - - - 1 - -] [ 1 - - 1 1 1 - - 1 - - - - 1 1 - - - 1 1 - 1 1 1] [ 1 1 1 1 - 1 - 1 - - 1 - 1 1 - - 1 - - 1 - - 1 -] [ 1 1 1 1 1 - 1 - - - - 1 1 1 - - - 1 1 - - - - 1] [ 1 1 - - - 1 1 - 1 - - - 1 - - 1 1 1 - - - 1 1 1] [ 1 1 - - 1 - - 1 - 1 - - - 1 1 - 1 1 - - 1 - 1 1] [ 1 - - - - 1 - - - 1 1 1 1 1 - - - 1 1 - 1 1 1 -] [ 1 - 1 1 - 1 1 1 - 1 - - - - 1 1 - 1 1 - - - 1 -] [ 1 1 1 1 - - - - 1 1 - - - - - - 1 1 1 1 1 1 - -] [ 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 -] [ 1 - - 1 1 - - 1 1 - - 1 1 - - 1 - 1 - 1 1 - 1 -] [ 1 - - 1 1 - - 1 - 1 1 - 1 - - 1 1 - 1 - - 1 - 1] [ 1 - - 1 - 1 1 - - 1 - 1 1 - 1 - 1 - - 1 1 - - 1] [ 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 48 Order = 96 = 2^5 * 3 (1, 32, 25, 8)(2, 37, 26, 13)(3, 36, 27, 12)(4, 33, 28, 9)(5, 18, 29, 42)(6, 38, 30, 14)(7, 15, 31, 39)(10, 17, 34, 41)(11, 16, 35, 40)(19, 21, 43, 45)(20, 22, 44, 46)(23, 24, 47, 48) (1, 34, 47, 11, 25, 10, 23, 35)(2, 4, 27, 44, 26, 28, 3, 20)(5, 15, 45, 14, 29, 39, 21, 38)(6, 32, 7, 48, 30, 8, 31, 24)(9, 17, 22, 40, 33, 41, 46, 16)(12, 19, 13, 42, 36, 43, 37, 18) (2, 3)(6, 31)(7, 30)(10, 35)(11, 34)(12, 13)(14, 15)(16, 41)(17, 40)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(26, 27)(36, 37)(38, 39) 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: <24, 8> <48, 18> <24, 6> <48, 8> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 - 1 1 - 1 - 1 - - 1 - 1 1 1 1 1 1 - - - - - -] [ 1 1 - - 1 - 1 - 1 1 - 1 - 1 1 1 1 1 - - - - - -] [ 1 1 1 1 1 1 1 - - - - - - 1 1 - - - 1 1 1 - - -] [ 1 1 1 1 - - 1 - - - - 1 1 - - - 1 1 - - 1 1 1 -] [ 1 1 1 - 1 1 - - - 1 1 - - - - 1 1 - - 1 - 1 1 -] [ 1 - - 1 1 1 1 1 1 - - - - - - 1 - 1 1 - - 1 1 -] [ 1 1 - 1 - - - - 1 - 1 1 1 1 - 1 - - 1 1 - 1 - -] [ 1 - 1 - - - 1 1 - 1 - 1 1 - 1 1 - - 1 1 - - 1 -] [ 1 - - 1 1 - - 1 1 - 1 1 - - 1 - 1 - - 1 1 - 1 -] [ 1 - 1 - 1 - - 1 - 1 1 1 - 1 - - - 1 1 - 1 1 - -] [ 1 1 - - - 1 - - 1 1 1 - 1 - 1 - - 1 1 - 1 - 1 -] [ 1 - - - - 1 1 1 1 1 - - 1 1 - - 1 - - 1 1 1 - -] [ 1 1 - 1 - 1 - 1 - 1 - 1 - - - 1 1 - 1 - 1 - - 1] [ 1 1 1 - 1 - - 1 1 - - - 1 - - - 1 1 1 1 - - - 1] [ 1 - 1 1 - - 1 - 1 1 1 - - - - 1 - 1 - 1 1 - - 1] [ 1 - - 1 1 1 - - - 1 - 1 1 - 1 - - 1 - 1 - 1 - 1] [ 1 - 1 - 1 1 - - 1 - - 1 1 1 - 1 - - - - 1 - 1 1] [ 1 - 1 - - 1 1 - 1 - 1 1 - - 1 - 1 - 1 - - 1 - 1] [ 1 - - 1 1 - 1 - - 1 1 - 1 1 - - 1 - 1 - - - 1 1] [ 1 1 - - - 1 1 1 - - 1 1 - 1 - - - 1 - 1 - - 1 1] [ 1 1 - - 1 - 1 1 - - 1 - 1 - 1 1 - - - - 1 1 - 1] [ 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 48 Order = 480 = 2^5 * 3 * 5 (1, 5, 14, 27, 19, 33, 25, 29, 38, 3, 43, 9)(2, 46, 13, 48, 31, 47, 26, 22, 37, 24, 7, 23)(4, 42, 34, 40, 11, 45, 28, 18, 10, 16, 35, 21)(6, 20, 8, 39, 12, 17, 30, 44, 32, 15, 36, 41) (2, 26)(3, 27)(4, 9, 29, 35, 36, 28, 33, 5, 11, 12)(6, 34, 32, 13, 7, 30, 10, 8, 37, 31)(14, 19, 42, 44, 16)(15, 45, 17, 47, 22)(18, 20, 40, 38, 43)(21, 41, 23, 46, 39) (4, 33, 29, 11, 36)(5, 35, 12, 28, 9)(6, 10, 32, 37, 7)(8, 13, 31, 30, 34)(14, 19, 42, 44, 16)(15, 45, 17, 47, 22)(18, 20, 40, 38, 43)(21, 41, 23, 46, 39) 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: <24, 13> <48, 32> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 - - - - - - - - 1 1 1 1 1 - 1 - 1 1 1 1 - 1 -] [ 1 - 1 1 1 1 1 1 - 1 - - - - - 1 - 1 - - 1 - 1 -] [ 1 1 - 1 1 - 1 - 1 - 1 1 - 1 - 1 - - - - 1 1 - -] [ 1 1 1 - - 1 - 1 - 1 1 1 1 - 1 - - - - - 1 1 - -] [ 1 1 1 - - 1 1 - 1 1 1 - - 1 - - - - - 1 - - 1 1] [ 1 1 - 1 1 - - 1 1 1 - 1 1 - - - - - 1 - - - 1 1] [ 1 1 1 - 1 - - 1 1 - - - 1 1 1 1 - 1 - 1 - - - -] [ 1 1 - 1 - 1 1 - - 1 - - 1 1 1 1 1 - 1 - - - - -] [ 1 1 1 1 - - - - - - - - 1 1 - - 1 1 - - 1 1 1 1] [ 1 - 1 1 - 1 - 1 1 - 1 1 - 1 - - 1 1 1 - - - - -] [ 1 - - - - 1 - 1 1 - - - - 1 1 1 - - 1 - 1 1 1 1] [ 1 1 1 - - - 1 1 - - - 1 - - - 1 1 - 1 1 1 - - 1] [ 1 1 - 1 - - 1 1 - - 1 - - - 1 - - 1 1 1 - 1 1 -] [ 1 1 - - 1 1 - - 1 1 - - - - - - 1 1 1 1 1 1 - -] [ 1 1 - - 1 1 - - - - 1 1 - - 1 1 1 1 - - - - 1 1] [ 1 - 1 1 - - - - 1 1 - 1 - - 1 1 1 - - 1 - 1 1 -] [ 1 - - - 1 1 1 1 - - - 1 1 1 - - 1 - - 1 - 1 1 -] [ 1 - 1 1 1 1 - - - - 1 - 1 - - 1 - - 1 1 - 1 - 1] [ 1 - - - - - 1 1 1 1 1 - 1 - - 1 1 1 - - - 1 - 1] [ 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 -] [ 1 - - 1 - 1 1 - 1 - - 1 1 - 1 - - 1 - 1 1 - - 1] [ 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 48 Order = 96 = 2^5 * 3 (1, 42, 29, 24, 28, 41)(2, 12, 16, 11, 27, 22)(3, 46, 26, 36, 40, 35)(4, 17, 25, 18, 5, 48)(6, 37, 21, 38, 31, 34)(7, 10, 30, 13, 45, 14)(8, 44, 39, 43, 9, 23)(15, 19, 33, 47, 32, 20) (1, 2, 25, 26)(3, 29, 27, 5)(4, 40, 28, 16)(6, 48, 30, 24)(7, 41, 31, 17)(8, 10, 32, 34)(9, 13, 33, 37)(11, 47, 35, 23)(12, 20, 36, 44)(14, 15, 38, 39)(18, 45, 42, 21)(19, 46, 43, 22) (2, 27)(3, 26)(4, 5)(6, 7)(8, 9)(11, 36)(12, 35)(13, 14)(17, 42)(18, 41)(19, 44)(20, 43)(21, 45)(22, 46)(23, 47)(24, 48)(28, 29)(30, 31)(32, 33)(37, 38) 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: <24, 6> <48, 8> <24, 8> <48, 18> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 - - - - - - - - - - - - 1 1 1 1 1 1 1 1 1 1 1] [ 1 1 1 1 - 1 - 1 1 - - - - 1 1 1 - - 1 1 - - - -] [ 1 1 1 1 1 - 1 - - 1 - - - 1 1 - 1 1 - - 1 - - -] [ 1 - 1 1 - - 1 1 - - 1 1 - - - 1 1 1 1 - - - - 1] [ 1 1 - 1 - 1 - - - 1 1 1 - - - - 1 - 1 1 1 1 - -] [ 1 1 1 - 1 - - - 1 - 1 1 - - - 1 - 1 - 1 1 - 1 -] [ 1 1 - - 1 1 1 1 - - 1 - - 1 - 1 1 - - - - 1 1 -] [ 1 - - 1 1 - - 1 1 1 1 - - 1 - - - 1 - 1 - 1 - 1] [ 1 - - 1 1 1 1 - 1 - - 1 - - 1 1 - - - - 1 1 - 1] [ 1 - 1 - - 1 1 - 1 1 1 - - 1 - - - - 1 - 1 - 1 1] [ 1 - 1 - 1 1 - 1 - 1 - 1 - - 1 - 1 - - 1 - - 1 1] [ 1 1 - - - - 1 1 1 1 - 1 - - 1 - - 1 1 - - 1 1 -] [ 1 - 1 1 - - - 1 - 1 - 1 1 1 - 1 - - - - 1 1 1 -] [ 1 - 1 1 - - 1 - 1 - 1 - 1 - 1 - 1 - - 1 - 1 1 -] [ 1 1 1 - - 1 - - - 1 1 - 1 - 1 1 - 1 - - - 1 - 1] [ 1 1 1 - 1 - - - 1 - - 1 1 1 - - 1 - 1 - - 1 - 1] [ 1 1 - 1 - 1 1 - - - - 1 1 1 - - - 1 - 1 - - 1 1] [ 1 1 - 1 1 - - 1 - - 1 - 1 - 1 - - - 1 - 1 - 1 1] [ 1 - - 1 1 1 - - 1 1 - - 1 - - 1 1 1 1 - - - 1 -] [ 1 - 1 - 1 1 1 1 - - - - 1 - - - - 1 1 1 1 1 - -] [ 1 1 - - - - 1 1 1 1 - - 1 - - 1 1 - - 1 1 - - 1] [ 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 48 Order = 576 = 2^6 * 3^2 (1, 5, 43, 32, 48, 11, 45, 9, 47, 6, 20, 37, 25, 29, 19, 8, 24, 35, 21, 33, 23, 30, 44, 13)(2, 42, 31, 40, 27, 46, 34, 15, 28, 38, 12, 41, 26, 18, 7, 16, 3, 22, 10, 39, 4, 14, 36, 17) (2, 26)(3, 4)(5, 13, 36, 11, 33, 31)(6, 8, 34, 30, 32, 10)(7, 29, 37, 12, 35, 9)(14, 16, 45)(15, 19, 18, 17, 44, 46)(20, 22, 39, 43, 42, 41)(21, 38, 40)(23, 48)(24, 47)(27, 28) (3, 28)(4, 27)(5, 37, 36, 35, 33, 7)(6, 32, 34)(8, 10, 30)(9, 31, 29, 13, 12, 11)(14, 16, 45)(15, 19, 18, 17, 44, 46)(20, 22, 39, 43, 42, 41)(21, 38, 40)(23, 48)(24, 47) (5, 36, 33)(6, 34, 32)(7, 37, 35)(8, 30, 10)(9, 29, 12)(11, 31, 13)(14, 45, 16)(15, 18, 44)(17, 46, 19)(20, 39, 42)(21, 40, 38)(22, 43, 41) Order of automorphism group: 576 Automorphism group has centre of order: 2 Number of regular subgroups: 9 Number of regular subgroups containing zeta: 9 Matrix is cocyclic over /Expanded matrix is group developed over: <24, 8> <48, 18> <24, 10> <48, 27> <24, 6> <48, 8> <24, 8> <48, 18> <24, 6> <48, 8> <24, 8> <48, 18> <24, 10> <48, 27> <24, 8> <48, 18> <24, 12> <48, 28> [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [ 1 - - - - - - - - - - - - 1 1 1 1 1 1 1 1 1 1 1] [ 1 1 1 - - 1 1 1 - 1 - - - 1 1 - 1 1 1 - - - - -] [ 1 1 1 1 1 - - 1 - - 1 - - 1 1 1 - - - 1 1 - - -] [ 1 1 - 1 1 1 1 - 1 - - - - 1 - 1 1 - - - - 1 1 -] [ 1 - 1 1 - - 1 - 1 1 1 - - 1 - - - - 1 - 1 1 - 1] [ 1 - - - 1 1 - 1 1 1 1 - - 1 - - - 1 - 1 - - 1 1] [ 1 - 1 - 1 1 1 - - - 1 - 1 - 1 1 - 1 - - - 1 - 1] [ 1 - 1 1 - 1 - 1 1 - - - 1 - - 1 1 - 1 1 - - - 1] [ 1 - - 1 1 - 1 1 - 1 - - 1 - 1 - 1 - - - 1 - 1 1] [ 1 1 1 - 1 - - - 1 1 - - 1 - - - 1 1 - 1 1 1 - -] [ 1 1 - 1 - 1 - - - 1 1 - 1 - 1 - - - 1 1 - 1 1 -] [ 1 1 - - - - 1 1 1 - 1 - 1 - - 1 - 1 1 - 1 - 1 -] [ 1 - 1 - 1 1 1 - - - 1 1 - - - - 1 - 1 1 1 - 1 -] [ 1 - 1 1 - - 1 1 1 - - 1 - - 1 - - 1 - 1 - 1 1 -] [ 1 - - 1 1 1 - 1 - 1 - 1 - - - 1 - 1 1 - 1 1 - -] [ 1 1 1 - 1 - - - 1 1 - 1 - - 1 1 - - 1 - - - 1 1] [ 1 1 - 1 - - 1 - - 1 1 1 - - - 1 1 1 - 1 - - - 1] [ 1 1 - - - 1 - 1 1 - 1 1 - - 1 - 1 - - - 1 1 - 1] [ 1 1 1 1 - 1 - - - - - 1 1 1 - - - 1 - - 1 - 1 1] [ 1 1 - - 1 - 1 1 - - - 1 1 1 - - - - 1 1 - 1 - 1] [ 1 - 1 - - - - 1 - 1 1 1 1 1 - 1 1 - - - - 1 1 -] [ 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 48 Order = 1536 = 2^9 * 3 (4, 28)(5, 29)(6, 34, 7, 13)(8, 9, 35, 36)(10, 31, 37, 30)(11, 12, 32, 33)(14, 42, 41, 15)(16, 21, 43, 20)(17, 39, 38, 18)(19, 44, 40, 45)(22, 46)(23, 47) (1, 8, 42, 4, 38, 9)(2, 41, 36, 23, 11, 15)(3, 44, 13, 22, 31, 40)(5, 21, 34, 24, 6, 19)(7, 16, 27, 20, 37, 46)(10, 48, 30, 43, 29, 45)(12, 47, 35, 39, 26, 17)(14, 33, 25, 32, 18, 28) (2, 26)(3, 27)(4, 28)(5, 29)(6, 31)(7, 30)(8, 11)(9, 12)(10, 13)(14, 41)(15, 42)(16, 43)(17, 38)(18, 39)(19, 40)(20, 21)(32, 35)(33, 36)(34, 37)(44, 45) (3, 27)(4, 28)(6, 33, 7, 12)(8, 37, 35, 10)(9, 31, 36, 30)(11, 34, 32, 13)(14, 16, 41, 43)(15, 21, 42, 20)(17, 19, 38, 40)(18, 44, 39, 45)(23, 47)(24, 48) (6, 7)(8, 35)(9, 36)(10, 37)(11, 32)(12, 33)(13, 34)(14, 41)(15, 42)(16, 43)(17, 38)(18, 39)(19, 40)(20, 21)(30, 31)(44, 45) (3, 5)(6, 7)(9, 10)(12, 13)(15, 16)(18, 19)(20, 21)(22, 24)(27, 29)(30, 31)(33, 34)(36, 37)(39, 40)(42, 43)(44, 45)(46, 48) 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: <24, 14> <48, 34> <24, 14> <48, 40> <24, 14> <48, 34> <24, 14> <48, 39>