G:= PermutationGroup<126 | \[ 2, 5, 8, 11, 1, 16, 19, 21, 9, 25, 28, 31, 34, 6, 38, 14, 43, 45, 47, 50, 3, 22, 57, 59, 61, 63, 66, 4, 20, 44, 60, 46, 70, 65, 74, 39, 42, 78, 81, 83, 86, 76, 80, 89, 90, 54, 7, 95, 40, 29, 64, 96, 53, 32, 24, 26, 73, 92, 55, 12, 10, 62, 56, 102, 13, 105, 107, 68, 71, 108, 110, 111, 23, 101, 103, 37, 52, 15, 115, 17, 36, 114, 49, 118, 85, 94, 117, 120, 30, 18, 67, 97, 79, 41, 123, 77, 58, 124, 84, 109, 35, 51, 122, 98, 27, 113, 91, 33, 119, 69, 125, 87, 126, 116, 93, 82, 112, 99, 100, 121, 88, 75, 48, 104, 72, 106 ], \[ 3, 6, 9, 12, 14, 17, 20, 22, 24, 26, 29, 32, 35, 34, 39, 41, 44, 46, 48, 51, 53, 55, 58, 16, 62, 64, 1, 37, 60, 67, 61, 68, 71, 72, 75, 11, 31, 79, 82, 84, 27, 38, 87, 74, 10, 92, 93, 90, 5, 95, 28, 94, 59, 47, 96, 4, 85, 76, 69, 23, 7, 100, 81, 50, 104, 30, 108, 109, 43, 21, 86, 112, 63, 40, 8, 36, 80, 114, 116, 107, 42, 54, 117, 2, 119, 118, 70, 15, 33, 57, 89, 121, 88, 83, 120, 13, 78, 122, 49, 113, 91, 18, 52, 66, 111, 56, 105, 110, 106, 65, 98, 99, 97, 25, 123, 73, 124, 101, 126, 45, 115, 77, 102, 125, 103, 19 ], \[ 4, 7, 10, 13, 15, 18, 3, 23, 19, 27, 30, 33, 36, 37, 40, 42, 39, 9, 49, 52, 54, 56, 35, 60, 16, 65, 64, 34, 66, 62, 22, 69, 11, 73, 76, 77, 1, 80, 74, 85, 50, 84, 88, 25, 91, 59, 94, 41, 20, 14, 67, 31, 97, 87, 82, 98, 96, 17, 45, 99, 24, 101, 8, 103, 29, 106, 109, 105, 51, 48, 102, 26, 55, 113, 78, 108, 79, 43, 75, 46, 110, 111, 57, 100, 112, 61, 93, 71, 121, 122, 123, 21, 2, 120, 124, 115, 89, 81, 28, 83, 114, 70, 63, 32, 12, 107, 58, 92, 44, 116, 38, 90, 118, 5, 125, 53, 126, 47, 104, 117, 6, 95, 86, 68, 119, 72 ]>; size:= 362880; name:= "3.L3(4).6"; compfactor:= < 1, 2, 4 >; M:= 3; A:= 6;