HSDatabase:= [rec( name := "HS", sbgname := "U3(5).2", filename := "U35.2", degree := 176, rank := 2, permchar := "1a + 175a", permchar2 := "1a + 175a", charnmbs := [ 1, 7 ], charnmbs2 := [ 1, 7 ], ctbl := [ [ 1, 175 ], [ 1, -1 ] ], mats := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 0, 175 ], [ 1, 174 ] ] ] ), rec( name := "HS", sbgname := "4.2^4:S5", degree := 5775, rank := 9, permchar := "1a + 77a + 154a + 175a + 693a + 825a + 1056a + 1386a + 1408a", charnmbs := [ 1, 3, 4, 7, 9, 13, 16, 17, 18 ], ctbl := [ [ 1, 30, 80, 128, 480, 640, 960, 1536, 1920 ], [ 1, 15, 20, -32, 60, 80, 0, 96, -240 ], [ 1, 15, 20, 8, 60, -20, 0, -144, 60 ], [ 1, -3, 14, 40, -48, 68, 36, -48, -60 ], [ 1, 5, -10, 8, 0, 20, -60, 16, 20 ], [ 1, 7, 4, 0, -28, -32, 16, 32, 0 ], [ 1, -5, 10, -12, -10, 10, -20, -4, 30 ], [ 1, -5, 0, 8, 20, -20, 0, 16, -20 ], [ 1, 0, -10, -7, 0, 10, 30, -24, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 30, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 5, 8, 0, 16, 0, 0, 0, 0 ], [ 0, 3, 3, 0, 12, 0, 12, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 30 ], [ 0, 1, 2, 0, 7, 8, 4, 0, 8 ], [ 0, 0, 0, 0, 6, 6, 3, 12, 3 ], [ 0, 0, 1, 0, 2, 2, 7, 8, 10 ], [ 0, 0, 0, 0, 0, 5, 5, 15, 5 ], [ 0, 0, 0, 2, 2, 1, 5, 4, 16 ] ], [ [ 0, 0, 80, 0, 0, 0, 0, 0, 0 ], [ 0, 8, 8, 0, 32, 0, 32, 0, 0 ], [ 1, 3, 4, 0, 12, 24, 12, 0, 24 ], [ 0, 0, 0, 10, 0, 10, 30, 0, 30 ], [ 0, 2, 2, 0, 16, 8, 12, 16, 24 ], [ 0, 0, 3, 2, 6, 15, 15, 24, 15 ], [ 0, 1, 1, 4, 6, 10, 8, 24, 26 ], [ 0, 0, 0, 0, 5, 10, 15, 30, 20 ], [ 0, 0, 1, 2, 6, 5, 13, 16, 37 ] ], [ [ 0, 0, 0, 128, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 128 ], [ 0, 0, 0, 16, 0, 16, 48, 0, 48 ], [ 1, 0, 10, 13, 0, 50, 30, 24, 0 ], [ 0, 0, 0, 0, 16, 0, 16, 32, 64 ], [ 0, 0, 2, 10, 0, 20, 24, 24, 48 ], [ 0, 0, 4, 4, 8, 16, 24, 32, 40 ], [ 0, 0, 0, 2, 10, 10, 20, 36, 50 ], [ 0, 2, 2, 0, 16, 16, 20, 40, 32 ] ], [ [ 0, 0, 0, 0, 480, 0, 0, 0, 0 ], [ 0, 16, 32, 0, 112, 128, 64, 0, 128 ], [ 0, 12, 12, 0, 96, 48, 72, 96, 144 ], [ 0, 0, 0, 0, 60, 0, 60, 120, 240 ], [ 1, 7, 16, 16, 48, 56, 88, 112, 136 ], [ 0, 6, 6, 0, 42, 48, 78, 156, 144 ], [ 0, 2, 6, 8, 44, 52, 76, 128, 164 ], [ 0, 0, 5, 10, 35, 65, 80, 150, 135 ], [ 0, 2, 6, 16, 34, 48, 82, 108, 184 ] ], [ [ 0, 0, 0, 0, 0, 640, 0, 0, 0 ], [ 0, 0, 0, 0, 128, 128, 64, 256, 64 ], [ 0, 0, 24, 16, 48, 120, 120, 192, 120 ], [ 0, 0, 10, 50, 0, 100, 120, 120, 240 ], [ 0, 8, 8, 0, 56, 64, 104, 208, 192 ], [ 1, 6, 15, 20, 48, 88, 114, 180, 168 ], [ 0, 2, 10, 16, 52, 76, 120, 160, 204 ], [ 0, 5, 10, 10, 65, 75, 100, 170, 205 ], [ 0, 1, 5, 16, 48, 56, 102, 164, 248 ] ], [ [ 0, 0, 0, 0, 0, 0, 960, 0, 0 ], [ 0, 0, 32, 0, 64, 64, 224, 256, 320 ], [ 0, 12, 12, 48, 72, 120, 96, 288, 312 ], [ 0, 0, 30, 30, 60, 120, 180, 240, 300 ], [ 0, 4, 12, 16, 88, 104, 152, 256, 328 ], [ 0, 3, 15, 24, 78, 114, 180, 240, 306 ], [ 1, 7, 8, 24, 76, 120, 140, 256, 328 ], [ 0, 5, 15, 20, 80, 100, 160, 260, 320 ], [ 0, 5, 13, 20, 82, 102, 164, 256, 318 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 1536, 0 ], [ 0, 0, 0, 0, 0, 256, 256, 768, 256 ], [ 0, 0, 0, 0, 96, 192, 288, 576, 384 ], [ 0, 0, 0, 24, 120, 120, 240, 432, 600 ], [ 0, 0, 16, 32, 112, 208, 256, 480, 432 ], [ 0, 12, 24, 24, 156, 180, 240, 408, 492 ], [ 0, 8, 24, 32, 128, 160, 256, 416, 512 ], [ 1, 15, 30, 36, 150, 170, 260, 364, 510 ], [ 0, 4, 16, 40, 108, 164, 256, 408, 540 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1920 ], [ 0, 0, 0, 128, 128, 64, 320, 256, 1024 ], [ 0, 0, 24, 48, 144, 120, 312, 384, 888 ], [ 0, 30, 30, 0, 240, 240, 300, 600, 480 ], [ 0, 8, 24, 64, 136, 192, 328, 432, 736 ], [ 0, 3, 15, 48, 144, 168, 306, 492, 744 ], [ 0, 10, 26, 40, 164, 204, 328, 512, 636 ], [ 0, 5, 20, 50, 135, 205, 320, 510, 675 ], [ 1, 16, 37, 32, 184, 248, 318, 540, 544 ] ] ] ), rec( name := "HS", sbgname := "A8 leq A8.2", filename := "A8", degree := 2200, rank := 9, permchar := "1a + 22a + 77a + 154abc + 175a + 693a + 770a", charnmbs := [ 1, 2, 3, 4, 5, 6, 7, 9, 10 ], ctbl := [ [ 1, 1, 28, 28, 105, 105, 336, 336, 1260 ], [ 1, -1, 0, 0, -35, 35, -112, 112, 0 ], [ 1, 1, -12, -12, 25, 25, 16, 16, -60 ], [ 1, 1, 8, 8, 15, 15, -24, -24, 0 ], [ 1, -1, -10, 10, 15, -15, -12, 12, 0 ], [ 1, -1, 10, -10, 15, -15, -12, 12, 0 ], [ 1, 1, 6, 6, -5, -5, 28, 28, -60 ], [ 1, 1, -2, -2, -5, -5, -4, -4, 20 ], [ 1, -1, 0, 0, -5, 5, 8, -8, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 28, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 28, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 15, 0, 0, 12, 0 ], [ 0, 1, 0, 0, 0, 15, 12, 0, 0 ], [ 0, 0, 4, 0, 0, 0, 0, 0, 24 ], [ 0, 0, 0, 4, 0, 0, 0, 0, 24 ], [ 0, 0, 0, 1, 0, 0, 6, 6, 15 ], [ 0, 0, 1, 0, 0, 0, 6, 6, 15 ], [ 0, 0, 0, 0, 2, 2, 4, 4, 16 ] ] , [ [ 0, 0, 0, 28, 0, 0, 0, 0, 0 ], [ 0, 0, 28, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 15, 12, 0, 0 ], [ 1, 0, 0, 0, 15, 0, 0, 12, 0 ], [ 0, 0, 0, 4, 0, 0, 0, 0, 24 ], [ 0, 0, 4, 0, 0, 0, 0, 0, 24 ], [ 0, 0, 1, 0, 0, 0, 6, 6, 15 ], [ 0, 0, 0, 1, 0, 0, 6, 6, 15 ], [ 0, 0, 0, 0, 2, 2, 4, 4, 16 ] ] , [ [ 0, 0, 0, 0, 105, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 105, 0, 0, 0 ], [ 0, 0, 15, 0, 0, 0, 0, 0, 90 ], [ 0, 0, 0, 15, 0, 0, 0, 0, 90 ], [ 1, 0, 0, 0, 12, 12, 0, 32, 48 ], [ 0, 1, 0, 0, 12, 12, 32, 0, 48 ], [ 0, 0, 0, 0, 0, 10, 5, 30, 60 ], [ 0, 0, 0, 0, 10, 0, 30, 5, 60 ], [ 0, 0, 2, 2, 4, 4, 16, 16, 61 ] ], [ [ 0, 0, 0, 0, 0, 105, 0, 0, 0 ], [ 0, 0, 0, 0, 105, 0, 0, 0, 0 ], [ 0, 0, 0, 15, 0, 0, 0, 0, 90 ], [ 0, 0, 15, 0, 0, 0, 0, 0, 90 ], [ 0, 1, 0, 0, 12, 12, 32, 0, 48 ], [ 1, 0, 0, 0, 12, 12, 0, 32, 48 ], [ 0, 0, 0, 0, 10, 0, 30, 5, 60 ], [ 0, 0, 0, 0, 0, 10, 5, 30, 60 ], [ 0, 0, 2, 2, 4, 4, 16, 16, 61 ] ], [ [ 0, 0, 0, 0, 0, 0, 336, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 336, 0 ], [ 0, 0, 0, 12, 0, 0, 72, 72, 180 ], [ 0, 0, 12, 0, 0, 0, 72, 72, 180 ], [ 0, 0, 0, 0, 0, 32, 16, 96, 192 ], [ 0, 0, 0, 0, 32, 0, 96, 16, 192 ], [ 1, 0, 6, 6, 5, 30, 12, 96, 180 ], [ 0, 1, 6, 6, 30, 5, 96, 12, 180 ], [ 0, 0, 4, 4, 16, 16, 48, 48, 200 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 336, 0 ], [ 0, 0, 0, 0, 0, 0, 336, 0, 0 ], [ 0, 0, 12, 0, 0, 0, 72, 72, 180 ], [ 0, 0, 0, 12, 0, 0, 72, 72, 180 ], [ 0, 0, 0, 0, 32, 0, 96, 16, 192 ], [ 0, 0, 0, 0, 0, 32, 16, 96, 192 ], [ 0, 1, 6, 6, 30, 5, 96, 12, 180 ], [ 1, 0, 6, 6, 5, 30, 12, 96, 180 ], [ 0, 0, 4, 4, 16, 16, 48, 48, 200 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1260 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1260 ] , [ 0, 0, 0, 0, 90, 90, 180, 180, 720 ], [ 0, 0, 0, 0, 90, 90, 180, 180, 720 ], [ 0, 0, 24, 24, 48, 48, 192, 192, 732 ], [ 0, 0, 24, 24, 48, 48, 192, 192, 732 ], [ 0, 0, 15, 15, 60, 60, 180, 180, 750 ], [ 0, 0, 15, 15, 60, 60, 180, 180, 750 ], [ 1, 1, 16, 16, 61, 61, 200, 200, 704 ] ] ] ), rec( name := "HS", sbgname := "4^3:L3(2)", filename := "4^3:L32", degree := 4125, rank := 9, permchar := "1a + 22a + 77a + 154a + 175a + 693a + 770a + 825a + 1408a", charnmbs := [ 1, 2, 3, 4, 7, 9, 10, 13, 18 ], ctbl := [ [ 1, 28, 64, 112, 336, 448, 896, 896, 1344 ], [ 1, -7, -36, 42, -84, 168, -224, 56, 84 ], [ 1, 13, 14, 32, 6, 28, 16, -164, 54 ], [ 1, 13, 4, 22, 36, -32, -64, 56, -36 ], [ 1, -5, 20, 2, 6, 52, 16, 16, -108 ], [ 1, 3, 4, 2, -34, -12, 16, 16, 4 ], [ 1, -7, -6, 12, 6, -12, 16, -4, -6 ], [ 1, 5, -10, -8, 6, 12, 16, -4, -18 ], [ 1, -2, 4, -8, 6, -2, -19, -4, 24 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 28, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 3, 0, 12, 12, 0, 0, 0, 0 ], [ 0, 0, 0, 7, 0, 0, 0, 0, 21 ], [ 0, 3, 4, 3, 6, 0, 0, 0, 12 ], [ 0, 1, 0, 2, 5, 4, 0, 8, 8 ], [ 0, 0, 0, 0, 3, 1, 12, 0, 12 ], [ 0, 0, 0, 0, 0, 6, 6, 4, 12 ], [ 0, 0, 0, 0, 3, 0, 4, 15, 6 ], [ 0, 0, 1, 1, 2, 4, 8, 4, 8 ] ], [ [ 0, 0, 64, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 16, 0, 0, 0, 0, 48 ], [ 1, 0, 0, 7, 0, 42, 0, 14, 0 ], [ 0, 4, 4, 0, 12, 0, 32, 0, 12 ], [ 0, 0, 0, 4, 4, 16, 0, 16, 24 ], [ 0, 0, 6, 0, 12, 0, 32, 8, 6 ], [ 0, 0, 0, 4, 0, 16, 4, 16, 24 ], [ 0, 0, 1, 0, 6, 4, 16, 22, 15 ], [ 0, 1, 0, 1, 6, 2, 16, 10, 28 ] ], [ [ 0, 0, 0, 112, 0, 0, 0, 0, 0 ], [ 0, 12, 16, 12, 24, 0, 0, 0, 48 ], [ 0, 7, 7, 0, 21, 0, 56, 0, 21 ], [ 1, 3, 0, 16, 12, 24, 0, 8, 48 ], [ 0, 2, 4, 4, 18, 0, 32, 24, 28 ], [ 0, 0, 0, 6, 0, 30, 8, 20, 48 ], [ 0, 0, 4, 0, 12, 4, 40, 16, 36 ], [ 0, 0, 0, 1, 9, 10, 16, 46, 30 ], [ 0, 1, 1, 4, 7, 16, 24, 20, 39 ] ], [ [ 0, 0, 0, 0, 336, 0, 0, 0, 0 ], [ 0, 12, 0, 24, 60, 48, 0, 96, 96 ], [ 0, 0, 0, 21, 21, 84, 0, 84, 126 ], [ 0, 6, 12, 12, 54, 0, 96, 72, 84 ], [ 1, 5, 4, 18, 4, 44, 48, 96, 116 ], [ 0, 3, 12, 0, 33, 12, 120, 60, 96 ], [ 0, 0, 0, 12, 18, 60, 54, 72, 120 ], [ 0, 3, 6, 9, 36, 30, 72, 78, 102 ], [ 0, 2, 6, 7, 29, 32, 80, 68, 112 ] ], [ [ 0, 0, 0, 0, 0, 448, 0, 0, 0 ], [ 0, 0, 0, 0, 48, 16, 192, 0, 192 ], [ 0, 0, 42, 0, 84, 0, 224, 56, 42 ], [ 0, 0, 0, 24, 0, 120, 32, 80, 192 ], [ 0, 4, 16, 0, 44, 16, 160, 80, 128 ], [ 1, 1, 0, 30, 12, 116, 24, 120, 144 ], [ 0, 6, 16, 4, 60, 12, 142, 88, 120 ], [ 0, 0, 4, 10, 30, 60, 88, 112, 144 ], [ 0, 4, 2, 16, 32, 48, 80, 96, 170 ] ], [ [ 0, 0, 0, 0, 0, 0, 896, 0, 0 ], [ 0, 0, 0, 0, 0, 192, 192, 128, 384 ], [ 0, 0, 0, 56, 0, 224, 56, 224, 336 ], [ 0, 0, 32, 0, 96, 32, 320, 128, 288 ], [ 0, 0, 0, 32, 48, 160, 144, 192, 320 ], [ 0, 12, 32, 8, 120, 24, 284, 176, 240 ], [ 1, 6, 4, 40, 54, 142, 117, 220, 312 ], [ 0, 4, 16, 16, 72, 88, 220, 192, 288 ], [ 0, 8, 16, 24, 80, 80, 208, 192, 288 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 896, 0 ], [ 0, 0, 0, 0, 96, 0, 128, 480, 192 ], [ 0, 0, 14, 0, 84, 56, 224, 308, 210 ], [ 0, 0, 0, 8, 72, 80, 128, 368, 240 ], [ 0, 8, 16, 24, 96, 80, 192, 208, 272 ], [ 0, 0, 8, 20, 60, 120, 176, 224, 288 ], [ 0, 4, 16, 16, 72, 88, 220, 192, 288 ], [ 1, 15, 22, 46, 78, 112, 192, 112, 318 ], [ 0, 4, 10, 20, 68, 96, 192, 212, 294 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1344 ], [ 0, 0, 48, 48, 96, 192, 384, 192, 384 ], [ 0, 21, 0, 21, 126, 42, 336, 210, 588 ], [ 0, 12, 12, 48, 84, 192, 288, 240, 468 ], [ 0, 8, 24, 28, 116, 128, 320, 272, 448 ], [ 0, 12, 6, 48, 96, 144, 240, 288, 510 ], [ 0, 12, 24, 36, 120, 120, 312, 288, 432 ], [ 0, 6, 15, 30, 102, 144, 288, 318, 441 ], [ 1, 8, 28, 39, 112, 170, 288, 294, 404 ] ] ] ), rec( name := "HS", sbgname := "A8.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 1100, rank := 5, permchar := "1a + 77a + 154a + 175a + 693a", charnmbs := [ 1, 3, 4, 7, 9 ], ctbl := [ [ 1, 28, 105, 336, 630 ], [ 1, -12, 25, 16, -30 ], [ 1, 8, 15, -24, 0 ], [ 1, 6, -5, 28, -30 ], [ 1, -2, -5, -4, 10 ] ] , mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 28, 0, 0, 0 ], [ 1, 0, 15, 12, 0 ], [ 0, 4, 0, 0, 24 ], [ 0, 1, 0, 12, 15 ], [ 0, 0, 4, 8, 16 ] ], [ [ 0, 0, 105, 0, 0 ], [ 0, 15, 0, 0, 90 ], [ 1, 0, 24, 32, 48 ], [ 0, 0, 10, 35, 60 ], [ 0, 4, 8, 32, 61 ] ], [ [ 0, 0, 0, 336, 0 ], [ 0, 12, 0, 144, 180 ], [ 0, 0, 32, 112, 192 ], [ 1, 12, 35, 108, 180 ], [ 0, 8, 32, 96, 200 ] ], [ [ 0, 0, 0, 0, 630 ], [ 0, 0, 90, 180, 360 ], [ 0, 24, 48, 192, 366 ], [ 0, 15, 60, 180, 375 ], [ 1, 16, 61, 200, 352 ] ] ] ), rec( name := "HS", sbgname := "L3(4).2_1", filename := "L34.2_1", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 1100, rank := 5, permchar := "1a + 22a + 77a + 175a + 825a", charnmbs := [ 1, 2, 3, 7, 13 ], ctbl := [ [ 1, 42, 105, 280, 672 ], [ 1, 12, -45, 80, -48 ], [ 1, 22, 5, -20, -8 ], [ 1, -2, 17, 16, -32 ], [ 1, -2, -3, -4, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 42, 0, 0, 0 ], [ 1, 20, 5, 0, 16 ], [ 0, 2, 8, 0, 32 ], [ 0, 0, 0, 18, 24 ], [ 0, 1, 5, 10, 26 ] ], [ [ 0, 0, 105, 0, 0 ], [ 0, 5, 20, 0, 80 ], [ 1, 8, 0, 64, 32 ], [ 0, 0, 24, 9, 72 ], [ 0, 5, 5, 30, 65 ] ], [ [ 0, 0, 0, 280, 0 ], [ 0, 0, 0, 120, 160 ], [ 0, 0, 64, 24, 192 ], [ 1, 18, 9, 108, 144 ], [ 0, 10, 30, 60, 180 ] ], [ [ 0, 0, 0, 0, 672 ], [ 0, 16, 80, 160, 416 ], [ 0, 32, 32, 192, 416 ], [ 0, 24, 72, 144, 432 ], [ 1, 26, 65, 180, 400 ] ] ] ), rec( name := "HS", sbgname := "M11", degree := 5600, rank := 9, permchar := "1a + 22a + 77a + 154b + 175a + 770a + 825a + 1056a + 2520a" , permchar2 := "1a + 22a + 77a + 154c + 175a + 770a + 825a + 1056a + 2520a" , charnmbs := [ 1, 2, 3, 5, 7, 10, 13, 16, 22 ], charnmbs2 := [ 1, 2, 3, 6, 7, 10, 13, 16, 22 ], ctbl := [ [ 1, 55, 132, 165, 495, 660, 792, 1320, 1980 ], [ 1, 5, 52, -85, 195, -140, 72, -280, 180 ], [ 1, -20, 37, 40, 45, 85, -138, -80, 30 ], [ 1, -19, -12, -21, 27, 84, 72, -24, -108 ], [ 1, 7, 4, 37, 63, -44, 24, 40, -132 ], [ 1, -4, 13, -16, -3, -11, -18, 56, -18 ], [ 1, 12, -11, -8, 13, 21, -26, 0, -2 ], [ 1, 6, 13, 4, -23, 9, 22, -24, -8 ], [ 1, -4, -7, 4, -3, -11, 2, -4, 22 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 55, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 18, 36, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 30, 10, 15 ], [ 0, 0, 0, 0, 3, 4, 24, 24, 0 ], [ 0, 2, 0, 1, 8, 0, 8, 16, 20 ], [ 0, 3, 0, 1, 0, 0, 6, 18, 27 ], [ 0, 0, 5, 5, 5, 5, 0, 10, 25 ], [ 0, 0, 1, 3, 6, 9, 6, 12, 18 ], [ 0, 0, 1, 0, 5, 9, 10, 12, 18 ] ], [ [ 0, 0, 132, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 72, 24, 36 ], [ 1, 0, 15, 0, 30, 20, 6, 0, 60 ], [ 0, 0, 0, 20, 0, 48, 0, 40, 24 ], [ 0, 0, 8, 0, 32, 4, 16, 8, 64 ], [ 0, 0, 4, 12, 3, 23, 6, 36, 48 ], [ 0, 5, 1, 0, 10, 5, 31, 30, 50 ], [ 0, 1, 0, 5, 3, 18, 18, 51, 36 ], [ 0, 1, 4, 2, 16, 16, 20, 24, 49 ] ], [ [ 0, 0, 0, 165, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 9, 12, 72, 72, 0 ], [ 0, 0, 0, 25, 0, 60, 0, 50, 30 ], [ 1, 0, 20, 0, 72, 0, 24, 0, 48 ], [ 0, 1, 0, 24, 0, 32, 8, 80, 20 ], [ 0, 1, 12, 0, 24, 12, 12, 14, 90 ], [ 0, 5, 0, 5, 5, 10, 30, 60, 50 ], [ 0, 3, 5, 0, 30, 7, 36, 18, 66 ], [ 0, 0, 2, 4, 5, 30, 20, 44, 60 ] ], [ [ 0, 0, 0, 0, 495, 0, 0, 0, 0 ], [ 0, 18, 0, 9, 72, 0, 72, 144, 180 ], [ 0, 0, 30, 0, 120, 15, 60, 30, 240 ], [ 0, 3, 0, 72, 0, 96, 24, 240, 60 ], [ 1, 8, 32, 0, 118, 16, 96, 32, 192 ], [ 0, 0, 3, 24, 12, 102, 48, 150, 156 ], [ 0, 5, 10, 5, 60, 40, 95, 110, 170 ], [ 0, 6, 3, 30, 12, 75, 66, 165, 138 ], [ 0, 5, 16, 5, 48, 52, 68, 92, 209 ] ], [ [ 0, 0, 0, 0, 0, 660, 0, 0, 0 ], [ 0, 36, 0, 12, 0, 0, 72, 216, 324 ], [ 0, 0, 20, 60, 15, 115, 30, 180, 240 ], [ 0, 4, 48, 0, 96, 48, 48, 56, 360 ], [ 0, 0, 4, 32, 16, 136, 64, 200, 208 ], [ 1, 0, 23, 12, 102, 96, 102, 108, 216 ], [ 0, 5, 5, 10, 40, 85, 135, 180, 200 ], [ 0, 9, 18, 7, 75, 54, 108, 125, 264 ], [ 0, 9, 16, 30, 52, 72, 80, 176, 225 ] ], [ [ 0, 0, 0, 0, 0, 0, 792, 0, 0 ], [ 0, 0, 72, 72, 72, 72, 0, 144, 360 ], [ 0, 30, 6, 0, 60, 30, 186, 180, 300 ], [ 0, 24, 0, 24, 24, 48, 144, 288, 240 ], [ 0, 8, 16, 8, 96, 64, 152, 176, 272 ], [ 0, 6, 6, 12, 48, 102, 162, 216, 240 ], [ 1, 0, 31, 30, 95, 135, 80, 150, 270 ], [ 0, 6, 18, 36, 66, 108, 90, 192, 276 ], [ 0, 10, 20, 20, 68, 80, 108, 184, 302 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 1320, 0 ], [ 0, 0, 24, 72, 144, 216, 144, 288, 432 ], [ 0, 10, 0, 50, 30, 180, 180, 510, 360 ], [ 0, 24, 40, 0, 240, 56, 288, 144, 528 ], [ 0, 16, 8, 80, 32, 200, 176, 440, 368 ], [ 0, 18, 36, 14, 150, 108, 216, 250, 528 ], [ 0, 10, 30, 60, 110, 180, 150, 320, 460 ], [ 1, 12, 51, 18, 165, 125, 192, 258, 498 ], [ 0, 12, 24, 44, 92, 176, 184, 332, 456 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1980 ], [ 0, 0, 36, 0, 180, 324, 360, 432, 648 ], [ 0, 15, 60, 30, 240, 240, 300, 360, 735 ], [ 0, 0, 24, 48, 60, 360, 240, 528, 720 ], [ 0, 20, 64, 20, 192, 208, 272, 368, 836 ], [ 0, 27, 48, 90, 156, 216, 240, 528, 675 ], [ 0, 25, 50, 50, 170, 200, 270, 460, 755 ], [ 0, 18, 36, 66, 138, 264, 276, 498, 684 ], [ 1, 18, 49, 60, 209, 225, 302, 456, 660 ] ] ] ), rec( name := "HS", sbgname := "M22", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 100, rank := 3, permchar := "1a + 22a + 77a", charnmbs := [ 1, 2, 3 ], ctbl := [ [ 1, 22, 77 ], [ 1, -8, 7 ], [ 1, 2, -3 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 22, 0 ], [ 1, 0, 21 ], [ 0, 6, 16 ] ], [ [ 0, 0, 77 ], [ 0, 21, 56 ], [ 1, 16, 60 ] ] ] ), rec( name := "HS", sbgname := "U3(5) leq U3(5).2", filename := "U35", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 352, rank := 4, permchar := "1a + 22a + 154b + 175a", permchar2 := "1a + 22a + 154b + 175a", charnmbs := [ 1, 2, 5, 7 ], charnmbs2 := [ 1, 2, 5, 7 ], ctbl := [ [ 1, 1, 175, 175 ], [ 1, -1, 35, -35 ], [ 1, -1, -5, 5 ], [ 1, 1, -1, -1 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ 0, 0, 175, 0 ], [ 0, 0, 0, 175 ], [ 1, 0, 102, 72 ], [ 0, 1, 72, 102 ] ], [ [ 0, 0, 0, 175 ], [ 0, 0, 175, 0 ], [ 0, 1, 72, 102 ], [ 1, 0, 102, 72 ] ] ] ), rec( name := "HS.2", sbgname := "A8.2x2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 1100, rank := 5, permchar := "1a^+ + 77a^+ + 154a^+ + 175a^+ + 693a^+", charnmbs := [ 1, 5, 7, 10, 14 ], ctbl := [ [ 1, 28, 105, 336, 630 ], [ 1, -12, 25, 16, -30 ], [ 1, 8, 15, -24, 0 ], [ 1, 6, -5, 28, -30 ], [ 1, -2, -5, -4, 10 ] ] , mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 28, 0, 0, 0 ], [ 1, 0, 15, 12, 0 ], [ 0, 4, 0, 0, 24 ], [ 0, 1, 0, 12, 15 ], [ 0, 0, 4, 8, 16 ] ], [ [ 0, 0, 105, 0, 0 ], [ 0, 15, 0, 0, 90 ], [ 1, 0, 24, 32, 48 ], [ 0, 0, 10, 35, 60 ], [ 0, 4, 8, 32, 61 ] ], [ [ 0, 0, 0, 336, 0 ], [ 0, 12, 0, 144, 180 ], [ 0, 0, 32, 112, 192 ], [ 1, 12, 35, 108, 180 ], [ 0, 8, 32, 96, 200 ] ], [ [ 0, 0, 0, 0, 630 ], [ 0, 0, 90, 180, 360 ], [ 0, 24, 48, 192, 366 ], [ 0, 15, 60, 180, 375 ], [ 1, 16, 61, 200, 352 ] ] ] ), rec( name := "HS.2", sbgname := "L3(4).2^2", filename := "L34.2^2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 1100, rank := 5, permchar := "1a^+ + 22a^+ + 77a^+ + 175a^+ + 825a^+", charnmbs := [ 1, 3, 5, 10, 19 ], ctbl := [ [ 1, 42, 105, 280, 672 ], [ 1, 12, -45, 80, -48 ], [ 1, 22, 5, -20, -8 ], [ 1, -2, 17, 16, -32 ], [ 1, -2, -3, -4, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 42, 0, 0, 0 ], [ 1, 20, 5, 0, 16 ], [ 0, 2, 8, 0, 32 ], [ 0, 0, 0, 18, 24 ], [ 0, 1, 5, 10, 26 ] ], [ [ 0, 0, 105, 0, 0 ], [ 0, 5, 20, 0, 80 ], [ 1, 8, 0, 64, 32 ], [ 0, 0, 24, 9, 72 ], [ 0, 5, 5, 30, 65 ] ], [ [ 0, 0, 0, 280, 0 ], [ 0, 0, 0, 120, 160 ], [ 0, 0, 64, 24, 192 ], [ 1, 18, 9, 108, 144 ], [ 0, 10, 30, 60, 180 ] ], [ [ 0, 0, 0, 0, 672 ], [ 0, 16, 80, 160, 416 ], [ 0, 32, 32, 192, 416 ], [ 0, 24, 72, 144, 432 ], [ 1, 26, 65, 180, 400 ] ] ] ), rec( name := "HS.2", sbgname := "M22.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 100, rank := 3, permchar := "1a^+ + 22a^+ + 77a^+", charnmbs := [ 1, 3, 5 ], ctbl := [ [ 1, 22, 77 ], [ 1, -8, 7 ], [ 1, 2, -3 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 22, 0 ], [ 1, 0, 21 ], [ 0, 6, 16 ] ], [ [ 0, 0, 77 ], [ 0, 21, 56 ], [ 1, 16, 60 ] ] ] ), rec( name := "HS.2", sbgname := "U3(5).2", filename := "U35.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 352, rank := 4, permchar := "1a^{+-} + 175a^{+-}", charnmbs := [ 1, 2, 10, 11 ], ctbl := [ [ 1, 50, 126, 175 ], [ 1, -50, -126, 175 ], [ 1, 6, -6, -1 ], [ 1, -6, 6, -1 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 50, 0, 0 ], [ 1, 0, 0, 49 ], [ 0, 0, 0, 50 ], [ 0, 14, 36, 0 ] ], [ [ 0, 0, 126, 0 ], [ 0, 0, 0, 126 ], [ 1, 0, 0, 125 ], [ 0, 36, 90, 0 ] ], [ [ 0, 0, 0, 175 ], [ 0, 49, 126, 0 ], [ 0, 50, 125, 0 ], [ 1, 0, 0, 174 ] ] ] ), rec( name := "HS.2", sbgname := "M22 leq M22.2", filename := "M22", degree := 200, rank := 6, permchar := "1a^{+-} + 22a^{+-} + 77a^{+-}", charnmbs := [ 1, 2, 3, 4, 5, 6 ], ctbl := [ [ 1, 1, 22, 22, 77, 77 ], [ 1, -1, -22, 22, -77, 77 ], [ 1, 1, -8, -8, 7, 7 ], [ 1, -1, 8, -8, -7, 7 ], [ 1, 1, 2, 2, -3, -3 ], [ 1, -1, -2, 2, 3, -3 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 22, 0, 0, 0 ], [ 0, 0, 0, 22, 0, 0 ], [ 1, 0, 0, 0, 0, 21 ], [ 0, 1, 0, 0, 21, 0 ], [ 0, 0, 0, 6, 0, 16 ], [ 0, 0, 6, 0, 16, 0 ] ], [ [ 0, 0, 0, 22, 0, 0 ], [ 0, 0, 22, 0, 0, 0 ], [ 0, 1, 0, 0, 21, 0 ], [ 1, 0, 0, 0, 0, 21 ], [ 0, 0, 6, 0, 16, 0 ], [ 0, 0, 0, 6, 0, 16 ] ], [ [ 0, 0, 0, 0, 77, 0 ], [ 0, 0, 0, 0, 0, 77 ], [ 0, 0, 0, 21, 0, 56 ], [ 0, 0, 21, 0, 56, 0 ], [ 1, 0, 0, 16, 0, 60 ], [ 0, 1, 16, 0, 60, 0 ] ], [ [ 0, 0, 0, 0, 0, 77 ], [ 0, 0, 0, 0, 77, 0 ], [ 0, 0, 21, 0, 56, 0 ], [ 0, 0, 0, 21, 0, 56 ], [ 0, 1, 16, 0, 60, 0 ], [ 1, 0, 0, 16, 0, 60 ] ] ] ), rec( name := "HS.2", sbgname := "L3(4).2_1 leq L3(4).2^2", filename := "L34.2_1", degree := 2200, rank := 10, permchar := "1a^{+-} + 22a^{+-} + 77a^{+-} + 175a^{+-} + 825a^{+-}", charnmbs := [ 1, 2, 3, 4, 5, 6, 10, 11, 19, 20 ], ctbl := [ [ 1, 1, 42, 42, 105, 105, 280, 280, 672, 672 ], [ 1, -1, -42, 42, 105, -105, 280, -280, 672, -672 ], [ 1, 1, 12, 12, -45, -45, 80, 80, -48, -48 ], [ 1, -1, -12, 12, -45, 45, 80, -80, -48, 48 ], [ 1, 1, 22, 22, 5, 5, -20, -20, -8, -8 ], [ 1, -1, -22, 22, 5, -5, -20, 20, -8, 8 ], [ 1, 1, -2, -2, 17, 17, 16, 16, -32, -32 ], [ 1, -1, 2, -2, 17, -17, 16, -16, -32, 32 ], [ 1, 1, -2, -2, -3, -3, -4, -4, 8, 8 ], [ 1, -1, 2, -2, -3, 3, -4, 4, 8, -8 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] , [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 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144, 0, 432, 0 ], [ 0, 1, 26, 0, 0, 65, 0, 180, 0, 400 ], [ 1, 0, 0, 26, 65, 0, 180, 0, 400, 0 ] ] ] ), rec( name := "HS.2", sbgname := "A8.2 leq A8.2x2", filename := "A8.2", degree := 2200, rank := 10, permchar := "1a^{+-} + 77a^{+-} + 154a^{+-} + 175a^{+-} + 693a^{+-}", charnmbs := [ 1, 2, 5, 6, 7, 8, 10, 11, 14, 15 ], ctbl := [ [ 1, 1, 28, 28, 105, 105, 336, 336, 630, 630 ], [ 1, -1, -28, 28, -105, 105, -336, 336, 630, -630 ], [ 1, 1, -12, -12, 25, 25, 16, 16, -30, -30 ], [ 1, -1, 12, -12, -25, 25, -16, 16, -30, 30 ], [ 1, 1, 8, 8, 15, 15, -24, -24, 0, 0 ], [ 1, -1, -8, 8, -15, 15, 24, -24, 0, 0 ], [ 1, 1, 6, 6, -5, -5, 28, 28, -30, -30 ], [ 1, -1, -6, 6, 5, -5, -28, 28, -30, 30 ], [ 1, 1, -2, -2, -5, -5, -4, -4, 10, 10 ], [ 1, -1, 2, -2, 5, -5, 4, -4, 10, -10 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] , [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 28, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 28, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 15, 0, 12, 0, 0 ], [ 0, 1, 0, 0, 15, 0, 12, 0, 0, 0 ], [ 0, 0, 0, 4, 0, 0, 0, 0, 24, 0 ], [ 0, 0, 4, 0, 0, 0, 0, 0, 0, 24 ], [ 0, 0, 0, 1, 0, 0, 0, 12, 15, 0 ], [ 0, 0, 1, 0, 0, 0, 12, 0, 0, 15 ], [ 0, 0, 0, 0, 4, 0, 8, 0, 0, 16 ], [ 0, 0, 0, 0, 0, 4, 0, 8, 16, 0 ] ], [ [ 0, 0, 0, 28, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 28, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 15, 0, 12, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 15, 0, 12, 0, 0 ], [ 0, 0, 4, 0, 0, 0, 0, 0, 0, 24 ], [ 0, 0, 0, 4, 0, 0, 0, 0, 24, 0 ], [ 0, 0, 1, 0, 0, 0, 12, 0, 0, 15 ], [ 0, 0, 0, 1, 0, 0, 0, 12, 15, 0 ], [ 0, 0, 0, 0, 0, 4, 0, 8, 16, 0 ], [ 0, 0, 0, 0, 4, 0, 8, 0, 0, 16 ] ], [ [ 0, 0, 0, 0, 105, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 105, 0, 0, 0, 0 ], [ 0, 0, 0, 15, 0, 0, 0, 0, 90, 0 ], [ 0, 0, 15, 0, 0, 0, 0, 0, 0, 90 ], [ 1, 0, 0, 0, 0, 24, 0, 32, 48, 0 ], [ 0, 1, 0, 0, 24, 0, 32, 0, 0, 48 ], [ 0, 0, 0, 0, 0, 10, 0, 35, 60, 0 ], [ 0, 0, 0, 0, 10, 0, 35, 0, 0, 60 ], [ 0, 0, 4, 0, 8, 0, 32, 0, 0, 61 ], [ 0, 0, 0, 4, 0, 8, 0, 32, 61, 0 ] ], [ [ 0, 0, 0, 0, 0, 105, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 105, 0, 0, 0, 0, 0 ], [ 0, 0, 15, 0, 0, 0, 0, 0, 0, 90 ], [ 0, 0, 0, 15, 0, 0, 0, 0, 90, 0 ], [ 0, 1, 0, 0, 24, 0, 32, 0, 0, 48 ], [ 1, 0, 0, 0, 0, 24, 0, 32, 48, 0 ], [ 0, 0, 0, 0, 10, 0, 35, 0, 0, 60 ], [ 0, 0, 0, 0, 0, 10, 0, 35, 60, 0 ], [ 0, 0, 0, 4, 0, 8, 0, 32, 61, 0 ], [ 0, 0, 4, 0, 8, 0, 32, 0, 0, 61 ] ], [ [ 0, 0, 0, 0, 0, 0, 336, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 336, 0, 0 ], [ 0, 0, 0, 12, 0, 0, 0, 144, 180, 0 ], [ 0, 0, 12, 0, 0, 0, 144, 0, 0, 180 ], [ 0, 0, 0, 0, 0, 32, 0, 112, 192, 0 ], [ 0, 0, 0, 0, 32, 0, 112, 0, 0, 192 ], [ 1, 0, 0, 12, 0, 35, 0, 108, 180, 0 ], [ 0, 1, 12, 0, 35, 0, 108, 0, 0, 180 ], [ 0, 0, 8, 0, 32, 0, 96, 0, 0, 200 ], [ 0, 0, 0, 8, 0, 32, 0, 96, 200, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 336, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 336, 0, 0, 0 ], [ 0, 0, 12, 0, 0, 0, 144, 0, 0, 180 ], [ 0, 0, 0, 12, 0, 0, 0, 144, 180, 0 ], [ 0, 0, 0, 0, 32, 0, 112, 0, 0, 192 ], [ 0, 0, 0, 0, 0, 32, 0, 112, 192, 0 ], [ 0, 1, 12, 0, 35, 0, 108, 0, 0, 180 ], [ 1, 0, 0, 12, 0, 35, 0, 108, 180, 0 ], [ 0, 0, 0, 8, 0, 32, 0, 96, 200, 0 ], [ 0, 0, 8, 0, 32, 0, 96, 0, 0, 200 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 630, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 630 ], [ 0, 0, 0, 0, 90, 0, 180, 0, 0, 360 ], [ 0, 0, 0, 0, 0, 90, 0, 180, 360, 0 ], [ 0, 0, 24, 0, 48, 0, 192, 0, 0, 366 ], [ 0, 0, 0, 24, 0, 48, 0, 192, 366, 0 ], [ 0, 0, 15, 0, 60, 0, 180, 0, 0, 375 ], [ 0, 0, 0, 15, 0, 60, 0, 180, 375, 0 ], [ 1, 0, 0, 16, 0, 61, 0, 200, 352, 0 ], [ 0, 1, 16, 0, 61, 0, 200, 0, 0, 352 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 630 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 630, 0 ], [ 0, 0, 0, 0, 0, 90, 0, 180, 360, 0 ], [ 0, 0, 0, 0, 90, 0, 180, 0, 0, 360 ], [ 0, 0, 0, 24, 0, 48, 0, 192, 366, 0 ], [ 0, 0, 24, 0, 48, 0, 192, 0, 0, 366 ], [ 0, 0, 0, 15, 0, 60, 0, 180, 375, 0 ], [ 0, 0, 15, 0, 60, 0, 180, 0, 0, 375 ], [ 0, 1, 16, 0, 61, 0, 200, 0, 0, 352 ], [ 1, 0, 0, 16, 0, 61, 0, 200, 352, 0 ] ] ] ), rec( name := "HS.2", sbgname := "U3(5) leq U3(5).2", filename := "U35", degree := 704, rank := 7, permchar := "1a^{+-} + 22a^{+-} + 154bc + 175a^{+-}", charnmbs := [ 1, 2, 3, 4, 9, 10, 11 ], ctbl := [ [ 1, 1, 50, 50, 175, 175, 252 ], [ 1, 1, -50, -50, 175, 175, -252 ], [ 1, -1, -20, 20, 35, -35, 0 ], [ 1, -1, 20, -20, 35, -35, 0 ], [ 1, -1, 0, 0, -5, 5, 0 ], [ 1, 1, 6, 6, -1, -1, -12 ], [ 1, 1, -6, -6, -1, -1, 12 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 50, 0, 0, 0, 0 ], [ 0, 0, 0, 50, 0, 0, 0 ], [ 1, 0, 0, 0, 42, 7, 0 ], [ 0, 1, 0, 0, 7, 42, 0 ], [ 0, 0, 12, 2, 0, 0, 36 ], [ 0, 0, 2, 12, 0, 0, 36 ], [ 0, 0, 0, 0, 25, 25, 0 ] ], [ [ 0, 0, 0, 50, 0, 0, 0 ], [ 0, 0, 50, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 7, 42, 0 ], [ 1, 0, 0, 0, 42, 7, 0 ], [ 0, 0, 2, 12, 0, 0, 36 ], [ 0, 0, 12, 2, 0, 0, 36 ], [ 0, 0, 0, 0, 25, 25, 0 ] ], [ [ 0, 0, 0, 0, 175, 0, 0 ], [ 0, 0, 0, 0, 0, 175, 0 ], [ 0, 0, 42, 7, 0, 0, 126 ], [ 0, 0, 7, 42, 0, 0, 126 ], [ 1, 0, 0, 0, 102, 72, 0 ], [ 0, 1, 0, 0, 72, 102, 0 ], [ 0, 0, 25, 25, 0, 0, 125 ] ], [ [ 0, 0, 0, 0, 0, 175, 0 ], [ 0, 0, 0, 0, 175, 0, 0 ], [ 0, 0, 7, 42, 0, 0, 126 ], [ 0, 0, 42, 7, 0, 0, 126 ], [ 0, 1, 0, 0, 72, 102, 0 ], [ 1, 0, 0, 0, 102, 72, 0 ], [ 0, 0, 25, 25, 0, 0, 125 ] ], [ [ 0, 0, 0, 0, 0, 0, 252 ], [ 0, 0, 0, 0, 0, 0, 252 ], [ 0, 0, 0, 0, 126, 126, 0 ], [ 0, 0, 0, 0, 126, 126, 0 ], [ 0, 0, 36, 36, 0, 0, 180 ], [ 0, 0, 36, 36, 0, 0, 180 ], [ 1, 1, 0, 0, 125, 125, 0 ] ] ] ), rec( name := "HS.2", sbgname := "A8.2 leq A8.2x2", filename := "A8.2", degree := 2200, rank := 8, permchar := "1a^+ + 22a^- + 77a^+ + 154a^+bc + 175a^+ + 693a^+ + 770a^-" , charnmbs := [ 1, 4, 5, 7, 9, 10, 14, 17 ], ctbl := [ [ 1, 1, 56, 105, 105, 336, 336, 1260 ], [ 1, -1, 0, 35, -35, -112, 112, 0 ], [ 1, 1, -24, 25, 25, 16, 16, -60 ], [ 1, 1, 16, 15, 15, -24, -24, 0 ], [ 1, -1, 0, -15, 15, -12, 12, 0 ] , [ 1, 1, 12, -5, -5, 28, 28, -60 ], [ 1, 1, -4, -5, -5, -4, -4, 20 ], [ 1, -1, 0, 5, -5, 8, -8, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 56, 0, 0, 0, 0, 0 ], [ 0, 0, 56, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 15, 15, 12, 12, 0 ], [ 0, 0, 8, 0, 0, 0, 0, 48 ], [ 0, 0, 8, 0, 0, 0, 0, 48 ], [ 0, 0, 2, 0, 0, 12, 12, 30 ], [ 0, 0, 2, 0, 0, 12, 12, 30 ], [ 0, 0, 0, 4, 4, 8, 8, 32 ] ], [ [ 0, 0, 0, 105, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 105, 0, 0, 0 ], [ 0, 0, 15, 0, 0, 0, 0, 90 ], [ 1, 0, 0, 12, 12, 0, 32, 48 ], [ 0, 1, 0, 12, 12, 32, 0, 48 ], [ 0, 0, 0, 0, 10, 30, 5, 60 ], [ 0, 0, 0, 10, 0, 5, 30, 60 ], [ 0, 0, 4, 4, 4, 16, 16, 61 ] ], [ [ 0, 0, 0, 0, 105, 0, 0, 0 ], [ 0, 0, 0, 105, 0, 0, 0, 0 ], [ 0, 0, 15, 0, 0, 0, 0, 90 ], [ 0, 1, 0, 12, 12, 32, 0, 48 ], [ 1, 0, 0, 12, 12, 0, 32, 48 ], [ 0, 0, 0, 10, 0, 5, 30, 60 ], [ 0, 0, 0, 0, 10, 30, 5, 60 ], [ 0, 0, 4, 4, 4, 16, 16, 61 ] ], [ [ 0, 0, 0, 0, 0, 336, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 336, 0 ], [ 0, 0, 12, 0, 0, 72, 72, 180 ], [ 0, 0, 0, 0, 32, 96, 16, 192 ], [ 0, 0, 0, 32, 0, 16, 96, 192 ], [ 1, 0, 12, 30, 5, 12, 96, 180 ], [ 0, 1, 12, 5, 30, 96, 12, 180 ], [ 0, 0, 8, 16, 16, 48, 48, 200 ] ], [ [ 0, 0, 0, 0, 0, 0, 336, 0 ], [ 0, 0, 0, 0, 0, 336, 0, 0 ], [ 0, 0, 12, 0, 0, 72, 72, 180 ], [ 0, 0, 0, 32, 0, 16, 96, 192 ], [ 0, 0, 0, 0, 32, 96, 16, 192 ], [ 0, 1, 12, 5, 30, 96, 12, 180 ], [ 1, 0, 12, 30, 5, 12, 96, 180 ], [ 0, 0, 8, 16, 16, 48, 48, 200 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 1260 ], [ 0, 0, 0, 0, 0, 0, 0, 1260 ], [ 0, 0, 0, 90, 90, 180, 180, 720 ], [ 0, 0, 48, 48, 48, 192, 192, 732 ], [ 0, 0, 48, 48, 48, 192, 192, 732 ], [ 0, 0, 30, 60, 60, 180, 180, 750 ], [ 0, 0, 30, 60, 60, 180, 180, 750 ], [ 1, 1, 32, 61, 61, 200, 200, 704 ] ] ] ), rec( name := "HS.2", sbgname := "A8x2 leq A8.2x2", filename := "A8x2", degree := 2200, rank := 8, permchar := "1a^+ + 22a^+ + 77a^+ + 154a^+bc + 175a^+ + 693a^+ + 770a^+" , charnmbs := [ 1, 3, 5, 7, 9, 10, 14, 16 ], ctbl := [ [ 1, 1, 56, 105, 105, 336, 336, 1260 ], [ 1, -1, 0, -35, 35, -112, 112, 0 ], [ 1, 1, -24, 25, 25, 16, 16, -60 ], [ 1, 1, 16, 15, 15, -24, -24, 0 ], [ 1, -1, 0, 15, -15, -12, 12, 0 ] , [ 1, 1, 12, -5, -5, 28, 28, -60 ], [ 1, 1, -4, -5, -5, -4, -4, 20 ], [ 1, -1, 0, -5, 5, 8, -8, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 56, 0, 0, 0, 0, 0 ], [ 0, 0, 56, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 15, 15, 12, 12, 0 ], [ 0, 0, 8, 0, 0, 0, 0, 48 ], [ 0, 0, 8, 0, 0, 0, 0, 48 ], [ 0, 0, 2, 0, 0, 12, 12, 30 ], [ 0, 0, 2, 0, 0, 12, 12, 30 ], [ 0, 0, 0, 4, 4, 8, 8, 32 ] ], [ [ 0, 0, 0, 105, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 105, 0, 0, 0 ], [ 0, 0, 15, 0, 0, 0, 0, 90 ], [ 1, 0, 0, 12, 12, 0, 32, 48 ], [ 0, 1, 0, 12, 12, 32, 0, 48 ], [ 0, 0, 0, 0, 10, 5, 30, 60 ], [ 0, 0, 0, 10, 0, 30, 5, 60 ], [ 0, 0, 4, 4, 4, 16, 16, 61 ] ], [ [ 0, 0, 0, 0, 105, 0, 0, 0 ], [ 0, 0, 0, 105, 0, 0, 0, 0 ], [ 0, 0, 15, 0, 0, 0, 0, 90 ], [ 0, 1, 0, 12, 12, 32, 0, 48 ], [ 1, 0, 0, 12, 12, 0, 32, 48 ], [ 0, 0, 0, 10, 0, 30, 5, 60 ], [ 0, 0, 0, 0, 10, 5, 30, 60 ], [ 0, 0, 4, 4, 4, 16, 16, 61 ] ], [ [ 0, 0, 0, 0, 0, 336, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 336, 0 ], [ 0, 0, 12, 0, 0, 72, 72, 180 ], [ 0, 0, 0, 0, 32, 16, 96, 192 ], [ 0, 0, 0, 32, 0, 96, 16, 192 ], [ 1, 0, 12, 5, 30, 12, 96, 180 ], [ 0, 1, 12, 30, 5, 96, 12, 180 ], [ 0, 0, 8, 16, 16, 48, 48, 200 ] ], [ [ 0, 0, 0, 0, 0, 0, 336, 0 ], [ 0, 0, 0, 0, 0, 336, 0, 0 ], [ 0, 0, 12, 0, 0, 72, 72, 180 ], [ 0, 0, 0, 32, 0, 96, 16, 192 ], [ 0, 0, 0, 0, 32, 16, 96, 192 ], [ 0, 1, 12, 30, 5, 96, 12, 180 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240, 0, 288, 0, 0, 468 ], [ 0, 0, 8, 0, 0, 24, 0, 28, 0, 116, 0, 128, 0, 320, 0, 272, 448, 0 ], [ 0, 0, 0, 8, 24, 0, 28, 0, 116, 0, 128, 0, 272, 0, 320, 0, 0, 448 ], [ 0, 0, 12, 0, 0, 6, 0, 48, 0, 96, 0, 144, 0, 240, 0, 288, 510, 0 ], [ 0, 0, 0, 12, 6, 0, 48, 0, 96, 0, 144, 0, 288, 0, 240, 0, 0, 510 ], [ 0, 0, 6, 0, 0, 15, 0, 30, 0, 102, 0, 144, 0, 288, 0, 318, 441, 0 ], [ 0, 0, 0, 12, 24, 0, 36, 0, 120, 0, 120, 0, 288, 0, 312, 0, 0, 432 ], [ 0, 0, 12, 0, 0, 24, 0, 36, 0, 120, 0, 120, 0, 312, 0, 288, 432, 0 ], [ 0, 0, 0, 6, 15, 0, 30, 0, 102, 0, 144, 0, 318, 0, 288, 0, 0, 441 ], [ 0, 1, 0, 8, 28, 0, 39, 0, 112, 0, 170, 0, 294, 0, 288, 0, 0, 404 ], [ 1, 0, 8, 0, 0, 28, 0, 39, 0, 112, 0, 170, 0, 288, 0, 294, 404, 0 ] ] ] ), rec( name := "HS.2", sbgname := "M11", degree := 11200, rank := 17, permchar := "1a^{+-} + 22a^{+-} + 77a^{+-} + 154bc + 175a^{+-} + 770a^{+-} + 825a^{\ +-} + 1056a^{+-} + 2520a^{+-}", charnmbs := [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 16, 17, 19, 20, 22, 23, 34, 35 ], ctbl 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54, 0, 0, 96, 156, 0, 0, 246, 348, 0, 456, 0, 618, 0 ], [ 0, 0, 0, 40, 0, 0, 130, 140, 0, 0, 230, 200, 0, 520, 0, 720, 0 ], [ 0, 0, 20, 0, 64, 20, 0, 0, 192, 208, 0, 0, 272, 0, 368, 0, 836 ], [ 0, 0, 27, 0, 48, 90, 0, 0, 156, 216, 0, 0, 240, 0, 528, 0, 675 ], [ 0, 3, 0, 27, 0, 0, 123, 138, 0, 0, 240, 276, 0, 450, 0, 723, 0 ], [ 0, 5, 0, 15, 0, 0, 145, 100, 0, 0, 230, 330, 0, 390, 0, 765, 0 ], [ 0, 0, 25, 0, 50, 50, 0, 0, 170, 200, 0, 0, 270, 0, 460, 0, 755 ], [ 0, 3, 0, 51, 0, 0, 114, 156, 0, 0, 225, 234, 0, 522, 0, 675, 0 ], [ 0, 0, 18, 0, 36, 66, 0, 0, 138, 264, 0, 0, 276, 0, 498, 0, 684 ], [ 0, 6, 0, 42, 0, 0, 103, 144, 0, 0, 241, 306, 0, 450, 0, 688, 0 ], [ 1, 0, 18, 0, 49, 60, 0, 0, 209, 225, 0, 0, 302, 0, 456, 0, 660 ] ] ] ), rec( name := "HS.2", sbgname := "4.2^4:S5 leq 2^{1+6}_+:S5", filename := "4.2^4:S5", degree := 11550, rank := 18, permchar := "1a^{+-} + 77a^{+-} + 154a^{+-} + 175a^{+-} + 693a^{+-} + 825a^{+-} + 1\ 056a^{+-} + 1386a^{+-} + 1408a^{+-}", charnmbs := [ 1, 2, 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0, 32, 184, 0, 248, 0, 318, 0, 0, 540, 544, 0 ], [ 0, 1, 0, 16, 0, 37, 32, 0, 0, 184, 0, 248, 0, 318, 540, 0, 0, 544 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1920 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1920, 0 ], [ 0, 0, 0, 0, 0, 0, 128, 0, 0, 128, 0, 64, 0, 320, 256, 0, 0, 1024 ], [ 0, 0, 0, 0, 0, 0, 0, 128, 128, 0, 64, 0, 320, 0, 0, 256, 1024, 0 ], [ 0, 0, 0, 0, 0, 24, 48, 0, 0, 144, 0, 120, 0, 312, 384, 0, 0, 888 ], [ 0, 0, 0, 0, 24, 0, 0, 48, 144, 0, 120, 0, 312, 0, 0, 384, 888, 0 ], [ 0, 0, 30, 0, 30, 0, 0, 0, 240, 0, 240, 0, 300, 0, 0, 600, 480, 0 ], [ 0, 0, 0, 30, 0, 30, 0, 0, 0, 240, 0, 240, 0, 300, 600, 0, 0, 480 ], [ 0, 0, 0, 8, 0, 24, 64, 0, 0, 136, 0, 192, 0, 328, 432, 0, 0, 736 ], [ 0, 0, 8, 0, 24, 0, 0, 64, 136, 0, 192, 0, 328, 0, 0, 432, 736, 0 ], [ 0, 0, 0, 3, 0, 15, 48, 0, 0, 144, 0, 168, 0, 306, 492, 0, 0, 744 ], [ 0, 0, 3, 0, 15, 0, 0, 48, 144, 0, 168, 0, 306, 0, 0, 492, 744, 0 ], [ 0, 0, 0, 10, 0, 26, 40, 0, 0, 164, 0, 204, 0, 328, 512, 0, 0, 636 ], [ 0, 0, 10, 0, 26, 0, 0, 40, 164, 0, 204, 0, 328, 0, 0, 512, 636, 0 ], [ 0, 0, 5, 0, 20, 0, 0, 50, 135, 0, 205, 0, 320, 0, 0, 510, 675, 0 ], [ 0, 0, 0, 5, 0, 20, 50, 0, 0, 135, 0, 205, 0, 320, 510, 0, 0, 675 ], [ 0, 1, 0, 16, 0, 37, 32, 0, 0, 184, 0, 248, 0, 318, 540, 0, 0, 544 ], [ 1, 0, 16, 0, 37, 0, 0, 32, 184, 0, 248, 0, 318, 0, 0, 540, 544, 0 ] ] ] ), rec( name := "HS.2", sbgname := "2^{1+6}_+:S5", filename := "2_+^1+6:S5", degree := 5775, rank := 9, permchar := "1a^+ + 77a^+ + 154a^+ + 175a^+ + 693a^+ + 825a^+ + 1056a^+ + 1386a^- +\ 1408a^+", charnmbs := [ 1, 5, 7, 10, 14, 19, 22, 25, 26 ], ctbl := [ [ 1, 30, 80, 128, 480, 640, 960, 1536, 1920 ], [ 1, 15, 20, -32, 60, 80, 0, 96, -240 ], [ 1, 15, 20, 8, 60, -20, 0, -144, 60 ], [ 1, -3, 14, 40, -48, 68, 36, -48, -60 ], [ 1, 5, -10, 8, 0, 20, -60, 16, 20 ], [ 1, 7, 4, 0, -28, -32, 16, 32, 0 ], [ 1, -5, 10, -12, -10, 10, -20, -4, 30 ], [ 1, -5, 0, 8, 20, -20, 0, 16, -20 ], [ 1, 0, -10, -7, 0, 10, 30, -24, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 30, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 5, 8, 0, 16, 0, 0, 0, 0 ], [ 0, 3, 3, 0, 12, 0, 12, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 30 ], [ 0, 1, 2, 0, 7, 8, 4, 0, 8 ], [ 0, 0, 0, 0, 6, 6, 3, 12, 3 ], [ 0, 0, 1, 0, 2, 2, 7, 8, 10 ], [ 0, 0, 0, 0, 0, 5, 5, 15, 5 ], [ 0, 0, 0, 2, 2, 1, 5, 4, 16 ] ], [ [ 0, 0, 80, 0, 0, 0, 0, 0, 0 ], [ 0, 8, 8, 0, 32, 0, 32, 0, 0 ], [ 1, 3, 4, 0, 12, 24, 12, 0, 24 ], [ 0, 0, 0, 10, 0, 10, 30, 0, 30 ], [ 0, 2, 2, 0, 16, 8, 12, 16, 24 ], [ 0, 0, 3, 2, 6, 15, 15, 24, 15 ], [ 0, 1, 1, 4, 6, 10, 8, 24, 26 ], [ 0, 0, 0, 0, 5, 10, 15, 30, 20 ], [ 0, 0, 1, 2, 6, 5, 13, 16, 37 ] ], [ [ 0, 0, 0, 128, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 128 ], [ 0, 0, 0, 16, 0, 16, 48, 0, 48 ], [ 1, 0, 10, 13, 0, 50, 30, 24, 0 ], [ 0, 0, 0, 0, 16, 0, 16, 32, 64 ], [ 0, 0, 2, 10, 0, 20, 24, 24, 48 ], [ 0, 0, 4, 4, 8, 16, 24, 32, 40 ], [ 0, 0, 0, 2, 10, 10, 20, 36, 50 ], [ 0, 2, 2, 0, 16, 16, 20, 40, 32 ] ], [ [ 0, 0, 0, 0, 480, 0, 0, 0, 0 ], [ 0, 16, 32, 0, 112, 128, 64, 0, 128 ], [ 0, 12, 12, 0, 96, 48, 72, 96, 144 ], [ 0, 0, 0, 0, 60, 0, 60, 120, 240 ], [ 1, 7, 16, 16, 48, 56, 88, 112, 136 ], [ 0, 6, 6, 0, 42, 48, 78, 156, 144 ], [ 0, 2, 6, 8, 44, 52, 76, 128, 164 ], [ 0, 0, 5, 10, 35, 65, 80, 150, 135 ], [ 0, 2, 6, 16, 34, 48, 82, 108, 184 ] ], [ [ 0, 0, 0, 0, 0, 640, 0, 0, 0 ], [ 0, 0, 0, 0, 128, 128, 64, 256, 64 ], [ 0, 0, 24, 16, 48, 120, 120, 192, 120 ], [ 0, 0, 10, 50, 0, 100, 120, 120, 240 ], [ 0, 8, 8, 0, 56, 64, 104, 208, 192 ], [ 1, 6, 15, 20, 48, 88, 114, 180, 168 ], [ 0, 2, 10, 16, 52, 76, 120, 160, 204 ], [ 0, 5, 10, 10, 65, 75, 100, 170, 205 ], [ 0, 1, 5, 16, 48, 56, 102, 164, 248 ] ], [ [ 0, 0, 0, 0, 0, 0, 960, 0, 0 ], [ 0, 0, 32, 0, 64, 64, 224, 256, 320 ], [ 0, 12, 12, 48, 72, 120, 96, 288, 312 ], [ 0, 0, 30, 30, 60, 120, 180, 240, 300 ], [ 0, 4, 12, 16, 88, 104, 152, 256, 328 ], [ 0, 3, 15, 24, 78, 114, 180, 240, 306 ], [ 1, 7, 8, 24, 76, 120, 140, 256, 328 ], [ 0, 5, 15, 20, 80, 100, 160, 260, 320 ], [ 0, 5, 13, 20, 82, 102, 164, 256, 318 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 1536, 0 ], [ 0, 0, 0, 0, 0, 256, 256, 768, 256 ], [ 0, 0, 0, 0, 96, 192, 288, 576, 384 ], [ 0, 0, 0, 24, 120, 120, 240, 432, 600 ], [ 0, 0, 16, 32, 112, 208, 256, 480, 432 ], [ 0, 12, 24, 24, 156, 180, 240, 408, 492 ], [ 0, 8, 24, 32, 128, 160, 256, 416, 512 ], [ 1, 15, 30, 36, 150, 170, 260, 364, 510 ], [ 0, 4, 16, 40, 108, 164, 256, 408, 540 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1920 ], [ 0, 0, 0, 128, 128, 64, 320, 256, 1024 ], [ 0, 0, 24, 48, 144, 120, 312, 384, 888 ], [ 0, 30, 30, 0, 240, 240, 300, 600, 480 ], [ 0, 8, 24, 64, 136, 192, 328, 432, 736 ], [ 0, 3, 15, 48, 144, 168, 306, 492, 744 ], [ 0, 10, 26, 40, 164, 204, 328, 512, 636 ], [ 0, 5, 20, 50, 135, 205, 320, 510, 675 ], [ 1, 16, 37, 32, 184, 248, 318, 540, 544 ] ] ] ), rec( name := "HS.2", sbgname := "L3(4).2_3 leq L3(4).2^2", filename := "L34.2_3", degree := 2200, rank := 9, permchar := "1a^+ + 22a^{+-} + 77a^{+-} + 175a^+ + 231a^- + 770a^- + 825a^+", charnmbs := [ 1, 3, 4, 5, 6, 10, 13, 17, 19 ], ctbl := [ [ 1, 1, 42, 42, 105, 105, 560, 672, 672 ], [ 1, 1, 12, 12, -45, -45, 160, -48, -48 ], [ 1, -1, -28, 28, -35, 35, 0, -112, 112 ], [ 1, 1, 22, 22, 5, 5, -40, -8, -8 ], [ 1, -1, -18, 18, 15, -15, 0, 48, -48 ], [ 1, 1, -2, -2, 17, 17, 32, -32, -32 ], [ 1, -1, 2, -2, 15, -15, 0, -32, 32 ], [ 1, -1, 2, -2, -5, 5, 0, 8, -8 ], [ 1, 1, -2, -2, -3, -3, -8, 8, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 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[ 0, 1, 8, 0, 0, 0, 64, 32, 0 ], [ 0, 0, 0, 0, 12, 12, 9, 36, 36 ], [ 0, 0, 0, 5, 0, 5, 30, 30, 35 ], [ 0, 0, 5, 0, 5, 0, 30, 35, 30 ] ], [ [ 0, 0, 0, 0, 0, 105, 0, 0, 0 ], [ 0, 0, 0, 0, 105, 0, 0, 0, 0 ], [ 0, 0, 5, 0, 20, 0, 0, 80, 0 ], [ 0, 0, 0, 5, 0, 20, 0, 0, 80 ], [ 0, 1, 8, 0, 0, 0, 64, 32, 0 ], [ 1, 0, 0, 8, 0, 0, 64, 0, 32 ], [ 0, 0, 0, 0, 12, 12, 9, 36, 36 ], [ 0, 0, 5, 0, 5, 0, 30, 35, 30 ], [ 0, 0, 0, 5, 0, 5, 30, 30, 35 ] ], [ [ 0, 0, 0, 0, 0, 0, 560, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 560, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 240, 160, 160 ], [ 0, 0, 0, 0, 0, 0, 240, 160, 160 ], [ 0, 0, 0, 0, 64, 64, 48, 192, 192 ], [ 0, 0, 0, 0, 64, 64, 48, 192, 192 ], [ 1, 1, 18, 18, 9, 9, 216, 144, 144 ], [ 0, 0, 10, 10, 30, 30, 120, 180, 180 ], [ 0, 0, 10, 10, 30, 30, 120, 180, 180 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 672, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 672 ], [ 0, 0, 0, 16, 0, 80, 160, 96, 320 ], [ 0, 0, 16, 0, 80, 0, 160, 320, 96 ], [ 0, 0, 0, 32, 0, 32, 192, 192, 224 ], [ 0, 0, 32, 0, 32, 0, 192, 224, 192 ], [ 0, 0, 12, 12, 36, 36, 144, 216, 216 ], [ 1, 0, 6, 20, 30, 35, 180, 180, 220 ], [ 0, 1, 20, 6, 35, 30, 180, 220, 180 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 672 ], [ 0, 0, 0, 0, 0, 0, 0, 672, 0 ], [ 0, 0, 16, 0, 80, 0, 160, 320, 96 ], [ 0, 0, 0, 16, 0, 80, 160, 96, 320 ], [ 0, 0, 32, 0, 32, 0, 192, 224, 192 ], [ 0, 0, 0, 32, 0, 32, 192, 192, 224 ], [ 0, 0, 12, 12, 36, 36, 144, 216, 216 ], [ 0, 1, 20, 6, 35, 30, 180, 220, 180 ], [ 1, 0, 6, 20, 30, 35, 180, 180, 220 ] ] ] ), rec( name := "HS.2", sbgname := "5^{1+2}_+:[2^5]", filename := "5_+^1+2:2^5", degree := 22176, rank := 15, permchar := "1a^+ + 175a^{+-} + 693a^+ + 825a^+ + 896ab + 1056a^+ + 1386a^- + 1408a\ ^+ + 1750a^- + 1925a^- + 2520a^{+-} + 2750a^- + 3200a^-", charnmbs := [ 1, 10, 11, 14, 19, 21, 22, 25, 26, 29, 31, 34, 35, 37, 39 ], ctbl := [ [ 1, 50, 125, 250, 250, 500, 1000, 1000, 1000, 2000, 2000, 2000, 4000, 4000, 4000 ], [ 1, 6, -7, 118, 30, 60, -56, 120, 32, -112, -112, -112, 128, 128, -224 ], [ 1, -6, 5, 130, -30, -60, 40, -120, -40, 80, 80, 80, -160, -160, 160 ], [ 1, 14, -7, -2, 30, 12, 72, -40, 32, 16, 16, 80, 64, -128, -160 ], [ 1, 6, 13, -2, 10, 60, -56, -40, -8, 48, -112, 48, -32, -32, 96 ], [ 1, 9, 8, -2, 0, -18, 37, 45, -58, -34, -34, 20, -16, 2, 40 ], [ 1, -6, 13, -2, 40, -18, -8, 20, -8, 96, 26, -30, -116, 52, -60 ], [ 1, 14, 13, -2, -10, -8, -8, 0, 72, -24, 36, -60, -56, -8, 40 ], [ 1, -1, -22, -2, 10, 32, 7, -5, -8, -64, 56, 20, -116, 52, 40 ], [ 1, -2, -3, -2, -22, 4, -40, 56, 8, 32, 32, 64, -16, -64, -48 ], [ 1, -10, 5, -2, -14, -4, 40, -8, 40, -16, -64, 32, -32, 64, -32 ], [ 1, -6, 3*E(5)-9*E(5)^2-9*E(5)^3+3*E(5)^4, -2, -2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4, -8*E(5)-16*E(5)^2-16*E(5)^3-8*E(5)^4, -16*E(5)-8*E(5)^2-8*E(5)^3-16*E(5)^4, -8*E(5)+8*E(5)^2+8*E(5)^3-8*E(5)^4, 16*E(5)^2+16*E(5)^3, -8*E(5)+16*E(5)^2+16*E(5)^3-8*E(5)^4, -32*E(5)^2-32*E(5)^3, 48*E(5)+32*E(5)^2+32*E(5)^3+48*E(5)^4, -40*E(5)-48*E(5)^2-48*E(5)^3-40*E(5)^4, 64*E(5)+32*E(5)^2+32*E(5)^3+64*E(5)^4, -40*E(5)-40*E(5)^4 ], [ 1, -6, -9*E(5)+3*E(5)^2+3*E(5)^3-9*E(5)^4, -2, 2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4, -16*E(5)-8*E(5)^2-8*E(5)^3-16*E(5)^4, -8*E(5)-16*E(5)^2-16*E(5)^3-8*E(5)^4, 8*E(5)-8*E(5)^2-8*E(5)^3+8*E(5)^4, 16*E(5)+16*E(5)^4, 16*E(5)-8*E(5)^2-8*E(5)^3+16*E(5)^4, -32*E(5)-32*E(5)^4, 32*E(5)+48*E(5)^2+48*E(5)^3+32*E(5)^4, -48*E(5)-40*E(5)^2-40*E(5)^3-48*E(5)^4, 32*E(5)+64*E(5)^2+64*E(5)^3+32*E(5)^4, -40*E(5)^2-40*E(5)^3 ], [ 1, -2, -3, -2, 14, -32, -40, -16, 8, -40, -4, 28, 56, 8, 24 ], [ 1, 5, -10, -2, -14, -4, -5, -23, -20, 44, -4, -28, 28, 64, -32 ] ] , mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], 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