## Conway graph on 1408 vertices ## Second subconstituent of the Conway graph on 2300 vertices ## Unique rank-3 SRG(1408,567,246,216) ## Aut. group PSU(6,2):2 conway1408:=EdgeOrbitsGraph(Group([ ( 1, 604, 387, 159, 530, 845,1307, 207, 324, 390, 981, 263)( 2, 722,1303, 606, 570, 155, 183, 156, 411, 659, 221,1126)( 3,1252,1186,1194,1195, 104, 655, 494, 114, 720, 217, 34)( 4,1384,1167, 234, 839,1079,1124,1321,1210, 431, 415, 507)( 5, 795, 571, 1380, 813, 75, 6,1184,1300, 681, 599, 757)( 7, 601,1273, 556, 266,1295, 593,1026, 303, 218,1149, 940)( 8,1254,1053,1306,1390, 400,1017, 460, 235, 858, 723, 637) ( 9, 751, 760, 721, 976, 988, 875, 978, 61,1038, 749, 50)( 10, 381, 679, 613, 252, 622,1239, 237,1193,1381, 225, 832)( 11, 446,1280,1144, 939, 51, 509, 100, 92, 423, 296,1201)( 12, 628, 26,1142, 954,1387,1238,1308, 834, 651, 204,1368)( 13, 88,1102, 152, 59,1100, 642, 490, 820,1130, 38, 818)( 14, 656,1147, 436, 54,1369,1197,1103, 1036,1400, 959,1389)( 15, 527, 805, 384,1040, 883,1021, 339, 590,1221, 705,1114) ( 16, 977,1025, 764, 881,1145, 455, 638, 350,1007, 842, 782)( 17, 180, 620, 258,1407, 735, 396, 542, 226, 35, 149, 312)( 18, 506, 172, 108, 539, 796, 602, 956, 167, 554, 1251,1332)( 19, 793,1214,1243, 372,1247, 691, 158,1215, 119, 190,1262)( 20,1158,1324, 341,1119, 896, 304, 823, 193,1034, 535,1204)( 21,1281,1000,1181, 667,1109, 215, 987, 208, 660,1330, 229)( 22, 41, 854, 72, 43, 254, 105, 770,1121, 65, 709, 214) ( 23, 775, 378, 427, 31,1146, 70, 279, 811, 970, 177, 318)( 24, 953,1043, 121, 321, 1152, 281, 951,1045, 739, 366, 452)( 25, 362, 403,1218, 139, 209,1253, 991,1135, 173, 885, 784)( 27, 675, 761, 320,1106, 573, 389, 439, 863,1372,1297, 127)( 28,1156, 408, 1006, 967,1316, 562, 549,1117, 762,1039, 972)( 29, 892, 203, 162, 558, 311, 767, 611, 594, 328, 375, 596)( 30, 308,1282, 765,1001, 325, 306,1086, 171, 216, 404, 338) ( 32, 333, 46, 521,1256, 833, 449, 63, 364, 299,1335, 148)( 33, 912, 242,1405, 798, 1246, 698, 641, 240, 432, 322, 336)( 36,1219,1392,1348, 79, 750,1095, 290, 993, 688, 1312, 870)( 37, 807,1020, 476,1054, 859, 461, 222, 230,1227, 116,1048)( 39,1183,1402, 271, 53, 580, 809, 246, 728,1315,1096, 752)( 40, 756,1050, 724, 453, 836, 126, 541, 205, 87, 543, 398)( 42,1134, 365, 669, 998, 644, 682, 374, 627, 438, 206, 397) ( 44, 819, 344, 175, 582, 420, 102, 241, 422,1188, 789, 497)( 45, 161, 671, 371, 921, 1382, 363, 141, 670,1140, 754, 525)( 47, 646, 867,1344, 485, 734,1322, 612, 248, 445, 914, 243)( 48, 388, 557, 251, 123, 331, 512,1377, 213, 633,1378, 947)( 49,1022,1091, 268, 783, 629,1341, 835, 589, 178,1176, 591)( 52,1350, 922, 353, 528, 470, 692, 90, 518, 882, 474, 450)( 55,1179,1370, 690,1098, 958,1361, 83, 963,1061, 170,1122) ( 56,1168, 714, 115, 986,1015, 113,1166, 380,1171, 471,1287)( 57, 373, 211,1270, 980, 814, 467, 652, 785, 478, 887,1137)( 58, 910, 711, 665, 715,1185, 680, 568, 712, 926, 815, 469)( 60, 614, 719, 473, 487, 232,1269,1084, 861, 974,1163,1019)( 62, 879, 504, 480, 786,1073, 201, 864, 560, 462, 150, 982)( 64,1379, 269, 200, 192, 585, 699, 989, 249, 700, 283, 228)( 66,1240, 515,1291,1320,1267,1367, 555,1206, 825, 492, 685) ( 67, 672,1279, 741, 942, 792, 95, 273,1198, 768,1265, 794)( 68, 513, 293, 827,1346, 289,1383,1065, 529,1292, 514,1220)( 69, 135, 164, 71,1376, 166,1205, 624,1062, 965, 931,1191)( 73, 418, 496,1169, 846, 181, 938, 393, 145, 74, 346,1087)( 76, 803, 615, 937, 428,1118,1170, 597, 816, 107, 394,1164)( 77,1127, 125,1355,1260,1165,1051,1129, 1052, 112, 964, 666)( 78,1235, 188, 830,1301, 219,1257, 272, 414,1143,1107, 893) ( 80, 305,1058,1261,1136,1175, 853, 359, 227, 566,1248,1030)( 81, 329, 717, 984, 923, 909, 85, 327, 817,1172, 943,1088)( 82, 841, 352, 133,1406, 840, 122, 426, 716, 886, 1319, 545)( 84, 979,1298, 906, 544,1385, 124, 635, 406, 189, 610, 769)( 86, 781,1294, 367,1343, 261, 540, 523,1029,1055,1010, 310)( 89, 733, 945, 806, 856,1264, 369,1310, 1028,1070,1066,1328)( 91, 174, 822, 639, 932, 391,1046, 169, 790, 755, 928, 569) ( 93,1360, 109,1278, 592, 927, 457,1271,1060, 537, 898,1342)( 94,1394, 186, 110, 382, 184, 511, 933, 788, 284, 625, 572)( 96, 465,1228, 674, 676, 430, 197, 288,1245,1047, 1174, 952)( 97, 522,1311, 574,1005, 356, 129, 524, 726, 944,1232, 354)( 98,1160, 351, 1334, 916, 358, 195, 538, 583, 298, 536, 894)( 99, 701,1305, 440,1356, 860) ( 101, 276, 202,1396, 516, 900, 199, 468, 799, 773, 661, 911)( 103, 657, 929, 663, 899, 1314,1363,1234, 434, 824,1139,1004)( 106, 111, 664, 851,1336, 307,1202, 277,1093, 584, 1386,1403)( 117,1275,1067, 808,1035, 392,1002,1069, 598,1362, 678, 157)( 118, 386, 264, 437,1018, 687,1189, 897, 355, 668,1141, 286)( 120, 621, 134,1153,1284, 531, 433, 244, 780,1329,1223, 368)( 128,1345, 458, 236, 383, 645,1056, 710, 746, 983,1318, 559) ( 130, 742, 479, 132, 581,1373, 828, 483, 771, 631,1132, 703)( 131, 731, 250, 962, 797, 379,1108, 265, 576,1216,1178, 253)( 136, 730,1296, 550, 607,1289, 561, 634, 231, 533, 917,1340)( 137, 985, 245,1008, 182, 623, 968, 220, 738, 971, 779, 865)( 138, 725, 313, 451, 147, 609, 918, 502, 777,1217,1085,1080)( 140, 267,1255,1397, 997, 285, 233, 801, 294, 326, 565,1353)( 142, 349, 441, 888, 935, 877, 763, 435, 936, 517, 857, 643) ( 143, 729, 323,1323, 992, 247, 274, 493, 587, 444, 930, 270)( 144, 708,1208, 466, 292, 1230,1213, 146, 961, 772, 774, 454)( 151, 800, 401,1366, 802,1401)( 153, 475,1326,1154, 477,1285)( 154, 302, 334,1283, 626, 278, 718, 766, 280, 880, 262, 662)( 160,1063,1150, 1057, 852, 575, 459, 871, 946,1277,1090, 187)( 163,1037, 402, 194, 198, 707) ( 165, 753, 617,1209, 632,1272, 176,1133, 904, 196,1157,1116)( 168, 745, 616,1371,1115, 481,1268, 694, 876,1233, 810, 740)( 179, 347,1031,1276)( 185, 995, 960, 499, 370,1151, 1033,1229,1097,1352, 256,1364)( 191, 630, 501,1032, 588, 534,1325,1159, 223,1044, 791, 990)( 210,1309,1211)( 212,1192, 758, 838, 684, 787, 600, 510,1226, 862,1190, 759) ( 224, 564, 443, 737,1250,1313, 618,1138,1359, 360, 495,1187)( 238, 508,1131, 702, 866, 315, 969, 650, 837,1003,1083,1099)( 239,1014,1339, 878, 482,1331, 895, 342,1011, 908, 1111, 924)( 255, 608, 890, 697, 996,1302, 693, 919, 407, 889,1110,1222)( 257, 412, 472, 579, 419, 901,1113, 447,1041, 605, 489, 425)( 259, 416,1374,1293, 913,1258, 491, 957, 337,1027,1112, 385)( 260, 975)( 275,1104,1094, 551, 532, 553,1290, 498, 442, 503, 872, 505)( 282,1092, 821, 330, 376, 399, 332, 316, 829, 736,1199, 915)( 287, 297, 520,1225, 1404,1101,1327, 713,1375, 706,1263,1304)( 291,1354, 603, 934,1388,1120)( 295, 448, 464, 973)( 300, 526, 424)( 301,1012, 619, 826, 567,1082,1076,1074, 903, 941, 395, 484) ( 309, 636,1081, 519, 578,1317, 417,1357, 405, 486, 843, 966)( 314, 500, 874,1224) ( 317,1155, 844, 409, 920, 488, 357, 812, 377, 319, 686, 658)( 335,1286, 999, 948,1398, 1274)( 340,1338, 869, 673)( 343, 683,1105, 345,1009,1049, 552,1337,1023,1068,1333, 925) ( 348, 884,1177, 563,1249,1071, 848,1299,1259, 695, 778,1148)( 361, 868,1128,1013, 677, 1288, 891, 410, 413,1123,1365,1125)( 421,1042, 748, 640,1196, 647, 586,1077, 648, 649, 1347, 595)( 429,1231, 950,1203)( 456,1207,1075, 949)( 463,1089,1180,1358, 850,1393, 1059,1016,1182,1349, 905, 689)( 546, 847,1173,1351, 744, 548)( 547, 804, 907, 704,1399, 831)( 577,1266,1244)( 653,1200)( 654,1391,1162, 849, 747,1024, 902,1408,1161, 696,1078, 743)( 727,1242,1212,1072)( 732, 855,1241,1064)( 776,1395, 994)( 873,1237, 955,1236), ( 1,1250, 436, 912, 989, 931, 584,1153,1030, 409)( 2,1200, 842, 865, 770, 784,1295, 1043, 533, 229)( 3,1271, 465, 526,1307, 544, 518, 59, 967, 382)( 4, 952, 180, 503, 1057, 523, 307, 275, 398, 832)( 5,1405, 689,1104,1229)( 6, 14,1135,1382, 385, 884, 1074, 507, 71, 415)( 7, 834, 235,1267, 148, 857, 554, 196, 263,1223)( 8, 265, 944, 562, 279, 280, 452,1148, 653,1128)( 9, 243, 822, 464, 17,1323, 304, 546, 287,1242) ( 10, 830, 652,1338,1139)( 11,1017,1056,1158, 752,1190, 902, 751,1309, 695) ( 12, 974, 472,1095, 599, 985, 220,1279, 158,1202)( 13,1145,1090, 192, 43) ( 15, 188,1167, 690,1188, 890, 960,1345, 473,1329)( 16, 532,1134, 940,1383) ( 18, 702, 217, 594,1189, 685, 876,1224, 821, 517)( 19, 674,1285,1280,1365, 342,1341, 586,1063, 691)( 20,1130, 904, 397, 921, 669, 694, 144,1201, 827)( 21, 686, 820, 189, 1010, 330,1112,1232,1001, 869)( 22,1133,1068,1215, 170, 683, 885,1255, 50, 745) ( 23, 962,1401, 900, 441)( 24,1391,1091, 999, 454, 295, 431, 111, 769, 980) ( 25, 181, 399, 434,1393,1161, 369, 706,1041, 169)( 26, 331,1120,1281,1404) ( 27,1227, 930,1346, 581, 658,1321, 794,1037,1086)( 28,1009, 48, 856, 514) ( 29, 267, 227, 577, 347,1060, 362,1193, 555,1252)( 30,1064, 806, 335,1381, 412,1083, 671, 236, 214)( 31, 115, 388, 767, 624,1079,1044, 370, 659, 487)( 32,1275, 897, 440, 887)( 33, 448, 917, 489,1377)( 34,1257, 413, 377, 137, 308, 836, 183,1013, 636) ( 35, 455, 365, 318,1376)( 36, 656, 948, 356,1175, 838, 693, 638, 757, 150) ( 37, 51, 102, 650, 264, 986,1236, 878,1353, 316)( 38, 494,1240, 321, 722) ( 39, 620, 94, 232, 578, 522,1156, 813,1085,1356)( 40, 154, 139,1373, 969) ( 41, 804,1324, 715,1277, 939, 392,1105, 256, 779)( 42, 422,1397, 875, 447,1160, 259, 168, 255, 559)( 44, 818, 934, 212, 719, 411, 963,1026, 290,1360)( 45,1244,1110, 643, 1296, 160, 167,1100, 739,1207)( 46,1053, 670, 692,1203)( 47,1052, 949, 406, 536,1005, 1101, 936, 899, 131)( 49, 424, 561, 309, 476)( 52,1263, 799,1253,1326, 534, 350, 621, 892, 995)( 53,1293, 165, 344, 274)( 54, 239, 358, 982,1039)( 55, 826,1222, 870,1278, 1355, 663, 241,1181,1166)( 56, 909,1340, 955, 82, 913, 525,1225, 343,1399) ( 57, 918, 202,1343, 288, 773, 730, 819, 673, 224)( 58,1094, 753,1033, 449, 87, 680, 70, 756, 708)( 60,1036, 216,1067, 230, 700,1004,1194,1059,1318)( 61, 420, 996,1306, 410,1284,1308,1368, 984,1014)( 62,1305,1220, 786, 95, 363, 176, 852, 699, 132) ( 63, 675,1291,1034, 570, 250, 322, 91, 619, 458)( 64,1311,1269, 81,1084, 946, 538, 439, 775, 121)( 65, 905,1192, 790, 194)( 66, 783, 242,1177,1024, 837, 640,1287, 429, 811)( 67, 120, 747, 257, 510, 500,1138, 234, 114, 486)( 68, 765, 433,1221,1357,1154, 771,1370, 801, 386)( 69, 803, 550,1300,1254, 106, 401, 213, 981, 537)( 72, 627, 345, 727, 879, 519,1042,1248,1245,1256)( 73, 251,1371,1180, 416,1333, 505, 244, 551, 906) ( 74, 777,1062, 583, 956, 291, 506,1336,1369,1330)( 75, 394, 785,1164,1000, 164, 228, 1396,1210,1349)( 76,1125,1342, 606,1378, 156, 85, 816, 573, 731)( 77,1178, 282, 361, 850, 736, 805, 922, 471,1097)( 78, 589,1331, 862, 376,1290, 867, 317, 233, 798) ( 79, 110,1092,1170, 630, 426, 474,1238, 329,1372)( 80, 129, 729, 261, 354,1392, 430, 178, 979, 186)( 83,1394, 547, 357,1262, 951, 637, 417, 339, 252)( 84,1334, 935, 585, 338)( 86, 463, 97,1407, 807)( 88, 490,1069, 873, 427,1389, 268, 975, 644,1214) ( 89,1358, 187, 614, 442, 567, 634, 750,1289, 735)( 90,1008,1011, 846,1122) ( 92, 286, 117, 323, 651, 119, 853, 711,1012, 576)( 93, 446, 994,1132, 340) ( 96, 808, 580, 153, 303)( 98, 238,1390, 246, 796, 590,1206, 378,1386, 665) ( 99, 319, 152, 957, 105, 352, 184, 628, 404, 738)( 100,1165,1348, 863,1054, 193, 749, 966, 615, 582)( 101, 432, 126, 136, 556,1142, 513, 549,1149,1354)( 103,1213, 641,1228, 973,1195,1406, 478, 764, 847)( 104, 625, 159, 716,1093)( 107,1302,1050,1150, 617, 635, 299, 972,1270,1319)( 108, 171,1297,1366, 284, 958, 781, 332, 782,1088)( 109,1046, 219, 992, 146,1172, 604, 954, 273, 911)( 112,1174,1098, 166,1027, 199,1274,1313,1015, 151) ( 113, 977, 231, 226, 928)( 116,1185, 903, 324, 569, 326, 888,1028, 795,1018) ( 118, 713,1137, 610, 197, 557,1016, 459, 703, 800)( 122,1119,1029, 920,1115) ( 123, 607, 248, 155,1400,1304, 593, 726, 965, 740)( 124, 712, 305,1359, 883) ( 125,1191, 575, 484, 845, 568,1379, 725, 959, 602)( 127, 792,1196, 915, 493, 858, 657, 732, 877, 737)( 128,1299, 714, 457,1374,1114, 728, 315,1159,1146)( 130,1408, 260, 978, 161)( 133, 776,1199,1261,1361, 709,1031, 592, 450, 333)( 134, 495, 542, 793, 841, 705, 1322,1182, 254, 381)( 135, 721,1076, 976, 341, 203, 924, 210,1022, 945)( 138, 145, 654, 1123, 564,1235,1344, 859, 461,1387)( 140, 402, 451,1265, 953, 613,1151, 759,1298, 893) ( 141, 707,1282, 895, 215, 990, 748,1124, 515, 379)( 142, 587,1155, 848, 221) ( 143,1179, 182, 383, 337,1082,1089, 993, 662,1218)( 147, 191,1099, 482, 925,1051, 367, 527, 855,1109)( 149, 997,1350, 666, 296,1316,1219,1070, 195,1217)( 157, 237,1385, 421, 418)( 162, 908, 240,1168, 941, 849, 717, 572, 375, 741)( 163, 470, 289,1081,1249, 348, 814, 359, 774, 477)( 172, 414, 597, 403, 177)( 173,1320, 720, 574,1351) ( 174, 710, 285,1310,1337,1143,1118, 868, 560, 437)( 175, 647, 405, 916,1243, 247, 642, 1157, 368,1136)( 179, 269, 942, 901, 479)( 185, 772, 947, 810, 488, 258, 364,1002, 491, 460)( 190, 501, 530, 351, 646, 302,1398,1096, 360,1237)( 198, 543,1364, 688, 320) ( 200, 668, 923, 932,1325, 898, 684, 746,1266, 579)( 201,1126,1072, 851, 509, 566, 528, 453, 206, 245)( 204,1212, 366, 839, 797, 297,1007,1025, 588, 835)( 205, 618,1327, 667, 327)( 207,1106, 516, 631,1363, 825, 371, 760, 874, 314)( 208,1047, 520,1226, 552, 349, 894, 881, 886, 612)( 209,1061, 521,1352,1187,1288, 355,1233,1259, 497)( 211, 508, 611, 312,1234, 864, 677, 743, 633,1147)( 218, 541,1075,1023,1402)( 222, 933, 718, 679, 988, 1116, 829,1384, 502, 991)( 223, 346, 742, 540,1246)( 225, 802, 529, 880, 443, 854, 425, 1347, 891, 595)( 249, 328,1264, 639,1163,1065,1048, 336,1216, 400)( 253, 987, 466,1108, 1211,1019, 840, 276, 889, 393)( 262, 271, 983, 866,1403)( 266, 469, 649,1113,1292, 763, 623, 298, 483, 353)( 270,1283, 664,1230, 293, 919, 844,1071,1073,1241)( 272, 724,1315, 1055, 511, 435, 553, 387, 605, 524)( 277, 306, 428,1117, 294, 682, 645, 698, 300, 871) ( 278, 768, 929, 926,1273)( 281, 419, 539, 468,1006)( 283,1040, 809,1021, 373,1328,1103, 1205, 833, 733)( 292,1209, 629, 390, 696, 632, 311, 697, 744, 334)( 301, 843, 824, 761, 601)( 310,1087, 817,1152,1183, 937, 395, 616, 910, 788)( 313,1186,1131, 778, 815) ( 325,1141,1184, 609, 701)( 372, 812, 545, 480, 872, 789,1032,1080, 467,1035) ( 374,1258, 603,1335, 661, 496, 791,1066, 462, 407)( 380, 512,1173, 860, 444,1038,1332, 1251, 456, 780)( 384,1162, 766,1362, 998, 970, 723,1268, 704,1102)( 389,1204, 391,1314, 1276, 558,1388, 971, 672, 828)( 396, 438, 485, 676, 445)( 408, 758,1107, 762,1231) ( 423,1198, 927, 882, 681)( 475,1197, 655,1294,1286)( 481,1272, 498,1058,1303, 608, 626, 678, 660,1003)( 492, 548, 823, 734, 504)( 499, 950)( 531, 563,1301, 861, 600,1127,1380, 598,1140,1247)( 535, 571, 968,1375,1171)( 565, 787,1144, 622,1317,1121,1049, 938, 687, 1239)( 591, 964,1077, 907,1367,1129, 755, 914,1208,1339)( 596,1176,1169,1078,1111) ( 648,1020, 961, 754,1395)( 831,1045,1260, 943, 896) ]),[[1,2]]);