Created on Mon Sep 06 2010, 16:00:29 CEST GENUS: 3 NUMBER OF RECORDS: 1404 NUMBER OF MAPS: 103 REFLEXIBLE MAPS: 63 CHIRAL MAPS: 40 #TYPE I: 78 #TYPE II: 25 CAYLEY MAPS: 100 NON-CAYLEY MAPS: 3 NON-CAYLEY REPRESENTATIVES: A3.191, A3.382, A3.1382 ISOMORPHISMS Representatives [ 1, 3, 13, 19, 25, 37, 43, 48, 145, 147, 173, 183, 191, 193, 319, 323, 335, 345, 349, 365, 366, 370, 374, 382, 386, 398, 400, 404, 415, 427, 429, 475, 495, 519, 871, 872, 873, 874, 876, 891, 895, 899, 907, 908, 909, 910, 916, 918, 921, 944, 945, 947, 950, 951, 952, 953, 955, 961, 966, 968, 969, 1004, 1028, 1034, 1036, 1046, 1047, 1048, 1049, 1050, 1052, 1053, 1059, 1062, 1063, 1064, 1066, 1074, 1076, 1077, 1104, 1108, 1148, 1268, 1271, 1272, 1274, 1276, 1277, 1278, 1280, 1283, 1286, 1291, 1296, 1306, 1327, 1351, 1352, 1378, 1382, 1384, 1397 ] Classes [ {@ 1, 2 @}, {@ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 @}, {@ 13, 14, 15, 16, 17, 18, 85, 86, 87, 88, 89, 90 @}, {@ 19, 20, 21, 22, 23, 24, 91, 92, 93, 94, 95, 96 @}, {@ 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144 @}, {@ 37, 38, 39, 40, 41, 42, 79, 80, 81, 82, 83, 84 @}, {@ 43, 44, 45, 46, 47, 52, 53, 54, 57, 58, 68, 74, 97, 98, 99, 100, 105, 107, 108, 109, 120, 121, 126, 128 @}, {@ 48, 49, 50, 51, 55, 56, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 75, 76, 77, 78, 101, 102, 103, 104, 106, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 122, 123, 124, 125, 127, 129, 130, 131, 132 @}, {@ 145, 146 @}, {@ 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172 @}, {@ 173, 174, 175, 176, 177, 178, 179, 180, 181, 182 @}, {@ 183, 184, 185, 186, 187, 188, 189, 190 @}, {@ 191, 192 @}, {@ 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318 @}, {@ 319, 320, 321, 322 @}, {@ 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334 @}, {@ 335, 336, 337, 338, 339, 340, 341, 342, 343, 344 @}, {@ 345, 346, 347, 348 @}, {@ 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364 @}, {@ 365, 368 @}, {@ 366, 367, 369, 373 @}, {@ 370, 371, 372 @}, {@ 374, 375, 376, 377, 378, 379, 380, 381 @}, {@ 382, 383, 384, 385 @}, {@ 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397 @}, {@ 398, 399, 401, 403, 407, 410, 411, 412, 419, 420, 425 @}, {@ 400, 402, 408, 409, 416, 422, 424, 426 @}, {@ 404, 405, 406, 413, 414, 417, 421, 423 @}, {@ 415, 418 @}, {@ 427, 428, 431, 432, 433, 436, 437, 440, 447, 448, 451, 452, 454, 458, 459, 460, 520, 521, 524, 525, 556, 582, 583, 584, 585, 590, 591, 592, 593, 598, 599, 600, 601, 606, 607, 608, 609, 630, 631, 634, 635, 638, 639, 642, 643, 646, 647, 649, 650, 653, 654, 658, 659, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 771, 772, 775, 776, 810, 811, 814, 815, 844, 849, 852, 855, 856, 859, 860, 863, 864, 865, 868 @}, {@ 429, 430, 434, 435, 438, 439, 441, 442, 443, 444, 445, 446, 449, 450, 453, 455, 456, 457, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 477, 478, 487, 488, 489, 490, 491, 492, 493, 494, 498, 499, 516, 557, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 812, 813, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 831, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 846, 847, 848, 851, 861 @}, {@ 475, 476, 479, 480, 481, 482, 483, 484, 485, 486, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 517, 518, 527, 528, 529, 530, 531 @}, {@ 495, 496, 497, 515, 532, 533, 534, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554 @}, {@ 519, 522, 523, 526, 535, 536, 537, 555, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 586, 587, 588, 589, 594, 595, 596, 597, 602, 603, 604, 605, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 632, 633, 636, 637, 640, 641, 644, 645, 648, 651, 652, 655, 656, 657, 660, 661, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 769, 770, 773, 774, 832, 845, 850, 853, 854, 857, 858, 862, 866, 867, 869, 870 @}, {@ 871, 878, 885, 887 @}, {@ 872, 875, 881, 883 @}, {@ 873, 879, 880, 889 @}, {@ 874, 877, 886, 890 @}, {@ 876, 882, 884, 888 @}, {@ 891, 892, 893, 894 @}, {@ 895, 896, 897, 898 @}, {@ 899, 900, 901, 902, 903, 904, 905, 906 @}, {@ 907, 913 @}, {@ 908, 911, 915 @}, {@ 909, 912 @}, {@ 910, 914 @}, {@ 916, 917, 930, 931 @}, {@ 918, 919, 920, 922, 923, 925, 927, 928, 932, 933, 934, 935, 936, 937, 940, 943 @}, {@ 921, 924, 926, 929, 938, 939, 941, 942 @}, {@ 944, 946, 948 @}, {@ 945, 954, 958 @}, {@ 947, 949 @}, {@ 950, 957, 965 @}, {@ 951, 959 @}, {@ 952, 956 @}, {@ 953, 962, 964 @}, {@ 955, 960 @}, {@ 961, 963 @}, {@ 966, 967, 970, 976, 979, 991, 994, 1003 @}, {@ 968, 971, 985, 992, 993, 998, 1001, 1002 @}, {@ 969, 972, 973, 974, 975, 977, 978, 980, 981, 982, 983, 984, 986, 987, 988, 989, 990, 995, 996, 997, 999, 1000 @}, {@ 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027 @}, {@ 1028, 1029, 1030, 1031, 1032, 1033 @}, {@ 1034, 1035, 1037, 1041, 1043, 1044 @}, {@ 1036, 1038, 1039, 1040, 1042, 1045 @}, {@ 1046, 1054 @}, {@ 1047, 1057 @}, {@ 1048, 1055 @}, {@ 1049, 1056 @}, {@ 1050, 1051 @}, {@ 1052, 1060 @}, {@ 1053, 1058 @}, {@ 1059, 1061 @}, {@ 1062, 1070 @}, {@ 1063, 1068 @}, {@ 1064, 1065, 1067, 1071, 1073 @}, {@ 1066, 1069, 1072 @}, {@ 1074, 1075 @}, {@ 1076, 1078, 1080, 1081, 1084, 1087, 1088, 1090, 1092, 1096, 1098, 1099, 1100, 1101, 1102, 1103, 1122, 1126, 1128, 1129, 1131, 1133, 1134, 1137, 1138, 1139, 1140, 1141, 1142, 1145, 1146, 1147 @}, {@ 1077, 1079, 1082, 1083, 1085, 1086, 1089, 1091, 1093, 1094, 1095, 1097, 1120, 1121, 1123, 1124, 1125, 1127, 1130, 1132, 1135, 1136, 1143, 1144 @}, {@ 1104, 1105, 1106, 1107, 1109, 1117, 1118, 1119 @}, {@ 1108, 1110, 1111, 1112, 1113, 1114, 1115, 1116 @}, {@ 1148, 1149, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267 @}, {@ 1268, 1269, 1270 @}, {@ 1271, 1279 @}, {@ 1272, 1273, 1275, 1281 @}, {@ 1274, 1288 @}, {@ 1276, 1282 @}, {@ 1277, 1287 @}, {@ 1278, 1290 @}, {@ 1280, 1285 @}, {@ 1283, 1284 @}, {@ 1286, 1289 @}, {@ 1291, 1292, 1293, 1294, 1295, 1297, 1298, 1299, 1300, 1301, 1302, 1303, 1304, 1305, 1307, 1308, 1309, 1310, 1315, 1316, 1317, 1318, 1324, 1325, 1332, 1333, 1334, 1337, 1338, 1339, 1374, 1376 @}, {@ 1296, 1311, 1312, 1313, 1314, 1319, 1320, 1321, 1322, 1323, 1329, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 1350, 1356 @}, {@ 1306, 1326, 1328, 1331, 1335, 1360, 1362, 1364 @}, {@ 1327, 1330, 1336, 1359, 1361, 1363, 1365, 1370 @}, {@ 1351, 1353, 1357, 1367, 1368, 1369, 1371, 1377 @}, {@ 1352, 1354, 1355, 1358, 1366, 1372, 1373, 1375 @}, {@ 1378, 1379, 1380, 1381 @}, {@ 1382, 1383, 1385, 1386, 1388, 1389, 1390, 1391, 1392, 1393, 1394, 1395, 1396 @}, {@ 1384, 1387, 1401, 1402, 1403, 1404 @}, {@ 1397, 1398, 1399, 1400 @} ] MAP : A3.1 NOTES : type I, reflexible, isomorphic to Trun({3,7}), representative. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7 ] UNIGROUP : < u.1, u.2 | u.1^2, u.2^3, (u.1 * u.2^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.1^2, x.2^3, (x.2 * x.1)^7, (x.1 * x.2 * x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (3, 14, 14) #DARTS : 504 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168)(169, 420)(170, 435)(171, 437)(172, 434)(173, 456)(174, 443)(175, 436)(176, 453)(177, 418)(178, 417)(179, 433)(180, 401)(181, 441)(182, 394)(183, 393)(184, 442)(185, 423)(186, 422)(187, 351)(188, 440)(189, 348)(190, 352)(191, 349)(192, 363)(193, 419)(194, 404)(195, 402)(196, 407)(197, 403)(198, 479)(199, 478)(200, 396)(201, 502)(202, 503)(203, 500)(204, 350)(205, 498)(206, 365)(207, 368)(208, 497)(209, 421)(210, 424)(211, 406)(212, 389)(213, 391)(214, 380)(215, 387)(216, 390)(217, 488)(218, 485)(219, 392)(220, 483)(221, 382)(222, 481)(223, 482)(224, 383)(225, 355)(226, 372)(227, 370)(228, 375)(229, 371)(230, 439)(231, 438)(232, 388)(233, 357)(234, 360)(235, 374)(236, 469)(237, 471)(238, 484)(239, 467)(240, 470)(241, 354)(242, 353)(243, 337)(244, 369)(245, 345)(246, 386)(247, 385)(248, 346)(249, 416)(250, 413)(251, 472)(252, 411)(253, 486)(254, 409)(255, 410)(256, 487)(257, 356)(258, 339)(259, 341)(260, 338)(261, 408)(262, 347)(263, 340)(264, 405)(265, 430)(266, 431)(267, 428)(268, 494)(269, 426)(270, 501)(271, 504)(272, 425)(273, 359)(274, 358)(275, 495)(276, 344)(277, 492)(278, 496)(279, 493)(280, 499)(281, 463)(282, 462)(283, 447)(284, 480)(285, 444)(286, 448)(287, 445)(288, 427)(289, 460)(290, 475)(291, 477)(292, 474)(293, 376)(294, 491)(295, 476)(296, 373)(297, 366)(298, 367)(299, 364)(300, 446)(301, 362)(302, 429)(303, 432)(304, 361)(305, 458)(306, 457)(307, 473)(308, 449)(309, 489)(310, 466)(311, 465)(312, 490)(313, 384)(314, 381)(315, 400)(316, 379)(317, 414)(318, 377)(319, 378)(320, 415)(321, 459)(322, 452)(323, 450)(324, 455)(325, 451)(326, 343)(327, 342)(328, 468)(329, 461)(330, 464)(331, 454)(332, 397)(333, 399)(334, 412)(335, 395)(336, 398) MAP : A3.2 NOTES : type I, reflexible, isomorphic to Trun({3,7}), isomorphic to A3.1. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7 ] UNIGROUP : < u.1, u.2 | u.1^2, u.2^3, (u.1 * u.2^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.1^2, x.2^3, (x.2 * x.1)^7, (x.1 * x.2 * x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (3, 14, 14) #DARTS : 504 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168)(169, 339)(170, 356)(171, 354)(172, 359)(173, 355)(174, 431)(175, 430)(176, 372)(177, 341)(178, 344)(179, 358)(180, 493)(181, 495)(182, 476)(183, 491)(184, 494)(185, 338)(186, 337)(187, 345)(188, 353)(189, 361)(190, 370)(191, 369)(192, 362)(193, 408)(194, 405)(195, 496)(196, 403)(197, 478)(198, 401)(199, 402)(200, 479)(201, 340)(202, 347)(203, 349)(204, 346)(205, 440)(206, 363)(207, 348)(208, 437)(209, 398)(210, 399)(211, 396)(212, 454)(213, 394)(214, 461)(215, 464)(216, 393)(217, 343)(218, 342)(219, 455)(220, 352)(221, 452)(222, 456)(223, 453)(224, 459)(225, 487)(226, 486)(227, 415)(228, 472)(229, 412)(230, 416)(231, 413)(232, 395)(233, 484)(234, 467)(235, 469)(236, 466)(237, 360)(238, 451)(239, 468)(240, 357)(241, 382)(242, 383)(243, 380)(244, 414)(245, 378)(246, 397)(247, 400)(248, 377)(249, 482)(250, 481)(251, 465)(252, 497)(253, 449)(254, 490)(255, 489)(256, 450)(257, 392)(258, 389)(259, 424)(260, 387)(261, 406)(262, 385)(263, 386)(264, 407)(265, 483)(266, 500)(267, 498)(268, 503)(269, 499)(270, 351)(271, 350)(272, 492)(273, 485)(274, 488)(275, 502)(276, 421)(277, 423)(278, 404)(279, 419)(280, 422)(281, 444)(282, 427)(283, 429)(284, 426)(285, 504)(286, 411)(287, 428)(288, 501)(289, 442)(290, 441)(291, 425)(292, 433)(293, 409)(294, 418)(295, 417)(296, 410)(297, 447)(298, 446)(299, 367)(300, 432)(301, 364)(302, 368)(303, 365)(304, 379)(305, 443)(306, 436)(307, 434)(308, 439)(309, 435)(310, 471)(311, 470)(312, 420)(313, 462)(314, 463)(315, 460)(316, 366)(317, 458)(318, 381)(319, 384)(320, 457)(321, 445)(322, 448)(323, 438)(324, 373)(325, 375)(326, 388)(327, 371)(328, 374)(329, 480)(330, 477)(331, 376)(332, 475)(333, 390)(334, 473)(335, 474)(336, 391) MAP : A3.3 NOTES : type I, reflexible, isomorphic to Trun({3,8}), representative. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (3, 16, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 99)(50, 133)(51, 102)(52, 136)(53, 130)(54, 97)(55, 108)(56, 132)(57, 100)(58, 98)(59, 119)(60, 142)(61, 101)(62, 140)(63, 115)(64, 104)(65, 134)(66, 138)(67, 129)(68, 137)(69, 141)(70, 131)(71, 126)(72, 144)(73, 120)(74, 117)(75, 110)(76, 135)(77, 114)(78, 107)(79, 113)(80, 116)(81, 111)(82, 109)(83, 143)(84, 112)(85, 106)(86, 127)(87, 139)(88, 105)(89, 128)(90, 125)(91, 124)(92, 123)(93, 122)(94, 103)(95, 118)(96, 121)(193, 248)(194, 279)(195, 242)(196, 266)(197, 254)(198, 247)(199, 280)(200, 274)(201, 263)(202, 249)(203, 271)(204, 262)(205, 264)(206, 273)(207, 270)(208, 283)(209, 267)(210, 256)(211, 281)(212, 284)(213, 260)(214, 285)(215, 250)(216, 286)(217, 255)(218, 278)(219, 276)(220, 272)(221, 287)(222, 265)(223, 282)(224, 275)(225, 245)(226, 241)(227, 268)(228, 257)(229, 259)(230, 244)(231, 243)(232, 246)(233, 277)(234, 251)(235, 258)(236, 261)(237, 252)(238, 253)(239, 288)(240, 269) MAP : A3.4 NOTES : type I, reflexible, isomorphic to Trun({3,8}), isomorphic to A3.3. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (3, 16, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 99)(50, 133)(51, 102)(52, 136)(53, 130)(54, 97)(55, 108)(56, 132)(57, 100)(58, 98)(59, 119)(60, 142)(61, 101)(62, 140)(63, 115)(64, 104)(65, 134)(66, 138)(67, 129)(68, 137)(69, 141)(70, 131)(71, 126)(72, 144)(73, 120)(74, 117)(75, 110)(76, 135)(77, 114)(78, 107)(79, 113)(80, 116)(81, 111)(82, 109)(83, 143)(84, 112)(85, 106)(86, 127)(87, 139)(88, 105)(89, 128)(90, 125)(91, 124)(92, 123)(93, 122)(94, 103)(95, 118)(96, 121)(193, 253)(194, 246)(195, 283)(196, 271)(197, 255)(198, 249)(199, 241)(200, 243)(201, 242)(202, 270)(203, 269)(204, 266)(205, 247)(206, 274)(207, 264)(208, 282)(209, 256)(210, 268)(211, 250)(212, 285)(213, 267)(214, 286)(215, 244)(216, 245)(217, 251)(218, 280)(219, 278)(220, 287)(221, 265)(222, 259)(223, 263)(224, 279)(225, 284)(226, 276)(227, 260)(228, 254)(229, 272)(230, 261)(231, 277)(232, 252)(233, 273)(234, 257)(235, 248)(236, 281)(237, 275)(238, 288)(239, 258)(240, 262) MAP : A3.5 NOTES : type I, reflexible, isomorphic to Trun({3,8}), isomorphic to A3.3. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (3, 16, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 102)(50, 106)(51, 97)(52, 105)(53, 109)(54, 99)(55, 142)(56, 112)(57, 136)(58, 133)(59, 126)(60, 103)(61, 130)(62, 123)(63, 129)(64, 132)(65, 127)(66, 125)(67, 111)(68, 128)(69, 122)(70, 143)(71, 107)(72, 121)(73, 144)(74, 141)(75, 140)(76, 139)(77, 138)(78, 119)(79, 134)(80, 137)(81, 115)(82, 101)(83, 118)(84, 104)(85, 98)(86, 113)(87, 124)(88, 100)(89, 116)(90, 114)(91, 135)(92, 110)(93, 117)(94, 108)(95, 131)(96, 120)(193, 260)(194, 267)(195, 261)(196, 245)(197, 268)(198, 284)(199, 281)(200, 285)(201, 254)(202, 276)(203, 241)(204, 259)(205, 272)(206, 287)(207, 283)(208, 252)(209, 286)(210, 280)(211, 256)(212, 251)(213, 265)(214, 250)(215, 274)(216, 279)(217, 243)(218, 255)(219, 288)(220, 244)(221, 246)(222, 248)(223, 253)(224, 271)(225, 258)(226, 275)(227, 263)(228, 262)(229, 257)(230, 264)(231, 278)(232, 273)(233, 282)(234, 247)(235, 266)(236, 269)(237, 270)(238, 277)(239, 249)(240, 242) MAP : A3.6 NOTES : type I, reflexible, isomorphic to Trun({3,8}), isomorphic to A3.3. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (3, 16, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 102)(50, 106)(51, 97)(52, 105)(53, 109)(54, 99)(55, 142)(56, 112)(57, 136)(58, 133)(59, 126)(60, 103)(61, 130)(62, 123)(63, 129)(64, 132)(65, 127)(66, 125)(67, 111)(68, 128)(69, 122)(70, 143)(71, 107)(72, 121)(73, 144)(74, 141)(75, 140)(76, 139)(77, 138)(78, 119)(79, 134)(80, 137)(81, 115)(82, 101)(83, 118)(84, 104)(85, 98)(86, 113)(87, 124)(88, 100)(89, 116)(90, 114)(91, 135)(92, 110)(93, 117)(94, 108)(95, 131)(96, 120)(193, 274)(194, 243)(195, 279)(196, 278)(197, 273)(198, 280)(199, 246)(200, 241)(201, 250)(202, 263)(203, 282)(204, 285)(205, 286)(206, 245)(207, 265)(208, 258)(209, 276)(210, 283)(211, 277)(212, 261)(213, 284)(214, 252)(215, 249)(216, 253)(217, 270)(218, 244)(219, 257)(220, 275)(221, 288)(222, 255)(223, 251)(224, 268)(225, 254)(226, 248)(227, 272)(228, 267)(229, 281)(230, 266)(231, 242)(232, 247)(233, 259)(234, 271)(235, 256)(236, 260)(237, 262)(238, 264)(239, 269)(240, 287) MAP : A3.7 NOTES : type I, reflexible, isomorphic to Trun({3,8}), isomorphic to A3.3. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (3, 16, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 102)(50, 106)(51, 97)(52, 105)(53, 109)(54, 99)(55, 142)(56, 112)(57, 136)(58, 133)(59, 126)(60, 103)(61, 130)(62, 123)(63, 129)(64, 132)(65, 127)(66, 125)(67, 111)(68, 128)(69, 122)(70, 143)(71, 107)(72, 121)(73, 144)(74, 141)(75, 140)(76, 139)(77, 138)(78, 119)(79, 134)(80, 137)(81, 115)(82, 101)(83, 118)(84, 104)(85, 98)(86, 113)(87, 124)(88, 100)(89, 116)(90, 114)(91, 135)(92, 110)(93, 117)(94, 108)(95, 131)(96, 120)(193, 247)(194, 249)(195, 248)(196, 263)(197, 264)(198, 242)(199, 253)(200, 283)(201, 246)(202, 259)(203, 265)(204, 280)(205, 241)(206, 276)(207, 245)(208, 257)(209, 282)(210, 287)(211, 270)(212, 275)(213, 278)(214, 288)(215, 271)(216, 255)(217, 269)(218, 252)(219, 261)(220, 258)(221, 251)(222, 250)(223, 244)(224, 277)(225, 281)(226, 254)(227, 285)(228, 274)(229, 279)(230, 267)(231, 272)(232, 266)(233, 284)(234, 256)(235, 243)(236, 273)(237, 260)(238, 262)(239, 268)(240, 286) MAP : A3.8 NOTES : type I, reflexible, isomorphic to Trun({3,8}), isomorphic to A3.3. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (3, 16, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 102)(50, 106)(51, 97)(52, 105)(53, 109)(54, 99)(55, 142)(56, 112)(57, 136)(58, 133)(59, 126)(60, 103)(61, 130)(62, 123)(63, 129)(64, 132)(65, 127)(66, 125)(67, 111)(68, 128)(69, 122)(70, 143)(71, 107)(72, 121)(73, 144)(74, 141)(75, 140)(76, 139)(77, 138)(78, 119)(79, 134)(80, 137)(81, 115)(82, 101)(83, 118)(84, 104)(85, 98)(86, 113)(87, 124)(88, 100)(89, 116)(90, 114)(91, 135)(92, 110)(93, 117)(94, 108)(95, 131)(96, 120)(193, 270)(194, 264)(195, 288)(196, 283)(197, 249)(198, 282)(199, 258)(200, 263)(201, 275)(202, 287)(203, 272)(204, 276)(205, 278)(206, 280)(207, 285)(208, 255)(209, 242)(210, 259)(211, 247)(212, 246)(213, 241)(214, 248)(215, 262)(216, 257)(217, 266)(218, 279)(219, 250)(220, 253)(221, 254)(222, 261)(223, 281)(224, 274)(225, 244)(226, 251)(227, 245)(228, 277)(229, 252)(230, 268)(231, 265)(232, 269)(233, 286)(234, 260)(235, 273)(236, 243)(237, 256)(238, 271)(239, 267)(240, 284) MAP : A3.9 NOTES : type I, reflexible, isomorphic to Trun({3,8}), isomorphic to A3.3. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 8 ] UNIGROUP : < u.1, u.2 | u.1^2, u.2^3, (u.1 * u.2^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.1^2, x.2^3, (x.1 * x.2 * x.1 * x.2^-1)^3, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (3, 16, 16) #DARTS : 288 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288) L = (1, 4)(2, 8)(3, 5)(6, 34)(7, 37)(9, 18)(10, 81)(11, 82)(12, 33)(13, 17)(14, 21)(15, 85)(16, 53)(19, 30)(20, 29)(22, 63)(23, 58)(24, 25)(26, 48)(27, 64)(28, 59)(31, 32)(35, 39)(36, 44)(38, 40)(41, 43)(42, 45)(46, 47)(49, 80)(50, 96)(51, 75)(52, 79)(54, 76)(55, 70)(56, 74)(57, 94)(60, 71)(61, 89)(62, 93)(65, 91)(66, 95)(67, 92)(68, 86)(69, 90)(72, 87)(73, 83)(77, 88)(78, 84)(97, 197)(98, 193)(99, 226)(100, 229)(101, 194)(102, 273)(103, 274)(104, 225)(105, 228)(106, 275)(107, 276)(108, 277)(109, 227)(110, 232)(111, 280)(112, 281)(113, 195)(114, 196)(115, 198)(116, 199)(117, 200)(118, 202)(119, 203)(120, 204)(121, 236)(122, 265)(123, 270)(124, 207)(125, 231)(126, 230)(127, 269)(128, 253)(129, 213)(130, 209)(131, 258)(132, 261)(133, 210)(134, 241)(135, 242)(136, 257)(137, 260)(138, 243)(139, 244)(140, 245)(141, 259)(142, 264)(143, 248)(144, 249)(145, 222)(146, 221)(147, 255)(148, 250)(149, 217)(150, 240)(151, 256)(152, 251)(153, 246)(154, 235)(155, 239)(156, 224)(157, 252)(158, 247)(159, 234)(160, 254)(161, 206)(162, 205)(163, 287)(164, 282)(165, 201)(166, 272)(167, 288)(168, 283)(169, 278)(170, 267)(171, 271)(172, 208)(173, 284)(174, 279)(175, 266)(176, 286)(177, 211)(178, 212)(179, 214)(180, 215)(181, 216)(182, 218)(183, 219)(184, 220)(185, 268)(186, 233)(187, 238)(188, 223)(189, 263)(190, 262)(191, 237)(192, 285) MAP : A3.10 NOTES : type I, reflexible, isomorphic to Trun({3,8}), isomorphic to A3.3. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (3, 16, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 99)(50, 133)(51, 102)(52, 136)(53, 130)(54, 97)(55, 108)(56, 132)(57, 100)(58, 98)(59, 119)(60, 142)(61, 101)(62, 140)(63, 115)(64, 104)(65, 134)(66, 138)(67, 129)(68, 137)(69, 141)(70, 131)(71, 126)(72, 144)(73, 120)(74, 117)(75, 110)(76, 135)(77, 114)(78, 107)(79, 113)(80, 116)(81, 111)(82, 109)(83, 143)(84, 112)(85, 106)(86, 127)(87, 139)(88, 105)(89, 128)(90, 125)(91, 124)(92, 123)(93, 122)(94, 103)(95, 118)(96, 121)(193, 261)(194, 257)(195, 284)(196, 273)(197, 275)(198, 260)(199, 259)(200, 262)(201, 245)(202, 267)(203, 274)(204, 277)(205, 268)(206, 269)(207, 256)(208, 285)(209, 264)(210, 247)(211, 258)(212, 282)(213, 270)(214, 263)(215, 248)(216, 242)(217, 279)(218, 265)(219, 287)(220, 278)(221, 280)(222, 241)(223, 286)(224, 251)(225, 283)(226, 272)(227, 249)(228, 252)(229, 276)(230, 253)(231, 266)(232, 254)(233, 271)(234, 246)(235, 244)(236, 288)(237, 255)(238, 281)(239, 250)(240, 243) MAP : A3.11 NOTES : type I, reflexible, isomorphic to Trun({3,8}), isomorphic to A3.3. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 8 ] UNIGROUP : < u.1, u.2 | u.1^2, u.2^3, (u.1 * u.2^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.1^2, x.2^3, (x.1 * x.2 * x.1 * x.2^-1)^3, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (3, 16, 16) #DARTS : 288 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288) L = (1, 4)(2, 8)(3, 5)(6, 34)(7, 37)(9, 18)(10, 81)(11, 82)(12, 33)(13, 17)(14, 21)(15, 85)(16, 53)(19, 30)(20, 29)(22, 63)(23, 58)(24, 25)(26, 48)(27, 64)(28, 59)(31, 32)(35, 39)(36, 44)(38, 40)(41, 43)(42, 45)(46, 47)(49, 80)(50, 96)(51, 75)(52, 79)(54, 76)(55, 70)(56, 74)(57, 94)(60, 71)(61, 89)(62, 93)(65, 91)(66, 95)(67, 92)(68, 86)(69, 90)(72, 87)(73, 83)(77, 88)(78, 84)(97, 194)(98, 197)(99, 209)(100, 210)(101, 193)(102, 211)(103, 212)(104, 213)(105, 261)(106, 214)(107, 215)(108, 216)(109, 258)(110, 257)(111, 220)(112, 268)(113, 226)(114, 229)(115, 273)(116, 274)(117, 225)(118, 275)(119, 276)(120, 277)(121, 245)(122, 278)(123, 279)(124, 280)(125, 242)(126, 241)(127, 284)(128, 252)(129, 200)(130, 195)(131, 205)(132, 201)(133, 196)(134, 222)(135, 221)(136, 206)(137, 282)(138, 255)(139, 250)(140, 217)(141, 287)(142, 283)(143, 251)(144, 246)(145, 230)(146, 231)(147, 234)(148, 235)(149, 236)(150, 249)(151, 254)(152, 239)(153, 240)(154, 244)(155, 248)(156, 253)(157, 224)(158, 256)(159, 243)(160, 247)(161, 232)(162, 227)(163, 237)(164, 233)(165, 228)(166, 286)(167, 285)(168, 238)(169, 218)(170, 271)(171, 266)(172, 281)(173, 223)(174, 219)(175, 267)(176, 262)(177, 198)(178, 199)(179, 202)(180, 203)(181, 204)(182, 265)(183, 270)(184, 207)(185, 208)(186, 260)(187, 264)(188, 269)(189, 288)(190, 272)(191, 259)(192, 263) MAP : A3.12 NOTES : type I, reflexible, isomorphic to Trun({3,8}), isomorphic to A3.3. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (3, 16, 16) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 99)(50, 133)(51, 102)(52, 136)(53, 130)(54, 97)(55, 108)(56, 132)(57, 100)(58, 98)(59, 119)(60, 142)(61, 101)(62, 140)(63, 115)(64, 104)(65, 134)(66, 138)(67, 129)(68, 137)(69, 141)(70, 131)(71, 126)(72, 144)(73, 120)(74, 117)(75, 110)(76, 135)(77, 114)(78, 107)(79, 113)(80, 116)(81, 111)(82, 109)(83, 143)(84, 112)(85, 106)(86, 127)(87, 139)(88, 105)(89, 128)(90, 125)(91, 124)(92, 123)(93, 122)(94, 103)(95, 118)(96, 121)(193, 251)(194, 288)(195, 265)(196, 268)(197, 244)(198, 269)(199, 282)(200, 270)(201, 287)(202, 262)(203, 260)(204, 256)(205, 271)(206, 249)(207, 266)(208, 259)(209, 277)(210, 273)(211, 252)(212, 241)(213, 243)(214, 276)(215, 275)(216, 278)(217, 261)(218, 283)(219, 242)(220, 245)(221, 284)(222, 285)(223, 272)(224, 253)(225, 280)(226, 263)(227, 274)(228, 250)(229, 286)(230, 279)(231, 264)(232, 258)(233, 247)(234, 281)(235, 255)(236, 246)(237, 248)(238, 257)(239, 254)(240, 267) MAP : A3.13 NOTES : type II, reflexible, isomorphic to DBar({3,7}), representative. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 7, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^3, x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-2 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1, (x.3 * x.2^-1)^7, x.3 * x.2 * x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 14) #DARTS : 1008 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504)(505, 673, 841)(506, 674, 842)(507, 675, 843)(508, 676, 844)(509, 677, 845)(510, 678, 846)(511, 679, 847)(512, 680, 848)(513, 681, 849)(514, 682, 850)(515, 683, 851)(516, 684, 852)(517, 685, 853)(518, 686, 854)(519, 687, 855)(520, 688, 856)(521, 689, 857)(522, 690, 858)(523, 691, 859)(524, 692, 860)(525, 693, 861)(526, 694, 862)(527, 695, 863)(528, 696, 864)(529, 697, 865)(530, 698, 866)(531, 699, 867)(532, 700, 868)(533, 701, 869)(534, 702, 870)(535, 703, 871)(536, 704, 872)(537, 705, 873)(538, 706, 874)(539, 707, 875)(540, 708, 876)(541, 709, 877)(542, 710, 878)(543, 711, 879)(544, 712, 880)(545, 713, 881)(546, 714, 882)(547, 715, 883)(548, 716, 884)(549, 717, 885)(550, 718, 886)(551, 719, 887)(552, 720, 888)(553, 721, 889)(554, 722, 890)(555, 723, 891)(556, 724, 892)(557, 725, 893)(558, 726, 894)(559, 727, 895)(560, 728, 896)(561, 729, 897)(562, 730, 898)(563, 731, 899)(564, 732, 900)(565, 733, 901)(566, 734, 902)(567, 735, 903)(568, 736, 904)(569, 737, 905)(570, 738, 906)(571, 739, 907)(572, 740, 908)(573, 741, 909)(574, 742, 910)(575, 743, 911)(576, 744, 912)(577, 745, 913)(578, 746, 914)(579, 747, 915)(580, 748, 916)(581, 749, 917)(582, 750, 918)(583, 751, 919)(584, 752, 920)(585, 753, 921)(586, 754, 922)(587, 755, 923)(588, 756, 924)(589, 757, 925)(590, 758, 926)(591, 759, 927)(592, 760, 928)(593, 761, 929)(594, 762, 930)(595, 763, 931)(596, 764, 932)(597, 765, 933)(598, 766, 934)(599, 767, 935)(600, 768, 936)(601, 769, 937)(602, 770, 938)(603, 771, 939)(604, 772, 940)(605, 773, 941)(606, 774, 942)(607, 775, 943)(608, 776, 944)(609, 777, 945)(610, 778, 946)(611, 779, 947)(612, 780, 948)(613, 781, 949)(614, 782, 950)(615, 783, 951)(616, 784, 952)(617, 785, 953)(618, 786, 954)(619, 787, 955)(620, 788, 956)(621, 789, 957)(622, 790, 958)(623, 791, 959)(624, 792, 960)(625, 793, 961)(626, 794, 962)(627, 795, 963)(628, 796, 964)(629, 797, 965)(630, 798, 966)(631, 799, 967)(632, 800, 968)(633, 801, 969)(634, 802, 970)(635, 803, 971)(636, 804, 972)(637, 805, 973)(638, 806, 974)(639, 807, 975)(640, 808, 976)(641, 809, 977)(642, 810, 978)(643, 811, 979)(644, 812, 980)(645, 813, 981)(646, 814, 982)(647, 815, 983)(648, 816, 984)(649, 817, 985)(650, 818, 986)(651, 819, 987)(652, 820, 988)(653, 821, 989)(654, 822, 990)(655, 823, 991)(656, 824, 992)(657, 825, 993)(658, 826, 994)(659, 827, 995)(660, 828, 996)(661, 829, 997)(662, 830, 998)(663, 831, 999)(664, 832, 1000)(665, 833, 1001)(666, 834, 1002)(667, 835, 1003)(668, 836, 1004)(669, 837, 1005)(670, 838, 1006)(671, 839, 1007)(672, 840, 1008) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 843)(170, 860)(171, 858)(172, 863)(173, 859)(174, 935)(175, 934)(176, 876)(177, 845)(178, 848)(179, 862)(180, 997)(181, 999)(182, 980)(183, 995)(184, 998)(185, 842)(186, 841)(187, 849)(188, 857)(189, 865)(190, 874)(191, 873)(192, 866)(193, 912)(194, 909)(195, 1000)(196, 907)(197, 982)(198, 905)(199, 906)(200, 983)(201, 844)(202, 851)(203, 853)(204, 850)(205, 944)(206, 867)(207, 852)(208, 941)(209, 902)(210, 903)(211, 900)(212, 958)(213, 898)(214, 965)(215, 968)(216, 897)(217, 847)(218, 846)(219, 959)(220, 856)(221, 956)(222, 960)(223, 957)(224, 963)(225, 991)(226, 990)(227, 919)(228, 976)(229, 916)(230, 920)(231, 917)(232, 899)(233, 988)(234, 971)(235, 973)(236, 970)(237, 864)(238, 955)(239, 972)(240, 861)(241, 886)(242, 887)(243, 884)(244, 918)(245, 882)(246, 901)(247, 904)(248, 881)(249, 986)(250, 985)(251, 969)(252, 1001)(253, 953)(254, 994)(255, 993)(256, 954)(257, 896)(258, 893)(259, 928)(260, 891)(261, 910)(262, 889)(263, 890)(264, 911)(265, 987)(266, 1004)(267, 1002)(268, 1007)(269, 1003)(270, 855)(271, 854)(272, 996)(273, 989)(274, 992)(275, 1006)(276, 925)(277, 927)(278, 908)(279, 923)(280, 926)(281, 948)(282, 931)(283, 933)(284, 930)(285, 1008)(286, 915)(287, 932)(288, 1005)(289, 946)(290, 945)(291, 929)(292, 937)(293, 913)(294, 922)(295, 921)(296, 914)(297, 951)(298, 950)(299, 871)(300, 936)(301, 868)(302, 872)(303, 869)(304, 883)(305, 947)(306, 940)(307, 938)(308, 943)(309, 939)(310, 975)(311, 974)(312, 924)(313, 966)(314, 967)(315, 964)(316, 870)(317, 962)(318, 885)(319, 888)(320, 961)(321, 949)(322, 952)(323, 942)(324, 877)(325, 879)(326, 892)(327, 875)(328, 878)(329, 984)(330, 981)(331, 880)(332, 979)(333, 894)(334, 977)(335, 978)(336, 895)(337, 674)(338, 673)(339, 681)(340, 689)(341, 697)(342, 706)(343, 705)(344, 698)(345, 675)(346, 692)(347, 690)(348, 695)(349, 691)(350, 767)(351, 766)(352, 708)(353, 676)(354, 683)(355, 685)(356, 682)(357, 776)(358, 699)(359, 684)(360, 773)(361, 677)(362, 680)(363, 694)(364, 829)(365, 831)(366, 812)(367, 827)(368, 830)(369, 679)(370, 678)(371, 791)(372, 688)(373, 788)(374, 792)(375, 789)(376, 795)(377, 744)(378, 741)(379, 832)(380, 739)(381, 814)(382, 737)(383, 738)(384, 815)(385, 734)(386, 735)(387, 732)(388, 790)(389, 730)(390, 797)(391, 800)(392, 729)(393, 728)(394, 725)(395, 760)(396, 723)(397, 742)(398, 721)(399, 722)(400, 743)(401, 718)(402, 719)(403, 716)(404, 750)(405, 714)(406, 733)(407, 736)(408, 713)(409, 821)(410, 824)(411, 838)(412, 757)(413, 759)(414, 740)(415, 755)(416, 758)(417, 823)(418, 822)(419, 751)(420, 808)(421, 748)(422, 752)(423, 749)(424, 731)(425, 819)(426, 836)(427, 834)(428, 839)(429, 835)(430, 687)(431, 686)(432, 828)(433, 820)(434, 803)(435, 805)(436, 802)(437, 696)(438, 787)(439, 804)(440, 693)(441, 818)(442, 817)(443, 801)(444, 833)(445, 785)(446, 826)(447, 825)(448, 786)(449, 781)(450, 784)(451, 774)(452, 709)(453, 711)(454, 724)(455, 707)(456, 710)(457, 816)(458, 813)(459, 712)(460, 811)(461, 726)(462, 809)(463, 810)(464, 727)(465, 779)(466, 772)(467, 770)(468, 775)(469, 771)(470, 807)(471, 806)(472, 756)(473, 798)(474, 799)(475, 796)(476, 702)(477, 794)(478, 717)(479, 720)(480, 793)(481, 778)(482, 777)(483, 761)(484, 769)(485, 745)(486, 754)(487, 753)(488, 746)(489, 783)(490, 782)(491, 703)(492, 768)(493, 700)(494, 704)(495, 701)(496, 715)(497, 780)(498, 763)(499, 765)(500, 762)(501, 840)(502, 747)(503, 764)(504, 837) MAP : A3.14 NOTES : type II, reflexible, isomorphic to DBar({3,7}), isomorphic to A3.13. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 7, 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3 * x.1^-1)^3, x.2^7, (x.3^-1 * x.2^-2)^4, (x.1 * x.2^-1)^7 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 14) #DARTS : 1008 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504)(505, 673, 841)(506, 674, 842)(507, 675, 843)(508, 676, 844)(509, 677, 845)(510, 678, 846)(511, 679, 847)(512, 680, 848)(513, 681, 849)(514, 682, 850)(515, 683, 851)(516, 684, 852)(517, 685, 853)(518, 686, 854)(519, 687, 855)(520, 688, 856)(521, 689, 857)(522, 690, 858)(523, 691, 859)(524, 692, 860)(525, 693, 861)(526, 694, 862)(527, 695, 863)(528, 696, 864)(529, 697, 865)(530, 698, 866)(531, 699, 867)(532, 700, 868)(533, 701, 869)(534, 702, 870)(535, 703, 871)(536, 704, 872)(537, 705, 873)(538, 706, 874)(539, 707, 875)(540, 708, 876)(541, 709, 877)(542, 710, 878)(543, 711, 879)(544, 712, 880)(545, 713, 881)(546, 714, 882)(547, 715, 883)(548, 716, 884)(549, 717, 885)(550, 718, 886)(551, 719, 887)(552, 720, 888)(553, 721, 889)(554, 722, 890)(555, 723, 891)(556, 724, 892)(557, 725, 893)(558, 726, 894)(559, 727, 895)(560, 728, 896)(561, 729, 897)(562, 730, 898)(563, 731, 899)(564, 732, 900)(565, 733, 901)(566, 734, 902)(567, 735, 903)(568, 736, 904)(569, 737, 905)(570, 738, 906)(571, 739, 907)(572, 740, 908)(573, 741, 909)(574, 742, 910)(575, 743, 911)(576, 744, 912)(577, 745, 913)(578, 746, 914)(579, 747, 915)(580, 748, 916)(581, 749, 917)(582, 750, 918)(583, 751, 919)(584, 752, 920)(585, 753, 921)(586, 754, 922)(587, 755, 923)(588, 756, 924)(589, 757, 925)(590, 758, 926)(591, 759, 927)(592, 760, 928)(593, 761, 929)(594, 762, 930)(595, 763, 931)(596, 764, 932)(597, 765, 933)(598, 766, 934)(599, 767, 935)(600, 768, 936)(601, 769, 937)(602, 770, 938)(603, 771, 939)(604, 772, 940)(605, 773, 941)(606, 774, 942)(607, 775, 943)(608, 776, 944)(609, 777, 945)(610, 778, 946)(611, 779, 947)(612, 780, 948)(613, 781, 949)(614, 782, 950)(615, 783, 951)(616, 784, 952)(617, 785, 953)(618, 786, 954)(619, 787, 955)(620, 788, 956)(621, 789, 957)(622, 790, 958)(623, 791, 959)(624, 792, 960)(625, 793, 961)(626, 794, 962)(627, 795, 963)(628, 796, 964)(629, 797, 965)(630, 798, 966)(631, 799, 967)(632, 800, 968)(633, 801, 969)(634, 802, 970)(635, 803, 971)(636, 804, 972)(637, 805, 973)(638, 806, 974)(639, 807, 975)(640, 808, 976)(641, 809, 977)(642, 810, 978)(643, 811, 979)(644, 812, 980)(645, 813, 981)(646, 814, 982)(647, 815, 983)(648, 816, 984)(649, 817, 985)(650, 818, 986)(651, 819, 987)(652, 820, 988)(653, 821, 989)(654, 822, 990)(655, 823, 991)(656, 824, 992)(657, 825, 993)(658, 826, 994)(659, 827, 995)(660, 828, 996)(661, 829, 997)(662, 830, 998)(663, 831, 999)(664, 832, 1000)(665, 833, 1001)(666, 834, 1002)(667, 835, 1003)(668, 836, 1004)(669, 837, 1005)(670, 838, 1006)(671, 839, 1007)(672, 840, 1008) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 932)(170, 915)(171, 917)(172, 914)(173, 976)(174, 899)(175, 916)(176, 973)(177, 930)(178, 929)(179, 913)(180, 945)(181, 897)(182, 938)(183, 937)(184, 898)(185, 935)(186, 934)(187, 863)(188, 920)(189, 860)(190, 864)(191, 861)(192, 843)(193, 931)(194, 948)(195, 946)(196, 951)(197, 947)(198, 967)(199, 966)(200, 940)(201, 998)(202, 999)(203, 996)(204, 862)(205, 994)(206, 845)(207, 848)(208, 993)(209, 933)(210, 936)(211, 950)(212, 869)(213, 871)(214, 852)(215, 867)(216, 870)(217, 1008)(218, 1005)(219, 872)(220, 1003)(221, 854)(222, 1001)(223, 1002)(224, 855)(225, 891)(226, 884)(227, 882)(228, 887)(229, 883)(230, 919)(231, 918)(232, 868)(233, 893)(234, 896)(235, 886)(236, 989)(237, 991)(238, 1004)(239, 987)(240, 990)(241, 890)(242, 889)(243, 873)(244, 881)(245, 857)(246, 866)(247, 865)(248, 858)(249, 928)(250, 925)(251, 992)(252, 923)(253, 1006)(254, 921)(255, 922)(256, 1007)(257, 892)(258, 875)(259, 877)(260, 874)(261, 952)(262, 859)(263, 876)(264, 949)(265, 910)(266, 911)(267, 908)(268, 982)(269, 906)(270, 997)(271, 1000)(272, 905)(273, 895)(274, 894)(275, 983)(276, 880)(277, 980)(278, 984)(279, 981)(280, 995)(281, 959)(282, 958)(283, 903)(284, 968)(285, 900)(286, 904)(287, 901)(288, 907)(289, 956)(290, 963)(291, 965)(292, 962)(293, 888)(294, 979)(295, 964)(296, 885)(297, 846)(298, 847)(299, 844)(300, 902)(301, 842)(302, 909)(303, 912)(304, 841)(305, 954)(306, 953)(307, 961)(308, 969)(309, 977)(310, 986)(311, 985)(312, 978)(313, 856)(314, 853)(315, 944)(316, 851)(317, 926)(318, 849)(319, 850)(320, 927)(321, 955)(322, 972)(323, 970)(324, 975)(325, 971)(326, 879)(327, 878)(328, 988)(329, 957)(330, 960)(331, 974)(332, 941)(333, 943)(334, 924)(335, 939)(336, 942)(337, 826)(338, 825)(339, 833)(340, 809)(341, 817)(342, 794)(343, 793)(344, 818)(345, 827)(346, 812)(347, 810)(348, 815)(349, 811)(350, 727)(351, 726)(352, 796)(353, 828)(354, 835)(355, 837)(356, 834)(357, 704)(358, 819)(359, 836)(360, 701)(361, 829)(362, 832)(363, 814)(364, 741)(365, 743)(366, 732)(367, 739)(368, 742)(369, 831)(370, 830)(371, 767)(372, 840)(373, 764)(374, 768)(375, 765)(376, 747)(377, 680)(378, 677)(379, 744)(380, 675)(381, 734)(382, 673)(383, 674)(384, 735)(385, 694)(386, 695)(387, 692)(388, 766)(389, 690)(390, 749)(391, 752)(392, 689)(393, 792)(394, 789)(395, 688)(396, 787)(397, 678)(398, 785)(399, 786)(400, 679)(401, 806)(402, 807)(403, 804)(404, 710)(405, 802)(406, 693)(407, 696)(408, 801)(409, 773)(410, 776)(411, 758)(412, 685)(413, 687)(414, 676)(415, 683)(416, 686)(417, 775)(418, 774)(419, 711)(420, 784)(421, 708)(422, 712)(423, 709)(424, 691)(425, 771)(426, 756)(427, 754)(428, 759)(429, 755)(430, 839)(431, 838)(432, 740)(433, 772)(434, 779)(435, 781)(436, 778)(437, 816)(438, 763)(439, 780)(440, 813)(441, 770)(442, 769)(443, 777)(444, 753)(445, 761)(446, 738)(447, 737)(448, 762)(449, 717)(450, 720)(451, 702)(452, 797)(453, 799)(454, 788)(455, 795)(456, 798)(457, 736)(458, 733)(459, 800)(460, 731)(461, 790)(462, 729)(463, 730)(464, 791)(465, 715)(466, 700)(467, 698)(468, 703)(469, 699)(470, 783)(471, 782)(472, 684)(473, 750)(474, 751)(475, 748)(476, 822)(477, 746)(478, 805)(479, 808)(480, 745)(481, 714)(482, 713)(483, 721)(484, 697)(485, 705)(486, 682)(487, 681)(488, 706)(489, 719)(490, 718)(491, 823)(492, 728)(493, 820)(494, 824)(495, 821)(496, 803)(497, 716)(498, 723)(499, 725)(500, 722)(501, 760)(502, 707)(503, 724)(504, 757) MAP : A3.15 NOTES : type II, reflexible, isomorphic to DBar({3,7}), isomorphic to A3.13. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 7 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^2, (x.1 * x.2)^2, (x.3 * x.2)^3, x.3^7, (x.3 * x.1^-1)^7, (x.3 * x.2 * x.3^-1 * x.2)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 14) #DARTS : 1008 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504)(505, 673, 841)(506, 674, 842)(507, 675, 843)(508, 676, 844)(509, 677, 845)(510, 678, 846)(511, 679, 847)(512, 680, 848)(513, 681, 849)(514, 682, 850)(515, 683, 851)(516, 684, 852)(517, 685, 853)(518, 686, 854)(519, 687, 855)(520, 688, 856)(521, 689, 857)(522, 690, 858)(523, 691, 859)(524, 692, 860)(525, 693, 861)(526, 694, 862)(527, 695, 863)(528, 696, 864)(529, 697, 865)(530, 698, 866)(531, 699, 867)(532, 700, 868)(533, 701, 869)(534, 702, 870)(535, 703, 871)(536, 704, 872)(537, 705, 873)(538, 706, 874)(539, 707, 875)(540, 708, 876)(541, 709, 877)(542, 710, 878)(543, 711, 879)(544, 712, 880)(545, 713, 881)(546, 714, 882)(547, 715, 883)(548, 716, 884)(549, 717, 885)(550, 718, 886)(551, 719, 887)(552, 720, 888)(553, 721, 889)(554, 722, 890)(555, 723, 891)(556, 724, 892)(557, 725, 893)(558, 726, 894)(559, 727, 895)(560, 728, 896)(561, 729, 897)(562, 730, 898)(563, 731, 899)(564, 732, 900)(565, 733, 901)(566, 734, 902)(567, 735, 903)(568, 736, 904)(569, 737, 905)(570, 738, 906)(571, 739, 907)(572, 740, 908)(573, 741, 909)(574, 742, 910)(575, 743, 911)(576, 744, 912)(577, 745, 913)(578, 746, 914)(579, 747, 915)(580, 748, 916)(581, 749, 917)(582, 750, 918)(583, 751, 919)(584, 752, 920)(585, 753, 921)(586, 754, 922)(587, 755, 923)(588, 756, 924)(589, 757, 925)(590, 758, 926)(591, 759, 927)(592, 760, 928)(593, 761, 929)(594, 762, 930)(595, 763, 931)(596, 764, 932)(597, 765, 933)(598, 766, 934)(599, 767, 935)(600, 768, 936)(601, 769, 937)(602, 770, 938)(603, 771, 939)(604, 772, 940)(605, 773, 941)(606, 774, 942)(607, 775, 943)(608, 776, 944)(609, 777, 945)(610, 778, 946)(611, 779, 947)(612, 780, 948)(613, 781, 949)(614, 782, 950)(615, 783, 951)(616, 784, 952)(617, 785, 953)(618, 786, 954)(619, 787, 955)(620, 788, 956)(621, 789, 957)(622, 790, 958)(623, 791, 959)(624, 792, 960)(625, 793, 961)(626, 794, 962)(627, 795, 963)(628, 796, 964)(629, 797, 965)(630, 798, 966)(631, 799, 967)(632, 800, 968)(633, 801, 969)(634, 802, 970)(635, 803, 971)(636, 804, 972)(637, 805, 973)(638, 806, 974)(639, 807, 975)(640, 808, 976)(641, 809, 977)(642, 810, 978)(643, 811, 979)(644, 812, 980)(645, 813, 981)(646, 814, 982)(647, 815, 983)(648, 816, 984)(649, 817, 985)(650, 818, 986)(651, 819, 987)(652, 820, 988)(653, 821, 989)(654, 822, 990)(655, 823, 991)(656, 824, 992)(657, 825, 993)(658, 826, 994)(659, 827, 995)(660, 828, 996)(661, 829, 997)(662, 830, 998)(663, 831, 999)(664, 832, 1000)(665, 833, 1001)(666, 834, 1002)(667, 835, 1003)(668, 836, 1004)(669, 837, 1005)(670, 838, 1006)(671, 839, 1007)(672, 840, 1008) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 842)(170, 841)(171, 849)(172, 857)(173, 865)(174, 874)(175, 873)(176, 866)(177, 843)(178, 860)(179, 858)(180, 863)(181, 859)(182, 935)(183, 934)(184, 876)(185, 844)(186, 851)(187, 853)(188, 850)(189, 944)(190, 867)(191, 852)(192, 941)(193, 845)(194, 848)(195, 862)(196, 997)(197, 999)(198, 980)(199, 995)(200, 998)(201, 847)(202, 846)(203, 959)(204, 856)(205, 956)(206, 960)(207, 957)(208, 963)(209, 912)(210, 909)(211, 1000)(212, 907)(213, 982)(214, 905)(215, 906)(216, 983)(217, 902)(218, 903)(219, 900)(220, 958)(221, 898)(222, 965)(223, 968)(224, 897)(225, 896)(226, 893)(227, 928)(228, 891)(229, 910)(230, 889)(231, 890)(232, 911)(233, 886)(234, 887)(235, 884)(236, 918)(237, 882)(238, 901)(239, 904)(240, 881)(241, 989)(242, 992)(243, 1006)(244, 925)(245, 927)(246, 908)(247, 923)(248, 926)(249, 991)(250, 990)(251, 919)(252, 976)(253, 916)(254, 920)(255, 917)(256, 899)(257, 987)(258, 1004)(259, 1002)(260, 1007)(261, 1003)(262, 855)(263, 854)(264, 996)(265, 988)(266, 971)(267, 973)(268, 970)(269, 864)(270, 955)(271, 972)(272, 861)(273, 986)(274, 985)(275, 969)(276, 1001)(277, 953)(278, 994)(279, 993)(280, 954)(281, 949)(282, 952)(283, 942)(284, 877)(285, 879)(286, 892)(287, 875)(288, 878)(289, 984)(290, 981)(291, 880)(292, 979)(293, 894)(294, 977)(295, 978)(296, 895)(297, 947)(298, 940)(299, 938)(300, 943)(301, 939)(302, 975)(303, 974)(304, 924)(305, 966)(306, 967)(307, 964)(308, 870)(309, 962)(310, 885)(311, 888)(312, 961)(313, 946)(314, 945)(315, 929)(316, 937)(317, 913)(318, 922)(319, 921)(320, 914)(321, 951)(322, 950)(323, 871)(324, 936)(325, 868)(326, 872)(327, 869)(328, 883)(329, 948)(330, 931)(331, 933)(332, 930)(333, 1008)(334, 915)(335, 932)(336, 1005)(337, 764)(338, 747)(339, 749)(340, 746)(341, 808)(342, 731)(343, 748)(344, 805)(345, 762)(346, 761)(347, 745)(348, 777)(349, 729)(350, 770)(351, 769)(352, 730)(353, 767)(354, 766)(355, 695)(356, 752)(357, 692)(358, 696)(359, 693)(360, 675)(361, 763)(362, 780)(363, 778)(364, 783)(365, 779)(366, 799)(367, 798)(368, 772)(369, 830)(370, 831)(371, 828)(372, 694)(373, 826)(374, 677)(375, 680)(376, 825)(377, 765)(378, 768)(379, 782)(380, 701)(381, 703)(382, 684)(383, 699)(384, 702)(385, 840)(386, 837)(387, 704)(388, 835)(389, 686)(390, 833)(391, 834)(392, 687)(393, 723)(394, 716)(395, 714)(396, 719)(397, 715)(398, 751)(399, 750)(400, 700)(401, 725)(402, 728)(403, 718)(404, 821)(405, 823)(406, 836)(407, 819)(408, 822)(409, 722)(410, 721)(411, 705)(412, 713)(413, 689)(414, 698)(415, 697)(416, 690)(417, 760)(418, 757)(419, 824)(420, 755)(421, 838)(422, 753)(423, 754)(424, 839)(425, 724)(426, 707)(427, 709)(428, 706)(429, 784)(430, 691)(431, 708)(432, 781)(433, 742)(434, 743)(435, 740)(436, 814)(437, 738)(438, 829)(439, 832)(440, 737)(441, 727)(442, 726)(443, 815)(444, 712)(445, 812)(446, 816)(447, 813)(448, 827)(449, 791)(450, 790)(451, 735)(452, 800)(453, 732)(454, 736)(455, 733)(456, 739)(457, 788)(458, 795)(459, 797)(460, 794)(461, 720)(462, 811)(463, 796)(464, 717)(465, 678)(466, 679)(467, 676)(468, 734)(469, 674)(470, 741)(471, 744)(472, 673)(473, 786)(474, 785)(475, 793)(476, 801)(477, 809)(478, 818)(479, 817)(480, 810)(481, 688)(482, 685)(483, 776)(484, 683)(485, 758)(486, 681)(487, 682)(488, 759)(489, 787)(490, 804)(491, 802)(492, 807)(493, 803)(494, 711)(495, 710)(496, 820)(497, 789)(498, 792)(499, 806)(500, 773)(501, 775)(502, 756)(503, 771)(504, 774) MAP : A3.16 NOTES : type II, reflexible, isomorphic to DBar({3,7}), isomorphic to A3.13. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 7, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^3, x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-2 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1, (x.3 * x.2^-1)^7, x.3 * x.2 * x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 14) #DARTS : 1008 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504)(505, 673, 841)(506, 674, 842)(507, 675, 843)(508, 676, 844)(509, 677, 845)(510, 678, 846)(511, 679, 847)(512, 680, 848)(513, 681, 849)(514, 682, 850)(515, 683, 851)(516, 684, 852)(517, 685, 853)(518, 686, 854)(519, 687, 855)(520, 688, 856)(521, 689, 857)(522, 690, 858)(523, 691, 859)(524, 692, 860)(525, 693, 861)(526, 694, 862)(527, 695, 863)(528, 696, 864)(529, 697, 865)(530, 698, 866)(531, 699, 867)(532, 700, 868)(533, 701, 869)(534, 702, 870)(535, 703, 871)(536, 704, 872)(537, 705, 873)(538, 706, 874)(539, 707, 875)(540, 708, 876)(541, 709, 877)(542, 710, 878)(543, 711, 879)(544, 712, 880)(545, 713, 881)(546, 714, 882)(547, 715, 883)(548, 716, 884)(549, 717, 885)(550, 718, 886)(551, 719, 887)(552, 720, 888)(553, 721, 889)(554, 722, 890)(555, 723, 891)(556, 724, 892)(557, 725, 893)(558, 726, 894)(559, 727, 895)(560, 728, 896)(561, 729, 897)(562, 730, 898)(563, 731, 899)(564, 732, 900)(565, 733, 901)(566, 734, 902)(567, 735, 903)(568, 736, 904)(569, 737, 905)(570, 738, 906)(571, 739, 907)(572, 740, 908)(573, 741, 909)(574, 742, 910)(575, 743, 911)(576, 744, 912)(577, 745, 913)(578, 746, 914)(579, 747, 915)(580, 748, 916)(581, 749, 917)(582, 750, 918)(583, 751, 919)(584, 752, 920)(585, 753, 921)(586, 754, 922)(587, 755, 923)(588, 756, 924)(589, 757, 925)(590, 758, 926)(591, 759, 927)(592, 760, 928)(593, 761, 929)(594, 762, 930)(595, 763, 931)(596, 764, 932)(597, 765, 933)(598, 766, 934)(599, 767, 935)(600, 768, 936)(601, 769, 937)(602, 770, 938)(603, 771, 939)(604, 772, 940)(605, 773, 941)(606, 774, 942)(607, 775, 943)(608, 776, 944)(609, 777, 945)(610, 778, 946)(611, 779, 947)(612, 780, 948)(613, 781, 949)(614, 782, 950)(615, 783, 951)(616, 784, 952)(617, 785, 953)(618, 786, 954)(619, 787, 955)(620, 788, 956)(621, 789, 957)(622, 790, 958)(623, 791, 959)(624, 792, 960)(625, 793, 961)(626, 794, 962)(627, 795, 963)(628, 796, 964)(629, 797, 965)(630, 798, 966)(631, 799, 967)(632, 800, 968)(633, 801, 969)(634, 802, 970)(635, 803, 971)(636, 804, 972)(637, 805, 973)(638, 806, 974)(639, 807, 975)(640, 808, 976)(641, 809, 977)(642, 810, 978)(643, 811, 979)(644, 812, 980)(645, 813, 981)(646, 814, 982)(647, 815, 983)(648, 816, 984)(649, 817, 985)(650, 818, 986)(651, 819, 987)(652, 820, 988)(653, 821, 989)(654, 822, 990)(655, 823, 991)(656, 824, 992)(657, 825, 993)(658, 826, 994)(659, 827, 995)(660, 828, 996)(661, 829, 997)(662, 830, 998)(663, 831, 999)(664, 832, 1000)(665, 833, 1001)(666, 834, 1002)(667, 835, 1003)(668, 836, 1004)(669, 837, 1005)(670, 838, 1006)(671, 839, 1007)(672, 840, 1008) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 843)(170, 860)(171, 858)(172, 863)(173, 859)(174, 935)(175, 934)(176, 876)(177, 845)(178, 848)(179, 862)(180, 997)(181, 999)(182, 980)(183, 995)(184, 998)(185, 842)(186, 841)(187, 849)(188, 857)(189, 865)(190, 874)(191, 873)(192, 866)(193, 912)(194, 909)(195, 1000)(196, 907)(197, 982)(198, 905)(199, 906)(200, 983)(201, 844)(202, 851)(203, 853)(204, 850)(205, 944)(206, 867)(207, 852)(208, 941)(209, 902)(210, 903)(211, 900)(212, 958)(213, 898)(214, 965)(215, 968)(216, 897)(217, 847)(218, 846)(219, 959)(220, 856)(221, 956)(222, 960)(223, 957)(224, 963)(225, 991)(226, 990)(227, 919)(228, 976)(229, 916)(230, 920)(231, 917)(232, 899)(233, 988)(234, 971)(235, 973)(236, 970)(237, 864)(238, 955)(239, 972)(240, 861)(241, 886)(242, 887)(243, 884)(244, 918)(245, 882)(246, 901)(247, 904)(248, 881)(249, 986)(250, 985)(251, 969)(252, 1001)(253, 953)(254, 994)(255, 993)(256, 954)(257, 896)(258, 893)(259, 928)(260, 891)(261, 910)(262, 889)(263, 890)(264, 911)(265, 987)(266, 1004)(267, 1002)(268, 1007)(269, 1003)(270, 855)(271, 854)(272, 996)(273, 989)(274, 992)(275, 1006)(276, 925)(277, 927)(278, 908)(279, 923)(280, 926)(281, 948)(282, 931)(283, 933)(284, 930)(285, 1008)(286, 915)(287, 932)(288, 1005)(289, 946)(290, 945)(291, 929)(292, 937)(293, 913)(294, 922)(295, 921)(296, 914)(297, 951)(298, 950)(299, 871)(300, 936)(301, 868)(302, 872)(303, 869)(304, 883)(305, 947)(306, 940)(307, 938)(308, 943)(309, 939)(310, 975)(311, 974)(312, 924)(313, 966)(314, 967)(315, 964)(316, 870)(317, 962)(318, 885)(319, 888)(320, 961)(321, 949)(322, 952)(323, 942)(324, 877)(325, 879)(326, 892)(327, 875)(328, 878)(329, 984)(330, 981)(331, 880)(332, 979)(333, 894)(334, 977)(335, 978)(336, 895)(337, 743)(338, 742)(339, 727)(340, 760)(341, 724)(342, 728)(343, 725)(344, 707)(345, 740)(346, 755)(347, 757)(348, 754)(349, 824)(350, 771)(351, 756)(352, 821)(353, 814)(354, 815)(355, 812)(356, 726)(357, 810)(358, 709)(359, 712)(360, 809)(361, 738)(362, 737)(363, 753)(364, 729)(365, 769)(366, 746)(367, 745)(368, 770)(369, 832)(370, 829)(371, 680)(372, 827)(373, 694)(374, 825)(375, 826)(376, 695)(377, 739)(378, 732)(379, 730)(380, 735)(381, 731)(382, 791)(383, 790)(384, 748)(385, 741)(386, 744)(387, 734)(388, 677)(389, 679)(390, 692)(391, 675)(392, 678)(393, 700)(394, 715)(395, 717)(396, 714)(397, 736)(398, 723)(399, 716)(400, 733)(401, 698)(402, 697)(403, 713)(404, 681)(405, 721)(406, 674)(407, 673)(408, 722)(409, 703)(410, 702)(411, 799)(412, 720)(413, 796)(414, 800)(415, 797)(416, 811)(417, 699)(418, 684)(419, 682)(420, 687)(421, 683)(422, 759)(423, 758)(424, 676)(425, 782)(426, 783)(427, 780)(428, 798)(429, 778)(430, 813)(431, 816)(432, 777)(433, 701)(434, 704)(435, 686)(436, 837)(437, 839)(438, 828)(439, 835)(440, 838)(441, 768)(442, 765)(443, 840)(444, 763)(445, 830)(446, 761)(447, 762)(448, 831)(449, 803)(450, 820)(451, 818)(452, 823)(453, 819)(454, 719)(455, 718)(456, 836)(457, 805)(458, 808)(459, 822)(460, 749)(461, 751)(462, 764)(463, 747)(464, 750)(465, 802)(466, 801)(467, 785)(468, 817)(469, 793)(470, 834)(471, 833)(472, 794)(473, 696)(474, 693)(475, 752)(476, 691)(477, 766)(478, 689)(479, 690)(480, 767)(481, 804)(482, 787)(483, 789)(484, 786)(485, 688)(486, 795)(487, 788)(488, 685)(489, 710)(490, 711)(491, 708)(492, 774)(493, 706)(494, 781)(495, 784)(496, 705)(497, 807)(498, 806)(499, 775)(500, 792)(501, 772)(502, 776)(503, 773)(504, 779) MAP : A3.17 NOTES : type II, reflexible, isomorphic to DBar({3,7}), isomorphic to A3.13. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 7 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^2, (x.1 * x.2)^2, (x.3 * x.2)^3, x.3^7, (x.3 * x.1^-1)^7, (x.3 * x.2 * x.3^-1 * x.2)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 14) #DARTS : 1008 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504)(505, 673, 841)(506, 674, 842)(507, 675, 843)(508, 676, 844)(509, 677, 845)(510, 678, 846)(511, 679, 847)(512, 680, 848)(513, 681, 849)(514, 682, 850)(515, 683, 851)(516, 684, 852)(517, 685, 853)(518, 686, 854)(519, 687, 855)(520, 688, 856)(521, 689, 857)(522, 690, 858)(523, 691, 859)(524, 692, 860)(525, 693, 861)(526, 694, 862)(527, 695, 863)(528, 696, 864)(529, 697, 865)(530, 698, 866)(531, 699, 867)(532, 700, 868)(533, 701, 869)(534, 702, 870)(535, 703, 871)(536, 704, 872)(537, 705, 873)(538, 706, 874)(539, 707, 875)(540, 708, 876)(541, 709, 877)(542, 710, 878)(543, 711, 879)(544, 712, 880)(545, 713, 881)(546, 714, 882)(547, 715, 883)(548, 716, 884)(549, 717, 885)(550, 718, 886)(551, 719, 887)(552, 720, 888)(553, 721, 889)(554, 722, 890)(555, 723, 891)(556, 724, 892)(557, 725, 893)(558, 726, 894)(559, 727, 895)(560, 728, 896)(561, 729, 897)(562, 730, 898)(563, 731, 899)(564, 732, 900)(565, 733, 901)(566, 734, 902)(567, 735, 903)(568, 736, 904)(569, 737, 905)(570, 738, 906)(571, 739, 907)(572, 740, 908)(573, 741, 909)(574, 742, 910)(575, 743, 911)(576, 744, 912)(577, 745, 913)(578, 746, 914)(579, 747, 915)(580, 748, 916)(581, 749, 917)(582, 750, 918)(583, 751, 919)(584, 752, 920)(585, 753, 921)(586, 754, 922)(587, 755, 923)(588, 756, 924)(589, 757, 925)(590, 758, 926)(591, 759, 927)(592, 760, 928)(593, 761, 929)(594, 762, 930)(595, 763, 931)(596, 764, 932)(597, 765, 933)(598, 766, 934)(599, 767, 935)(600, 768, 936)(601, 769, 937)(602, 770, 938)(603, 771, 939)(604, 772, 940)(605, 773, 941)(606, 774, 942)(607, 775, 943)(608, 776, 944)(609, 777, 945)(610, 778, 946)(611, 779, 947)(612, 780, 948)(613, 781, 949)(614, 782, 950)(615, 783, 951)(616, 784, 952)(617, 785, 953)(618, 786, 954)(619, 787, 955)(620, 788, 956)(621, 789, 957)(622, 790, 958)(623, 791, 959)(624, 792, 960)(625, 793, 961)(626, 794, 962)(627, 795, 963)(628, 796, 964)(629, 797, 965)(630, 798, 966)(631, 799, 967)(632, 800, 968)(633, 801, 969)(634, 802, 970)(635, 803, 971)(636, 804, 972)(637, 805, 973)(638, 806, 974)(639, 807, 975)(640, 808, 976)(641, 809, 977)(642, 810, 978)(643, 811, 979)(644, 812, 980)(645, 813, 981)(646, 814, 982)(647, 815, 983)(648, 816, 984)(649, 817, 985)(650, 818, 986)(651, 819, 987)(652, 820, 988)(653, 821, 989)(654, 822, 990)(655, 823, 991)(656, 824, 992)(657, 825, 993)(658, 826, 994)(659, 827, 995)(660, 828, 996)(661, 829, 997)(662, 830, 998)(663, 831, 999)(664, 832, 1000)(665, 833, 1001)(666, 834, 1002)(667, 835, 1003)(668, 836, 1004)(669, 837, 1005)(670, 838, 1006)(671, 839, 1007)(672, 840, 1008) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 842)(170, 841)(171, 849)(172, 857)(173, 865)(174, 874)(175, 873)(176, 866)(177, 843)(178, 860)(179, 858)(180, 863)(181, 859)(182, 935)(183, 934)(184, 876)(185, 844)(186, 851)(187, 853)(188, 850)(189, 944)(190, 867)(191, 852)(192, 941)(193, 845)(194, 848)(195, 862)(196, 997)(197, 999)(198, 980)(199, 995)(200, 998)(201, 847)(202, 846)(203, 959)(204, 856)(205, 956)(206, 960)(207, 957)(208, 963)(209, 912)(210, 909)(211, 1000)(212, 907)(213, 982)(214, 905)(215, 906)(216, 983)(217, 902)(218, 903)(219, 900)(220, 958)(221, 898)(222, 965)(223, 968)(224, 897)(225, 896)(226, 893)(227, 928)(228, 891)(229, 910)(230, 889)(231, 890)(232, 911)(233, 886)(234, 887)(235, 884)(236, 918)(237, 882)(238, 901)(239, 904)(240, 881)(241, 989)(242, 992)(243, 1006)(244, 925)(245, 927)(246, 908)(247, 923)(248, 926)(249, 991)(250, 990)(251, 919)(252, 976)(253, 916)(254, 920)(255, 917)(256, 899)(257, 987)(258, 1004)(259, 1002)(260, 1007)(261, 1003)(262, 855)(263, 854)(264, 996)(265, 988)(266, 971)(267, 973)(268, 970)(269, 864)(270, 955)(271, 972)(272, 861)(273, 986)(274, 985)(275, 969)(276, 1001)(277, 953)(278, 994)(279, 993)(280, 954)(281, 949)(282, 952)(283, 942)(284, 877)(285, 879)(286, 892)(287, 875)(288, 878)(289, 984)(290, 981)(291, 880)(292, 979)(293, 894)(294, 977)(295, 978)(296, 895)(297, 947)(298, 940)(299, 938)(300, 943)(301, 939)(302, 975)(303, 974)(304, 924)(305, 966)(306, 967)(307, 964)(308, 870)(309, 962)(310, 885)(311, 888)(312, 961)(313, 946)(314, 945)(315, 929)(316, 937)(317, 913)(318, 922)(319, 921)(320, 914)(321, 951)(322, 950)(323, 871)(324, 936)(325, 868)(326, 872)(327, 869)(328, 883)(329, 948)(330, 931)(331, 933)(332, 930)(333, 1008)(334, 915)(335, 932)(336, 1005)(337, 808)(338, 805)(339, 696)(340, 803)(341, 710)(342, 801)(343, 802)(344, 711)(345, 822)(346, 823)(347, 820)(348, 718)(349, 818)(350, 725)(351, 728)(352, 817)(353, 749)(354, 752)(355, 766)(356, 693)(357, 695)(358, 708)(359, 691)(360, 694)(361, 751)(362, 750)(363, 719)(364, 736)(365, 716)(366, 720)(367, 717)(368, 723)(369, 747)(370, 764)(371, 762)(372, 767)(373, 763)(374, 831)(375, 830)(376, 780)(377, 748)(378, 731)(379, 733)(380, 730)(381, 800)(382, 739)(383, 732)(384, 797)(385, 746)(386, 745)(387, 729)(388, 761)(389, 737)(390, 778)(391, 777)(392, 738)(393, 685)(394, 688)(395, 678)(396, 789)(397, 791)(398, 804)(399, 787)(400, 790)(401, 776)(402, 773)(403, 792)(404, 771)(405, 806)(406, 769)(407, 770)(408, 807)(409, 683)(410, 676)(411, 674)(412, 679)(413, 675)(414, 735)(415, 734)(416, 692)(417, 758)(418, 759)(419, 756)(420, 838)(421, 754)(422, 821)(423, 824)(424, 753)(425, 682)(426, 681)(427, 697)(428, 673)(429, 713)(430, 690)(431, 689)(432, 714)(433, 687)(434, 686)(435, 839)(436, 704)(437, 836)(438, 840)(439, 837)(440, 819)(441, 684)(442, 699)(443, 701)(444, 698)(445, 768)(446, 715)(447, 700)(448, 765)(449, 810)(450, 809)(451, 825)(452, 793)(453, 833)(454, 786)(455, 785)(456, 834)(457, 811)(458, 796)(459, 794)(460, 799)(461, 795)(462, 703)(463, 702)(464, 788)(465, 812)(466, 827)(467, 829)(468, 826)(469, 680)(470, 835)(471, 828)(472, 677)(473, 813)(474, 816)(475, 798)(476, 781)(477, 783)(478, 772)(479, 779)(480, 782)(481, 815)(482, 814)(483, 743)(484, 832)(485, 740)(486, 744)(487, 741)(488, 755)(489, 712)(490, 709)(491, 784)(492, 707)(493, 774)(494, 705)(495, 706)(496, 775)(497, 726)(498, 727)(499, 724)(500, 742)(501, 722)(502, 757)(503, 760)(504, 721) MAP : A3.18 NOTES : type II, reflexible, isomorphic to DBar({3,7}), isomorphic to A3.13. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 7, 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3 * x.1^-1)^3, x.2^7, (x.3^-1 * x.2^-2)^4, (x.1 * x.2^-1)^7 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 14) #DARTS : 1008 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504)(505, 673, 841)(506, 674, 842)(507, 675, 843)(508, 676, 844)(509, 677, 845)(510, 678, 846)(511, 679, 847)(512, 680, 848)(513, 681, 849)(514, 682, 850)(515, 683, 851)(516, 684, 852)(517, 685, 853)(518, 686, 854)(519, 687, 855)(520, 688, 856)(521, 689, 857)(522, 690, 858)(523, 691, 859)(524, 692, 860)(525, 693, 861)(526, 694, 862)(527, 695, 863)(528, 696, 864)(529, 697, 865)(530, 698, 866)(531, 699, 867)(532, 700, 868)(533, 701, 869)(534, 702, 870)(535, 703, 871)(536, 704, 872)(537, 705, 873)(538, 706, 874)(539, 707, 875)(540, 708, 876)(541, 709, 877)(542, 710, 878)(543, 711, 879)(544, 712, 880)(545, 713, 881)(546, 714, 882)(547, 715, 883)(548, 716, 884)(549, 717, 885)(550, 718, 886)(551, 719, 887)(552, 720, 888)(553, 721, 889)(554, 722, 890)(555, 723, 891)(556, 724, 892)(557, 725, 893)(558, 726, 894)(559, 727, 895)(560, 728, 896)(561, 729, 897)(562, 730, 898)(563, 731, 899)(564, 732, 900)(565, 733, 901)(566, 734, 902)(567, 735, 903)(568, 736, 904)(569, 737, 905)(570, 738, 906)(571, 739, 907)(572, 740, 908)(573, 741, 909)(574, 742, 910)(575, 743, 911)(576, 744, 912)(577, 745, 913)(578, 746, 914)(579, 747, 915)(580, 748, 916)(581, 749, 917)(582, 750, 918)(583, 751, 919)(584, 752, 920)(585, 753, 921)(586, 754, 922)(587, 755, 923)(588, 756, 924)(589, 757, 925)(590, 758, 926)(591, 759, 927)(592, 760, 928)(593, 761, 929)(594, 762, 930)(595, 763, 931)(596, 764, 932)(597, 765, 933)(598, 766, 934)(599, 767, 935)(600, 768, 936)(601, 769, 937)(602, 770, 938)(603, 771, 939)(604, 772, 940)(605, 773, 941)(606, 774, 942)(607, 775, 943)(608, 776, 944)(609, 777, 945)(610, 778, 946)(611, 779, 947)(612, 780, 948)(613, 781, 949)(614, 782, 950)(615, 783, 951)(616, 784, 952)(617, 785, 953)(618, 786, 954)(619, 787, 955)(620, 788, 956)(621, 789, 957)(622, 790, 958)(623, 791, 959)(624, 792, 960)(625, 793, 961)(626, 794, 962)(627, 795, 963)(628, 796, 964)(629, 797, 965)(630, 798, 966)(631, 799, 967)(632, 800, 968)(633, 801, 969)(634, 802, 970)(635, 803, 971)(636, 804, 972)(637, 805, 973)(638, 806, 974)(639, 807, 975)(640, 808, 976)(641, 809, 977)(642, 810, 978)(643, 811, 979)(644, 812, 980)(645, 813, 981)(646, 814, 982)(647, 815, 983)(648, 816, 984)(649, 817, 985)(650, 818, 986)(651, 819, 987)(652, 820, 988)(653, 821, 989)(654, 822, 990)(655, 823, 991)(656, 824, 992)(657, 825, 993)(658, 826, 994)(659, 827, 995)(660, 828, 996)(661, 829, 997)(662, 830, 998)(663, 831, 999)(664, 832, 1000)(665, 833, 1001)(666, 834, 1002)(667, 835, 1003)(668, 836, 1004)(669, 837, 1005)(670, 838, 1006)(671, 839, 1007)(672, 840, 1008) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 845)(170, 848)(171, 862)(172, 997)(173, 999)(174, 980)(175, 995)(176, 998)(177, 912)(178, 909)(179, 1000)(180, 907)(181, 982)(182, 905)(183, 906)(184, 983)(185, 843)(186, 860)(187, 858)(188, 863)(189, 859)(190, 935)(191, 934)(192, 876)(193, 902)(194, 903)(195, 900)(196, 958)(197, 898)(198, 965)(199, 968)(200, 897)(201, 842)(202, 841)(203, 849)(204, 857)(205, 865)(206, 874)(207, 873)(208, 866)(209, 847)(210, 846)(211, 959)(212, 856)(213, 956)(214, 960)(215, 957)(216, 963)(217, 844)(218, 851)(219, 853)(220, 850)(221, 944)(222, 867)(223, 852)(224, 941)(225, 986)(226, 985)(227, 969)(228, 1001)(229, 953)(230, 994)(231, 993)(232, 954)(233, 987)(234, 1004)(235, 1002)(236, 1007)(237, 1003)(238, 855)(239, 854)(240, 996)(241, 988)(242, 971)(243, 973)(244, 970)(245, 864)(246, 955)(247, 972)(248, 861)(249, 989)(250, 992)(251, 1006)(252, 925)(253, 927)(254, 908)(255, 923)(256, 926)(257, 991)(258, 990)(259, 919)(260, 976)(261, 916)(262, 920)(263, 917)(264, 899)(265, 896)(266, 893)(267, 928)(268, 891)(269, 910)(270, 889)(271, 890)(272, 911)(273, 886)(274, 887)(275, 884)(276, 918)(277, 882)(278, 901)(279, 904)(280, 881)(281, 984)(282, 981)(283, 880)(284, 979)(285, 894)(286, 977)(287, 978)(288, 895)(289, 966)(290, 967)(291, 964)(292, 870)(293, 962)(294, 885)(295, 888)(296, 961)(297, 949)(298, 952)(299, 942)(300, 877)(301, 879)(302, 892)(303, 875)(304, 878)(305, 951)(306, 950)(307, 871)(308, 936)(309, 868)(310, 872)(311, 869)(312, 883)(313, 947)(314, 940)(315, 938)(316, 943)(317, 939)(318, 975)(319, 974)(320, 924)(321, 948)(322, 931)(323, 933)(324, 930)(325, 1008)(326, 915)(327, 932)(328, 1005)(329, 946)(330, 945)(331, 929)(332, 937)(333, 913)(334, 922)(335, 921)(336, 914)(337, 745)(338, 746)(339, 747)(340, 748)(341, 749)(342, 750)(343, 751)(344, 752)(345, 729)(346, 730)(347, 731)(348, 732)(349, 733)(350, 734)(351, 735)(352, 736)(353, 761)(354, 762)(355, 763)(356, 764)(357, 765)(358, 766)(359, 767)(360, 768)(361, 737)(362, 738)(363, 739)(364, 740)(365, 741)(366, 742)(367, 743)(368, 744)(369, 777)(370, 778)(371, 779)(372, 780)(373, 781)(374, 782)(375, 783)(376, 784)(377, 753)(378, 754)(379, 755)(380, 756)(381, 757)(382, 758)(383, 759)(384, 760)(385, 769)(386, 770)(387, 771)(388, 772)(389, 773)(390, 774)(391, 775)(392, 776)(393, 817)(394, 818)(395, 819)(396, 820)(397, 821)(398, 822)(399, 823)(400, 824)(401, 801)(402, 802)(403, 803)(404, 804)(405, 805)(406, 806)(407, 807)(408, 808)(409, 833)(410, 834)(411, 835)(412, 836)(413, 837)(414, 838)(415, 839)(416, 840)(417, 785)(418, 786)(419, 787)(420, 788)(421, 789)(422, 790)(423, 791)(424, 792)(425, 825)(426, 826)(427, 827)(428, 828)(429, 829)(430, 830)(431, 831)(432, 832)(433, 793)(434, 794)(435, 795)(436, 796)(437, 797)(438, 798)(439, 799)(440, 800)(441, 809)(442, 810)(443, 811)(444, 812)(445, 813)(446, 814)(447, 815)(448, 816)(449, 713)(450, 714)(451, 715)(452, 716)(453, 717)(454, 718)(455, 719)(456, 720)(457, 721)(458, 722)(459, 723)(460, 724)(461, 725)(462, 726)(463, 727)(464, 728)(465, 697)(466, 698)(467, 699)(468, 700)(469, 701)(470, 702)(471, 703)(472, 704)(473, 705)(474, 706)(475, 707)(476, 708)(477, 709)(478, 710)(479, 711)(480, 712)(481, 681)(482, 682)(483, 683)(484, 684)(485, 685)(486, 686)(487, 687)(488, 688)(489, 689)(490, 690)(491, 691)(492, 692)(493, 693)(494, 694)(495, 695)(496, 696)(497, 673)(498, 674)(499, 675)(500, 676)(501, 677)(502, 678)(503, 679)(504, 680) MAP : A3.19 NOTES : type II, reflexible, isomorphic to DBar({3,8}), representative. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^2, (x.1 * x.2)^2, (x.3^-1 * x.2)^3, x.3^2 * x.2 * x.3^-1 * x.2 * x.3^2 * x.2 * x.3^3 * x.2, (x.3^2 * x.2 * x.3^-3 * x.2)^2, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 16) #DARTS : 576 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288)(289, 385, 481)(290, 386, 482)(291, 387, 483)(292, 388, 484)(293, 389, 485)(294, 390, 486)(295, 391, 487)(296, 392, 488)(297, 393, 489)(298, 394, 490)(299, 395, 491)(300, 396, 492)(301, 397, 493)(302, 398, 494)(303, 399, 495)(304, 400, 496)(305, 401, 497)(306, 402, 498)(307, 403, 499)(308, 404, 500)(309, 405, 501)(310, 406, 502)(311, 407, 503)(312, 408, 504)(313, 409, 505)(314, 410, 506)(315, 411, 507)(316, 412, 508)(317, 413, 509)(318, 414, 510)(319, 415, 511)(320, 416, 512)(321, 417, 513)(322, 418, 514)(323, 419, 515)(324, 420, 516)(325, 421, 517)(326, 422, 518)(327, 423, 519)(328, 424, 520)(329, 425, 521)(330, 426, 522)(331, 427, 523)(332, 428, 524)(333, 429, 525)(334, 430, 526)(335, 431, 527)(336, 432, 528)(337, 433, 529)(338, 434, 530)(339, 435, 531)(340, 436, 532)(341, 437, 533)(342, 438, 534)(343, 439, 535)(344, 440, 536)(345, 441, 537)(346, 442, 538)(347, 443, 539)(348, 444, 540)(349, 445, 541)(350, 446, 542)(351, 447, 543)(352, 448, 544)(353, 449, 545)(354, 450, 546)(355, 451, 547)(356, 452, 548)(357, 453, 549)(358, 454, 550)(359, 455, 551)(360, 456, 552)(361, 457, 553)(362, 458, 554)(363, 459, 555)(364, 460, 556)(365, 461, 557)(366, 462, 558)(367, 463, 559)(368, 464, 560)(369, 465, 561)(370, 466, 562)(371, 467, 563)(372, 468, 564)(373, 469, 565)(374, 470, 566)(375, 471, 567)(376, 472, 568)(377, 473, 569)(378, 474, 570)(379, 475, 571)(380, 476, 572)(381, 477, 573)(382, 478, 574)(383, 479, 575)(384, 480, 576) L = (1, 289)(2, 290)(3, 291)(4, 292)(5, 293)(6, 294)(7, 295)(8, 296)(9, 297)(10, 298)(11, 299)(12, 300)(13, 301)(14, 302)(15, 303)(16, 304)(17, 305)(18, 306)(19, 307)(20, 308)(21, 309)(22, 310)(23, 311)(24, 312)(25, 313)(26, 314)(27, 315)(28, 316)(29, 317)(30, 318)(31, 319)(32, 320)(33, 321)(34, 322)(35, 323)(36, 324)(37, 325)(38, 326)(39, 327)(40, 328)(41, 329)(42, 330)(43, 331)(44, 332)(45, 333)(46, 334)(47, 335)(48, 336)(49, 337)(50, 338)(51, 339)(52, 340)(53, 341)(54, 342)(55, 343)(56, 344)(57, 345)(58, 346)(59, 347)(60, 348)(61, 349)(62, 350)(63, 351)(64, 352)(65, 353)(66, 354)(67, 355)(68, 356)(69, 357)(70, 358)(71, 359)(72, 360)(73, 361)(74, 362)(75, 363)(76, 364)(77, 365)(78, 366)(79, 367)(80, 368)(81, 369)(82, 370)(83, 371)(84, 372)(85, 373)(86, 374)(87, 375)(88, 376)(89, 377)(90, 378)(91, 379)(92, 380)(93, 381)(94, 382)(95, 383)(96, 384)(97, 484)(98, 488)(99, 485)(100, 481)(101, 483)(102, 514)(103, 517)(104, 482)(105, 498)(106, 561)(107, 562)(108, 513)(109, 497)(110, 501)(111, 565)(112, 533)(113, 493)(114, 489)(115, 510)(116, 509)(117, 494)(118, 543)(119, 538)(120, 505)(121, 504)(122, 528)(123, 544)(124, 539)(125, 500)(126, 499)(127, 512)(128, 511)(129, 492)(130, 486)(131, 519)(132, 524)(133, 487)(134, 520)(135, 515)(136, 518)(137, 523)(138, 525)(139, 521)(140, 516)(141, 522)(142, 527)(143, 526)(144, 506)(145, 560)(146, 576)(147, 555)(148, 559)(149, 496)(150, 556)(151, 550)(152, 554)(153, 574)(154, 503)(155, 508)(156, 551)(157, 569)(158, 573)(159, 502)(160, 507)(161, 571)(162, 575)(163, 572)(164, 566)(165, 570)(166, 535)(167, 540)(168, 567)(169, 563)(170, 536)(171, 531)(172, 534)(173, 568)(174, 564)(175, 532)(176, 529)(177, 490)(178, 491)(179, 553)(180, 558)(181, 495)(182, 548)(183, 552)(184, 557)(185, 541)(186, 549)(187, 545)(188, 547)(189, 542)(190, 537)(191, 546)(192, 530)(193, 394)(194, 395)(195, 457)(196, 462)(197, 399)(198, 452)(199, 456)(200, 461)(201, 445)(202, 453)(203, 449)(204, 451)(205, 446)(206, 441)(207, 450)(208, 434)(209, 396)(210, 390)(211, 423)(212, 428)(213, 391)(214, 424)(215, 419)(216, 422)(217, 427)(218, 429)(219, 425)(220, 420)(221, 426)(222, 431)(223, 430)(224, 410)(225, 464)(226, 480)(227, 459)(228, 463)(229, 400)(230, 460)(231, 454)(232, 458)(233, 478)(234, 407)(235, 412)(236, 455)(237, 473)(238, 477)(239, 406)(240, 411)(241, 397)(242, 393)(243, 414)(244, 413)(245, 398)(246, 447)(247, 442)(248, 409)(249, 408)(250, 432)(251, 448)(252, 443)(253, 404)(254, 403)(255, 416)(256, 415)(257, 388)(258, 392)(259, 389)(260, 385)(261, 387)(262, 418)(263, 421)(264, 386)(265, 402)(266, 465)(267, 466)(268, 417)(269, 401)(270, 405)(271, 469)(272, 437)(273, 475)(274, 479)(275, 476)(276, 470)(277, 474)(278, 439)(279, 444)(280, 471)(281, 467)(282, 440)(283, 435)(284, 438)(285, 472)(286, 468)(287, 436)(288, 433) MAP : A3.20 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A3.19. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^2, (x.1 * x.2)^2, (x.3^-1 * x.2)^3, x.3^2 * x.2 * x.3^-1 * x.2 * x.3^2 * x.2 * x.3^3 * x.2, (x.3^2 * x.2 * x.3^-3 * x.2)^2, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 16) #DARTS : 576 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288)(289, 385, 481)(290, 386, 482)(291, 387, 483)(292, 388, 484)(293, 389, 485)(294, 390, 486)(295, 391, 487)(296, 392, 488)(297, 393, 489)(298, 394, 490)(299, 395, 491)(300, 396, 492)(301, 397, 493)(302, 398, 494)(303, 399, 495)(304, 400, 496)(305, 401, 497)(306, 402, 498)(307, 403, 499)(308, 404, 500)(309, 405, 501)(310, 406, 502)(311, 407, 503)(312, 408, 504)(313, 409, 505)(314, 410, 506)(315, 411, 507)(316, 412, 508)(317, 413, 509)(318, 414, 510)(319, 415, 511)(320, 416, 512)(321, 417, 513)(322, 418, 514)(323, 419, 515)(324, 420, 516)(325, 421, 517)(326, 422, 518)(327, 423, 519)(328, 424, 520)(329, 425, 521)(330, 426, 522)(331, 427, 523)(332, 428, 524)(333, 429, 525)(334, 430, 526)(335, 431, 527)(336, 432, 528)(337, 433, 529)(338, 434, 530)(339, 435, 531)(340, 436, 532)(341, 437, 533)(342, 438, 534)(343, 439, 535)(344, 440, 536)(345, 441, 537)(346, 442, 538)(347, 443, 539)(348, 444, 540)(349, 445, 541)(350, 446, 542)(351, 447, 543)(352, 448, 544)(353, 449, 545)(354, 450, 546)(355, 451, 547)(356, 452, 548)(357, 453, 549)(358, 454, 550)(359, 455, 551)(360, 456, 552)(361, 457, 553)(362, 458, 554)(363, 459, 555)(364, 460, 556)(365, 461, 557)(366, 462, 558)(367, 463, 559)(368, 464, 560)(369, 465, 561)(370, 466, 562)(371, 467, 563)(372, 468, 564)(373, 469, 565)(374, 470, 566)(375, 471, 567)(376, 472, 568)(377, 473, 569)(378, 474, 570)(379, 475, 571)(380, 476, 572)(381, 477, 573)(382, 478, 574)(383, 479, 575)(384, 480, 576) L = (1, 289)(2, 290)(3, 291)(4, 292)(5, 293)(6, 294)(7, 295)(8, 296)(9, 297)(10, 298)(11, 299)(12, 300)(13, 301)(14, 302)(15, 303)(16, 304)(17, 305)(18, 306)(19, 307)(20, 308)(21, 309)(22, 310)(23, 311)(24, 312)(25, 313)(26, 314)(27, 315)(28, 316)(29, 317)(30, 318)(31, 319)(32, 320)(33, 321)(34, 322)(35, 323)(36, 324)(37, 325)(38, 326)(39, 327)(40, 328)(41, 329)(42, 330)(43, 331)(44, 332)(45, 333)(46, 334)(47, 335)(48, 336)(49, 337)(50, 338)(51, 339)(52, 340)(53, 341)(54, 342)(55, 343)(56, 344)(57, 345)(58, 346)(59, 347)(60, 348)(61, 349)(62, 350)(63, 351)(64, 352)(65, 353)(66, 354)(67, 355)(68, 356)(69, 357)(70, 358)(71, 359)(72, 360)(73, 361)(74, 362)(75, 363)(76, 364)(77, 365)(78, 366)(79, 367)(80, 368)(81, 369)(82, 370)(83, 371)(84, 372)(85, 373)(86, 374)(87, 375)(88, 376)(89, 377)(90, 378)(91, 379)(92, 380)(93, 381)(94, 382)(95, 383)(96, 384)(97, 484)(98, 488)(99, 485)(100, 481)(101, 483)(102, 514)(103, 517)(104, 482)(105, 498)(106, 561)(107, 562)(108, 513)(109, 497)(110, 501)(111, 565)(112, 533)(113, 493)(114, 489)(115, 510)(116, 509)(117, 494)(118, 543)(119, 538)(120, 505)(121, 504)(122, 528)(123, 544)(124, 539)(125, 500)(126, 499)(127, 512)(128, 511)(129, 492)(130, 486)(131, 519)(132, 524)(133, 487)(134, 520)(135, 515)(136, 518)(137, 523)(138, 525)(139, 521)(140, 516)(141, 522)(142, 527)(143, 526)(144, 506)(145, 560)(146, 576)(147, 555)(148, 559)(149, 496)(150, 556)(151, 550)(152, 554)(153, 574)(154, 503)(155, 508)(156, 551)(157, 569)(158, 573)(159, 502)(160, 507)(161, 571)(162, 575)(163, 572)(164, 566)(165, 570)(166, 535)(167, 540)(168, 567)(169, 563)(170, 536)(171, 531)(172, 534)(173, 568)(174, 564)(175, 532)(176, 529)(177, 490)(178, 491)(179, 553)(180, 558)(181, 495)(182, 548)(183, 552)(184, 557)(185, 541)(186, 549)(187, 545)(188, 547)(189, 542)(190, 537)(191, 546)(192, 530)(193, 387)(194, 388)(195, 390)(196, 391)(197, 392)(198, 394)(199, 395)(200, 396)(201, 428)(202, 457)(203, 462)(204, 399)(205, 423)(206, 422)(207, 461)(208, 445)(209, 389)(210, 385)(211, 418)(212, 421)(213, 386)(214, 465)(215, 466)(216, 417)(217, 420)(218, 467)(219, 468)(220, 469)(221, 419)(222, 424)(223, 472)(224, 473)(225, 398)(226, 397)(227, 479)(228, 474)(229, 393)(230, 464)(231, 480)(232, 475)(233, 470)(234, 459)(235, 463)(236, 400)(237, 476)(238, 471)(239, 458)(240, 478)(241, 403)(242, 404)(243, 406)(244, 407)(245, 408)(246, 410)(247, 411)(248, 412)(249, 460)(250, 425)(251, 430)(252, 415)(253, 455)(254, 454)(255, 429)(256, 477)(257, 405)(258, 401)(259, 450)(260, 453)(261, 402)(262, 433)(263, 434)(264, 449)(265, 452)(266, 435)(267, 436)(268, 437)(269, 451)(270, 456)(271, 440)(272, 441)(273, 414)(274, 413)(275, 447)(276, 442)(277, 409)(278, 432)(279, 448)(280, 443)(281, 438)(282, 427)(283, 431)(284, 416)(285, 444)(286, 439)(287, 426)(288, 446) MAP : A3.21 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A3.19. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3 * x.1^-1)^3, (x.3 * x.2^2)^3, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 16) #DARTS : 576 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288)(289, 385, 481)(290, 386, 482)(291, 387, 483)(292, 388, 484)(293, 389, 485)(294, 390, 486)(295, 391, 487)(296, 392, 488)(297, 393, 489)(298, 394, 490)(299, 395, 491)(300, 396, 492)(301, 397, 493)(302, 398, 494)(303, 399, 495)(304, 400, 496)(305, 401, 497)(306, 402, 498)(307, 403, 499)(308, 404, 500)(309, 405, 501)(310, 406, 502)(311, 407, 503)(312, 408, 504)(313, 409, 505)(314, 410, 506)(315, 411, 507)(316, 412, 508)(317, 413, 509)(318, 414, 510)(319, 415, 511)(320, 416, 512)(321, 417, 513)(322, 418, 514)(323, 419, 515)(324, 420, 516)(325, 421, 517)(326, 422, 518)(327, 423, 519)(328, 424, 520)(329, 425, 521)(330, 426, 522)(331, 427, 523)(332, 428, 524)(333, 429, 525)(334, 430, 526)(335, 431, 527)(336, 432, 528)(337, 433, 529)(338, 434, 530)(339, 435, 531)(340, 436, 532)(341, 437, 533)(342, 438, 534)(343, 439, 535)(344, 440, 536)(345, 441, 537)(346, 442, 538)(347, 443, 539)(348, 444, 540)(349, 445, 541)(350, 446, 542)(351, 447, 543)(352, 448, 544)(353, 449, 545)(354, 450, 546)(355, 451, 547)(356, 452, 548)(357, 453, 549)(358, 454, 550)(359, 455, 551)(360, 456, 552)(361, 457, 553)(362, 458, 554)(363, 459, 555)(364, 460, 556)(365, 461, 557)(366, 462, 558)(367, 463, 559)(368, 464, 560)(369, 465, 561)(370, 466, 562)(371, 467, 563)(372, 468, 564)(373, 469, 565)(374, 470, 566)(375, 471, 567)(376, 472, 568)(377, 473, 569)(378, 474, 570)(379, 475, 571)(380, 476, 572)(381, 477, 573)(382, 478, 574)(383, 479, 575)(384, 480, 576) L = (1, 289)(2, 290)(3, 291)(4, 292)(5, 293)(6, 294)(7, 295)(8, 296)(9, 297)(10, 298)(11, 299)(12, 300)(13, 301)(14, 302)(15, 303)(16, 304)(17, 305)(18, 306)(19, 307)(20, 308)(21, 309)(22, 310)(23, 311)(24, 312)(25, 313)(26, 314)(27, 315)(28, 316)(29, 317)(30, 318)(31, 319)(32, 320)(33, 321)(34, 322)(35, 323)(36, 324)(37, 325)(38, 326)(39, 327)(40, 328)(41, 329)(42, 330)(43, 331)(44, 332)(45, 333)(46, 334)(47, 335)(48, 336)(49, 337)(50, 338)(51, 339)(52, 340)(53, 341)(54, 342)(55, 343)(56, 344)(57, 345)(58, 346)(59, 347)(60, 348)(61, 349)(62, 350)(63, 351)(64, 352)(65, 353)(66, 354)(67, 355)(68, 356)(69, 357)(70, 358)(71, 359)(72, 360)(73, 361)(74, 362)(75, 363)(76, 364)(77, 365)(78, 366)(79, 367)(80, 368)(81, 369)(82, 370)(83, 371)(84, 372)(85, 373)(86, 374)(87, 375)(88, 376)(89, 377)(90, 378)(91, 379)(92, 380)(93, 381)(94, 382)(95, 383)(96, 384)(97, 490)(98, 491)(99, 553)(100, 558)(101, 495)(102, 548)(103, 552)(104, 557)(105, 541)(106, 549)(107, 545)(108, 547)(109, 542)(110, 537)(111, 546)(112, 530)(113, 492)(114, 486)(115, 519)(116, 524)(117, 487)(118, 520)(119, 515)(120, 518)(121, 523)(122, 525)(123, 521)(124, 516)(125, 522)(126, 527)(127, 526)(128, 506)(129, 560)(130, 576)(131, 555)(132, 559)(133, 496)(134, 556)(135, 550)(136, 554)(137, 574)(138, 503)(139, 508)(140, 551)(141, 569)(142, 573)(143, 502)(144, 507)(145, 493)(146, 489)(147, 510)(148, 509)(149, 494)(150, 543)(151, 538)(152, 505)(153, 504)(154, 528)(155, 544)(156, 539)(157, 500)(158, 499)(159, 512)(160, 511)(161, 484)(162, 488)(163, 485)(164, 481)(165, 483)(166, 514)(167, 517)(168, 482)(169, 498)(170, 561)(171, 562)(172, 513)(173, 497)(174, 501)(175, 565)(176, 533)(177, 571)(178, 575)(179, 572)(180, 566)(181, 570)(182, 535)(183, 540)(184, 567)(185, 563)(186, 536)(187, 531)(188, 534)(189, 568)(190, 564)(191, 532)(192, 529)(193, 442)(194, 443)(195, 409)(196, 414)(197, 447)(198, 404)(199, 408)(200, 413)(201, 397)(202, 405)(203, 401)(204, 403)(205, 398)(206, 393)(207, 402)(208, 386)(209, 444)(210, 438)(211, 471)(212, 476)(213, 439)(214, 472)(215, 467)(216, 470)(217, 475)(218, 477)(219, 473)(220, 468)(221, 474)(222, 479)(223, 478)(224, 458)(225, 416)(226, 432)(227, 411)(228, 415)(229, 448)(230, 412)(231, 406)(232, 410)(233, 430)(234, 455)(235, 460)(236, 407)(237, 425)(238, 429)(239, 454)(240, 459)(241, 445)(242, 441)(243, 462)(244, 461)(245, 446)(246, 399)(247, 394)(248, 457)(249, 456)(250, 480)(251, 400)(252, 395)(253, 452)(254, 451)(255, 464)(256, 463)(257, 436)(258, 440)(259, 437)(260, 433)(261, 435)(262, 466)(263, 469)(264, 434)(265, 450)(266, 417)(267, 418)(268, 465)(269, 449)(270, 453)(271, 421)(272, 389)(273, 427)(274, 431)(275, 428)(276, 422)(277, 426)(278, 391)(279, 396)(280, 423)(281, 419)(282, 392)(283, 387)(284, 390)(285, 424)(286, 420)(287, 388)(288, 385) MAP : A3.22 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A3.19. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^3, x.2^-1 * x.3 * x.2 * x.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2 * x.3^-1, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 16) #DARTS : 576 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288)(289, 385, 481)(290, 386, 482)(291, 387, 483)(292, 388, 484)(293, 389, 485)(294, 390, 486)(295, 391, 487)(296, 392, 488)(297, 393, 489)(298, 394, 490)(299, 395, 491)(300, 396, 492)(301, 397, 493)(302, 398, 494)(303, 399, 495)(304, 400, 496)(305, 401, 497)(306, 402, 498)(307, 403, 499)(308, 404, 500)(309, 405, 501)(310, 406, 502)(311, 407, 503)(312, 408, 504)(313, 409, 505)(314, 410, 506)(315, 411, 507)(316, 412, 508)(317, 413, 509)(318, 414, 510)(319, 415, 511)(320, 416, 512)(321, 417, 513)(322, 418, 514)(323, 419, 515)(324, 420, 516)(325, 421, 517)(326, 422, 518)(327, 423, 519)(328, 424, 520)(329, 425, 521)(330, 426, 522)(331, 427, 523)(332, 428, 524)(333, 429, 525)(334, 430, 526)(335, 431, 527)(336, 432, 528)(337, 433, 529)(338, 434, 530)(339, 435, 531)(340, 436, 532)(341, 437, 533)(342, 438, 534)(343, 439, 535)(344, 440, 536)(345, 441, 537)(346, 442, 538)(347, 443, 539)(348, 444, 540)(349, 445, 541)(350, 446, 542)(351, 447, 543)(352, 448, 544)(353, 449, 545)(354, 450, 546)(355, 451, 547)(356, 452, 548)(357, 453, 549)(358, 454, 550)(359, 455, 551)(360, 456, 552)(361, 457, 553)(362, 458, 554)(363, 459, 555)(364, 460, 556)(365, 461, 557)(366, 462, 558)(367, 463, 559)(368, 464, 560)(369, 465, 561)(370, 466, 562)(371, 467, 563)(372, 468, 564)(373, 469, 565)(374, 470, 566)(375, 471, 567)(376, 472, 568)(377, 473, 569)(378, 474, 570)(379, 475, 571)(380, 476, 572)(381, 477, 573)(382, 478, 574)(383, 479, 575)(384, 480, 576) L = (1, 289)(2, 290)(3, 291)(4, 292)(5, 293)(6, 294)(7, 295)(8, 296)(9, 297)(10, 298)(11, 299)(12, 300)(13, 301)(14, 302)(15, 303)(16, 304)(17, 305)(18, 306)(19, 307)(20, 308)(21, 309)(22, 310)(23, 311)(24, 312)(25, 313)(26, 314)(27, 315)(28, 316)(29, 317)(30, 318)(31, 319)(32, 320)(33, 321)(34, 322)(35, 323)(36, 324)(37, 325)(38, 326)(39, 327)(40, 328)(41, 329)(42, 330)(43, 331)(44, 332)(45, 333)(46, 334)(47, 335)(48, 336)(49, 337)(50, 338)(51, 339)(52, 340)(53, 341)(54, 342)(55, 343)(56, 344)(57, 345)(58, 346)(59, 347)(60, 348)(61, 349)(62, 350)(63, 351)(64, 352)(65, 353)(66, 354)(67, 355)(68, 356)(69, 357)(70, 358)(71, 359)(72, 360)(73, 361)(74, 362)(75, 363)(76, 364)(77, 365)(78, 366)(79, 367)(80, 368)(81, 369)(82, 370)(83, 371)(84, 372)(85, 373)(86, 374)(87, 375)(88, 376)(89, 377)(90, 378)(91, 379)(92, 380)(93, 381)(94, 382)(95, 383)(96, 384)(97, 482)(98, 485)(99, 497)(100, 498)(101, 481)(102, 499)(103, 500)(104, 501)(105, 549)(106, 502)(107, 503)(108, 504)(109, 546)(110, 545)(111, 508)(112, 556)(113, 514)(114, 517)(115, 561)(116, 562)(117, 513)(118, 563)(119, 564)(120, 565)(121, 533)(122, 566)(123, 567)(124, 568)(125, 530)(126, 529)(127, 572)(128, 540)(129, 488)(130, 483)(131, 493)(132, 489)(133, 484)(134, 510)(135, 509)(136, 494)(137, 570)(138, 543)(139, 538)(140, 505)(141, 575)(142, 571)(143, 539)(144, 534)(145, 518)(146, 519)(147, 522)(148, 523)(149, 524)(150, 537)(151, 542)(152, 527)(153, 528)(154, 532)(155, 536)(156, 541)(157, 512)(158, 544)(159, 531)(160, 535)(161, 520)(162, 515)(163, 525)(164, 521)(165, 516)(166, 574)(167, 573)(168, 526)(169, 506)(170, 559)(171, 554)(172, 569)(173, 511)(174, 507)(175, 555)(176, 550)(177, 486)(178, 487)(179, 490)(180, 491)(181, 492)(182, 553)(183, 558)(184, 495)(185, 496)(186, 548)(187, 552)(188, 557)(189, 576)(190, 560)(191, 547)(192, 551)(193, 388)(194, 392)(195, 389)(196, 385)(197, 387)(198, 418)(199, 421)(200, 386)(201, 402)(202, 465)(203, 466)(204, 417)(205, 401)(206, 405)(207, 469)(208, 437)(209, 397)(210, 393)(211, 414)(212, 413)(213, 398)(214, 447)(215, 442)(216, 409)(217, 408)(218, 432)(219, 448)(220, 443)(221, 404)(222, 403)(223, 416)(224, 415)(225, 396)(226, 390)(227, 423)(228, 428)(229, 391)(230, 424)(231, 419)(232, 422)(233, 427)(234, 429)(235, 425)(236, 420)(237, 426)(238, 431)(239, 430)(240, 410)(241, 464)(242, 480)(243, 459)(244, 463)(245, 400)(246, 460)(247, 454)(248, 458)(249, 478)(250, 407)(251, 412)(252, 455)(253, 473)(254, 477)(255, 406)(256, 411)(257, 475)(258, 479)(259, 476)(260, 470)(261, 474)(262, 439)(263, 444)(264, 471)(265, 467)(266, 440)(267, 435)(268, 438)(269, 472)(270, 468)(271, 436)(272, 433)(273, 394)(274, 395)(275, 457)(276, 462)(277, 399)(278, 452)(279, 456)(280, 461)(281, 445)(282, 453)(283, 449)(284, 451)(285, 446)(286, 441)(287, 450)(288, 434) MAP : A3.23 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A3.19. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^3, x.2^-1 * x.3 * x.2 * x.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2 * x.3^-1, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 16) #DARTS : 576 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288)(289, 385, 481)(290, 386, 482)(291, 387, 483)(292, 388, 484)(293, 389, 485)(294, 390, 486)(295, 391, 487)(296, 392, 488)(297, 393, 489)(298, 394, 490)(299, 395, 491)(300, 396, 492)(301, 397, 493)(302, 398, 494)(303, 399, 495)(304, 400, 496)(305, 401, 497)(306, 402, 498)(307, 403, 499)(308, 404, 500)(309, 405, 501)(310, 406, 502)(311, 407, 503)(312, 408, 504)(313, 409, 505)(314, 410, 506)(315, 411, 507)(316, 412, 508)(317, 413, 509)(318, 414, 510)(319, 415, 511)(320, 416, 512)(321, 417, 513)(322, 418, 514)(323, 419, 515)(324, 420, 516)(325, 421, 517)(326, 422, 518)(327, 423, 519)(328, 424, 520)(329, 425, 521)(330, 426, 522)(331, 427, 523)(332, 428, 524)(333, 429, 525)(334, 430, 526)(335, 431, 527)(336, 432, 528)(337, 433, 529)(338, 434, 530)(339, 435, 531)(340, 436, 532)(341, 437, 533)(342, 438, 534)(343, 439, 535)(344, 440, 536)(345, 441, 537)(346, 442, 538)(347, 443, 539)(348, 444, 540)(349, 445, 541)(350, 446, 542)(351, 447, 543)(352, 448, 544)(353, 449, 545)(354, 450, 546)(355, 451, 547)(356, 452, 548)(357, 453, 549)(358, 454, 550)(359, 455, 551)(360, 456, 552)(361, 457, 553)(362, 458, 554)(363, 459, 555)(364, 460, 556)(365, 461, 557)(366, 462, 558)(367, 463, 559)(368, 464, 560)(369, 465, 561)(370, 466, 562)(371, 467, 563)(372, 468, 564)(373, 469, 565)(374, 470, 566)(375, 471, 567)(376, 472, 568)(377, 473, 569)(378, 474, 570)(379, 475, 571)(380, 476, 572)(381, 477, 573)(382, 478, 574)(383, 479, 575)(384, 480, 576) L = (1, 289)(2, 290)(3, 291)(4, 292)(5, 293)(6, 294)(7, 295)(8, 296)(9, 297)(10, 298)(11, 299)(12, 300)(13, 301)(14, 302)(15, 303)(16, 304)(17, 305)(18, 306)(19, 307)(20, 308)(21, 309)(22, 310)(23, 311)(24, 312)(25, 313)(26, 314)(27, 315)(28, 316)(29, 317)(30, 318)(31, 319)(32, 320)(33, 321)(34, 322)(35, 323)(36, 324)(37, 325)(38, 326)(39, 327)(40, 328)(41, 329)(42, 330)(43, 331)(44, 332)(45, 333)(46, 334)(47, 335)(48, 336)(49, 337)(50, 338)(51, 339)(52, 340)(53, 341)(54, 342)(55, 343)(56, 344)(57, 345)(58, 346)(59, 347)(60, 348)(61, 349)(62, 350)(63, 351)(64, 352)(65, 353)(66, 354)(67, 355)(68, 356)(69, 357)(70, 358)(71, 359)(72, 360)(73, 361)(74, 362)(75, 363)(76, 364)(77, 365)(78, 366)(79, 367)(80, 368)(81, 369)(82, 370)(83, 371)(84, 372)(85, 373)(86, 374)(87, 375)(88, 376)(89, 377)(90, 378)(91, 379)(92, 380)(93, 381)(94, 382)(95, 383)(96, 384)(97, 482)(98, 485)(99, 497)(100, 498)(101, 481)(102, 499)(103, 500)(104, 501)(105, 549)(106, 502)(107, 503)(108, 504)(109, 546)(110, 545)(111, 508)(112, 556)(113, 514)(114, 517)(115, 561)(116, 562)(117, 513)(118, 563)(119, 564)(120, 565)(121, 533)(122, 566)(123, 567)(124, 568)(125, 530)(126, 529)(127, 572)(128, 540)(129, 488)(130, 483)(131, 493)(132, 489)(133, 484)(134, 510)(135, 509)(136, 494)(137, 570)(138, 543)(139, 538)(140, 505)(141, 575)(142, 571)(143, 539)(144, 534)(145, 518)(146, 519)(147, 522)(148, 523)(149, 524)(150, 537)(151, 542)(152, 527)(153, 528)(154, 532)(155, 536)(156, 541)(157, 512)(158, 544)(159, 531)(160, 535)(161, 520)(162, 515)(163, 525)(164, 521)(165, 516)(166, 574)(167, 573)(168, 526)(169, 506)(170, 559)(171, 554)(172, 569)(173, 511)(174, 507)(175, 555)(176, 550)(177, 486)(178, 487)(179, 490)(180, 491)(181, 492)(182, 553)(183, 558)(184, 495)(185, 496)(186, 548)(187, 552)(188, 557)(189, 576)(190, 560)(191, 547)(192, 551)(193, 416)(194, 432)(195, 411)(196, 415)(197, 448)(198, 412)(199, 406)(200, 410)(201, 430)(202, 455)(203, 460)(204, 407)(205, 425)(206, 429)(207, 454)(208, 459)(209, 427)(210, 431)(211, 428)(212, 422)(213, 426)(214, 391)(215, 396)(216, 423)(217, 419)(218, 392)(219, 387)(220, 390)(221, 424)(222, 420)(223, 388)(224, 385)(225, 442)(226, 443)(227, 409)(228, 414)(229, 447)(230, 404)(231, 408)(232, 413)(233, 397)(234, 405)(235, 401)(236, 403)(237, 398)(238, 393)(239, 402)(240, 386)(241, 436)(242, 440)(243, 437)(244, 433)(245, 435)(246, 466)(247, 469)(248, 434)(249, 450)(250, 417)(251, 418)(252, 465)(253, 449)(254, 453)(255, 421)(256, 389)(257, 445)(258, 441)(259, 462)(260, 461)(261, 446)(262, 399)(263, 394)(264, 457)(265, 456)(266, 480)(267, 400)(268, 395)(269, 452)(270, 451)(271, 464)(272, 463)(273, 444)(274, 438)(275, 471)(276, 476)(277, 439)(278, 472)(279, 467)(280, 470)(281, 475)(282, 477)(283, 473)(284, 468)(285, 474)(286, 479)(287, 478)(288, 458) MAP : A3.24 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A3.19. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3 * x.1^-1)^3, (x.3 * x.2^2)^3, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 16) #DARTS : 576 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288)(289, 385, 481)(290, 386, 482)(291, 387, 483)(292, 388, 484)(293, 389, 485)(294, 390, 486)(295, 391, 487)(296, 392, 488)(297, 393, 489)(298, 394, 490)(299, 395, 491)(300, 396, 492)(301, 397, 493)(302, 398, 494)(303, 399, 495)(304, 400, 496)(305, 401, 497)(306, 402, 498)(307, 403, 499)(308, 404, 500)(309, 405, 501)(310, 406, 502)(311, 407, 503)(312, 408, 504)(313, 409, 505)(314, 410, 506)(315, 411, 507)(316, 412, 508)(317, 413, 509)(318, 414, 510)(319, 415, 511)(320, 416, 512)(321, 417, 513)(322, 418, 514)(323, 419, 515)(324, 420, 516)(325, 421, 517)(326, 422, 518)(327, 423, 519)(328, 424, 520)(329, 425, 521)(330, 426, 522)(331, 427, 523)(332, 428, 524)(333, 429, 525)(334, 430, 526)(335, 431, 527)(336, 432, 528)(337, 433, 529)(338, 434, 530)(339, 435, 531)(340, 436, 532)(341, 437, 533)(342, 438, 534)(343, 439, 535)(344, 440, 536)(345, 441, 537)(346, 442, 538)(347, 443, 539)(348, 444, 540)(349, 445, 541)(350, 446, 542)(351, 447, 543)(352, 448, 544)(353, 449, 545)(354, 450, 546)(355, 451, 547)(356, 452, 548)(357, 453, 549)(358, 454, 550)(359, 455, 551)(360, 456, 552)(361, 457, 553)(362, 458, 554)(363, 459, 555)(364, 460, 556)(365, 461, 557)(366, 462, 558)(367, 463, 559)(368, 464, 560)(369, 465, 561)(370, 466, 562)(371, 467, 563)(372, 468, 564)(373, 469, 565)(374, 470, 566)(375, 471, 567)(376, 472, 568)(377, 473, 569)(378, 474, 570)(379, 475, 571)(380, 476, 572)(381, 477, 573)(382, 478, 574)(383, 479, 575)(384, 480, 576) L = (1, 289)(2, 290)(3, 291)(4, 292)(5, 293)(6, 294)(7, 295)(8, 296)(9, 297)(10, 298)(11, 299)(12, 300)(13, 301)(14, 302)(15, 303)(16, 304)(17, 305)(18, 306)(19, 307)(20, 308)(21, 309)(22, 310)(23, 311)(24, 312)(25, 313)(26, 314)(27, 315)(28, 316)(29, 317)(30, 318)(31, 319)(32, 320)(33, 321)(34, 322)(35, 323)(36, 324)(37, 325)(38, 326)(39, 327)(40, 328)(41, 329)(42, 330)(43, 331)(44, 332)(45, 333)(46, 334)(47, 335)(48, 336)(49, 337)(50, 338)(51, 339)(52, 340)(53, 341)(54, 342)(55, 343)(56, 344)(57, 345)(58, 346)(59, 347)(60, 348)(61, 349)(62, 350)(63, 351)(64, 352)(65, 353)(66, 354)(67, 355)(68, 356)(69, 357)(70, 358)(71, 359)(72, 360)(73, 361)(74, 362)(75, 363)(76, 364)(77, 365)(78, 366)(79, 367)(80, 368)(81, 369)(82, 370)(83, 371)(84, 372)(85, 373)(86, 374)(87, 375)(88, 376)(89, 377)(90, 378)(91, 379)(92, 380)(93, 381)(94, 382)(95, 383)(96, 384)(97, 483)(98, 484)(99, 486)(100, 487)(101, 488)(102, 490)(103, 491)(104, 492)(105, 524)(106, 553)(107, 558)(108, 495)(109, 519)(110, 518)(111, 557)(112, 541)(113, 485)(114, 481)(115, 514)(116, 517)(117, 482)(118, 561)(119, 562)(120, 513)(121, 516)(122, 563)(123, 564)(124, 565)(125, 515)(126, 520)(127, 568)(128, 569)(129, 494)(130, 493)(131, 575)(132, 570)(133, 489)(134, 560)(135, 576)(136, 571)(137, 566)(138, 555)(139, 559)(140, 496)(141, 572)(142, 567)(143, 554)(144, 574)(145, 499)(146, 500)(147, 502)(148, 503)(149, 504)(150, 506)(151, 507)(152, 508)(153, 556)(154, 521)(155, 526)(156, 511)(157, 551)(158, 550)(159, 525)(160, 573)(161, 501)(162, 497)(163, 546)(164, 549)(165, 498)(166, 529)(167, 530)(168, 545)(169, 548)(170, 531)(171, 532)(172, 533)(173, 547)(174, 552)(175, 536)(176, 537)(177, 510)(178, 509)(179, 543)(180, 538)(181, 505)(182, 528)(183, 544)(184, 539)(185, 534)(186, 523)(187, 527)(188, 512)(189, 540)(190, 535)(191, 522)(192, 542)(193, 389)(194, 385)(195, 418)(196, 421)(197, 386)(198, 465)(199, 466)(200, 417)(201, 420)(202, 467)(203, 468)(204, 469)(205, 419)(206, 424)(207, 472)(208, 473)(209, 387)(210, 388)(211, 390)(212, 391)(213, 392)(214, 394)(215, 395)(216, 396)(217, 428)(218, 457)(219, 462)(220, 399)(221, 423)(222, 422)(223, 461)(224, 445)(225, 405)(226, 401)(227, 450)(228, 453)(229, 402)(230, 433)(231, 434)(232, 449)(233, 452)(234, 435)(235, 436)(236, 437)(237, 451)(238, 456)(239, 440)(240, 441)(241, 414)(242, 413)(243, 447)(244, 442)(245, 409)(246, 432)(247, 448)(248, 443)(249, 438)(250, 427)(251, 431)(252, 416)(253, 444)(254, 439)(255, 426)(256, 446)(257, 398)(258, 397)(259, 479)(260, 474)(261, 393)(262, 464)(263, 480)(264, 475)(265, 470)(266, 459)(267, 463)(268, 400)(269, 476)(270, 471)(271, 458)(272, 478)(273, 403)(274, 404)(275, 406)(276, 407)(277, 408)(278, 410)(279, 411)(280, 412)(281, 460)(282, 425)(283, 430)(284, 415)(285, 455)(286, 454)(287, 429)(288, 477) MAP : A3.25 NOTES : type II, reflexible, isomorphic to DBar({3,12}), representative. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 12 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^3, x.3^-2 * x.2 * x.3^3 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 24) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 249)(51, 241)(52, 245)(53, 244)(54, 250)(55, 266)(56, 251)(57, 242)(58, 246)(59, 248)(60, 264)(61, 282)(62, 265)(63, 280)(64, 277)(65, 263)(66, 262)(67, 270)(68, 286)(69, 269)(70, 258)(71, 257)(72, 252)(73, 254)(74, 247)(75, 279)(76, 285)(77, 261)(78, 259)(79, 278)(80, 274)(81, 288)(82, 272)(83, 287)(84, 283)(85, 256)(86, 271)(87, 267)(88, 255)(89, 284)(90, 253)(91, 276)(92, 281)(93, 268)(94, 260)(95, 275)(96, 273)(97, 211)(98, 217)(99, 209)(100, 213)(101, 212)(102, 218)(103, 234)(104, 219)(105, 210)(106, 214)(107, 216)(108, 232)(109, 202)(110, 233)(111, 200)(112, 197)(113, 231)(114, 230)(115, 238)(116, 206)(117, 237)(118, 226)(119, 225)(120, 220)(121, 222)(122, 215)(123, 199)(124, 205)(125, 229)(126, 227)(127, 198)(128, 194)(129, 208)(130, 240)(131, 207)(132, 203)(133, 224)(134, 239)(135, 235)(136, 223)(137, 204)(138, 221)(139, 196)(140, 201)(141, 236)(142, 228)(143, 195)(144, 193) MAP : A3.26 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 12 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^3, x.3^-2 * x.2 * x.3^3 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 24) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 249)(51, 241)(52, 245)(53, 244)(54, 250)(55, 266)(56, 251)(57, 242)(58, 246)(59, 248)(60, 264)(61, 282)(62, 265)(63, 280)(64, 277)(65, 263)(66, 262)(67, 270)(68, 286)(69, 269)(70, 258)(71, 257)(72, 252)(73, 254)(74, 247)(75, 279)(76, 285)(77, 261)(78, 259)(79, 278)(80, 274)(81, 288)(82, 272)(83, 287)(84, 283)(85, 256)(86, 271)(87, 267)(88, 255)(89, 284)(90, 253)(91, 276)(92, 281)(93, 268)(94, 260)(95, 275)(96, 273)(97, 198)(98, 205)(99, 194)(100, 193)(101, 199)(102, 236)(103, 239)(104, 206)(105, 197)(106, 200)(107, 195)(108, 196)(109, 235)(110, 240)(111, 201)(112, 202)(113, 214)(114, 221)(115, 210)(116, 209)(117, 215)(118, 204)(119, 207)(120, 222)(121, 213)(122, 216)(123, 211)(124, 212)(125, 203)(126, 208)(127, 217)(128, 218)(129, 230)(130, 237)(131, 226)(132, 225)(133, 231)(134, 220)(135, 223)(136, 238)(137, 229)(138, 232)(139, 227)(140, 228)(141, 219)(142, 224)(143, 233)(144, 234) MAP : A3.27 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 12, 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.3 * x.2^-1)^2, (x.3 * x.1^-1)^3, x.2^-2 * x.3 * x.2^2 * x.3 * x.2^-2, (x.1 * x.2^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 24) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 244)(50, 243)(51, 251)(52, 252)(53, 249)(54, 241)(55, 245)(56, 250)(57, 255)(58, 256)(59, 269)(60, 262)(61, 242)(62, 248)(63, 263)(64, 270)(65, 260)(66, 259)(67, 267)(68, 268)(69, 265)(70, 257)(71, 261)(72, 266)(73, 271)(74, 272)(75, 285)(76, 278)(77, 258)(78, 264)(79, 279)(80, 286)(81, 276)(82, 275)(83, 283)(84, 284)(85, 281)(86, 273)(87, 277)(88, 282)(89, 287)(90, 288)(91, 253)(92, 246)(93, 274)(94, 280)(95, 247)(96, 254)(97, 197)(98, 193)(99, 200)(100, 216)(101, 194)(102, 195)(103, 196)(104, 198)(105, 232)(106, 229)(107, 213)(108, 210)(109, 201)(110, 203)(111, 209)(112, 211)(113, 238)(114, 222)(115, 231)(116, 237)(117, 206)(118, 215)(119, 221)(120, 199)(121, 230)(122, 226)(123, 220)(124, 223)(125, 214)(126, 204)(127, 219)(128, 212)(129, 235)(130, 239)(131, 228)(132, 233)(133, 236)(134, 240)(135, 208)(136, 205)(137, 227)(138, 225)(139, 234)(140, 202)(141, 224)(142, 207)(143, 218)(144, 217) MAP : A3.28 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 12, 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.3 * x.2^-1)^2, (x.3 * x.1^-1)^3, x.2^-2 * x.3 * x.2^2 * x.3 * x.2^-2, (x.1 * x.2^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 24) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 260)(50, 259)(51, 267)(52, 268)(53, 265)(54, 257)(55, 261)(56, 266)(57, 271)(58, 272)(59, 285)(60, 278)(61, 258)(62, 264)(63, 279)(64, 286)(65, 276)(66, 275)(67, 283)(68, 284)(69, 281)(70, 273)(71, 277)(72, 282)(73, 287)(74, 288)(75, 253)(76, 246)(77, 274)(78, 280)(79, 247)(80, 254)(81, 244)(82, 243)(83, 251)(84, 252)(85, 249)(86, 241)(87, 245)(88, 250)(89, 255)(90, 256)(91, 269)(92, 262)(93, 242)(94, 248)(95, 263)(96, 270)(97, 194)(98, 197)(99, 198)(100, 199)(101, 193)(102, 200)(103, 216)(104, 195)(105, 205)(106, 236)(107, 206)(108, 222)(109, 232)(110, 213)(111, 238)(112, 231)(113, 207)(114, 204)(115, 208)(116, 224)(117, 203)(118, 221)(119, 214)(120, 196)(121, 240)(122, 239)(123, 223)(124, 219)(125, 215)(126, 210)(127, 220)(128, 237)(129, 234)(130, 218)(131, 233)(132, 227)(133, 202)(134, 217)(135, 211)(136, 201)(137, 228)(138, 235)(139, 225)(140, 229)(141, 212)(142, 209)(143, 226)(144, 230) MAP : A3.29 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 12 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^3, x.3^-2 * x.2 * x.3^3 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 24) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 249)(51, 241)(52, 245)(53, 244)(54, 250)(55, 266)(56, 251)(57, 242)(58, 246)(59, 248)(60, 264)(61, 282)(62, 265)(63, 280)(64, 277)(65, 263)(66, 262)(67, 270)(68, 286)(69, 269)(70, 258)(71, 257)(72, 252)(73, 254)(74, 247)(75, 279)(76, 285)(77, 261)(78, 259)(79, 278)(80, 274)(81, 288)(82, 272)(83, 287)(84, 283)(85, 256)(86, 271)(87, 267)(88, 255)(89, 284)(90, 253)(91, 276)(92, 281)(93, 268)(94, 260)(95, 275)(96, 273)(97, 240)(98, 224)(99, 239)(100, 235)(101, 208)(102, 223)(103, 219)(104, 207)(105, 236)(106, 205)(107, 228)(108, 233)(109, 220)(110, 212)(111, 227)(112, 225)(113, 195)(114, 201)(115, 193)(116, 197)(117, 196)(118, 202)(119, 218)(120, 203)(121, 194)(122, 198)(123, 200)(124, 216)(125, 234)(126, 217)(127, 232)(128, 229)(129, 215)(130, 214)(131, 222)(132, 238)(133, 221)(134, 210)(135, 209)(136, 204)(137, 206)(138, 199)(139, 231)(140, 237)(141, 213)(142, 211)(143, 230)(144, 226) MAP : A3.30 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 12, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^3, x.2^-1 * x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3^-1, x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.2^-1 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1, x.3^-3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 24) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 242)(50, 245)(51, 246)(52, 247)(53, 241)(54, 248)(55, 264)(56, 243)(57, 253)(58, 284)(59, 254)(60, 270)(61, 280)(62, 261)(63, 286)(64, 279)(65, 255)(66, 252)(67, 256)(68, 272)(69, 251)(70, 269)(71, 262)(72, 244)(73, 288)(74, 287)(75, 271)(76, 267)(77, 263)(78, 258)(79, 268)(80, 285)(81, 282)(82, 266)(83, 281)(84, 275)(85, 250)(86, 265)(87, 259)(88, 249)(89, 276)(90, 283)(91, 273)(92, 277)(93, 260)(94, 257)(95, 274)(96, 278)(97, 195)(98, 201)(99, 193)(100, 197)(101, 196)(102, 202)(103, 218)(104, 203)(105, 194)(106, 198)(107, 200)(108, 216)(109, 234)(110, 217)(111, 232)(112, 229)(113, 215)(114, 214)(115, 222)(116, 238)(117, 221)(118, 210)(119, 209)(120, 204)(121, 206)(122, 199)(123, 231)(124, 237)(125, 213)(126, 211)(127, 230)(128, 226)(129, 240)(130, 224)(131, 239)(132, 235)(133, 208)(134, 223)(135, 219)(136, 207)(137, 236)(138, 205)(139, 228)(140, 233)(141, 220)(142, 212)(143, 227)(144, 225) MAP : A3.31 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 12, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^3, x.2^-1 * x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3^-1, x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.2^-1 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1, x.3^-3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 24) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 242)(50, 245)(51, 246)(52, 247)(53, 241)(54, 248)(55, 264)(56, 243)(57, 253)(58, 284)(59, 254)(60, 270)(61, 280)(62, 261)(63, 286)(64, 279)(65, 255)(66, 252)(67, 256)(68, 272)(69, 251)(70, 269)(71, 262)(72, 244)(73, 288)(74, 287)(75, 271)(76, 267)(77, 263)(78, 258)(79, 268)(80, 285)(81, 282)(82, 266)(83, 281)(84, 275)(85, 250)(86, 265)(87, 259)(88, 249)(89, 276)(90, 283)(91, 273)(92, 277)(93, 260)(94, 257)(95, 274)(96, 278)(97, 208)(98, 240)(99, 207)(100, 203)(101, 224)(102, 239)(103, 235)(104, 223)(105, 204)(106, 221)(107, 196)(108, 201)(109, 236)(110, 228)(111, 195)(112, 193)(113, 211)(114, 217)(115, 209)(116, 213)(117, 212)(118, 218)(119, 234)(120, 219)(121, 210)(122, 214)(123, 216)(124, 232)(125, 202)(126, 233)(127, 200)(128, 197)(129, 231)(130, 230)(131, 238)(132, 206)(133, 237)(134, 226)(135, 225)(136, 220)(137, 222)(138, 215)(139, 199)(140, 205)(141, 229)(142, 227)(143, 198)(144, 194) MAP : A3.32 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 12, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^3, x.2^-1 * x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3^-1, x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.2^-1 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1, x.3^-3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 24) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 245)(50, 241)(51, 248)(52, 264)(53, 242)(54, 243)(55, 244)(56, 246)(57, 280)(58, 277)(59, 261)(60, 258)(61, 249)(62, 251)(63, 257)(64, 259)(65, 286)(66, 270)(67, 279)(68, 285)(69, 254)(70, 263)(71, 269)(72, 247)(73, 278)(74, 274)(75, 268)(76, 271)(77, 262)(78, 252)(79, 267)(80, 260)(81, 283)(82, 287)(83, 276)(84, 281)(85, 284)(86, 288)(87, 256)(88, 253)(89, 275)(90, 273)(91, 282)(92, 250)(93, 272)(94, 255)(95, 266)(96, 265)(97, 195)(98, 201)(99, 193)(100, 197)(101, 196)(102, 202)(103, 218)(104, 203)(105, 194)(106, 198)(107, 200)(108, 216)(109, 234)(110, 217)(111, 232)(112, 229)(113, 215)(114, 214)(115, 222)(116, 238)(117, 221)(118, 210)(119, 209)(120, 204)(121, 206)(122, 199)(123, 231)(124, 237)(125, 213)(126, 211)(127, 230)(128, 226)(129, 240)(130, 224)(131, 239)(132, 235)(133, 208)(134, 223)(135, 219)(136, 207)(137, 236)(138, 205)(139, 228)(140, 233)(141, 220)(142, 212)(143, 227)(144, 225) MAP : A3.33 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 12 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^3, x.3^-2 * x.2 * x.3^3 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 24) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 249)(51, 241)(52, 245)(53, 244)(54, 250)(55, 266)(56, 251)(57, 242)(58, 246)(59, 248)(60, 264)(61, 282)(62, 265)(63, 280)(64, 277)(65, 263)(66, 262)(67, 270)(68, 286)(69, 269)(70, 258)(71, 257)(72, 252)(73, 254)(74, 247)(75, 279)(76, 285)(77, 261)(78, 259)(79, 278)(80, 274)(81, 288)(82, 272)(83, 287)(84, 283)(85, 256)(86, 271)(87, 267)(88, 255)(89, 284)(90, 253)(91, 276)(92, 281)(93, 268)(94, 260)(95, 275)(96, 273)(97, 196)(98, 195)(99, 203)(100, 204)(101, 201)(102, 193)(103, 197)(104, 202)(105, 207)(106, 208)(107, 221)(108, 214)(109, 194)(110, 200)(111, 215)(112, 222)(113, 212)(114, 211)(115, 219)(116, 220)(117, 217)(118, 209)(119, 213)(120, 218)(121, 223)(122, 224)(123, 237)(124, 230)(125, 210)(126, 216)(127, 231)(128, 238)(129, 228)(130, 227)(131, 235)(132, 236)(133, 233)(134, 225)(135, 229)(136, 234)(137, 239)(138, 240)(139, 205)(140, 198)(141, 226)(142, 232)(143, 199)(144, 206) MAP : A3.34 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 12, 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.3 * x.2^-1)^2, (x.3 * x.1^-1)^3, x.2^-2 * x.3 * x.2^2 * x.3 * x.2^-2, (x.1 * x.2^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 24) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 278)(50, 285)(51, 274)(52, 273)(53, 279)(54, 268)(55, 271)(56, 286)(57, 277)(58, 280)(59, 275)(60, 276)(61, 267)(62, 272)(63, 281)(64, 282)(65, 246)(66, 253)(67, 242)(68, 241)(69, 247)(70, 284)(71, 287)(72, 254)(73, 245)(74, 248)(75, 243)(76, 244)(77, 283)(78, 288)(79, 249)(80, 250)(81, 262)(82, 269)(83, 258)(84, 257)(85, 263)(86, 252)(87, 255)(88, 270)(89, 261)(90, 264)(91, 259)(92, 260)(93, 251)(94, 256)(95, 265)(96, 266)(97, 197)(98, 193)(99, 200)(100, 216)(101, 194)(102, 195)(103, 196)(104, 198)(105, 232)(106, 229)(107, 213)(108, 210)(109, 201)(110, 203)(111, 209)(112, 211)(113, 238)(114, 222)(115, 231)(116, 237)(117, 206)(118, 215)(119, 221)(120, 199)(121, 230)(122, 226)(123, 220)(124, 223)(125, 214)(126, 204)(127, 219)(128, 212)(129, 235)(130, 239)(131, 228)(132, 233)(133, 236)(134, 240)(135, 208)(136, 205)(137, 227)(138, 225)(139, 234)(140, 202)(141, 224)(142, 207)(143, 218)(144, 217) MAP : A3.35 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 12, 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.3 * x.2^-1)^2, (x.3 * x.1^-1)^3, x.2^-2 * x.3 * x.2^2 * x.3 * x.2^-2, (x.1 * x.2^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 24) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 253)(51, 242)(52, 241)(53, 247)(54, 284)(55, 287)(56, 254)(57, 245)(58, 248)(59, 243)(60, 244)(61, 283)(62, 288)(63, 249)(64, 250)(65, 262)(66, 269)(67, 258)(68, 257)(69, 263)(70, 252)(71, 255)(72, 270)(73, 261)(74, 264)(75, 259)(76, 260)(77, 251)(78, 256)(79, 265)(80, 266)(81, 278)(82, 285)(83, 274)(84, 273)(85, 279)(86, 268)(87, 271)(88, 286)(89, 277)(90, 280)(91, 275)(92, 276)(93, 267)(94, 272)(95, 281)(96, 282)(97, 194)(98, 197)(99, 198)(100, 199)(101, 193)(102, 200)(103, 216)(104, 195)(105, 205)(106, 236)(107, 206)(108, 222)(109, 232)(110, 213)(111, 238)(112, 231)(113, 207)(114, 204)(115, 208)(116, 224)(117, 203)(118, 221)(119, 214)(120, 196)(121, 240)(122, 239)(123, 223)(124, 219)(125, 215)(126, 210)(127, 220)(128, 237)(129, 234)(130, 218)(131, 233)(132, 227)(133, 202)(134, 217)(135, 211)(136, 201)(137, 228)(138, 235)(139, 225)(140, 229)(141, 212)(142, 209)(143, 226)(144, 230) MAP : A3.36 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 12, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^3, x.2^-1 * x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3^-1, x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.2^-1 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1, x.3^-3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 6, 24) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 245)(50, 241)(51, 248)(52, 264)(53, 242)(54, 243)(55, 244)(56, 246)(57, 280)(58, 277)(59, 261)(60, 258)(61, 249)(62, 251)(63, 257)(64, 259)(65, 286)(66, 270)(67, 279)(68, 285)(69, 254)(70, 263)(71, 269)(72, 247)(73, 278)(74, 274)(75, 268)(76, 271)(77, 262)(78, 252)(79, 267)(80, 260)(81, 283)(82, 287)(83, 276)(84, 281)(85, 284)(86, 288)(87, 256)(88, 253)(89, 275)(90, 273)(91, 282)(92, 250)(93, 272)(94, 255)(95, 266)(96, 265)(97, 208)(98, 240)(99, 207)(100, 203)(101, 224)(102, 239)(103, 235)(104, 223)(105, 204)(106, 221)(107, 196)(108, 201)(109, 236)(110, 228)(111, 195)(112, 193)(113, 211)(114, 217)(115, 209)(116, 213)(117, 212)(118, 218)(119, 234)(120, 219)(121, 210)(122, 214)(123, 216)(124, 232)(125, 202)(126, 233)(127, 200)(128, 197)(129, 231)(130, 230)(131, 238)(132, 206)(133, 237)(134, 226)(135, 225)(136, 220)(137, 222)(138, 215)(139, 199)(140, 205)(141, 229)(142, 227)(143, 198)(144, 194) MAP : A3.37 NOTES : type II, reflexible, isomorphic to DBar({4,6}), representative. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 6, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^4, x.3 * x.2 * x.3 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2^-2, x.2^-1 * x.3 * x.2^2 * x.3 * x.2^-1 * x.3^-1 * x.2^-2 * x.3^-1, x.3 * x.2^-1 * x.3 * x.2^2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-2, (x.2 * x.3^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 12) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 262)(51, 247)(52, 258)(53, 241)(54, 288)(55, 245)(56, 286)(57, 271)(58, 252)(59, 269)(60, 272)(61, 267)(62, 250)(63, 265)(64, 268)(65, 253)(66, 248)(67, 249)(68, 278)(69, 255)(70, 276)(71, 251)(72, 242)(73, 275)(74, 270)(75, 279)(76, 266)(77, 273)(78, 256)(79, 277)(80, 254)(81, 263)(82, 284)(83, 261)(84, 264)(85, 259)(86, 282)(87, 257)(88, 260)(89, 285)(90, 280)(91, 281)(92, 246)(93, 287)(94, 244)(95, 283)(96, 274)(97, 196)(98, 197)(99, 232)(100, 193)(101, 194)(102, 199)(103, 198)(104, 237)(105, 216)(106, 211)(107, 238)(108, 215)(109, 236)(110, 209)(111, 234)(112, 219)(113, 206)(114, 231)(115, 202)(116, 229)(117, 224)(118, 227)(119, 204)(120, 201)(121, 220)(122, 221)(123, 208)(124, 217)(125, 218)(126, 223)(127, 222)(128, 213)(129, 240)(130, 235)(131, 214)(132, 239)(133, 212)(134, 233)(135, 210)(136, 195)(137, 230)(138, 207)(139, 226)(140, 205)(141, 200)(142, 203)(143, 228)(144, 225) MAP : A3.38 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A3.37. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^4, (x.2 * x.3^-1)^2, (x.3 * x.2^2)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 12) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 242)(50, 249)(51, 244)(52, 251)(53, 246)(54, 253)(55, 280)(56, 279)(57, 250)(58, 257)(59, 252)(60, 259)(61, 254)(62, 261)(63, 272)(64, 271)(65, 258)(66, 241)(67, 260)(68, 243)(69, 262)(70, 245)(71, 288)(72, 287)(73, 282)(74, 265)(75, 284)(76, 267)(77, 286)(78, 269)(79, 264)(80, 263)(81, 266)(82, 273)(83, 268)(84, 275)(85, 270)(86, 277)(87, 256)(88, 255)(89, 274)(90, 281)(91, 276)(92, 283)(93, 278)(94, 285)(95, 248)(96, 247)(97, 223)(98, 204)(99, 221)(100, 224)(101, 219)(102, 202)(103, 217)(104, 220)(105, 205)(106, 200)(107, 201)(108, 230)(109, 207)(110, 228)(111, 203)(112, 194)(113, 195)(114, 214)(115, 199)(116, 210)(117, 193)(118, 240)(119, 197)(120, 238)(121, 237)(122, 232)(123, 233)(124, 198)(125, 239)(126, 196)(127, 235)(128, 226)(129, 227)(130, 222)(131, 231)(132, 218)(133, 225)(134, 208)(135, 229)(136, 206)(137, 215)(138, 236)(139, 213)(140, 216)(141, 211)(142, 234)(143, 209)(144, 212) MAP : A3.39 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A3.37. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 6 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^4, x.3^-2 * x.2 * x.3^3 * x.2^-1 * x.3^-1, x.3^-1 * x.2 * x.3 * x.2 * x.3^-2 * x.2^-1 * x.3 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 12) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 244)(50, 245)(51, 280)(52, 241)(53, 242)(54, 247)(55, 246)(56, 285)(57, 264)(58, 259)(59, 286)(60, 263)(61, 284)(62, 257)(63, 282)(64, 267)(65, 254)(66, 279)(67, 250)(68, 277)(69, 272)(70, 275)(71, 252)(72, 249)(73, 268)(74, 269)(75, 256)(76, 265)(77, 266)(78, 271)(79, 270)(80, 261)(81, 288)(82, 283)(83, 262)(84, 287)(85, 260)(86, 281)(87, 258)(88, 243)(89, 278)(90, 255)(91, 274)(92, 253)(93, 248)(94, 251)(95, 276)(96, 273)(97, 194)(98, 201)(99, 196)(100, 203)(101, 198)(102, 205)(103, 232)(104, 231)(105, 202)(106, 209)(107, 204)(108, 211)(109, 206)(110, 213)(111, 224)(112, 223)(113, 210)(114, 193)(115, 212)(116, 195)(117, 214)(118, 197)(119, 240)(120, 239)(121, 234)(122, 217)(123, 236)(124, 219)(125, 238)(126, 221)(127, 216)(128, 215)(129, 218)(130, 225)(131, 220)(132, 227)(133, 222)(134, 229)(135, 208)(136, 207)(137, 226)(138, 233)(139, 228)(140, 235)(141, 230)(142, 237)(143, 200)(144, 199) MAP : A3.40 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A3.37. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 6 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^4, x.3^-2 * x.2 * x.3^3 * x.2^-1 * x.3^-1, x.3^-1 * x.2 * x.3 * x.2 * x.3^-2 * x.2^-1 * x.3 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 12) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 253)(50, 248)(51, 249)(52, 278)(53, 255)(54, 276)(55, 251)(56, 242)(57, 243)(58, 262)(59, 247)(60, 258)(61, 241)(62, 288)(63, 245)(64, 286)(65, 271)(66, 252)(67, 269)(68, 272)(69, 267)(70, 250)(71, 265)(72, 268)(73, 263)(74, 284)(75, 261)(76, 264)(77, 259)(78, 282)(79, 257)(80, 260)(81, 285)(82, 280)(83, 281)(84, 246)(85, 287)(86, 244)(87, 283)(88, 274)(89, 275)(90, 270)(91, 279)(92, 266)(93, 273)(94, 256)(95, 277)(96, 254)(97, 194)(98, 201)(99, 196)(100, 203)(101, 198)(102, 205)(103, 232)(104, 231)(105, 202)(106, 209)(107, 204)(108, 211)(109, 206)(110, 213)(111, 224)(112, 223)(113, 210)(114, 193)(115, 212)(116, 195)(117, 214)(118, 197)(119, 240)(120, 239)(121, 234)(122, 217)(123, 236)(124, 219)(125, 238)(126, 221)(127, 216)(128, 215)(129, 218)(130, 225)(131, 220)(132, 227)(133, 222)(134, 229)(135, 208)(136, 207)(137, 226)(138, 233)(139, 228)(140, 235)(141, 230)(142, 237)(143, 200)(144, 199) MAP : A3.41 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A3.37. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 6, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^4, x.3 * x.2 * x.3 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2^-2, x.2^-1 * x.3 * x.2^2 * x.3 * x.2^-1 * x.3^-1 * x.2^-2 * x.3^-1, x.3 * x.2^-1 * x.3 * x.2^2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-2, (x.2 * x.3^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 12) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 287)(51, 242)(52, 285)(53, 280)(54, 283)(55, 244)(56, 241)(57, 260)(58, 261)(59, 288)(60, 257)(61, 258)(62, 263)(63, 262)(64, 269)(65, 256)(66, 251)(67, 270)(68, 255)(69, 268)(70, 249)(71, 266)(72, 275)(73, 272)(74, 267)(75, 254)(76, 271)(77, 252)(78, 265)(79, 250)(80, 259)(81, 286)(82, 247)(83, 282)(84, 245)(85, 264)(86, 243)(87, 284)(88, 281)(89, 276)(90, 277)(91, 248)(92, 273)(93, 274)(94, 279)(95, 278)(96, 253)(97, 205)(98, 200)(99, 201)(100, 230)(101, 207)(102, 228)(103, 203)(104, 194)(105, 195)(106, 214)(107, 199)(108, 210)(109, 193)(110, 240)(111, 197)(112, 238)(113, 223)(114, 204)(115, 221)(116, 224)(117, 219)(118, 202)(119, 217)(120, 220)(121, 215)(122, 236)(123, 213)(124, 216)(125, 211)(126, 234)(127, 209)(128, 212)(129, 237)(130, 232)(131, 233)(132, 198)(133, 239)(134, 196)(135, 235)(136, 226)(137, 227)(138, 222)(139, 231)(140, 218)(141, 225)(142, 208)(143, 229)(144, 206) MAP : A3.42 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A3.37. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^4, (x.2 * x.3^-1)^2, (x.3 * x.2^2)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 12) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 242)(50, 249)(51, 244)(52, 251)(53, 246)(54, 253)(55, 280)(56, 279)(57, 250)(58, 257)(59, 252)(60, 259)(61, 254)(62, 261)(63, 272)(64, 271)(65, 258)(66, 241)(67, 260)(68, 243)(69, 262)(70, 245)(71, 288)(72, 287)(73, 282)(74, 265)(75, 284)(76, 267)(77, 286)(78, 269)(79, 264)(80, 263)(81, 266)(82, 273)(83, 268)(84, 275)(85, 270)(86, 277)(87, 256)(88, 255)(89, 274)(90, 281)(91, 276)(92, 283)(93, 278)(94, 285)(95, 248)(96, 247)(97, 200)(98, 195)(99, 230)(100, 199)(101, 228)(102, 193)(103, 226)(104, 235)(105, 214)(106, 223)(107, 210)(108, 221)(109, 240)(110, 219)(111, 212)(112, 209)(113, 204)(114, 205)(115, 224)(116, 201)(117, 202)(118, 207)(119, 206)(120, 229)(121, 222)(122, 215)(123, 218)(124, 213)(125, 208)(126, 211)(127, 220)(128, 217)(129, 236)(130, 237)(131, 216)(132, 233)(133, 234)(134, 239)(135, 238)(136, 197)(137, 232)(138, 227)(139, 198)(140, 231)(141, 196)(142, 225)(143, 194)(144, 203) MAP : A3.43 NOTES : type II, reflexible, isomorphic to DBar({4,8}), representative. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 162)(34, 161)(35, 166)(36, 165)(37, 164)(38, 163)(39, 179)(40, 186)(41, 188)(42, 172)(43, 180)(44, 170)(45, 177)(46, 187)(47, 182)(48, 178)(49, 173)(50, 176)(51, 167)(52, 171)(53, 190)(54, 175)(55, 191)(56, 185)(57, 184)(58, 168)(59, 174)(60, 169)(61, 192)(62, 181)(63, 183)(64, 189)(65, 132)(66, 148)(67, 130)(68, 138)(69, 154)(70, 146)(71, 145)(72, 134)(73, 135)(74, 143)(75, 156)(76, 159)(77, 149)(78, 153)(79, 160)(80, 155)(81, 133)(82, 139)(83, 129)(84, 140)(85, 136)(86, 144)(87, 141)(88, 131)(89, 147)(90, 150)(91, 137)(92, 151)(93, 158)(94, 152)(95, 157)(96, 142) MAP : A3.44 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 162)(34, 161)(35, 166)(36, 165)(37, 164)(38, 163)(39, 179)(40, 186)(41, 188)(42, 172)(43, 180)(44, 170)(45, 177)(46, 187)(47, 182)(48, 178)(49, 173)(50, 176)(51, 167)(52, 171)(53, 190)(54, 175)(55, 191)(56, 185)(57, 184)(58, 168)(59, 174)(60, 169)(61, 192)(62, 181)(63, 183)(64, 189)(65, 142)(66, 158)(67, 157)(68, 153)(69, 137)(70, 141)(71, 144)(72, 151)(73, 150)(74, 147)(75, 136)(76, 131)(77, 139)(78, 138)(79, 129)(80, 133)(81, 155)(82, 149)(83, 160)(84, 152)(85, 156)(86, 145)(87, 146)(88, 159)(89, 143)(90, 135)(91, 154)(92, 134)(93, 148)(94, 140)(95, 130)(96, 132) MAP : A3.45 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^4, x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1, x.3^-3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 165)(34, 171)(35, 161)(36, 172)(37, 168)(38, 176)(39, 173)(40, 163)(41, 179)(42, 182)(43, 169)(44, 183)(45, 190)(46, 184)(47, 189)(48, 174)(49, 164)(50, 180)(51, 162)(52, 170)(53, 186)(54, 178)(55, 177)(56, 166)(57, 167)(58, 175)(59, 188)(60, 191)(61, 181)(62, 185)(63, 192)(64, 187)(65, 130)(66, 129)(67, 134)(68, 133)(69, 132)(70, 131)(71, 147)(72, 154)(73, 156)(74, 140)(75, 148)(76, 138)(77, 145)(78, 155)(79, 150)(80, 146)(81, 141)(82, 144)(83, 135)(84, 139)(85, 158)(86, 143)(87, 159)(88, 153)(89, 152)(90, 136)(91, 142)(92, 137)(93, 160)(94, 149)(95, 151)(96, 157) MAP : A3.46 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^4, x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1, x.3^-3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 182)(34, 183)(35, 170)(36, 189)(37, 178)(38, 169)(39, 168)(40, 180)(41, 164)(42, 187)(43, 177)(44, 181)(45, 163)(46, 162)(47, 184)(48, 179)(49, 175)(50, 191)(51, 172)(52, 192)(53, 176)(54, 188)(55, 186)(56, 171)(57, 165)(58, 174)(59, 173)(60, 190)(61, 166)(62, 161)(63, 185)(64, 167)(65, 130)(66, 129)(67, 134)(68, 133)(69, 132)(70, 131)(71, 147)(72, 154)(73, 156)(74, 140)(75, 148)(76, 138)(77, 145)(78, 155)(79, 150)(80, 146)(81, 141)(82, 144)(83, 135)(84, 139)(85, 158)(86, 143)(87, 159)(88, 153)(89, 152)(90, 136)(91, 142)(92, 137)(93, 160)(94, 149)(95, 151)(96, 157) MAP : A3.47 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^4, x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1, x.3^-3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 190)(34, 174)(35, 173)(36, 169)(37, 185)(38, 189)(39, 192)(40, 167)(41, 166)(42, 163)(43, 184)(44, 179)(45, 187)(46, 186)(47, 177)(48, 181)(49, 171)(50, 165)(51, 176)(52, 168)(53, 172)(54, 161)(55, 162)(56, 175)(57, 191)(58, 183)(59, 170)(60, 182)(61, 164)(62, 188)(63, 178)(64, 180)(65, 130)(66, 129)(67, 134)(68, 133)(69, 132)(70, 131)(71, 147)(72, 154)(73, 156)(74, 140)(75, 148)(76, 138)(77, 145)(78, 155)(79, 150)(80, 146)(81, 141)(82, 144)(83, 135)(84, 139)(85, 158)(86, 143)(87, 159)(88, 153)(89, 152)(90, 136)(91, 142)(92, 137)(93, 160)(94, 149)(95, 151)(96, 157) MAP : A3.48 NOTES : type II, reflexible, isomorphic to DBar({4,8}), representative. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 187)(34, 180)(35, 182)(36, 186)(37, 189)(38, 165)(39, 177)(40, 178)(41, 188)(42, 184)(43, 169)(44, 161)(45, 163)(46, 179)(47, 181)(48, 164)(49, 176)(50, 175)(51, 191)(52, 172)(53, 190)(54, 167)(55, 174)(56, 192)(57, 183)(58, 173)(59, 166)(60, 168)(61, 162)(62, 171)(63, 170)(64, 185)(65, 131)(66, 137)(67, 153)(68, 133)(69, 136)(70, 154)(71, 152)(72, 147)(73, 138)(74, 145)(75, 148)(76, 158)(77, 155)(78, 146)(79, 151)(80, 159)(81, 130)(82, 134)(83, 132)(84, 135)(85, 129)(86, 140)(87, 141)(88, 139)(89, 149)(90, 142)(91, 143)(92, 157)(93, 144)(94, 160)(95, 156)(96, 150) MAP : A3.49 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-1 * x.3 * x.2^2 * x.3^-1 * x.2^-1, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 181)(34, 177)(35, 161)(36, 179)(37, 164)(38, 178)(39, 180)(40, 165)(41, 162)(42, 169)(43, 184)(44, 182)(45, 183)(46, 186)(47, 187)(48, 189)(49, 170)(50, 174)(51, 168)(52, 171)(53, 185)(54, 192)(55, 175)(56, 167)(57, 163)(58, 166)(59, 173)(60, 191)(61, 188)(62, 172)(63, 176)(64, 190)(65, 150)(66, 156)(67, 151)(68, 157)(69, 146)(70, 141)(71, 160)(72, 159)(73, 152)(74, 144)(75, 140)(76, 139)(77, 134)(78, 143)(79, 142)(80, 138)(81, 148)(82, 133)(83, 154)(84, 145)(85, 155)(86, 129)(87, 131)(88, 137)(89, 158)(90, 147)(91, 149)(92, 130)(93, 132)(94, 153)(95, 136)(96, 135) MAP : A3.50 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-1 * x.3 * x.2^2 * x.3^-1 * x.2^-1, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 181)(34, 177)(35, 161)(36, 179)(37, 164)(38, 178)(39, 180)(40, 165)(41, 162)(42, 169)(43, 184)(44, 182)(45, 183)(46, 186)(47, 187)(48, 189)(49, 170)(50, 174)(51, 168)(52, 171)(53, 185)(54, 192)(55, 175)(56, 167)(57, 163)(58, 166)(59, 173)(60, 191)(61, 188)(62, 172)(63, 176)(64, 190)(65, 136)(66, 131)(67, 130)(68, 153)(69, 135)(70, 137)(71, 133)(72, 129)(73, 134)(74, 149)(75, 147)(76, 154)(77, 152)(78, 145)(79, 148)(80, 155)(81, 142)(82, 160)(83, 139)(84, 143)(85, 138)(86, 159)(87, 156)(88, 141)(89, 132)(90, 140)(91, 144)(92, 151)(93, 158)(94, 157)(95, 150)(96, 146) MAP : A3.51 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 172)(34, 189)(35, 173)(36, 176)(37, 166)(38, 187)(39, 182)(40, 188)(41, 171)(42, 191)(43, 190)(44, 180)(45, 186)(46, 183)(47, 178)(48, 177)(49, 167)(50, 168)(51, 174)(52, 162)(53, 175)(54, 163)(55, 185)(56, 170)(57, 192)(58, 164)(59, 161)(60, 169)(61, 165)(62, 181)(63, 179)(64, 184)(65, 149)(66, 145)(67, 129)(68, 147)(69, 132)(70, 146)(71, 148)(72, 133)(73, 130)(74, 137)(75, 152)(76, 150)(77, 151)(78, 154)(79, 155)(80, 157)(81, 138)(82, 142)(83, 136)(84, 139)(85, 153)(86, 160)(87, 143)(88, 135)(89, 131)(90, 134)(91, 141)(92, 159)(93, 156)(94, 140)(95, 144)(96, 158) MAP : A3.52 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^4, x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1, x.3^-3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 163)(34, 179)(35, 168)(36, 177)(37, 161)(38, 184)(39, 185)(40, 165)(41, 171)(42, 180)(43, 162)(44, 164)(45, 167)(46, 176)(47, 186)(48, 166)(49, 183)(50, 182)(51, 169)(52, 178)(53, 189)(54, 170)(55, 172)(56, 174)(57, 190)(58, 181)(59, 192)(60, 187)(61, 175)(62, 173)(63, 188)(64, 191)(65, 130)(66, 129)(67, 134)(68, 133)(69, 132)(70, 131)(71, 147)(72, 154)(73, 156)(74, 140)(75, 148)(76, 138)(77, 145)(78, 155)(79, 150)(80, 146)(81, 141)(82, 144)(83, 135)(84, 139)(85, 158)(86, 143)(87, 159)(88, 153)(89, 152)(90, 136)(91, 142)(92, 137)(93, 160)(94, 149)(95, 151)(96, 157) MAP : A3.53 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2)^2, x.3 * x.2^2 * x.3^-1 * x.2^-2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 164)(34, 180)(35, 162)(36, 170)(37, 186)(38, 178)(39, 177)(40, 166)(41, 167)(42, 175)(43, 188)(44, 191)(45, 181)(46, 185)(47, 192)(48, 187)(49, 165)(50, 171)(51, 161)(52, 172)(53, 168)(54, 176)(55, 173)(56, 163)(57, 179)(58, 182)(59, 169)(60, 183)(61, 190)(62, 184)(63, 189)(64, 174)(65, 133)(66, 139)(67, 129)(68, 140)(69, 136)(70, 144)(71, 141)(72, 131)(73, 147)(74, 150)(75, 137)(76, 151)(77, 158)(78, 152)(79, 157)(80, 142)(81, 132)(82, 148)(83, 130)(84, 138)(85, 154)(86, 146)(87, 145)(88, 134)(89, 135)(90, 143)(91, 156)(92, 159)(93, 149)(94, 153)(95, 160)(96, 155) MAP : A3.54 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 162)(34, 161)(35, 166)(36, 165)(37, 164)(38, 163)(39, 179)(40, 186)(41, 188)(42, 172)(43, 180)(44, 170)(45, 177)(46, 187)(47, 182)(48, 178)(49, 173)(50, 176)(51, 167)(52, 171)(53, 190)(54, 175)(55, 191)(56, 185)(57, 184)(58, 168)(59, 174)(60, 169)(61, 192)(62, 181)(63, 183)(64, 189)(65, 143)(66, 159)(67, 140)(68, 160)(69, 144)(70, 156)(71, 154)(72, 139)(73, 133)(74, 142)(75, 141)(76, 158)(77, 134)(78, 129)(79, 153)(80, 135)(81, 150)(82, 151)(83, 138)(84, 157)(85, 146)(86, 137)(87, 136)(88, 148)(89, 132)(90, 155)(91, 145)(92, 149)(93, 131)(94, 130)(95, 152)(96, 147) MAP : A3.55 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-1 * x.3 * x.2^2 * x.3^-1 * x.2^-1, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 181)(34, 177)(35, 161)(36, 179)(37, 164)(38, 178)(39, 180)(40, 165)(41, 162)(42, 169)(43, 184)(44, 182)(45, 183)(46, 186)(47, 187)(48, 189)(49, 170)(50, 174)(51, 168)(52, 171)(53, 185)(54, 192)(55, 175)(56, 167)(57, 163)(58, 166)(59, 173)(60, 191)(61, 188)(62, 172)(63, 176)(64, 190)(65, 158)(66, 144)(67, 155)(68, 159)(69, 154)(70, 143)(71, 140)(72, 157)(73, 148)(74, 156)(75, 160)(76, 135)(77, 142)(78, 141)(79, 134)(80, 130)(81, 152)(82, 147)(83, 146)(84, 137)(85, 151)(86, 153)(87, 149)(88, 145)(89, 150)(90, 133)(91, 131)(92, 138)(93, 136)(94, 129)(95, 132)(96, 139) MAP : A3.56 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^2 * x.2 * x.3^2 * x.2^-1, x.3^8, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 164)(34, 181)(35, 170)(36, 161)(37, 171)(38, 177)(39, 179)(40, 185)(41, 174)(42, 163)(43, 165)(44, 178)(45, 180)(46, 169)(47, 184)(48, 183)(49, 166)(50, 172)(51, 167)(52, 173)(53, 162)(54, 189)(55, 176)(56, 175)(57, 168)(58, 192)(59, 188)(60, 187)(61, 182)(62, 191)(63, 190)(64, 186)(65, 130)(66, 134)(67, 132)(68, 135)(69, 129)(70, 140)(71, 141)(72, 139)(73, 149)(74, 142)(75, 143)(76, 157)(77, 144)(78, 160)(79, 156)(80, 150)(81, 131)(82, 137)(83, 153)(84, 133)(85, 136)(86, 154)(87, 152)(88, 147)(89, 138)(90, 145)(91, 148)(92, 158)(93, 155)(94, 146)(95, 151)(96, 159) MAP : A3.57 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2)^2, x.3 * x.2^2 * x.3^-1 * x.2^-2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 175)(34, 191)(35, 172)(36, 192)(37, 176)(38, 188)(39, 186)(40, 171)(41, 165)(42, 174)(43, 173)(44, 190)(45, 166)(46, 161)(47, 185)(48, 167)(49, 182)(50, 183)(51, 170)(52, 189)(53, 178)(54, 169)(55, 168)(56, 180)(57, 164)(58, 187)(59, 177)(60, 181)(61, 163)(62, 162)(63, 184)(64, 179)(65, 150)(66, 151)(67, 138)(68, 157)(69, 146)(70, 137)(71, 136)(72, 148)(73, 132)(74, 155)(75, 145)(76, 149)(77, 131)(78, 130)(79, 152)(80, 147)(81, 143)(82, 159)(83, 140)(84, 160)(85, 144)(86, 156)(87, 154)(88, 139)(89, 133)(90, 142)(91, 141)(92, 158)(93, 134)(94, 129)(95, 153)(96, 135) MAP : A3.58 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2)^2, x.3 * x.2^2 * x.3^-1 * x.2^-2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 164)(34, 180)(35, 162)(36, 170)(37, 186)(38, 178)(39, 177)(40, 166)(41, 167)(42, 175)(43, 188)(44, 191)(45, 181)(46, 185)(47, 192)(48, 187)(49, 165)(50, 171)(51, 161)(52, 172)(53, 168)(54, 176)(55, 173)(56, 163)(57, 179)(58, 182)(59, 169)(60, 183)(61, 190)(62, 184)(63, 189)(64, 174)(65, 158)(66, 142)(67, 141)(68, 137)(69, 153)(70, 157)(71, 160)(72, 135)(73, 134)(74, 131)(75, 152)(76, 147)(77, 155)(78, 154)(79, 145)(80, 149)(81, 139)(82, 133)(83, 144)(84, 136)(85, 140)(86, 129)(87, 130)(88, 143)(89, 159)(90, 151)(91, 138)(92, 150)(93, 132)(94, 156)(95, 146)(96, 148) MAP : A3.59 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-1 * x.3 * x.2^2 * x.3^-1 * x.2^-1, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 163)(34, 169)(35, 185)(36, 165)(37, 168)(38, 186)(39, 184)(40, 179)(41, 170)(42, 177)(43, 180)(44, 190)(45, 187)(46, 178)(47, 183)(48, 191)(49, 162)(50, 166)(51, 164)(52, 167)(53, 161)(54, 172)(55, 173)(56, 171)(57, 181)(58, 174)(59, 175)(60, 189)(61, 176)(62, 192)(63, 188)(64, 182)(65, 158)(66, 144)(67, 155)(68, 159)(69, 154)(70, 143)(71, 140)(72, 157)(73, 148)(74, 156)(75, 160)(76, 135)(77, 142)(78, 141)(79, 134)(80, 130)(81, 152)(82, 147)(83, 146)(84, 137)(85, 151)(86, 153)(87, 149)(88, 145)(89, 150)(90, 133)(91, 131)(92, 138)(93, 136)(94, 129)(95, 132)(96, 139) MAP : A3.60 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-1 * x.3 * x.2^2 * x.3^-1 * x.2^-1, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 181)(34, 177)(35, 161)(36, 179)(37, 164)(38, 178)(39, 180)(40, 165)(41, 162)(42, 169)(43, 184)(44, 182)(45, 183)(46, 186)(47, 187)(48, 189)(49, 170)(50, 174)(51, 168)(52, 171)(53, 185)(54, 192)(55, 175)(56, 167)(57, 163)(58, 166)(59, 173)(60, 191)(61, 188)(62, 172)(63, 176)(64, 190)(65, 132)(66, 149)(67, 138)(68, 129)(69, 139)(70, 145)(71, 147)(72, 153)(73, 142)(74, 131)(75, 133)(76, 146)(77, 148)(78, 137)(79, 152)(80, 151)(81, 134)(82, 140)(83, 135)(84, 141)(85, 130)(86, 157)(87, 144)(88, 143)(89, 136)(90, 160)(91, 156)(92, 155)(93, 150)(94, 159)(95, 158)(96, 154) MAP : A3.61 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 172)(34, 189)(35, 173)(36, 176)(37, 166)(38, 187)(39, 182)(40, 188)(41, 171)(42, 191)(43, 190)(44, 180)(45, 186)(46, 183)(47, 178)(48, 177)(49, 167)(50, 168)(51, 174)(52, 162)(53, 175)(54, 163)(55, 185)(56, 170)(57, 192)(58, 164)(59, 161)(60, 169)(61, 165)(62, 181)(63, 179)(64, 184)(65, 131)(66, 137)(67, 153)(68, 133)(69, 136)(70, 154)(71, 152)(72, 147)(73, 138)(74, 145)(75, 148)(76, 158)(77, 155)(78, 146)(79, 151)(80, 159)(81, 130)(82, 134)(83, 132)(84, 135)(85, 129)(86, 140)(87, 141)(88, 139)(89, 149)(90, 142)(91, 143)(92, 157)(93, 144)(94, 160)(95, 156)(96, 150) MAP : A3.62 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 165)(34, 161)(35, 177)(36, 163)(37, 180)(38, 162)(39, 164)(40, 181)(41, 178)(42, 185)(43, 168)(44, 166)(45, 167)(46, 170)(47, 171)(48, 173)(49, 186)(50, 190)(51, 184)(52, 187)(53, 169)(54, 176)(55, 191)(56, 183)(57, 179)(58, 182)(59, 189)(60, 175)(61, 172)(62, 188)(63, 192)(64, 174)(65, 149)(66, 145)(67, 129)(68, 147)(69, 132)(70, 146)(71, 148)(72, 133)(73, 130)(74, 137)(75, 152)(76, 150)(77, 151)(78, 154)(79, 155)(80, 157)(81, 138)(82, 142)(83, 136)(84, 139)(85, 153)(86, 160)(87, 143)(88, 135)(89, 131)(90, 134)(91, 141)(92, 159)(93, 156)(94, 140)(95, 144)(96, 158) MAP : A3.63 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 162)(34, 166)(35, 164)(36, 167)(37, 161)(38, 172)(39, 173)(40, 171)(41, 181)(42, 174)(43, 175)(44, 189)(45, 176)(46, 192)(47, 188)(48, 182)(49, 163)(50, 169)(51, 185)(52, 165)(53, 168)(54, 186)(55, 184)(56, 179)(57, 170)(58, 177)(59, 180)(60, 190)(61, 187)(62, 178)(63, 183)(64, 191)(65, 131)(66, 137)(67, 153)(68, 133)(69, 136)(70, 154)(71, 152)(72, 147)(73, 138)(74, 145)(75, 148)(76, 158)(77, 155)(78, 146)(79, 151)(80, 159)(81, 130)(82, 134)(83, 132)(84, 135)(85, 129)(86, 140)(87, 141)(88, 139)(89, 149)(90, 142)(91, 143)(92, 157)(93, 144)(94, 160)(95, 156)(96, 150) MAP : A3.64 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 162)(34, 166)(35, 164)(36, 167)(37, 161)(38, 172)(39, 173)(40, 171)(41, 181)(42, 174)(43, 175)(44, 189)(45, 176)(46, 192)(47, 188)(48, 182)(49, 163)(50, 169)(51, 185)(52, 165)(53, 168)(54, 186)(55, 184)(56, 179)(57, 170)(58, 177)(59, 180)(60, 190)(61, 187)(62, 178)(63, 183)(64, 191)(65, 149)(66, 145)(67, 129)(68, 147)(69, 132)(70, 146)(71, 148)(72, 133)(73, 130)(74, 137)(75, 152)(76, 150)(77, 151)(78, 154)(79, 155)(80, 157)(81, 138)(82, 142)(83, 136)(84, 139)(85, 153)(86, 160)(87, 143)(88, 135)(89, 131)(90, 134)(91, 141)(92, 159)(93, 156)(94, 140)(95, 144)(96, 158) MAP : A3.65 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 165)(34, 161)(35, 177)(36, 163)(37, 180)(38, 162)(39, 164)(40, 181)(41, 178)(42, 185)(43, 168)(44, 166)(45, 167)(46, 170)(47, 171)(48, 173)(49, 186)(50, 190)(51, 184)(52, 187)(53, 169)(54, 176)(55, 191)(56, 183)(57, 179)(58, 182)(59, 189)(60, 175)(61, 172)(62, 188)(63, 192)(64, 174)(65, 131)(66, 137)(67, 153)(68, 133)(69, 136)(70, 154)(71, 152)(72, 147)(73, 138)(74, 145)(75, 148)(76, 158)(77, 155)(78, 146)(79, 151)(80, 159)(81, 130)(82, 134)(83, 132)(84, 135)(85, 129)(86, 140)(87, 141)(88, 139)(89, 149)(90, 142)(91, 143)(92, 157)(93, 144)(94, 160)(95, 156)(96, 150) MAP : A3.66 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^2 * x.2 * x.3^2 * x.2^-1, x.3^8, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 168)(34, 163)(35, 162)(36, 185)(37, 167)(38, 169)(39, 165)(40, 161)(41, 166)(42, 181)(43, 179)(44, 186)(45, 184)(46, 177)(47, 180)(48, 187)(49, 174)(50, 192)(51, 171)(52, 175)(53, 170)(54, 191)(55, 188)(56, 173)(57, 164)(58, 172)(59, 176)(60, 183)(61, 190)(62, 189)(63, 182)(64, 178)(65, 133)(66, 129)(67, 145)(68, 131)(69, 148)(70, 130)(71, 132)(72, 149)(73, 146)(74, 153)(75, 136)(76, 134)(77, 135)(78, 138)(79, 139)(80, 141)(81, 154)(82, 158)(83, 152)(84, 155)(85, 137)(86, 144)(87, 159)(88, 151)(89, 147)(90, 150)(91, 157)(92, 143)(93, 140)(94, 156)(95, 160)(96, 142) MAP : A3.67 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-1 * x.3 * x.2^2 * x.3^-1 * x.2^-1, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 163)(34, 169)(35, 185)(36, 165)(37, 168)(38, 186)(39, 184)(40, 179)(41, 170)(42, 177)(43, 180)(44, 190)(45, 187)(46, 178)(47, 183)(48, 191)(49, 162)(50, 166)(51, 164)(52, 167)(53, 161)(54, 172)(55, 173)(56, 171)(57, 181)(58, 174)(59, 175)(60, 189)(61, 176)(62, 192)(63, 188)(64, 182)(65, 132)(66, 149)(67, 138)(68, 129)(69, 139)(70, 145)(71, 147)(72, 153)(73, 142)(74, 131)(75, 133)(76, 146)(77, 148)(78, 137)(79, 152)(80, 151)(81, 134)(82, 140)(83, 135)(84, 141)(85, 130)(86, 157)(87, 144)(88, 143)(89, 136)(90, 160)(91, 156)(92, 155)(93, 150)(94, 159)(95, 158)(96, 154) MAP : A3.68 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 162)(34, 161)(35, 166)(36, 165)(37, 164)(38, 163)(39, 179)(40, 186)(41, 188)(42, 172)(43, 180)(44, 170)(45, 177)(46, 187)(47, 182)(48, 178)(49, 173)(50, 176)(51, 167)(52, 171)(53, 190)(54, 175)(55, 191)(56, 185)(57, 184)(58, 168)(59, 174)(60, 169)(61, 192)(62, 181)(63, 183)(64, 189)(65, 147)(66, 131)(67, 152)(68, 129)(69, 145)(70, 136)(71, 137)(72, 149)(73, 155)(74, 132)(75, 146)(76, 148)(77, 151)(78, 160)(79, 138)(80, 150)(81, 135)(82, 134)(83, 153)(84, 130)(85, 141)(86, 154)(87, 156)(88, 158)(89, 142)(90, 133)(91, 144)(92, 139)(93, 159)(94, 157)(95, 140)(96, 143) MAP : A3.69 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-1 * x.3 * x.2^2 * x.3^-1 * x.2^-1, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 163)(34, 169)(35, 185)(36, 165)(37, 168)(38, 186)(39, 184)(40, 179)(41, 170)(42, 177)(43, 180)(44, 190)(45, 187)(46, 178)(47, 183)(48, 191)(49, 162)(50, 166)(51, 164)(52, 167)(53, 161)(54, 172)(55, 173)(56, 171)(57, 181)(58, 174)(59, 175)(60, 189)(61, 176)(62, 192)(63, 188)(64, 182)(65, 136)(66, 131)(67, 130)(68, 153)(69, 135)(70, 137)(71, 133)(72, 129)(73, 134)(74, 149)(75, 147)(76, 154)(77, 152)(78, 145)(79, 148)(80, 155)(81, 142)(82, 160)(83, 139)(84, 143)(85, 138)(86, 159)(87, 156)(88, 141)(89, 132)(90, 140)(91, 144)(92, 151)(93, 158)(94, 157)(95, 150)(96, 146) MAP : A3.70 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 187)(34, 180)(35, 182)(36, 186)(37, 189)(38, 165)(39, 177)(40, 178)(41, 188)(42, 184)(43, 169)(44, 161)(45, 163)(46, 179)(47, 181)(48, 164)(49, 176)(50, 175)(51, 191)(52, 172)(53, 190)(54, 167)(55, 174)(56, 192)(57, 183)(58, 173)(59, 166)(60, 168)(61, 162)(62, 171)(63, 170)(64, 185)(65, 149)(66, 145)(67, 129)(68, 147)(69, 132)(70, 146)(71, 148)(72, 133)(73, 130)(74, 137)(75, 152)(76, 150)(77, 151)(78, 154)(79, 155)(80, 157)(81, 138)(82, 142)(83, 136)(84, 139)(85, 153)(86, 160)(87, 143)(88, 135)(89, 131)(90, 134)(91, 141)(92, 159)(93, 156)(94, 140)(95, 144)(96, 158) MAP : A3.71 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^2 * x.2 * x.3^2 * x.2^-1, x.3^8, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 164)(34, 181)(35, 170)(36, 161)(37, 171)(38, 177)(39, 179)(40, 185)(41, 174)(42, 163)(43, 165)(44, 178)(45, 180)(46, 169)(47, 184)(48, 183)(49, 166)(50, 172)(51, 167)(52, 173)(53, 162)(54, 189)(55, 176)(56, 175)(57, 168)(58, 192)(59, 188)(60, 187)(61, 182)(62, 191)(63, 190)(64, 186)(65, 133)(66, 129)(67, 145)(68, 131)(69, 148)(70, 130)(71, 132)(72, 149)(73, 146)(74, 153)(75, 136)(76, 134)(77, 135)(78, 138)(79, 139)(80, 141)(81, 154)(82, 158)(83, 152)(84, 155)(85, 137)(86, 144)(87, 159)(88, 151)(89, 147)(90, 150)(91, 157)(92, 143)(93, 140)(94, 156)(95, 160)(96, 142) MAP : A3.72 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-1 * x.3 * x.2^2 * x.3^-1 * x.2^-1, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 163)(34, 169)(35, 185)(36, 165)(37, 168)(38, 186)(39, 184)(40, 179)(41, 170)(42, 177)(43, 180)(44, 190)(45, 187)(46, 178)(47, 183)(48, 191)(49, 162)(50, 166)(51, 164)(52, 167)(53, 161)(54, 172)(55, 173)(56, 171)(57, 181)(58, 174)(59, 175)(60, 189)(61, 176)(62, 192)(63, 188)(64, 182)(65, 150)(66, 156)(67, 151)(68, 157)(69, 146)(70, 141)(71, 160)(72, 159)(73, 152)(74, 144)(75, 140)(76, 139)(77, 134)(78, 143)(79, 142)(80, 138)(81, 148)(82, 133)(83, 154)(84, 145)(85, 155)(86, 129)(87, 131)(88, 137)(89, 158)(90, 147)(91, 149)(92, 130)(93, 132)(94, 153)(95, 136)(96, 135) MAP : A3.73 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^2 * x.2 * x.3^2 * x.2^-1, x.3^8, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 168)(34, 163)(35, 162)(36, 185)(37, 167)(38, 169)(39, 165)(40, 161)(41, 166)(42, 181)(43, 179)(44, 186)(45, 184)(46, 177)(47, 180)(48, 187)(49, 174)(50, 192)(51, 171)(52, 175)(53, 170)(54, 191)(55, 188)(56, 173)(57, 164)(58, 172)(59, 176)(60, 183)(61, 190)(62, 189)(63, 182)(64, 178)(65, 140)(66, 157)(67, 141)(68, 144)(69, 134)(70, 155)(71, 150)(72, 156)(73, 139)(74, 159)(75, 158)(76, 148)(77, 154)(78, 151)(79, 146)(80, 145)(81, 135)(82, 136)(83, 142)(84, 130)(85, 143)(86, 131)(87, 153)(88, 138)(89, 160)(90, 132)(91, 129)(92, 137)(93, 133)(94, 149)(95, 147)(96, 152) MAP : A3.74 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 2, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2)^2, x.3 * x.2^2 * x.3^-1 * x.2^-2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 175)(34, 191)(35, 172)(36, 192)(37, 176)(38, 188)(39, 186)(40, 171)(41, 165)(42, 174)(43, 173)(44, 190)(45, 166)(46, 161)(47, 185)(48, 167)(49, 182)(50, 183)(51, 170)(52, 189)(53, 178)(54, 169)(55, 168)(56, 180)(57, 164)(58, 187)(59, 177)(60, 181)(61, 163)(62, 162)(63, 184)(64, 179)(65, 131)(66, 147)(67, 136)(68, 145)(69, 129)(70, 152)(71, 153)(72, 133)(73, 139)(74, 148)(75, 130)(76, 132)(77, 135)(78, 144)(79, 154)(80, 134)(81, 151)(82, 150)(83, 137)(84, 146)(85, 157)(86, 138)(87, 140)(88, 142)(89, 158)(90, 149)(91, 160)(92, 155)(93, 143)(94, 141)(95, 156)(96, 159) MAP : A3.75 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^2 * x.2 * x.3^2 * x.2^-1, x.3^8, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 164)(34, 181)(35, 170)(36, 161)(37, 171)(38, 177)(39, 179)(40, 185)(41, 174)(42, 163)(43, 165)(44, 178)(45, 180)(46, 169)(47, 184)(48, 183)(49, 166)(50, 172)(51, 167)(52, 173)(53, 162)(54, 189)(55, 176)(56, 175)(57, 168)(58, 192)(59, 188)(60, 187)(61, 182)(62, 191)(63, 190)(64, 186)(65, 140)(66, 157)(67, 141)(68, 144)(69, 134)(70, 155)(71, 150)(72, 156)(73, 139)(74, 159)(75, 158)(76, 148)(77, 154)(78, 151)(79, 146)(80, 145)(81, 135)(82, 136)(83, 142)(84, 130)(85, 143)(86, 131)(87, 153)(88, 138)(89, 160)(90, 132)(91, 129)(92, 137)(93, 133)(94, 149)(95, 147)(96, 152) MAP : A3.76 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^2 * x.2 * x.3^2 * x.2^-1, x.3^8, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 168)(34, 163)(35, 162)(36, 185)(37, 167)(38, 169)(39, 165)(40, 161)(41, 166)(42, 181)(43, 179)(44, 186)(45, 184)(46, 177)(47, 180)(48, 187)(49, 174)(50, 192)(51, 171)(52, 175)(53, 170)(54, 191)(55, 188)(56, 173)(57, 164)(58, 172)(59, 176)(60, 183)(61, 190)(62, 189)(63, 182)(64, 178)(65, 130)(66, 134)(67, 132)(68, 135)(69, 129)(70, 140)(71, 141)(72, 139)(73, 149)(74, 142)(75, 143)(76, 157)(77, 144)(78, 160)(79, 156)(80, 150)(81, 131)(82, 137)(83, 153)(84, 133)(85, 136)(86, 154)(87, 152)(88, 147)(89, 138)(90, 145)(91, 148)(92, 158)(93, 155)(94, 146)(95, 151)(96, 159) MAP : A3.77 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^2 * x.2 * x.3^2 * x.2^-1, x.3^8, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 168)(34, 163)(35, 162)(36, 185)(37, 167)(38, 169)(39, 165)(40, 161)(41, 166)(42, 181)(43, 179)(44, 186)(45, 184)(46, 177)(47, 180)(48, 187)(49, 174)(50, 192)(51, 171)(52, 175)(53, 170)(54, 191)(55, 188)(56, 173)(57, 164)(58, 172)(59, 176)(60, 183)(61, 190)(62, 189)(63, 182)(64, 178)(65, 155)(66, 148)(67, 150)(68, 154)(69, 157)(70, 133)(71, 145)(72, 146)(73, 156)(74, 152)(75, 137)(76, 129)(77, 131)(78, 147)(79, 149)(80, 132)(81, 144)(82, 143)(83, 159)(84, 140)(85, 158)(86, 135)(87, 142)(88, 160)(89, 151)(90, 141)(91, 134)(92, 136)(93, 130)(94, 139)(95, 138)(96, 153) MAP : A3.78 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^2 * x.2 * x.3^2 * x.2^-1, x.3^8, (x.2 * x.3^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 8, 16) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 164)(34, 181)(35, 170)(36, 161)(37, 171)(38, 177)(39, 179)(40, 185)(41, 174)(42, 163)(43, 165)(44, 178)(45, 180)(46, 169)(47, 184)(48, 183)(49, 166)(50, 172)(51, 167)(52, 173)(53, 162)(54, 189)(55, 176)(56, 175)(57, 168)(58, 192)(59, 188)(60, 187)(61, 182)(62, 191)(63, 190)(64, 186)(65, 155)(66, 148)(67, 150)(68, 154)(69, 157)(70, 133)(71, 145)(72, 146)(73, 156)(74, 152)(75, 137)(76, 129)(77, 131)(78, 147)(79, 149)(80, 132)(81, 144)(82, 143)(83, 159)(84, 140)(85, 158)(86, 135)(87, 142)(88, 160)(89, 151)(90, 141)(91, 134)(92, 136)(93, 130)(94, 139)(95, 138)(96, 153) MAP : A3.79 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A3.37. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2 * x.3^-1 * x.2^-3 * x.3 * x.2^2, (x.2 * x.3^-1)^4, x.3 * x.2^-1 * x.3 * x.2^2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^2, (x.1 * x.2^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 12, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 242)(50, 249)(51, 244)(52, 251)(53, 246)(54, 253)(55, 280)(56, 279)(57, 250)(58, 257)(59, 252)(60, 259)(61, 254)(62, 261)(63, 272)(64, 271)(65, 258)(66, 241)(67, 260)(68, 243)(69, 262)(70, 245)(71, 288)(72, 287)(73, 282)(74, 265)(75, 284)(76, 267)(77, 286)(78, 269)(79, 264)(80, 263)(81, 266)(82, 273)(83, 268)(84, 275)(85, 270)(86, 277)(87, 256)(88, 255)(89, 274)(90, 281)(91, 276)(92, 283)(93, 278)(94, 285)(95, 248)(96, 247)(97, 205)(98, 200)(99, 201)(100, 230)(101, 207)(102, 228)(103, 203)(104, 194)(105, 195)(106, 214)(107, 199)(108, 210)(109, 193)(110, 240)(111, 197)(112, 238)(113, 223)(114, 204)(115, 221)(116, 224)(117, 219)(118, 202)(119, 217)(120, 220)(121, 215)(122, 236)(123, 213)(124, 216)(125, 211)(126, 234)(127, 209)(128, 212)(129, 237)(130, 232)(131, 233)(132, 198)(133, 239)(134, 196)(135, 235)(136, 226)(137, 227)(138, 222)(139, 231)(140, 218)(141, 225)(142, 208)(143, 229)(144, 206) MAP : A3.80 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A3.37. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2 * x.3^-1 * x.2^-3 * x.3 * x.2^2, (x.2 * x.3^-1)^4, x.3 * x.2^-1 * x.3 * x.2^2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^2, (x.1 * x.2^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 12, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 242)(50, 249)(51, 244)(52, 251)(53, 246)(54, 253)(55, 280)(56, 279)(57, 250)(58, 257)(59, 252)(60, 259)(61, 254)(62, 261)(63, 272)(64, 271)(65, 258)(66, 241)(67, 260)(68, 243)(69, 262)(70, 245)(71, 288)(72, 287)(73, 282)(74, 265)(75, 284)(76, 267)(77, 286)(78, 269)(79, 264)(80, 263)(81, 266)(82, 273)(83, 268)(84, 275)(85, 270)(86, 277)(87, 256)(88, 255)(89, 274)(90, 281)(91, 276)(92, 283)(93, 278)(94, 285)(95, 248)(96, 247)(97, 196)(98, 197)(99, 232)(100, 193)(101, 194)(102, 199)(103, 198)(104, 237)(105, 216)(106, 211)(107, 238)(108, 215)(109, 236)(110, 209)(111, 234)(112, 219)(113, 206)(114, 231)(115, 202)(116, 229)(117, 224)(118, 227)(119, 204)(120, 201)(121, 220)(122, 221)(123, 208)(124, 217)(125, 218)(126, 223)(127, 222)(128, 213)(129, 240)(130, 235)(131, 214)(132, 239)(133, 212)(134, 233)(135, 210)(136, 195)(137, 230)(138, 207)(139, 226)(140, 205)(141, 200)(142, 203)(143, 228)(144, 225) MAP : A3.81 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A3.37. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 6 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^4, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1 * x.3^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 12, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 262)(51, 247)(52, 258)(53, 241)(54, 288)(55, 245)(56, 286)(57, 271)(58, 252)(59, 269)(60, 272)(61, 267)(62, 250)(63, 265)(64, 268)(65, 253)(66, 248)(67, 249)(68, 278)(69, 255)(70, 276)(71, 251)(72, 242)(73, 275)(74, 270)(75, 279)(76, 266)(77, 273)(78, 256)(79, 277)(80, 254)(81, 263)(82, 284)(83, 261)(84, 264)(85, 259)(86, 282)(87, 257)(88, 260)(89, 285)(90, 280)(91, 281)(92, 246)(93, 287)(94, 244)(95, 283)(96, 274)(97, 236)(98, 237)(99, 216)(100, 233)(101, 234)(102, 239)(103, 238)(104, 197)(105, 232)(106, 227)(107, 198)(108, 231)(109, 196)(110, 225)(111, 194)(112, 203)(113, 222)(114, 215)(115, 218)(116, 213)(117, 208)(118, 211)(119, 220)(120, 217)(121, 204)(122, 205)(123, 224)(124, 201)(125, 202)(126, 207)(127, 206)(128, 229)(129, 200)(130, 195)(131, 230)(132, 199)(133, 228)(134, 193)(135, 226)(136, 235)(137, 214)(138, 223)(139, 210)(140, 221)(141, 240)(142, 219)(143, 212)(144, 209) MAP : A3.82 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A3.37. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 6, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^4, x.3^2 * x.2 * x.3 * x.2 * x.3^-2 * x.2^-1 * x.3 * x.2^-1, x.3^-1 * x.2 * x.3^2 * x.2 * x.3^-1 * x.2^-1 * x.3^-2 * x.2^-1, x.3^2 * x.2 * x.3^-1 * x.2 * x.3^-2 * x.2^-1 * x.3^-1 * x.2^-1, (x.2 * x.3^-1)^6, x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 12, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 253)(50, 248)(51, 249)(52, 278)(53, 255)(54, 276)(55, 251)(56, 242)(57, 243)(58, 262)(59, 247)(60, 258)(61, 241)(62, 288)(63, 245)(64, 286)(65, 271)(66, 252)(67, 269)(68, 272)(69, 267)(70, 250)(71, 265)(72, 268)(73, 263)(74, 284)(75, 261)(76, 264)(77, 259)(78, 282)(79, 257)(80, 260)(81, 285)(82, 280)(83, 281)(84, 246)(85, 287)(86, 244)(87, 283)(88, 274)(89, 275)(90, 270)(91, 279)(92, 266)(93, 273)(94, 256)(95, 277)(96, 254)(97, 198)(98, 239)(99, 194)(100, 237)(101, 232)(102, 235)(103, 196)(104, 193)(105, 212)(106, 213)(107, 240)(108, 209)(109, 210)(110, 215)(111, 214)(112, 221)(113, 208)(114, 203)(115, 222)(116, 207)(117, 220)(118, 201)(119, 218)(120, 227)(121, 224)(122, 219)(123, 206)(124, 223)(125, 204)(126, 217)(127, 202)(128, 211)(129, 238)(130, 199)(131, 234)(132, 197)(133, 216)(134, 195)(135, 236)(136, 233)(137, 228)(138, 229)(139, 200)(140, 225)(141, 226)(142, 231)(143, 230)(144, 205) MAP : A3.83 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A3.37. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 6 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^4, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1 * x.3^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 12, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 287)(51, 242)(52, 285)(53, 280)(54, 283)(55, 244)(56, 241)(57, 260)(58, 261)(59, 288)(60, 257)(61, 258)(62, 263)(63, 262)(64, 269)(65, 256)(66, 251)(67, 270)(68, 255)(69, 268)(70, 249)(71, 266)(72, 275)(73, 272)(74, 267)(75, 254)(76, 271)(77, 252)(78, 265)(79, 250)(80, 259)(81, 286)(82, 247)(83, 282)(84, 245)(85, 264)(86, 243)(87, 284)(88, 281)(89, 276)(90, 277)(91, 248)(92, 273)(93, 274)(94, 279)(95, 278)(96, 253)(97, 238)(98, 199)(99, 234)(100, 197)(101, 216)(102, 195)(103, 236)(104, 233)(105, 228)(106, 229)(107, 200)(108, 225)(109, 226)(110, 231)(111, 230)(112, 205)(113, 224)(114, 219)(115, 206)(116, 223)(117, 204)(118, 217)(119, 202)(120, 211)(121, 208)(122, 203)(123, 222)(124, 207)(125, 220)(126, 201)(127, 218)(128, 227)(129, 198)(130, 239)(131, 194)(132, 237)(133, 232)(134, 235)(135, 196)(136, 193)(137, 212)(138, 213)(139, 240)(140, 209)(141, 210)(142, 215)(143, 214)(144, 221) MAP : A3.84 NOTES : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A3.37. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 6, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^4, x.3^2 * x.2 * x.3 * x.2 * x.3^-2 * x.2^-1 * x.3 * x.2^-1, x.3^-1 * x.2 * x.3^2 * x.2 * x.3^-1 * x.2^-1 * x.3^-2 * x.2^-1, x.3^2 * x.2 * x.3^-1 * x.2 * x.3^-2 * x.2^-1 * x.3^-1 * x.2^-1, (x.2 * x.3^-1)^6, x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 12, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 244)(50, 245)(51, 280)(52, 241)(53, 242)(54, 247)(55, 246)(56, 285)(57, 264)(58, 259)(59, 286)(60, 263)(61, 284)(62, 257)(63, 282)(64, 267)(65, 254)(66, 279)(67, 250)(68, 277)(69, 272)(70, 275)(71, 252)(72, 249)(73, 268)(74, 269)(75, 256)(76, 265)(77, 266)(78, 271)(79, 270)(80, 261)(81, 288)(82, 283)(83, 262)(84, 287)(85, 260)(86, 281)(87, 258)(88, 243)(89, 278)(90, 255)(91, 274)(92, 253)(93, 248)(94, 251)(95, 276)(96, 273)(97, 195)(98, 214)(99, 199)(100, 210)(101, 193)(102, 240)(103, 197)(104, 238)(105, 223)(106, 204)(107, 221)(108, 224)(109, 219)(110, 202)(111, 217)(112, 220)(113, 205)(114, 200)(115, 201)(116, 230)(117, 207)(118, 228)(119, 203)(120, 194)(121, 227)(122, 222)(123, 231)(124, 218)(125, 225)(126, 208)(127, 229)(128, 206)(129, 215)(130, 236)(131, 213)(132, 216)(133, 211)(134, 234)(135, 209)(136, 212)(137, 237)(138, 232)(139, 233)(140, 198)(141, 239)(142, 196)(143, 235)(144, 226) MAP : A3.85 NOTES : type II, reflexible, isomorphic to DBar({3,7}), isomorphic to A3.13. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 7, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^3, x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3 * x.2 * x.3 * x.2, x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2^-1, x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 14, 6) #DARTS : 1008 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504)(505, 673, 841)(506, 674, 842)(507, 675, 843)(508, 676, 844)(509, 677, 845)(510, 678, 846)(511, 679, 847)(512, 680, 848)(513, 681, 849)(514, 682, 850)(515, 683, 851)(516, 684, 852)(517, 685, 853)(518, 686, 854)(519, 687, 855)(520, 688, 856)(521, 689, 857)(522, 690, 858)(523, 691, 859)(524, 692, 860)(525, 693, 861)(526, 694, 862)(527, 695, 863)(528, 696, 864)(529, 697, 865)(530, 698, 866)(531, 699, 867)(532, 700, 868)(533, 701, 869)(534, 702, 870)(535, 703, 871)(536, 704, 872)(537, 705, 873)(538, 706, 874)(539, 707, 875)(540, 708, 876)(541, 709, 877)(542, 710, 878)(543, 711, 879)(544, 712, 880)(545, 713, 881)(546, 714, 882)(547, 715, 883)(548, 716, 884)(549, 717, 885)(550, 718, 886)(551, 719, 887)(552, 720, 888)(553, 721, 889)(554, 722, 890)(555, 723, 891)(556, 724, 892)(557, 725, 893)(558, 726, 894)(559, 727, 895)(560, 728, 896)(561, 729, 897)(562, 730, 898)(563, 731, 899)(564, 732, 900)(565, 733, 901)(566, 734, 902)(567, 735, 903)(568, 736, 904)(569, 737, 905)(570, 738, 906)(571, 739, 907)(572, 740, 908)(573, 741, 909)(574, 742, 910)(575, 743, 911)(576, 744, 912)(577, 745, 913)(578, 746, 914)(579, 747, 915)(580, 748, 916)(581, 749, 917)(582, 750, 918)(583, 751, 919)(584, 752, 920)(585, 753, 921)(586, 754, 922)(587, 755, 923)(588, 756, 924)(589, 757, 925)(590, 758, 926)(591, 759, 927)(592, 760, 928)(593, 761, 929)(594, 762, 930)(595, 763, 931)(596, 764, 932)(597, 765, 933)(598, 766, 934)(599, 767, 935)(600, 768, 936)(601, 769, 937)(602, 770, 938)(603, 771, 939)(604, 772, 940)(605, 773, 941)(606, 774, 942)(607, 775, 943)(608, 776, 944)(609, 777, 945)(610, 778, 946)(611, 779, 947)(612, 780, 948)(613, 781, 949)(614, 782, 950)(615, 783, 951)(616, 784, 952)(617, 785, 953)(618, 786, 954)(619, 787, 955)(620, 788, 956)(621, 789, 957)(622, 790, 958)(623, 791, 959)(624, 792, 960)(625, 793, 961)(626, 794, 962)(627, 795, 963)(628, 796, 964)(629, 797, 965)(630, 798, 966)(631, 799, 967)(632, 800, 968)(633, 801, 969)(634, 802, 970)(635, 803, 971)(636, 804, 972)(637, 805, 973)(638, 806, 974)(639, 807, 975)(640, 808, 976)(641, 809, 977)(642, 810, 978)(643, 811, 979)(644, 812, 980)(645, 813, 981)(646, 814, 982)(647, 815, 983)(648, 816, 984)(649, 817, 985)(650, 818, 986)(651, 819, 987)(652, 820, 988)(653, 821, 989)(654, 822, 990)(655, 823, 991)(656, 824, 992)(657, 825, 993)(658, 826, 994)(659, 827, 995)(660, 828, 996)(661, 829, 997)(662, 830, 998)(663, 831, 999)(664, 832, 1000)(665, 833, 1001)(666, 834, 1002)(667, 835, 1003)(668, 836, 1004)(669, 837, 1005)(670, 838, 1006)(671, 839, 1007)(672, 840, 1008) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 842)(170, 841)(171, 849)(172, 857)(173, 865)(174, 874)(175, 873)(176, 866)(177, 843)(178, 860)(179, 858)(180, 863)(181, 859)(182, 935)(183, 934)(184, 876)(185, 844)(186, 851)(187, 853)(188, 850)(189, 944)(190, 867)(191, 852)(192, 941)(193, 845)(194, 848)(195, 862)(196, 997)(197, 999)(198, 980)(199, 995)(200, 998)(201, 847)(202, 846)(203, 959)(204, 856)(205, 956)(206, 960)(207, 957)(208, 963)(209, 912)(210, 909)(211, 1000)(212, 907)(213, 982)(214, 905)(215, 906)(216, 983)(217, 902)(218, 903)(219, 900)(220, 958)(221, 898)(222, 965)(223, 968)(224, 897)(225, 896)(226, 893)(227, 928)(228, 891)(229, 910)(230, 889)(231, 890)(232, 911)(233, 886)(234, 887)(235, 884)(236, 918)(237, 882)(238, 901)(239, 904)(240, 881)(241, 989)(242, 992)(243, 1006)(244, 925)(245, 927)(246, 908)(247, 923)(248, 926)(249, 991)(250, 990)(251, 919)(252, 976)(253, 916)(254, 920)(255, 917)(256, 899)(257, 987)(258, 1004)(259, 1002)(260, 1007)(261, 1003)(262, 855)(263, 854)(264, 996)(265, 988)(266, 971)(267, 973)(268, 970)(269, 864)(270, 955)(271, 972)(272, 861)(273, 986)(274, 985)(275, 969)(276, 1001)(277, 953)(278, 994)(279, 993)(280, 954)(281, 949)(282, 952)(283, 942)(284, 877)(285, 879)(286, 892)(287, 875)(288, 878)(289, 984)(290, 981)(291, 880)(292, 979)(293, 894)(294, 977)(295, 978)(296, 895)(297, 947)(298, 940)(299, 938)(300, 943)(301, 939)(302, 975)(303, 974)(304, 924)(305, 966)(306, 967)(307, 964)(308, 870)(309, 962)(310, 885)(311, 888)(312, 961)(313, 946)(314, 945)(315, 929)(316, 937)(317, 913)(318, 922)(319, 921)(320, 914)(321, 951)(322, 950)(323, 871)(324, 936)(325, 868)(326, 872)(327, 869)(328, 883)(329, 948)(330, 931)(331, 933)(332, 930)(333, 1008)(334, 915)(335, 932)(336, 1005)(337, 675)(338, 692)(339, 690)(340, 695)(341, 691)(342, 767)(343, 766)(344, 708)(345, 677)(346, 680)(347, 694)(348, 829)(349, 831)(350, 812)(351, 827)(352, 830)(353, 674)(354, 673)(355, 681)(356, 689)(357, 697)(358, 706)(359, 705)(360, 698)(361, 744)(362, 741)(363, 832)(364, 739)(365, 814)(366, 737)(367, 738)(368, 815)(369, 676)(370, 683)(371, 685)(372, 682)(373, 776)(374, 699)(375, 684)(376, 773)(377, 734)(378, 735)(379, 732)(380, 790)(381, 730)(382, 797)(383, 800)(384, 729)(385, 679)(386, 678)(387, 791)(388, 688)(389, 788)(390, 792)(391, 789)(392, 795)(393, 823)(394, 822)(395, 751)(396, 808)(397, 748)(398, 752)(399, 749)(400, 731)(401, 820)(402, 803)(403, 805)(404, 802)(405, 696)(406, 787)(407, 804)(408, 693)(409, 718)(410, 719)(411, 716)(412, 750)(413, 714)(414, 733)(415, 736)(416, 713)(417, 818)(418, 817)(419, 801)(420, 833)(421, 785)(422, 826)(423, 825)(424, 786)(425, 728)(426, 725)(427, 760)(428, 723)(429, 742)(430, 721)(431, 722)(432, 743)(433, 819)(434, 836)(435, 834)(436, 839)(437, 835)(438, 687)(439, 686)(440, 828)(441, 821)(442, 824)(443, 838)(444, 757)(445, 759)(446, 740)(447, 755)(448, 758)(449, 780)(450, 763)(451, 765)(452, 762)(453, 840)(454, 747)(455, 764)(456, 837)(457, 778)(458, 777)(459, 761)(460, 769)(461, 745)(462, 754)(463, 753)(464, 746)(465, 783)(466, 782)(467, 703)(468, 768)(469, 700)(470, 704)(471, 701)(472, 715)(473, 779)(474, 772)(475, 770)(476, 775)(477, 771)(478, 807)(479, 806)(480, 756)(481, 798)(482, 799)(483, 796)(484, 702)(485, 794)(486, 717)(487, 720)(488, 793)(489, 781)(490, 784)(491, 774)(492, 709)(493, 711)(494, 724)(495, 707)(496, 710)(497, 816)(498, 813)(499, 712)(500, 811)(501, 726)(502, 809)(503, 810)(504, 727) MAP : A3.86 NOTES : type II, reflexible, isomorphic to DBar({3,7}), isomorphic to A3.13. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 7, 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^2, (x.3 * x.1^-1)^2, (x.2 * x.3)^3, x.2^7, (x.1 * x.2^-1)^7, (x.2^-2 * x.3 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 14, 6) #DARTS : 1008 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504)(505, 673, 841)(506, 674, 842)(507, 675, 843)(508, 676, 844)(509, 677, 845)(510, 678, 846)(511, 679, 847)(512, 680, 848)(513, 681, 849)(514, 682, 850)(515, 683, 851)(516, 684, 852)(517, 685, 853)(518, 686, 854)(519, 687, 855)(520, 688, 856)(521, 689, 857)(522, 690, 858)(523, 691, 859)(524, 692, 860)(525, 693, 861)(526, 694, 862)(527, 695, 863)(528, 696, 864)(529, 697, 865)(530, 698, 866)(531, 699, 867)(532, 700, 868)(533, 701, 869)(534, 702, 870)(535, 703, 871)(536, 704, 872)(537, 705, 873)(538, 706, 874)(539, 707, 875)(540, 708, 876)(541, 709, 877)(542, 710, 878)(543, 711, 879)(544, 712, 880)(545, 713, 881)(546, 714, 882)(547, 715, 883)(548, 716, 884)(549, 717, 885)(550, 718, 886)(551, 719, 887)(552, 720, 888)(553, 721, 889)(554, 722, 890)(555, 723, 891)(556, 724, 892)(557, 725, 893)(558, 726, 894)(559, 727, 895)(560, 728, 896)(561, 729, 897)(562, 730, 898)(563, 731, 899)(564, 732, 900)(565, 733, 901)(566, 734, 902)(567, 735, 903)(568, 736, 904)(569, 737, 905)(570, 738, 906)(571, 739, 907)(572, 740, 908)(573, 741, 909)(574, 742, 910)(575, 743, 911)(576, 744, 912)(577, 745, 913)(578, 746, 914)(579, 747, 915)(580, 748, 916)(581, 749, 917)(582, 750, 918)(583, 751, 919)(584, 752, 920)(585, 753, 921)(586, 754, 922)(587, 755, 923)(588, 756, 924)(589, 757, 925)(590, 758, 926)(591, 759, 927)(592, 760, 928)(593, 761, 929)(594, 762, 930)(595, 763, 931)(596, 764, 932)(597, 765, 933)(598, 766, 934)(599, 767, 935)(600, 768, 936)(601, 769, 937)(602, 770, 938)(603, 771, 939)(604, 772, 940)(605, 773, 941)(606, 774, 942)(607, 775, 943)(608, 776, 944)(609, 777, 945)(610, 778, 946)(611, 779, 947)(612, 780, 948)(613, 781, 949)(614, 782, 950)(615, 783, 951)(616, 784, 952)(617, 785, 953)(618, 786, 954)(619, 787, 955)(620, 788, 956)(621, 789, 957)(622, 790, 958)(623, 791, 959)(624, 792, 960)(625, 793, 961)(626, 794, 962)(627, 795, 963)(628, 796, 964)(629, 797, 965)(630, 798, 966)(631, 799, 967)(632, 800, 968)(633, 801, 969)(634, 802, 970)(635, 803, 971)(636, 804, 972)(637, 805, 973)(638, 806, 974)(639, 807, 975)(640, 808, 976)(641, 809, 977)(642, 810, 978)(643, 811, 979)(644, 812, 980)(645, 813, 981)(646, 814, 982)(647, 815, 983)(648, 816, 984)(649, 817, 985)(650, 818, 986)(651, 819, 987)(652, 820, 988)(653, 821, 989)(654, 822, 990)(655, 823, 991)(656, 824, 992)(657, 825, 993)(658, 826, 994)(659, 827, 995)(660, 828, 996)(661, 829, 997)(662, 830, 998)(663, 831, 999)(664, 832, 1000)(665, 833, 1001)(666, 834, 1002)(667, 835, 1003)(668, 836, 1004)(669, 837, 1005)(670, 838, 1006)(671, 839, 1007)(672, 840, 1008) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 845)(170, 848)(171, 862)(172, 997)(173, 999)(174, 980)(175, 995)(176, 998)(177, 912)(178, 909)(179, 1000)(180, 907)(181, 982)(182, 905)(183, 906)(184, 983)(185, 843)(186, 860)(187, 858)(188, 863)(189, 859)(190, 935)(191, 934)(192, 876)(193, 902)(194, 903)(195, 900)(196, 958)(197, 898)(198, 965)(199, 968)(200, 897)(201, 842)(202, 841)(203, 849)(204, 857)(205, 865)(206, 874)(207, 873)(208, 866)(209, 847)(210, 846)(211, 959)(212, 856)(213, 956)(214, 960)(215, 957)(216, 963)(217, 844)(218, 851)(219, 853)(220, 850)(221, 944)(222, 867)(223, 852)(224, 941)(225, 986)(226, 985)(227, 969)(228, 1001)(229, 953)(230, 994)(231, 993)(232, 954)(233, 987)(234, 1004)(235, 1002)(236, 1007)(237, 1003)(238, 855)(239, 854)(240, 996)(241, 988)(242, 971)(243, 973)(244, 970)(245, 864)(246, 955)(247, 972)(248, 861)(249, 989)(250, 992)(251, 1006)(252, 925)(253, 927)(254, 908)(255, 923)(256, 926)(257, 991)(258, 990)(259, 919)(260, 976)(261, 916)(262, 920)(263, 917)(264, 899)(265, 896)(266, 893)(267, 928)(268, 891)(269, 910)(270, 889)(271, 890)(272, 911)(273, 886)(274, 887)(275, 884)(276, 918)(277, 882)(278, 901)(279, 904)(280, 881)(281, 984)(282, 981)(283, 880)(284, 979)(285, 894)(286, 977)(287, 978)(288, 895)(289, 966)(290, 967)(291, 964)(292, 870)(293, 962)(294, 885)(295, 888)(296, 961)(297, 949)(298, 952)(299, 942)(300, 877)(301, 879)(302, 892)(303, 875)(304, 878)(305, 951)(306, 950)(307, 871)(308, 936)(309, 868)(310, 872)(311, 869)(312, 883)(313, 947)(314, 940)(315, 938)(316, 943)(317, 939)(318, 975)(319, 974)(320, 924)(321, 948)(322, 931)(323, 933)(324, 930)(325, 1008)(326, 915)(327, 932)(328, 1005)(329, 946)(330, 945)(331, 929)(332, 937)(333, 913)(334, 922)(335, 921)(336, 914)(337, 691)(338, 708)(339, 706)(340, 711)(341, 707)(342, 775)(343, 774)(344, 724)(345, 693)(346, 696)(347, 710)(348, 805)(349, 807)(350, 820)(351, 803)(352, 806)(353, 690)(354, 689)(355, 673)(356, 705)(357, 681)(358, 722)(359, 721)(360, 682)(361, 752)(362, 749)(363, 808)(364, 747)(365, 822)(366, 745)(367, 746)(368, 823)(369, 692)(370, 675)(371, 677)(372, 674)(373, 744)(374, 683)(375, 676)(376, 741)(377, 766)(378, 767)(379, 764)(380, 830)(381, 762)(382, 837)(383, 840)(384, 761)(385, 695)(386, 694)(387, 831)(388, 680)(389, 828)(390, 832)(391, 829)(392, 835)(393, 799)(394, 798)(395, 783)(396, 816)(397, 780)(398, 784)(399, 781)(400, 763)(401, 796)(402, 811)(403, 813)(404, 810)(405, 712)(406, 827)(407, 812)(408, 709)(409, 702)(410, 703)(411, 700)(412, 782)(413, 698)(414, 765)(415, 768)(416, 697)(417, 794)(418, 793)(419, 809)(420, 785)(421, 825)(422, 802)(423, 801)(424, 826)(425, 720)(426, 717)(427, 736)(428, 715)(429, 750)(430, 713)(431, 714)(432, 751)(433, 795)(434, 788)(435, 786)(436, 791)(437, 787)(438, 679)(439, 678)(440, 804)(441, 797)(442, 800)(443, 790)(444, 733)(445, 735)(446, 748)(447, 731)(448, 734)(449, 756)(450, 771)(451, 773)(452, 770)(453, 792)(454, 779)(455, 772)(456, 789)(457, 754)(458, 753)(459, 769)(460, 737)(461, 777)(462, 730)(463, 729)(464, 778)(465, 759)(466, 758)(467, 687)(468, 776)(469, 684)(470, 688)(471, 685)(472, 699)(473, 755)(474, 740)(475, 738)(476, 743)(477, 739)(478, 815)(479, 814)(480, 732)(481, 838)(482, 839)(483, 836)(484, 686)(485, 834)(486, 701)(487, 704)(488, 833)(489, 757)(490, 760)(491, 742)(492, 725)(493, 727)(494, 716)(495, 723)(496, 726)(497, 824)(498, 821)(499, 728)(500, 819)(501, 718)(502, 817)(503, 818)(504, 719) MAP : A3.87 NOTES : type II, reflexible, isomorphic to DBar({3,7}), isomorphic to A3.13. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 7 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^3, (u.3 * u.1^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.1 * x.2^-1)^3, x.3 * x.2 * x.3 * x.2^-1 * x.3^-5 * x.2^-1, (x.3^-2 * x.2^-1)^4, (x.3 * x.1^-1)^7 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 14, 6) #DARTS : 1008 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504)(505, 673, 841)(506, 674, 842)(507, 675, 843)(508, 676, 844)(509, 677, 845)(510, 678, 846)(511, 679, 847)(512, 680, 848)(513, 681, 849)(514, 682, 850)(515, 683, 851)(516, 684, 852)(517, 685, 853)(518, 686, 854)(519, 687, 855)(520, 688, 856)(521, 689, 857)(522, 690, 858)(523, 691, 859)(524, 692, 860)(525, 693, 861)(526, 694, 862)(527, 695, 863)(528, 696, 864)(529, 697, 865)(530, 698, 866)(531, 699, 867)(532, 700, 868)(533, 701, 869)(534, 702, 870)(535, 703, 871)(536, 704, 872)(537, 705, 873)(538, 706, 874)(539, 707, 875)(540, 708, 876)(541, 709, 877)(542, 710, 878)(543, 711, 879)(544, 712, 880)(545, 713, 881)(546, 714, 882)(547, 715, 883)(548, 716, 884)(549, 717, 885)(550, 718, 886)(551, 719, 887)(552, 720, 888)(553, 721, 889)(554, 722, 890)(555, 723, 891)(556, 724, 892)(557, 725, 893)(558, 726, 894)(559, 727, 895)(560, 728, 896)(561, 729, 897)(562, 730, 898)(563, 731, 899)(564, 732, 900)(565, 733, 901)(566, 734, 902)(567, 735, 903)(568, 736, 904)(569, 737, 905)(570, 738, 906)(571, 739, 907)(572, 740, 908)(573, 741, 909)(574, 742, 910)(575, 743, 911)(576, 744, 912)(577, 745, 913)(578, 746, 914)(579, 747, 915)(580, 748, 916)(581, 749, 917)(582, 750, 918)(583, 751, 919)(584, 752, 920)(585, 753, 921)(586, 754, 922)(587, 755, 923)(588, 756, 924)(589, 757, 925)(590, 758, 926)(591, 759, 927)(592, 760, 928)(593, 761, 929)(594, 762, 930)(595, 763, 931)(596, 764, 932)(597, 765, 933)(598, 766, 934)(599, 767, 935)(600, 768, 936)(601, 769, 937)(602, 770, 938)(603, 771, 939)(604, 772, 940)(605, 773, 941)(606, 774, 942)(607, 775, 943)(608, 776, 944)(609, 777, 945)(610, 778, 946)(611, 779, 947)(612, 780, 948)(613, 781, 949)(614, 782, 950)(615, 783, 951)(616, 784, 952)(617, 785, 953)(618, 786, 954)(619, 787, 955)(620, 788, 956)(621, 789, 957)(622, 790, 958)(623, 791, 959)(624, 792, 960)(625, 793, 961)(626, 794, 962)(627, 795, 963)(628, 796, 964)(629, 797, 965)(630, 798, 966)(631, 799, 967)(632, 800, 968)(633, 801, 969)(634, 802, 970)(635, 803, 971)(636, 804, 972)(637, 805, 973)(638, 806, 974)(639, 807, 975)(640, 808, 976)(641, 809, 977)(642, 810, 978)(643, 811, 979)(644, 812, 980)(645, 813, 981)(646, 814, 982)(647, 815, 983)(648, 816, 984)(649, 817, 985)(650, 818, 986)(651, 819, 987)(652, 820, 988)(653, 821, 989)(654, 822, 990)(655, 823, 991)(656, 824, 992)(657, 825, 993)(658, 826, 994)(659, 827, 995)(660, 828, 996)(661, 829, 997)(662, 830, 998)(663, 831, 999)(664, 832, 1000)(665, 833, 1001)(666, 834, 1002)(667, 835, 1003)(668, 836, 1004)(669, 837, 1005)(670, 838, 1006)(671, 839, 1007)(672, 840, 1008) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 843)(170, 860)(171, 858)(172, 863)(173, 859)(174, 935)(175, 934)(176, 876)(177, 845)(178, 848)(179, 862)(180, 997)(181, 999)(182, 980)(183, 995)(184, 998)(185, 842)(186, 841)(187, 849)(188, 857)(189, 865)(190, 874)(191, 873)(192, 866)(193, 912)(194, 909)(195, 1000)(196, 907)(197, 982)(198, 905)(199, 906)(200, 983)(201, 844)(202, 851)(203, 853)(204, 850)(205, 944)(206, 867)(207, 852)(208, 941)(209, 902)(210, 903)(211, 900)(212, 958)(213, 898)(214, 965)(215, 968)(216, 897)(217, 847)(218, 846)(219, 959)(220, 856)(221, 956)(222, 960)(223, 957)(224, 963)(225, 991)(226, 990)(227, 919)(228, 976)(229, 916)(230, 920)(231, 917)(232, 899)(233, 988)(234, 971)(235, 973)(236, 970)(237, 864)(238, 955)(239, 972)(240, 861)(241, 886)(242, 887)(243, 884)(244, 918)(245, 882)(246, 901)(247, 904)(248, 881)(249, 986)(250, 985)(251, 969)(252, 1001)(253, 953)(254, 994)(255, 993)(256, 954)(257, 896)(258, 893)(259, 928)(260, 891)(261, 910)(262, 889)(263, 890)(264, 911)(265, 987)(266, 1004)(267, 1002)(268, 1007)(269, 1003)(270, 855)(271, 854)(272, 996)(273, 989)(274, 992)(275, 1006)(276, 925)(277, 927)(278, 908)(279, 923)(280, 926)(281, 948)(282, 931)(283, 933)(284, 930)(285, 1008)(286, 915)(287, 932)(288, 1005)(289, 946)(290, 945)(291, 929)(292, 937)(293, 913)(294, 922)(295, 921)(296, 914)(297, 951)(298, 950)(299, 871)(300, 936)(301, 868)(302, 872)(303, 869)(304, 883)(305, 947)(306, 940)(307, 938)(308, 943)(309, 939)(310, 975)(311, 974)(312, 924)(313, 966)(314, 967)(315, 964)(316, 870)(317, 962)(318, 885)(319, 888)(320, 961)(321, 949)(322, 952)(323, 942)(324, 877)(325, 879)(326, 892)(327, 875)(328, 878)(329, 984)(330, 981)(331, 880)(332, 979)(333, 894)(334, 977)(335, 978)(336, 895)(337, 706)(338, 705)(339, 689)(340, 721)(341, 673)(342, 714)(343, 713)(344, 674)(345, 707)(346, 724)(347, 722)(348, 727)(349, 723)(350, 743)(351, 742)(352, 716)(353, 708)(354, 691)(355, 693)(356, 690)(357, 752)(358, 675)(359, 692)(360, 749)(361, 709)(362, 712)(363, 726)(364, 813)(365, 815)(366, 796)(367, 811)(368, 814)(369, 711)(370, 710)(371, 807)(372, 696)(373, 804)(374, 808)(375, 805)(376, 787)(377, 784)(378, 781)(379, 816)(380, 779)(381, 798)(382, 777)(383, 778)(384, 799)(385, 774)(386, 775)(387, 772)(388, 806)(389, 770)(390, 789)(391, 792)(392, 769)(393, 704)(394, 701)(395, 768)(396, 699)(397, 782)(398, 697)(399, 698)(400, 783)(401, 686)(402, 687)(403, 684)(404, 758)(405, 682)(406, 773)(407, 776)(408, 681)(409, 837)(410, 840)(411, 830)(412, 765)(413, 767)(414, 780)(415, 763)(416, 766)(417, 839)(418, 838)(419, 759)(420, 824)(421, 756)(422, 760)(423, 757)(424, 771)(425, 835)(426, 828)(427, 826)(428, 831)(429, 827)(430, 695)(431, 694)(432, 812)(433, 836)(434, 819)(435, 821)(436, 818)(437, 728)(438, 803)(439, 820)(440, 725)(441, 834)(442, 833)(443, 817)(444, 825)(445, 801)(446, 810)(447, 809)(448, 802)(449, 733)(450, 736)(451, 750)(452, 717)(453, 719)(454, 700)(455, 715)(456, 718)(457, 800)(458, 797)(459, 720)(460, 795)(461, 702)(462, 793)(463, 794)(464, 703)(465, 731)(466, 748)(467, 746)(468, 751)(469, 747)(470, 823)(471, 822)(472, 764)(473, 790)(474, 791)(475, 788)(476, 678)(477, 786)(478, 685)(479, 688)(480, 785)(481, 730)(482, 729)(483, 737)(484, 745)(485, 753)(486, 762)(487, 761)(488, 754)(489, 735)(490, 734)(491, 679)(492, 744)(493, 676)(494, 680)(495, 677)(496, 683)(497, 732)(498, 739)(499, 741)(500, 738)(501, 832)(502, 755)(503, 740)(504, 829) MAP : A3.88 NOTES : type II, reflexible, isomorphic to DBar({3,7}), isomorphic to A3.13. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 7 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^3, (u.3 * u.1^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.1 * x.2^-1)^3, x.3 * x.2 * x.3 * x.2^-1 * x.3^-5 * x.2^-1, (x.3^-2 * x.2^-1)^4, (x.3 * x.1^-1)^7 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 14, 6) #DARTS : 1008 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504)(505, 673, 841)(506, 674, 842)(507, 675, 843)(508, 676, 844)(509, 677, 845)(510, 678, 846)(511, 679, 847)(512, 680, 848)(513, 681, 849)(514, 682, 850)(515, 683, 851)(516, 684, 852)(517, 685, 853)(518, 686, 854)(519, 687, 855)(520, 688, 856)(521, 689, 857)(522, 690, 858)(523, 691, 859)(524, 692, 860)(525, 693, 861)(526, 694, 862)(527, 695, 863)(528, 696, 864)(529, 697, 865)(530, 698, 866)(531, 699, 867)(532, 700, 868)(533, 701, 869)(534, 702, 870)(535, 703, 871)(536, 704, 872)(537, 705, 873)(538, 706, 874)(539, 707, 875)(540, 708, 876)(541, 709, 877)(542, 710, 878)(543, 711, 879)(544, 712, 880)(545, 713, 881)(546, 714, 882)(547, 715, 883)(548, 716, 884)(549, 717, 885)(550, 718, 886)(551, 719, 887)(552, 720, 888)(553, 721, 889)(554, 722, 890)(555, 723, 891)(556, 724, 892)(557, 725, 893)(558, 726, 894)(559, 727, 895)(560, 728, 896)(561, 729, 897)(562, 730, 898)(563, 731, 899)(564, 732, 900)(565, 733, 901)(566, 734, 902)(567, 735, 903)(568, 736, 904)(569, 737, 905)(570, 738, 906)(571, 739, 907)(572, 740, 908)(573, 741, 909)(574, 742, 910)(575, 743, 911)(576, 744, 912)(577, 745, 913)(578, 746, 914)(579, 747, 915)(580, 748, 916)(581, 749, 917)(582, 750, 918)(583, 751, 919)(584, 752, 920)(585, 753, 921)(586, 754, 922)(587, 755, 923)(588, 756, 924)(589, 757, 925)(590, 758, 926)(591, 759, 927)(592, 760, 928)(593, 761, 929)(594, 762, 930)(595, 763, 931)(596, 764, 932)(597, 765, 933)(598, 766, 934)(599, 767, 935)(600, 768, 936)(601, 769, 937)(602, 770, 938)(603, 771, 939)(604, 772, 940)(605, 773, 941)(606, 774, 942)(607, 775, 943)(608, 776, 944)(609, 777, 945)(610, 778, 946)(611, 779, 947)(612, 780, 948)(613, 781, 949)(614, 782, 950)(615, 783, 951)(616, 784, 952)(617, 785, 953)(618, 786, 954)(619, 787, 955)(620, 788, 956)(621, 789, 957)(622, 790, 958)(623, 791, 959)(624, 792, 960)(625, 793, 961)(626, 794, 962)(627, 795, 963)(628, 796, 964)(629, 797, 965)(630, 798, 966)(631, 799, 967)(632, 800, 968)(633, 801, 969)(634, 802, 970)(635, 803, 971)(636, 804, 972)(637, 805, 973)(638, 806, 974)(639, 807, 975)(640, 808, 976)(641, 809, 977)(642, 810, 978)(643, 811, 979)(644, 812, 980)(645, 813, 981)(646, 814, 982)(647, 815, 983)(648, 816, 984)(649, 817, 985)(650, 818, 986)(651, 819, 987)(652, 820, 988)(653, 821, 989)(654, 822, 990)(655, 823, 991)(656, 824, 992)(657, 825, 993)(658, 826, 994)(659, 827, 995)(660, 828, 996)(661, 829, 997)(662, 830, 998)(663, 831, 999)(664, 832, 1000)(665, 833, 1001)(666, 834, 1002)(667, 835, 1003)(668, 836, 1004)(669, 837, 1005)(670, 838, 1006)(671, 839, 1007)(672, 840, 1008) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 843)(170, 860)(171, 858)(172, 863)(173, 859)(174, 935)(175, 934)(176, 876)(177, 845)(178, 848)(179, 862)(180, 997)(181, 999)(182, 980)(183, 995)(184, 998)(185, 842)(186, 841)(187, 849)(188, 857)(189, 865)(190, 874)(191, 873)(192, 866)(193, 912)(194, 909)(195, 1000)(196, 907)(197, 982)(198, 905)(199, 906)(200, 983)(201, 844)(202, 851)(203, 853)(204, 850)(205, 944)(206, 867)(207, 852)(208, 941)(209, 902)(210, 903)(211, 900)(212, 958)(213, 898)(214, 965)(215, 968)(216, 897)(217, 847)(218, 846)(219, 959)(220, 856)(221, 956)(222, 960)(223, 957)(224, 963)(225, 991)(226, 990)(227, 919)(228, 976)(229, 916)(230, 920)(231, 917)(232, 899)(233, 988)(234, 971)(235, 973)(236, 970)(237, 864)(238, 955)(239, 972)(240, 861)(241, 886)(242, 887)(243, 884)(244, 918)(245, 882)(246, 901)(247, 904)(248, 881)(249, 986)(250, 985)(251, 969)(252, 1001)(253, 953)(254, 994)(255, 993)(256, 954)(257, 896)(258, 893)(259, 928)(260, 891)(261, 910)(262, 889)(263, 890)(264, 911)(265, 987)(266, 1004)(267, 1002)(268, 1007)(269, 1003)(270, 855)(271, 854)(272, 996)(273, 989)(274, 992)(275, 1006)(276, 925)(277, 927)(278, 908)(279, 923)(280, 926)(281, 948)(282, 931)(283, 933)(284, 930)(285, 1008)(286, 915)(287, 932)(288, 1005)(289, 946)(290, 945)(291, 929)(292, 937)(293, 913)(294, 922)(295, 921)(296, 914)(297, 951)(298, 950)(299, 871)(300, 936)(301, 868)(302, 872)(303, 869)(304, 883)(305, 947)(306, 940)(307, 938)(308, 943)(309, 939)(310, 975)(311, 974)(312, 924)(313, 966)(314, 967)(315, 964)(316, 870)(317, 962)(318, 885)(319, 888)(320, 961)(321, 949)(322, 952)(323, 942)(324, 877)(325, 879)(326, 892)(327, 875)(328, 878)(329, 984)(330, 981)(331, 880)(332, 979)(333, 894)(334, 977)(335, 978)(336, 895)(337, 704)(338, 701)(339, 768)(340, 699)(341, 782)(342, 697)(343, 698)(344, 783)(345, 686)(346, 687)(347, 684)(348, 758)(349, 682)(350, 773)(351, 776)(352, 681)(353, 837)(354, 840)(355, 830)(356, 765)(357, 767)(358, 780)(359, 763)(360, 766)(361, 839)(362, 838)(363, 759)(364, 824)(365, 756)(366, 760)(367, 757)(368, 771)(369, 835)(370, 828)(371, 826)(372, 831)(373, 827)(374, 695)(375, 694)(376, 812)(377, 836)(378, 819)(379, 821)(380, 818)(381, 728)(382, 803)(383, 820)(384, 725)(385, 834)(386, 833)(387, 817)(388, 825)(389, 801)(390, 810)(391, 809)(392, 802)(393, 733)(394, 736)(395, 750)(396, 717)(397, 719)(398, 700)(399, 715)(400, 718)(401, 800)(402, 797)(403, 720)(404, 795)(405, 702)(406, 793)(407, 794)(408, 703)(409, 731)(410, 748)(411, 746)(412, 751)(413, 747)(414, 823)(415, 822)(416, 764)(417, 790)(418, 791)(419, 788)(420, 678)(421, 786)(422, 685)(423, 688)(424, 785)(425, 730)(426, 729)(427, 737)(428, 745)(429, 753)(430, 762)(431, 761)(432, 754)(433, 735)(434, 734)(435, 679)(436, 744)(437, 676)(438, 680)(439, 677)(440, 683)(441, 732)(442, 739)(443, 741)(444, 738)(445, 832)(446, 755)(447, 740)(448, 829)(449, 706)(450, 705)(451, 689)(452, 721)(453, 673)(454, 714)(455, 713)(456, 674)(457, 707)(458, 724)(459, 722)(460, 727)(461, 723)(462, 743)(463, 742)(464, 716)(465, 708)(466, 691)(467, 693)(468, 690)(469, 752)(470, 675)(471, 692)(472, 749)(473, 709)(474, 712)(475, 726)(476, 813)(477, 815)(478, 796)(479, 811)(480, 814)(481, 711)(482, 710)(483, 807)(484, 696)(485, 804)(486, 808)(487, 805)(488, 787)(489, 784)(490, 781)(491, 816)(492, 779)(493, 798)(494, 777)(495, 778)(496, 799)(497, 774)(498, 775)(499, 772)(500, 806)(501, 770)(502, 789)(503, 792)(504, 769) MAP : A3.89 NOTES : type II, reflexible, isomorphic to DBar({3,7}), isomorphic to A3.13. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 7, 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^2, (x.3 * x.1^-1)^2, (x.2 * x.3)^3, x.2^7, (x.1 * x.2^-1)^7, (x.2^-2 * x.3 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 14, 6) #DARTS : 1008 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504)(505, 673, 841)(506, 674, 842)(507, 675, 843)(508, 676, 844)(509, 677, 845)(510, 678, 846)(511, 679, 847)(512, 680, 848)(513, 681, 849)(514, 682, 850)(515, 683, 851)(516, 684, 852)(517, 685, 853)(518, 686, 854)(519, 687, 855)(520, 688, 856)(521, 689, 857)(522, 690, 858)(523, 691, 859)(524, 692, 860)(525, 693, 861)(526, 694, 862)(527, 695, 863)(528, 696, 864)(529, 697, 865)(530, 698, 866)(531, 699, 867)(532, 700, 868)(533, 701, 869)(534, 702, 870)(535, 703, 871)(536, 704, 872)(537, 705, 873)(538, 706, 874)(539, 707, 875)(540, 708, 876)(541, 709, 877)(542, 710, 878)(543, 711, 879)(544, 712, 880)(545, 713, 881)(546, 714, 882)(547, 715, 883)(548, 716, 884)(549, 717, 885)(550, 718, 886)(551, 719, 887)(552, 720, 888)(553, 721, 889)(554, 722, 890)(555, 723, 891)(556, 724, 892)(557, 725, 893)(558, 726, 894)(559, 727, 895)(560, 728, 896)(561, 729, 897)(562, 730, 898)(563, 731, 899)(564, 732, 900)(565, 733, 901)(566, 734, 902)(567, 735, 903)(568, 736, 904)(569, 737, 905)(570, 738, 906)(571, 739, 907)(572, 740, 908)(573, 741, 909)(574, 742, 910)(575, 743, 911)(576, 744, 912)(577, 745, 913)(578, 746, 914)(579, 747, 915)(580, 748, 916)(581, 749, 917)(582, 750, 918)(583, 751, 919)(584, 752, 920)(585, 753, 921)(586, 754, 922)(587, 755, 923)(588, 756, 924)(589, 757, 925)(590, 758, 926)(591, 759, 927)(592, 760, 928)(593, 761, 929)(594, 762, 930)(595, 763, 931)(596, 764, 932)(597, 765, 933)(598, 766, 934)(599, 767, 935)(600, 768, 936)(601, 769, 937)(602, 770, 938)(603, 771, 939)(604, 772, 940)(605, 773, 941)(606, 774, 942)(607, 775, 943)(608, 776, 944)(609, 777, 945)(610, 778, 946)(611, 779, 947)(612, 780, 948)(613, 781, 949)(614, 782, 950)(615, 783, 951)(616, 784, 952)(617, 785, 953)(618, 786, 954)(619, 787, 955)(620, 788, 956)(621, 789, 957)(622, 790, 958)(623, 791, 959)(624, 792, 960)(625, 793, 961)(626, 794, 962)(627, 795, 963)(628, 796, 964)(629, 797, 965)(630, 798, 966)(631, 799, 967)(632, 800, 968)(633, 801, 969)(634, 802, 970)(635, 803, 971)(636, 804, 972)(637, 805, 973)(638, 806, 974)(639, 807, 975)(640, 808, 976)(641, 809, 977)(642, 810, 978)(643, 811, 979)(644, 812, 980)(645, 813, 981)(646, 814, 982)(647, 815, 983)(648, 816, 984)(649, 817, 985)(650, 818, 986)(651, 819, 987)(652, 820, 988)(653, 821, 989)(654, 822, 990)(655, 823, 991)(656, 824, 992)(657, 825, 993)(658, 826, 994)(659, 827, 995)(660, 828, 996)(661, 829, 997)(662, 830, 998)(663, 831, 999)(664, 832, 1000)(665, 833, 1001)(666, 834, 1002)(667, 835, 1003)(668, 836, 1004)(669, 837, 1005)(670, 838, 1006)(671, 839, 1007)(672, 840, 1008) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 932)(170, 915)(171, 917)(172, 914)(173, 976)(174, 899)(175, 916)(176, 973)(177, 930)(178, 929)(179, 913)(180, 945)(181, 897)(182, 938)(183, 937)(184, 898)(185, 935)(186, 934)(187, 863)(188, 920)(189, 860)(190, 864)(191, 861)(192, 843)(193, 931)(194, 948)(195, 946)(196, 951)(197, 947)(198, 967)(199, 966)(200, 940)(201, 998)(202, 999)(203, 996)(204, 862)(205, 994)(206, 845)(207, 848)(208, 993)(209, 933)(210, 936)(211, 950)(212, 869)(213, 871)(214, 852)(215, 867)(216, 870)(217, 1008)(218, 1005)(219, 872)(220, 1003)(221, 854)(222, 1001)(223, 1002)(224, 855)(225, 891)(226, 884)(227, 882)(228, 887)(229, 883)(230, 919)(231, 918)(232, 868)(233, 893)(234, 896)(235, 886)(236, 989)(237, 991)(238, 1004)(239, 987)(240, 990)(241, 890)(242, 889)(243, 873)(244, 881)(245, 857)(246, 866)(247, 865)(248, 858)(249, 928)(250, 925)(251, 992)(252, 923)(253, 1006)(254, 921)(255, 922)(256, 1007)(257, 892)(258, 875)(259, 877)(260, 874)(261, 952)(262, 859)(263, 876)(264, 949)(265, 910)(266, 911)(267, 908)(268, 982)(269, 906)(270, 997)(271, 1000)(272, 905)(273, 895)(274, 894)(275, 983)(276, 880)(277, 980)(278, 984)(279, 981)(280, 995)(281, 959)(282, 958)(283, 903)(284, 968)(285, 900)(286, 904)(287, 901)(288, 907)(289, 956)(290, 963)(291, 965)(292, 962)(293, 888)(294, 979)(295, 964)(296, 885)(297, 846)(298, 847)(299, 844)(300, 902)(301, 842)(302, 909)(303, 912)(304, 841)(305, 954)(306, 953)(307, 961)(308, 969)(309, 977)(310, 986)(311, 985)(312, 978)(313, 856)(314, 853)(315, 944)(316, 851)(317, 926)(318, 849)(319, 850)(320, 927)(321, 955)(322, 972)(323, 970)(324, 975)(325, 971)(326, 879)(327, 878)(328, 988)(329, 957)(330, 960)(331, 974)(332, 941)(333, 943)(334, 924)(335, 939)(336, 942)(337, 674)(338, 673)(339, 681)(340, 689)(341, 697)(342, 706)(343, 705)(344, 698)(345, 675)(346, 692)(347, 690)(348, 695)(349, 691)(350, 767)(351, 766)(352, 708)(353, 676)(354, 683)(355, 685)(356, 682)(357, 776)(358, 699)(359, 684)(360, 773)(361, 677)(362, 680)(363, 694)(364, 829)(365, 831)(366, 812)(367, 827)(368, 830)(369, 679)(370, 678)(371, 791)(372, 688)(373, 788)(374, 792)(375, 789)(376, 795)(377, 744)(378, 741)(379, 832)(380, 739)(381, 814)(382, 737)(383, 738)(384, 815)(385, 734)(386, 735)(387, 732)(388, 790)(389, 730)(390, 797)(391, 800)(392, 729)(393, 728)(394, 725)(395, 760)(396, 723)(397, 742)(398, 721)(399, 722)(400, 743)(401, 718)(402, 719)(403, 716)(404, 750)(405, 714)(406, 733)(407, 736)(408, 713)(409, 821)(410, 824)(411, 838)(412, 757)(413, 759)(414, 740)(415, 755)(416, 758)(417, 823)(418, 822)(419, 751)(420, 808)(421, 748)(422, 752)(423, 749)(424, 731)(425, 819)(426, 836)(427, 834)(428, 839)(429, 835)(430, 687)(431, 686)(432, 828)(433, 820)(434, 803)(435, 805)(436, 802)(437, 696)(438, 787)(439, 804)(440, 693)(441, 818)(442, 817)(443, 801)(444, 833)(445, 785)(446, 826)(447, 825)(448, 786)(449, 781)(450, 784)(451, 774)(452, 709)(453, 711)(454, 724)(455, 707)(456, 710)(457, 816)(458, 813)(459, 712)(460, 811)(461, 726)(462, 809)(463, 810)(464, 727)(465, 779)(466, 772)(467, 770)(468, 775)(469, 771)(470, 807)(471, 806)(472, 756)(473, 798)(474, 799)(475, 796)(476, 702)(477, 794)(478, 717)(479, 720)(480, 793)(481, 778)(482, 777)(483, 761)(484, 769)(485, 745)(486, 754)(487, 753)(488, 746)(489, 783)(490, 782)(491, 703)(492, 768)(493, 700)(494, 704)(495, 701)(496, 715)(497, 780)(498, 763)(499, 765)(500, 762)(501, 840)(502, 747)(503, 764)(504, 837) MAP : A3.90 NOTES : type II, reflexible, isomorphic to DBar({3,7}), isomorphic to A3.13. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 7, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^3, x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3 * x.2 * x.3 * x.2, x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2^-1, x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 14, 6) #DARTS : 1008 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504)(505, 673, 841)(506, 674, 842)(507, 675, 843)(508, 676, 844)(509, 677, 845)(510, 678, 846)(511, 679, 847)(512, 680, 848)(513, 681, 849)(514, 682, 850)(515, 683, 851)(516, 684, 852)(517, 685, 853)(518, 686, 854)(519, 687, 855)(520, 688, 856)(521, 689, 857)(522, 690, 858)(523, 691, 859)(524, 692, 860)(525, 693, 861)(526, 694, 862)(527, 695, 863)(528, 696, 864)(529, 697, 865)(530, 698, 866)(531, 699, 867)(532, 700, 868)(533, 701, 869)(534, 702, 870)(535, 703, 871)(536, 704, 872)(537, 705, 873)(538, 706, 874)(539, 707, 875)(540, 708, 876)(541, 709, 877)(542, 710, 878)(543, 711, 879)(544, 712, 880)(545, 713, 881)(546, 714, 882)(547, 715, 883)(548, 716, 884)(549, 717, 885)(550, 718, 886)(551, 719, 887)(552, 720, 888)(553, 721, 889)(554, 722, 890)(555, 723, 891)(556, 724, 892)(557, 725, 893)(558, 726, 894)(559, 727, 895)(560, 728, 896)(561, 729, 897)(562, 730, 898)(563, 731, 899)(564, 732, 900)(565, 733, 901)(566, 734, 902)(567, 735, 903)(568, 736, 904)(569, 737, 905)(570, 738, 906)(571, 739, 907)(572, 740, 908)(573, 741, 909)(574, 742, 910)(575, 743, 911)(576, 744, 912)(577, 745, 913)(578, 746, 914)(579, 747, 915)(580, 748, 916)(581, 749, 917)(582, 750, 918)(583, 751, 919)(584, 752, 920)(585, 753, 921)(586, 754, 922)(587, 755, 923)(588, 756, 924)(589, 757, 925)(590, 758, 926)(591, 759, 927)(592, 760, 928)(593, 761, 929)(594, 762, 930)(595, 763, 931)(596, 764, 932)(597, 765, 933)(598, 766, 934)(599, 767, 935)(600, 768, 936)(601, 769, 937)(602, 770, 938)(603, 771, 939)(604, 772, 940)(605, 773, 941)(606, 774, 942)(607, 775, 943)(608, 776, 944)(609, 777, 945)(610, 778, 946)(611, 779, 947)(612, 780, 948)(613, 781, 949)(614, 782, 950)(615, 783, 951)(616, 784, 952)(617, 785, 953)(618, 786, 954)(619, 787, 955)(620, 788, 956)(621, 789, 957)(622, 790, 958)(623, 791, 959)(624, 792, 960)(625, 793, 961)(626, 794, 962)(627, 795, 963)(628, 796, 964)(629, 797, 965)(630, 798, 966)(631, 799, 967)(632, 800, 968)(633, 801, 969)(634, 802, 970)(635, 803, 971)(636, 804, 972)(637, 805, 973)(638, 806, 974)(639, 807, 975)(640, 808, 976)(641, 809, 977)(642, 810, 978)(643, 811, 979)(644, 812, 980)(645, 813, 981)(646, 814, 982)(647, 815, 983)(648, 816, 984)(649, 817, 985)(650, 818, 986)(651, 819, 987)(652, 820, 988)(653, 821, 989)(654, 822, 990)(655, 823, 991)(656, 824, 992)(657, 825, 993)(658, 826, 994)(659, 827, 995)(660, 828, 996)(661, 829, 997)(662, 830, 998)(663, 831, 999)(664, 832, 1000)(665, 833, 1001)(666, 834, 1002)(667, 835, 1003)(668, 836, 1004)(669, 837, 1005)(670, 838, 1006)(671, 839, 1007)(672, 840, 1008) L = (1, 505)(2, 506)(3, 507)(4, 508)(5, 509)(6, 510)(7, 511)(8, 512)(9, 513)(10, 514)(11, 515)(12, 516)(13, 517)(14, 518)(15, 519)(16, 520)(17, 521)(18, 522)(19, 523)(20, 524)(21, 525)(22, 526)(23, 527)(24, 528)(25, 529)(26, 530)(27, 531)(28, 532)(29, 533)(30, 534)(31, 535)(32, 536)(33, 537)(34, 538)(35, 539)(36, 540)(37, 541)(38, 542)(39, 543)(40, 544)(41, 545)(42, 546)(43, 547)(44, 548)(45, 549)(46, 550)(47, 551)(48, 552)(49, 553)(50, 554)(51, 555)(52, 556)(53, 557)(54, 558)(55, 559)(56, 560)(57, 561)(58, 562)(59, 563)(60, 564)(61, 565)(62, 566)(63, 567)(64, 568)(65, 569)(66, 570)(67, 571)(68, 572)(69, 573)(70, 574)(71, 575)(72, 576)(73, 577)(74, 578)(75, 579)(76, 580)(77, 581)(78, 582)(79, 583)(80, 584)(81, 585)(82, 586)(83, 587)(84, 588)(85, 589)(86, 590)(87, 591)(88, 592)(89, 593)(90, 594)(91, 595)(92, 596)(93, 597)(94, 598)(95, 599)(96, 600)(97, 601)(98, 602)(99, 603)(100, 604)(101, 605)(102, 606)(103, 607)(104, 608)(105, 609)(106, 610)(107, 611)(108, 612)(109, 613)(110, 614)(111, 615)(112, 616)(113, 617)(114, 618)(115, 619)(116, 620)(117, 621)(118, 622)(119, 623)(120, 624)(121, 625)(122, 626)(123, 627)(124, 628)(125, 629)(126, 630)(127, 631)(128, 632)(129, 633)(130, 634)(131, 635)(132, 636)(133, 637)(134, 638)(135, 639)(136, 640)(137, 641)(138, 642)(139, 643)(140, 644)(141, 645)(142, 646)(143, 647)(144, 648)(145, 649)(146, 650)(147, 651)(148, 652)(149, 653)(150, 654)(151, 655)(152, 656)(153, 657)(154, 658)(155, 659)(156, 660)(157, 661)(158, 662)(159, 663)(160, 664)(161, 665)(162, 666)(163, 667)(164, 668)(165, 669)(166, 670)(167, 671)(168, 672)(169, 842)(170, 841)(171, 849)(172, 857)(173, 865)(174, 874)(175, 873)(176, 866)(177, 843)(178, 860)(179, 858)(180, 863)(181, 859)(182, 935)(183, 934)(184, 876)(185, 844)(186, 851)(187, 853)(188, 850)(189, 944)(190, 867)(191, 852)(192, 941)(193, 845)(194, 848)(195, 862)(196, 997)(197, 999)(198, 980)(199, 995)(200, 998)(201, 847)(202, 846)(203, 959)(204, 856)(205, 956)(206, 960)(207, 957)(208, 963)(209, 912)(210, 909)(211, 1000)(212, 907)(213, 982)(214, 905)(215, 906)(216, 983)(217, 902)(218, 903)(219, 900)(220, 958)(221, 898)(222, 965)(223, 968)(224, 897)(225, 896)(226, 893)(227, 928)(228, 891)(229, 910)(230, 889)(231, 890)(232, 911)(233, 886)(234, 887)(235, 884)(236, 918)(237, 882)(238, 901)(239, 904)(240, 881)(241, 989)(242, 992)(243, 1006)(244, 925)(245, 927)(246, 908)(247, 923)(248, 926)(249, 991)(250, 990)(251, 919)(252, 976)(253, 916)(254, 920)(255, 917)(256, 899)(257, 987)(258, 1004)(259, 1002)(260, 1007)(261, 1003)(262, 855)(263, 854)(264, 996)(265, 988)(266, 971)(267, 973)(268, 970)(269, 864)(270, 955)(271, 972)(272, 861)(273, 986)(274, 985)(275, 969)(276, 1001)(277, 953)(278, 994)(279, 993)(280, 954)(281, 949)(282, 952)(283, 942)(284, 877)(285, 879)(286, 892)(287, 875)(288, 878)(289, 984)(290, 981)(291, 880)(292, 979)(293, 894)(294, 977)(295, 978)(296, 895)(297, 947)(298, 940)(299, 938)(300, 943)(301, 939)(302, 975)(303, 974)(304, 924)(305, 966)(306, 967)(307, 964)(308, 870)(309, 962)(310, 885)(311, 888)(312, 961)(313, 946)(314, 945)(315, 929)(316, 937)(317, 913)(318, 922)(319, 921)(320, 914)(321, 951)(322, 950)(323, 871)(324, 936)(325, 868)(326, 872)(327, 869)(328, 883)(329, 948)(330, 931)(331, 933)(332, 930)(333, 1008)(334, 915)(335, 932)(336, 1005)(337, 756)(338, 771)(339, 773)(340, 770)(341, 792)(342, 779)(343, 772)(344, 789)(345, 754)(346, 753)(347, 769)(348, 737)(349, 777)(350, 730)(351, 729)(352, 778)(353, 759)(354, 758)(355, 687)(356, 776)(357, 684)(358, 688)(359, 685)(360, 699)(361, 755)(362, 740)(363, 738)(364, 743)(365, 739)(366, 815)(367, 814)(368, 732)(369, 838)(370, 839)(371, 836)(372, 686)(373, 834)(374, 701)(375, 704)(376, 833)(377, 757)(378, 760)(379, 742)(380, 725)(381, 727)(382, 716)(383, 723)(384, 726)(385, 824)(386, 821)(387, 728)(388, 819)(389, 718)(390, 817)(391, 818)(392, 719)(393, 691)(394, 708)(395, 706)(396, 711)(397, 707)(398, 775)(399, 774)(400, 724)(401, 693)(402, 696)(403, 710)(404, 805)(405, 807)(406, 820)(407, 803)(408, 806)(409, 690)(410, 689)(411, 673)(412, 705)(413, 681)(414, 722)(415, 721)(416, 682)(417, 752)(418, 749)(419, 808)(420, 747)(421, 822)(422, 745)(423, 746)(424, 823)(425, 692)(426, 675)(427, 677)(428, 674)(429, 744)(430, 683)(431, 676)(432, 741)(433, 766)(434, 767)(435, 764)(436, 830)(437, 762)(438, 837)(439, 840)(440, 761)(441, 695)(442, 694)(443, 831)(444, 680)(445, 828)(446, 832)(447, 829)(448, 835)(449, 799)(450, 798)(451, 783)(452, 816)(453, 780)(454, 784)(455, 781)(456, 763)(457, 796)(458, 811)(459, 813)(460, 810)(461, 712)(462, 827)(463, 812)(464, 709)(465, 702)(466, 703)(467, 700)(468, 782)(469, 698)(470, 765)(471, 768)(472, 697)(473, 794)(474, 793)(475, 809)(476, 785)(477, 825)(478, 802)(479, 801)(480, 826)(481, 720)(482, 717)(483, 736)(484, 715)(485, 750)(486, 713)(487, 714)(488, 751)(489, 795)(490, 788)(491, 786)(492, 791)(493, 787)(494, 679)(495, 678)(496, 804)(497, 797)(498, 800)(499, 790)(500, 733)(501, 735)(502, 748)(503, 731)(504, 734) MAP : A3.91 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A3.19. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^3, (u.3 * u.1^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.2 * x.3^-1)^2, (x.1 * x.2^-1)^3, x.3^8, (x.3^-2 * x.2^-1)^3, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 6) #DARTS : 576 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288)(289, 385, 481)(290, 386, 482)(291, 387, 483)(292, 388, 484)(293, 389, 485)(294, 390, 486)(295, 391, 487)(296, 392, 488)(297, 393, 489)(298, 394, 490)(299, 395, 491)(300, 396, 492)(301, 397, 493)(302, 398, 494)(303, 399, 495)(304, 400, 496)(305, 401, 497)(306, 402, 498)(307, 403, 499)(308, 404, 500)(309, 405, 501)(310, 406, 502)(311, 407, 503)(312, 408, 504)(313, 409, 505)(314, 410, 506)(315, 411, 507)(316, 412, 508)(317, 413, 509)(318, 414, 510)(319, 415, 511)(320, 416, 512)(321, 417, 513)(322, 418, 514)(323, 419, 515)(324, 420, 516)(325, 421, 517)(326, 422, 518)(327, 423, 519)(328, 424, 520)(329, 425, 521)(330, 426, 522)(331, 427, 523)(332, 428, 524)(333, 429, 525)(334, 430, 526)(335, 431, 527)(336, 432, 528)(337, 433, 529)(338, 434, 530)(339, 435, 531)(340, 436, 532)(341, 437, 533)(342, 438, 534)(343, 439, 535)(344, 440, 536)(345, 441, 537)(346, 442, 538)(347, 443, 539)(348, 444, 540)(349, 445, 541)(350, 446, 542)(351, 447, 543)(352, 448, 544)(353, 449, 545)(354, 450, 546)(355, 451, 547)(356, 452, 548)(357, 453, 549)(358, 454, 550)(359, 455, 551)(360, 456, 552)(361, 457, 553)(362, 458, 554)(363, 459, 555)(364, 460, 556)(365, 461, 557)(366, 462, 558)(367, 463, 559)(368, 464, 560)(369, 465, 561)(370, 466, 562)(371, 467, 563)(372, 468, 564)(373, 469, 565)(374, 470, 566)(375, 471, 567)(376, 472, 568)(377, 473, 569)(378, 474, 570)(379, 475, 571)(380, 476, 572)(381, 477, 573)(382, 478, 574)(383, 479, 575)(384, 480, 576) L = (1, 289)(2, 290)(3, 291)(4, 292)(5, 293)(6, 294)(7, 295)(8, 296)(9, 297)(10, 298)(11, 299)(12, 300)(13, 301)(14, 302)(15, 303)(16, 304)(17, 305)(18, 306)(19, 307)(20, 308)(21, 309)(22, 310)(23, 311)(24, 312)(25, 313)(26, 314)(27, 315)(28, 316)(29, 317)(30, 318)(31, 319)(32, 320)(33, 321)(34, 322)(35, 323)(36, 324)(37, 325)(38, 326)(39, 327)(40, 328)(41, 329)(42, 330)(43, 331)(44, 332)(45, 333)(46, 334)(47, 335)(48, 336)(49, 337)(50, 338)(51, 339)(52, 340)(53, 341)(54, 342)(55, 343)(56, 344)(57, 345)(58, 346)(59, 347)(60, 348)(61, 349)(62, 350)(63, 351)(64, 352)(65, 353)(66, 354)(67, 355)(68, 356)(69, 357)(70, 358)(71, 359)(72, 360)(73, 361)(74, 362)(75, 363)(76, 364)(77, 365)(78, 366)(79, 367)(80, 368)(81, 369)(82, 370)(83, 371)(84, 372)(85, 373)(86, 374)(87, 375)(88, 376)(89, 377)(90, 378)(91, 379)(92, 380)(93, 381)(94, 382)(95, 383)(96, 384)(97, 482)(98, 485)(99, 497)(100, 498)(101, 481)(102, 499)(103, 500)(104, 501)(105, 549)(106, 502)(107, 503)(108, 504)(109, 546)(110, 545)(111, 508)(112, 556)(113, 514)(114, 517)(115, 561)(116, 562)(117, 513)(118, 563)(119, 564)(120, 565)(121, 533)(122, 566)(123, 567)(124, 568)(125, 530)(126, 529)(127, 572)(128, 540)(129, 488)(130, 483)(131, 493)(132, 489)(133, 484)(134, 510)(135, 509)(136, 494)(137, 570)(138, 543)(139, 538)(140, 505)(141, 575)(142, 571)(143, 539)(144, 534)(145, 518)(146, 519)(147, 522)(148, 523)(149, 524)(150, 537)(151, 542)(152, 527)(153, 528)(154, 532)(155, 536)(156, 541)(157, 512)(158, 544)(159, 531)(160, 535)(161, 520)(162, 515)(163, 525)(164, 521)(165, 516)(166, 574)(167, 573)(168, 526)(169, 506)(170, 559)(171, 554)(172, 569)(173, 511)(174, 507)(175, 555)(176, 550)(177, 486)(178, 487)(179, 490)(180, 491)(181, 492)(182, 553)(183, 558)(184, 495)(185, 496)(186, 548)(187, 552)(188, 557)(189, 576)(190, 560)(191, 547)(192, 551)(193, 446)(194, 445)(195, 431)(196, 426)(197, 441)(198, 416)(199, 432)(200, 427)(201, 422)(202, 411)(203, 415)(204, 448)(205, 428)(206, 423)(207, 410)(208, 430)(209, 462)(210, 461)(211, 399)(212, 394)(213, 457)(214, 480)(215, 400)(216, 395)(217, 390)(218, 475)(219, 479)(220, 464)(221, 396)(222, 391)(223, 474)(224, 398)(225, 435)(226, 436)(227, 438)(228, 439)(229, 440)(230, 442)(231, 443)(232, 444)(233, 476)(234, 409)(235, 414)(236, 447)(237, 471)(238, 470)(239, 413)(240, 397)(241, 453)(242, 449)(243, 402)(244, 405)(245, 450)(246, 385)(247, 386)(248, 401)(249, 404)(250, 387)(251, 388)(252, 389)(253, 403)(254, 408)(255, 392)(256, 393)(257, 451)(258, 452)(259, 454)(260, 455)(261, 456)(262, 458)(263, 459)(264, 460)(265, 412)(266, 473)(267, 478)(268, 463)(269, 407)(270, 406)(271, 477)(272, 429)(273, 437)(274, 433)(275, 466)(276, 469)(277, 434)(278, 417)(279, 418)(280, 465)(281, 468)(282, 419)(283, 420)(284, 421)(285, 467)(286, 472)(287, 424)(288, 425) MAP : A3.92 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A3.19. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.2 * x.3^-1)^3, x.2^5 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^2, x.3 * x.2^-2 * x.3 * x.2^2 * x.3^-1 * x.2^2 * x.3^-1 * x.2^-2, x.2^-2 * x.3 * x.2^2 * x.3 * x.2^2 * x.3^-1 * x.2^-2 * x.3^-1, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 6) #DARTS : 576 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288)(289, 385, 481)(290, 386, 482)(291, 387, 483)(292, 388, 484)(293, 389, 485)(294, 390, 486)(295, 391, 487)(296, 392, 488)(297, 393, 489)(298, 394, 490)(299, 395, 491)(300, 396, 492)(301, 397, 493)(302, 398, 494)(303, 399, 495)(304, 400, 496)(305, 401, 497)(306, 402, 498)(307, 403, 499)(308, 404, 500)(309, 405, 501)(310, 406, 502)(311, 407, 503)(312, 408, 504)(313, 409, 505)(314, 410, 506)(315, 411, 507)(316, 412, 508)(317, 413, 509)(318, 414, 510)(319, 415, 511)(320, 416, 512)(321, 417, 513)(322, 418, 514)(323, 419, 515)(324, 420, 516)(325, 421, 517)(326, 422, 518)(327, 423, 519)(328, 424, 520)(329, 425, 521)(330, 426, 522)(331, 427, 523)(332, 428, 524)(333, 429, 525)(334, 430, 526)(335, 431, 527)(336, 432, 528)(337, 433, 529)(338, 434, 530)(339, 435, 531)(340, 436, 532)(341, 437, 533)(342, 438, 534)(343, 439, 535)(344, 440, 536)(345, 441, 537)(346, 442, 538)(347, 443, 539)(348, 444, 540)(349, 445, 541)(350, 446, 542)(351, 447, 543)(352, 448, 544)(353, 449, 545)(354, 450, 546)(355, 451, 547)(356, 452, 548)(357, 453, 549)(358, 454, 550)(359, 455, 551)(360, 456, 552)(361, 457, 553)(362, 458, 554)(363, 459, 555)(364, 460, 556)(365, 461, 557)(366, 462, 558)(367, 463, 559)(368, 464, 560)(369, 465, 561)(370, 466, 562)(371, 467, 563)(372, 468, 564)(373, 469, 565)(374, 470, 566)(375, 471, 567)(376, 472, 568)(377, 473, 569)(378, 474, 570)(379, 475, 571)(380, 476, 572)(381, 477, 573)(382, 478, 574)(383, 479, 575)(384, 480, 576) L = (1, 289)(2, 290)(3, 291)(4, 292)(5, 293)(6, 294)(7, 295)(8, 296)(9, 297)(10, 298)(11, 299)(12, 300)(13, 301)(14, 302)(15, 303)(16, 304)(17, 305)(18, 306)(19, 307)(20, 308)(21, 309)(22, 310)(23, 311)(24, 312)(25, 313)(26, 314)(27, 315)(28, 316)(29, 317)(30, 318)(31, 319)(32, 320)(33, 321)(34, 322)(35, 323)(36, 324)(37, 325)(38, 326)(39, 327)(40, 328)(41, 329)(42, 330)(43, 331)(44, 332)(45, 333)(46, 334)(47, 335)(48, 336)(49, 337)(50, 338)(51, 339)(52, 340)(53, 341)(54, 342)(55, 343)(56, 344)(57, 345)(58, 346)(59, 347)(60, 348)(61, 349)(62, 350)(63, 351)(64, 352)(65, 353)(66, 354)(67, 355)(68, 356)(69, 357)(70, 358)(71, 359)(72, 360)(73, 361)(74, 362)(75, 363)(76, 364)(77, 365)(78, 366)(79, 367)(80, 368)(81, 369)(82, 370)(83, 371)(84, 372)(85, 373)(86, 374)(87, 375)(88, 376)(89, 377)(90, 378)(91, 379)(92, 380)(93, 381)(94, 382)(95, 383)(96, 384)(97, 483)(98, 484)(99, 486)(100, 487)(101, 488)(102, 490)(103, 491)(104, 492)(105, 524)(106, 553)(107, 558)(108, 495)(109, 519)(110, 518)(111, 557)(112, 541)(113, 485)(114, 481)(115, 514)(116, 517)(117, 482)(118, 561)(119, 562)(120, 513)(121, 516)(122, 563)(123, 564)(124, 565)(125, 515)(126, 520)(127, 568)(128, 569)(129, 494)(130, 493)(131, 575)(132, 570)(133, 489)(134, 560)(135, 576)(136, 571)(137, 566)(138, 555)(139, 559)(140, 496)(141, 572)(142, 567)(143, 554)(144, 574)(145, 499)(146, 500)(147, 502)(148, 503)(149, 504)(150, 506)(151, 507)(152, 508)(153, 556)(154, 521)(155, 526)(156, 511)(157, 551)(158, 550)(159, 525)(160, 573)(161, 501)(162, 497)(163, 546)(164, 549)(165, 498)(166, 529)(167, 530)(168, 545)(169, 548)(170, 531)(171, 532)(172, 533)(173, 547)(174, 552)(175, 536)(176, 537)(177, 510)(178, 509)(179, 543)(180, 538)(181, 505)(182, 528)(183, 544)(184, 539)(185, 534)(186, 523)(187, 527)(188, 512)(189, 540)(190, 535)(191, 522)(192, 542)(193, 388)(194, 392)(195, 389)(196, 385)(197, 387)(198, 418)(199, 421)(200, 386)(201, 402)(202, 465)(203, 466)(204, 417)(205, 401)(206, 405)(207, 469)(208, 437)(209, 397)(210, 393)(211, 414)(212, 413)(213, 398)(214, 447)(215, 442)(216, 409)(217, 408)(218, 432)(219, 448)(220, 443)(221, 404)(222, 403)(223, 416)(224, 415)(225, 396)(226, 390)(227, 423)(228, 428)(229, 391)(230, 424)(231, 419)(232, 422)(233, 427)(234, 429)(235, 425)(236, 420)(237, 426)(238, 431)(239, 430)(240, 410)(241, 464)(242, 480)(243, 459)(244, 463)(245, 400)(246, 460)(247, 454)(248, 458)(249, 478)(250, 407)(251, 412)(252, 455)(253, 473)(254, 477)(255, 406)(256, 411)(257, 475)(258, 479)(259, 476)(260, 470)(261, 474)(262, 439)(263, 444)(264, 471)(265, 467)(266, 440)(267, 435)(268, 438)(269, 472)(270, 468)(271, 436)(272, 433)(273, 394)(274, 395)(275, 457)(276, 462)(277, 399)(278, 452)(279, 456)(280, 461)(281, 445)(282, 453)(283, 449)(284, 451)(285, 446)(286, 441)(287, 450)(288, 434) MAP : A3.93 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A3.19. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.2 * x.3^-1)^3, x.2^5 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^2, x.3 * x.2^-2 * x.3 * x.2^2 * x.3^-1 * x.2^2 * x.3^-1 * x.2^-2, x.2^-2 * x.3 * x.2^2 * x.3 * x.2^2 * x.3^-1 * x.2^-2 * x.3^-1, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 6) #DARTS : 576 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288)(289, 385, 481)(290, 386, 482)(291, 387, 483)(292, 388, 484)(293, 389, 485)(294, 390, 486)(295, 391, 487)(296, 392, 488)(297, 393, 489)(298, 394, 490)(299, 395, 491)(300, 396, 492)(301, 397, 493)(302, 398, 494)(303, 399, 495)(304, 400, 496)(305, 401, 497)(306, 402, 498)(307, 403, 499)(308, 404, 500)(309, 405, 501)(310, 406, 502)(311, 407, 503)(312, 408, 504)(313, 409, 505)(314, 410, 506)(315, 411, 507)(316, 412, 508)(317, 413, 509)(318, 414, 510)(319, 415, 511)(320, 416, 512)(321, 417, 513)(322, 418, 514)(323, 419, 515)(324, 420, 516)(325, 421, 517)(326, 422, 518)(327, 423, 519)(328, 424, 520)(329, 425, 521)(330, 426, 522)(331, 427, 523)(332, 428, 524)(333, 429, 525)(334, 430, 526)(335, 431, 527)(336, 432, 528)(337, 433, 529)(338, 434, 530)(339, 435, 531)(340, 436, 532)(341, 437, 533)(342, 438, 534)(343, 439, 535)(344, 440, 536)(345, 441, 537)(346, 442, 538)(347, 443, 539)(348, 444, 540)(349, 445, 541)(350, 446, 542)(351, 447, 543)(352, 448, 544)(353, 449, 545)(354, 450, 546)(355, 451, 547)(356, 452, 548)(357, 453, 549)(358, 454, 550)(359, 455, 551)(360, 456, 552)(361, 457, 553)(362, 458, 554)(363, 459, 555)(364, 460, 556)(365, 461, 557)(366, 462, 558)(367, 463, 559)(368, 464, 560)(369, 465, 561)(370, 466, 562)(371, 467, 563)(372, 468, 564)(373, 469, 565)(374, 470, 566)(375, 471, 567)(376, 472, 568)(377, 473, 569)(378, 474, 570)(379, 475, 571)(380, 476, 572)(381, 477, 573)(382, 478, 574)(383, 479, 575)(384, 480, 576) L = (1, 289)(2, 290)(3, 291)(4, 292)(5, 293)(6, 294)(7, 295)(8, 296)(9, 297)(10, 298)(11, 299)(12, 300)(13, 301)(14, 302)(15, 303)(16, 304)(17, 305)(18, 306)(19, 307)(20, 308)(21, 309)(22, 310)(23, 311)(24, 312)(25, 313)(26, 314)(27, 315)(28, 316)(29, 317)(30, 318)(31, 319)(32, 320)(33, 321)(34, 322)(35, 323)(36, 324)(37, 325)(38, 326)(39, 327)(40, 328)(41, 329)(42, 330)(43, 331)(44, 332)(45, 333)(46, 334)(47, 335)(48, 336)(49, 337)(50, 338)(51, 339)(52, 340)(53, 341)(54, 342)(55, 343)(56, 344)(57, 345)(58, 346)(59, 347)(60, 348)(61, 349)(62, 350)(63, 351)(64, 352)(65, 353)(66, 354)(67, 355)(68, 356)(69, 357)(70, 358)(71, 359)(72, 360)(73, 361)(74, 362)(75, 363)(76, 364)(77, 365)(78, 366)(79, 367)(80, 368)(81, 369)(82, 370)(83, 371)(84, 372)(85, 373)(86, 374)(87, 375)(88, 376)(89, 377)(90, 378)(91, 379)(92, 380)(93, 381)(94, 382)(95, 383)(96, 384)(97, 490)(98, 491)(99, 553)(100, 558)(101, 495)(102, 548)(103, 552)(104, 557)(105, 541)(106, 549)(107, 545)(108, 547)(109, 542)(110, 537)(111, 546)(112, 530)(113, 492)(114, 486)(115, 519)(116, 524)(117, 487)(118, 520)(119, 515)(120, 518)(121, 523)(122, 525)(123, 521)(124, 516)(125, 522)(126, 527)(127, 526)(128, 506)(129, 560)(130, 576)(131, 555)(132, 559)(133, 496)(134, 556)(135, 550)(136, 554)(137, 574)(138, 503)(139, 508)(140, 551)(141, 569)(142, 573)(143, 502)(144, 507)(145, 493)(146, 489)(147, 510)(148, 509)(149, 494)(150, 543)(151, 538)(152, 505)(153, 504)(154, 528)(155, 544)(156, 539)(157, 500)(158, 499)(159, 512)(160, 511)(161, 484)(162, 488)(163, 485)(164, 481)(165, 483)(166, 514)(167, 517)(168, 482)(169, 498)(170, 561)(171, 562)(172, 513)(173, 497)(174, 501)(175, 565)(176, 533)(177, 571)(178, 575)(179, 572)(180, 566)(181, 570)(182, 535)(183, 540)(184, 567)(185, 563)(186, 536)(187, 531)(188, 534)(189, 568)(190, 564)(191, 532)(192, 529)(193, 388)(194, 392)(195, 389)(196, 385)(197, 387)(198, 418)(199, 421)(200, 386)(201, 402)(202, 465)(203, 466)(204, 417)(205, 401)(206, 405)(207, 469)(208, 437)(209, 397)(210, 393)(211, 414)(212, 413)(213, 398)(214, 447)(215, 442)(216, 409)(217, 408)(218, 432)(219, 448)(220, 443)(221, 404)(222, 403)(223, 416)(224, 415)(225, 396)(226, 390)(227, 423)(228, 428)(229, 391)(230, 424)(231, 419)(232, 422)(233, 427)(234, 429)(235, 425)(236, 420)(237, 426)(238, 431)(239, 430)(240, 410)(241, 464)(242, 480)(243, 459)(244, 463)(245, 400)(246, 460)(247, 454)(248, 458)(249, 478)(250, 407)(251, 412)(252, 455)(253, 473)(254, 477)(255, 406)(256, 411)(257, 475)(258, 479)(259, 476)(260, 470)(261, 474)(262, 439)(263, 444)(264, 471)(265, 467)(266, 440)(267, 435)(268, 438)(269, 472)(270, 468)(271, 436)(272, 433)(273, 394)(274, 395)(275, 457)(276, 462)(277, 399)(278, 452)(279, 456)(280, 461)(281, 445)(282, 453)(283, 449)(284, 451)(285, 446)(286, 441)(287, 450)(288, 434) MAP : A3.94 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A3.19. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^3, x.3^-1 * x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 * x.3 * x.2^-1, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 6) #DARTS : 576 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288)(289, 385, 481)(290, 386, 482)(291, 387, 483)(292, 388, 484)(293, 389, 485)(294, 390, 486)(295, 391, 487)(296, 392, 488)(297, 393, 489)(298, 394, 490)(299, 395, 491)(300, 396, 492)(301, 397, 493)(302, 398, 494)(303, 399, 495)(304, 400, 496)(305, 401, 497)(306, 402, 498)(307, 403, 499)(308, 404, 500)(309, 405, 501)(310, 406, 502)(311, 407, 503)(312, 408, 504)(313, 409, 505)(314, 410, 506)(315, 411, 507)(316, 412, 508)(317, 413, 509)(318, 414, 510)(319, 415, 511)(320, 416, 512)(321, 417, 513)(322, 418, 514)(323, 419, 515)(324, 420, 516)(325, 421, 517)(326, 422, 518)(327, 423, 519)(328, 424, 520)(329, 425, 521)(330, 426, 522)(331, 427, 523)(332, 428, 524)(333, 429, 525)(334, 430, 526)(335, 431, 527)(336, 432, 528)(337, 433, 529)(338, 434, 530)(339, 435, 531)(340, 436, 532)(341, 437, 533)(342, 438, 534)(343, 439, 535)(344, 440, 536)(345, 441, 537)(346, 442, 538)(347, 443, 539)(348, 444, 540)(349, 445, 541)(350, 446, 542)(351, 447, 543)(352, 448, 544)(353, 449, 545)(354, 450, 546)(355, 451, 547)(356, 452, 548)(357, 453, 549)(358, 454, 550)(359, 455, 551)(360, 456, 552)(361, 457, 553)(362, 458, 554)(363, 459, 555)(364, 460, 556)(365, 461, 557)(366, 462, 558)(367, 463, 559)(368, 464, 560)(369, 465, 561)(370, 466, 562)(371, 467, 563)(372, 468, 564)(373, 469, 565)(374, 470, 566)(375, 471, 567)(376, 472, 568)(377, 473, 569)(378, 474, 570)(379, 475, 571)(380, 476, 572)(381, 477, 573)(382, 478, 574)(383, 479, 575)(384, 480, 576) L = (1, 289)(2, 290)(3, 291)(4, 292)(5, 293)(6, 294)(7, 295)(8, 296)(9, 297)(10, 298)(11, 299)(12, 300)(13, 301)(14, 302)(15, 303)(16, 304)(17, 305)(18, 306)(19, 307)(20, 308)(21, 309)(22, 310)(23, 311)(24, 312)(25, 313)(26, 314)(27, 315)(28, 316)(29, 317)(30, 318)(31, 319)(32, 320)(33, 321)(34, 322)(35, 323)(36, 324)(37, 325)(38, 326)(39, 327)(40, 328)(41, 329)(42, 330)(43, 331)(44, 332)(45, 333)(46, 334)(47, 335)(48, 336)(49, 337)(50, 338)(51, 339)(52, 340)(53, 341)(54, 342)(55, 343)(56, 344)(57, 345)(58, 346)(59, 347)(60, 348)(61, 349)(62, 350)(63, 351)(64, 352)(65, 353)(66, 354)(67, 355)(68, 356)(69, 357)(70, 358)(71, 359)(72, 360)(73, 361)(74, 362)(75, 363)(76, 364)(77, 365)(78, 366)(79, 367)(80, 368)(81, 369)(82, 370)(83, 371)(84, 372)(85, 373)(86, 374)(87, 375)(88, 376)(89, 377)(90, 378)(91, 379)(92, 380)(93, 381)(94, 382)(95, 383)(96, 384)(97, 484)(98, 488)(99, 485)(100, 481)(101, 483)(102, 514)(103, 517)(104, 482)(105, 498)(106, 561)(107, 562)(108, 513)(109, 497)(110, 501)(111, 565)(112, 533)(113, 493)(114, 489)(115, 510)(116, 509)(117, 494)(118, 543)(119, 538)(120, 505)(121, 504)(122, 528)(123, 544)(124, 539)(125, 500)(126, 499)(127, 512)(128, 511)(129, 492)(130, 486)(131, 519)(132, 524)(133, 487)(134, 520)(135, 515)(136, 518)(137, 523)(138, 525)(139, 521)(140, 516)(141, 522)(142, 527)(143, 526)(144, 506)(145, 560)(146, 576)(147, 555)(148, 559)(149, 496)(150, 556)(151, 550)(152, 554)(153, 574)(154, 503)(155, 508)(156, 551)(157, 569)(158, 573)(159, 502)(160, 507)(161, 571)(162, 575)(163, 572)(164, 566)(165, 570)(166, 535)(167, 540)(168, 567)(169, 563)(170, 536)(171, 531)(172, 534)(173, 568)(174, 564)(175, 532)(176, 529)(177, 490)(178, 491)(179, 553)(180, 558)(181, 495)(182, 548)(183, 552)(184, 557)(185, 541)(186, 549)(187, 545)(188, 547)(189, 542)(190, 537)(191, 546)(192, 530)(193, 386)(194, 389)(195, 401)(196, 402)(197, 385)(198, 403)(199, 404)(200, 405)(201, 453)(202, 406)(203, 407)(204, 408)(205, 450)(206, 449)(207, 412)(208, 460)(209, 418)(210, 421)(211, 465)(212, 466)(213, 417)(214, 467)(215, 468)(216, 469)(217, 437)(218, 470)(219, 471)(220, 472)(221, 434)(222, 433)(223, 476)(224, 444)(225, 392)(226, 387)(227, 397)(228, 393)(229, 388)(230, 414)(231, 413)(232, 398)(233, 474)(234, 447)(235, 442)(236, 409)(237, 479)(238, 475)(239, 443)(240, 438)(241, 422)(242, 423)(243, 426)(244, 427)(245, 428)(246, 441)(247, 446)(248, 431)(249, 432)(250, 436)(251, 440)(252, 445)(253, 416)(254, 448)(255, 435)(256, 439)(257, 424)(258, 419)(259, 429)(260, 425)(261, 420)(262, 478)(263, 477)(264, 430)(265, 410)(266, 463)(267, 458)(268, 473)(269, 415)(270, 411)(271, 459)(272, 454)(273, 390)(274, 391)(275, 394)(276, 395)(277, 396)(278, 457)(279, 462)(280, 399)(281, 400)(282, 452)(283, 456)(284, 461)(285, 480)(286, 464)(287, 451)(288, 455) MAP : A3.95 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A3.19. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^3, (u.3 * u.1^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.2 * x.3^-1)^2, (x.1 * x.2^-1)^3, x.3^8, (x.3^-2 * x.2^-1)^3, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 6) #DARTS : 576 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288)(289, 385, 481)(290, 386, 482)(291, 387, 483)(292, 388, 484)(293, 389, 485)(294, 390, 486)(295, 391, 487)(296, 392, 488)(297, 393, 489)(298, 394, 490)(299, 395, 491)(300, 396, 492)(301, 397, 493)(302, 398, 494)(303, 399, 495)(304, 400, 496)(305, 401, 497)(306, 402, 498)(307, 403, 499)(308, 404, 500)(309, 405, 501)(310, 406, 502)(311, 407, 503)(312, 408, 504)(313, 409, 505)(314, 410, 506)(315, 411, 507)(316, 412, 508)(317, 413, 509)(318, 414, 510)(319, 415, 511)(320, 416, 512)(321, 417, 513)(322, 418, 514)(323, 419, 515)(324, 420, 516)(325, 421, 517)(326, 422, 518)(327, 423, 519)(328, 424, 520)(329, 425, 521)(330, 426, 522)(331, 427, 523)(332, 428, 524)(333, 429, 525)(334, 430, 526)(335, 431, 527)(336, 432, 528)(337, 433, 529)(338, 434, 530)(339, 435, 531)(340, 436, 532)(341, 437, 533)(342, 438, 534)(343, 439, 535)(344, 440, 536)(345, 441, 537)(346, 442, 538)(347, 443, 539)(348, 444, 540)(349, 445, 541)(350, 446, 542)(351, 447, 543)(352, 448, 544)(353, 449, 545)(354, 450, 546)(355, 451, 547)(356, 452, 548)(357, 453, 549)(358, 454, 550)(359, 455, 551)(360, 456, 552)(361, 457, 553)(362, 458, 554)(363, 459, 555)(364, 460, 556)(365, 461, 557)(366, 462, 558)(367, 463, 559)(368, 464, 560)(369, 465, 561)(370, 466, 562)(371, 467, 563)(372, 468, 564)(373, 469, 565)(374, 470, 566)(375, 471, 567)(376, 472, 568)(377, 473, 569)(378, 474, 570)(379, 475, 571)(380, 476, 572)(381, 477, 573)(382, 478, 574)(383, 479, 575)(384, 480, 576) L = (1, 289)(2, 290)(3, 291)(4, 292)(5, 293)(6, 294)(7, 295)(8, 296)(9, 297)(10, 298)(11, 299)(12, 300)(13, 301)(14, 302)(15, 303)(16, 304)(17, 305)(18, 306)(19, 307)(20, 308)(21, 309)(22, 310)(23, 311)(24, 312)(25, 313)(26, 314)(27, 315)(28, 316)(29, 317)(30, 318)(31, 319)(32, 320)(33, 321)(34, 322)(35, 323)(36, 324)(37, 325)(38, 326)(39, 327)(40, 328)(41, 329)(42, 330)(43, 331)(44, 332)(45, 333)(46, 334)(47, 335)(48, 336)(49, 337)(50, 338)(51, 339)(52, 340)(53, 341)(54, 342)(55, 343)(56, 344)(57, 345)(58, 346)(59, 347)(60, 348)(61, 349)(62, 350)(63, 351)(64, 352)(65, 353)(66, 354)(67, 355)(68, 356)(69, 357)(70, 358)(71, 359)(72, 360)(73, 361)(74, 362)(75, 363)(76, 364)(77, 365)(78, 366)(79, 367)(80, 368)(81, 369)(82, 370)(83, 371)(84, 372)(85, 373)(86, 374)(87, 375)(88, 376)(89, 377)(90, 378)(91, 379)(92, 380)(93, 381)(94, 382)(95, 383)(96, 384)(97, 482)(98, 485)(99, 497)(100, 498)(101, 481)(102, 499)(103, 500)(104, 501)(105, 549)(106, 502)(107, 503)(108, 504)(109, 546)(110, 545)(111, 508)(112, 556)(113, 514)(114, 517)(115, 561)(116, 562)(117, 513)(118, 563)(119, 564)(120, 565)(121, 533)(122, 566)(123, 567)(124, 568)(125, 530)(126, 529)(127, 572)(128, 540)(129, 488)(130, 483)(131, 493)(132, 489)(133, 484)(134, 510)(135, 509)(136, 494)(137, 570)(138, 543)(139, 538)(140, 505)(141, 575)(142, 571)(143, 539)(144, 534)(145, 518)(146, 519)(147, 522)(148, 523)(149, 524)(150, 537)(151, 542)(152, 527)(153, 528)(154, 532)(155, 536)(156, 541)(157, 512)(158, 544)(159, 531)(160, 535)(161, 520)(162, 515)(163, 525)(164, 521)(165, 516)(166, 574)(167, 573)(168, 526)(169, 506)(170, 559)(171, 554)(172, 569)(173, 511)(174, 507)(175, 555)(176, 550)(177, 486)(178, 487)(179, 490)(180, 491)(181, 492)(182, 553)(183, 558)(184, 495)(185, 496)(186, 548)(187, 552)(188, 557)(189, 576)(190, 560)(191, 547)(192, 551)(193, 392)(194, 387)(195, 397)(196, 393)(197, 388)(198, 414)(199, 413)(200, 398)(201, 474)(202, 447)(203, 442)(204, 409)(205, 479)(206, 475)(207, 443)(208, 438)(209, 390)(210, 391)(211, 394)(212, 395)(213, 396)(214, 457)(215, 462)(216, 399)(217, 400)(218, 452)(219, 456)(220, 461)(221, 480)(222, 464)(223, 451)(224, 455)(225, 386)(226, 389)(227, 401)(228, 402)(229, 385)(230, 403)(231, 404)(232, 405)(233, 453)(234, 406)(235, 407)(236, 408)(237, 450)(238, 449)(239, 412)(240, 460)(241, 424)(242, 419)(243, 429)(244, 425)(245, 420)(246, 478)(247, 477)(248, 430)(249, 410)(250, 463)(251, 458)(252, 473)(253, 415)(254, 411)(255, 459)(256, 454)(257, 422)(258, 423)(259, 426)(260, 427)(261, 428)(262, 441)(263, 446)(264, 431)(265, 432)(266, 436)(267, 440)(268, 445)(269, 416)(270, 448)(271, 435)(272, 439)(273, 418)(274, 421)(275, 465)(276, 466)(277, 417)(278, 467)(279, 468)(280, 469)(281, 437)(282, 470)(283, 471)(284, 472)(285, 434)(286, 433)(287, 476)(288, 444) MAP : A3.96 NOTES : type II, reflexible, isomorphic to DBar({3,8}), isomorphic to A3.19. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^3, x.3^-1 * x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 * x.3 * x.2^-1, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 6) #DARTS : 576 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288)(289, 385, 481)(290, 386, 482)(291, 387, 483)(292, 388, 484)(293, 389, 485)(294, 390, 486)(295, 391, 487)(296, 392, 488)(297, 393, 489)(298, 394, 490)(299, 395, 491)(300, 396, 492)(301, 397, 493)(302, 398, 494)(303, 399, 495)(304, 400, 496)(305, 401, 497)(306, 402, 498)(307, 403, 499)(308, 404, 500)(309, 405, 501)(310, 406, 502)(311, 407, 503)(312, 408, 504)(313, 409, 505)(314, 410, 506)(315, 411, 507)(316, 412, 508)(317, 413, 509)(318, 414, 510)(319, 415, 511)(320, 416, 512)(321, 417, 513)(322, 418, 514)(323, 419, 515)(324, 420, 516)(325, 421, 517)(326, 422, 518)(327, 423, 519)(328, 424, 520)(329, 425, 521)(330, 426, 522)(331, 427, 523)(332, 428, 524)(333, 429, 525)(334, 430, 526)(335, 431, 527)(336, 432, 528)(337, 433, 529)(338, 434, 530)(339, 435, 531)(340, 436, 532)(341, 437, 533)(342, 438, 534)(343, 439, 535)(344, 440, 536)(345, 441, 537)(346, 442, 538)(347, 443, 539)(348, 444, 540)(349, 445, 541)(350, 446, 542)(351, 447, 543)(352, 448, 544)(353, 449, 545)(354, 450, 546)(355, 451, 547)(356, 452, 548)(357, 453, 549)(358, 454, 550)(359, 455, 551)(360, 456, 552)(361, 457, 553)(362, 458, 554)(363, 459, 555)(364, 460, 556)(365, 461, 557)(366, 462, 558)(367, 463, 559)(368, 464, 560)(369, 465, 561)(370, 466, 562)(371, 467, 563)(372, 468, 564)(373, 469, 565)(374, 470, 566)(375, 471, 567)(376, 472, 568)(377, 473, 569)(378, 474, 570)(379, 475, 571)(380, 476, 572)(381, 477, 573)(382, 478, 574)(383, 479, 575)(384, 480, 576) L = (1, 289)(2, 290)(3, 291)(4, 292)(5, 293)(6, 294)(7, 295)(8, 296)(9, 297)(10, 298)(11, 299)(12, 300)(13, 301)(14, 302)(15, 303)(16, 304)(17, 305)(18, 306)(19, 307)(20, 308)(21, 309)(22, 310)(23, 311)(24, 312)(25, 313)(26, 314)(27, 315)(28, 316)(29, 317)(30, 318)(31, 319)(32, 320)(33, 321)(34, 322)(35, 323)(36, 324)(37, 325)(38, 326)(39, 327)(40, 328)(41, 329)(42, 330)(43, 331)(44, 332)(45, 333)(46, 334)(47, 335)(48, 336)(49, 337)(50, 338)(51, 339)(52, 340)(53, 341)(54, 342)(55, 343)(56, 344)(57, 345)(58, 346)(59, 347)(60, 348)(61, 349)(62, 350)(63, 351)(64, 352)(65, 353)(66, 354)(67, 355)(68, 356)(69, 357)(70, 358)(71, 359)(72, 360)(73, 361)(74, 362)(75, 363)(76, 364)(77, 365)(78, 366)(79, 367)(80, 368)(81, 369)(82, 370)(83, 371)(84, 372)(85, 373)(86, 374)(87, 375)(88, 376)(89, 377)(90, 378)(91, 379)(92, 380)(93, 381)(94, 382)(95, 383)(96, 384)(97, 484)(98, 488)(99, 485)(100, 481)(101, 483)(102, 514)(103, 517)(104, 482)(105, 498)(106, 561)(107, 562)(108, 513)(109, 497)(110, 501)(111, 565)(112, 533)(113, 493)(114, 489)(115, 510)(116, 509)(117, 494)(118, 543)(119, 538)(120, 505)(121, 504)(122, 528)(123, 544)(124, 539)(125, 500)(126, 499)(127, 512)(128, 511)(129, 492)(130, 486)(131, 519)(132, 524)(133, 487)(134, 520)(135, 515)(136, 518)(137, 523)(138, 525)(139, 521)(140, 516)(141, 522)(142, 527)(143, 526)(144, 506)(145, 560)(146, 576)(147, 555)(148, 559)(149, 496)(150, 556)(151, 550)(152, 554)(153, 574)(154, 503)(155, 508)(156, 551)(157, 569)(158, 573)(159, 502)(160, 507)(161, 571)(162, 575)(163, 572)(164, 566)(165, 570)(166, 535)(167, 540)(168, 567)(169, 563)(170, 536)(171, 531)(172, 534)(173, 568)(174, 564)(175, 532)(176, 529)(177, 490)(178, 491)(179, 553)(180, 558)(181, 495)(182, 548)(183, 552)(184, 557)(185, 541)(186, 549)(187, 545)(188, 547)(189, 542)(190, 537)(191, 546)(192, 530)(193, 389)(194, 385)(195, 418)(196, 421)(197, 386)(198, 465)(199, 466)(200, 417)(201, 420)(202, 467)(203, 468)(204, 469)(205, 419)(206, 424)(207, 472)(208, 473)(209, 387)(210, 388)(211, 390)(212, 391)(213, 392)(214, 394)(215, 395)(216, 396)(217, 428)(218, 457)(219, 462)(220, 399)(221, 423)(222, 422)(223, 461)(224, 445)(225, 405)(226, 401)(227, 450)(228, 453)(229, 402)(230, 433)(231, 434)(232, 449)(233, 452)(234, 435)(235, 436)(236, 437)(237, 451)(238, 456)(239, 440)(240, 441)(241, 414)(242, 413)(243, 447)(244, 442)(245, 409)(246, 432)(247, 448)(248, 443)(249, 438)(250, 427)(251, 431)(252, 416)(253, 444)(254, 439)(255, 426)(256, 446)(257, 398)(258, 397)(259, 479)(260, 474)(261, 393)(262, 464)(263, 480)(264, 475)(265, 470)(266, 459)(267, 463)(268, 400)(269, 476)(270, 471)(271, 458)(272, 478)(273, 403)(274, 404)(275, 406)(276, 407)(277, 408)(278, 410)(279, 411)(280, 412)(281, 460)(282, 425)(283, 430)(284, 415)(285, 455)(286, 454)(287, 429)(288, 477) MAP : A3.97 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.3 * x.2^2 * x.3^-1 * x.2^-2, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 175)(34, 191)(35, 172)(36, 192)(37, 176)(38, 188)(39, 186)(40, 171)(41, 165)(42, 174)(43, 173)(44, 190)(45, 166)(46, 161)(47, 185)(48, 167)(49, 182)(50, 183)(51, 170)(52, 189)(53, 178)(54, 169)(55, 168)(56, 180)(57, 164)(58, 187)(59, 177)(60, 181)(61, 163)(62, 162)(63, 184)(64, 179)(65, 144)(66, 141)(67, 143)(68, 158)(69, 139)(70, 135)(71, 134)(72, 140)(73, 138)(74, 137)(75, 133)(76, 136)(77, 130)(78, 148)(79, 131)(80, 129)(81, 160)(82, 157)(83, 159)(84, 142)(85, 155)(86, 151)(87, 150)(88, 156)(89, 154)(90, 153)(91, 149)(92, 152)(93, 146)(94, 132)(95, 147)(96, 145) MAP : A3.98 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2)^2, x.3^-1 * x.2^-1 * x.3^3 * x.2^-1, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 163)(34, 179)(35, 168)(36, 177)(37, 161)(38, 184)(39, 185)(40, 165)(41, 171)(42, 180)(43, 162)(44, 164)(45, 167)(46, 176)(47, 186)(48, 166)(49, 183)(50, 182)(51, 169)(52, 178)(53, 189)(54, 170)(55, 172)(56, 174)(57, 190)(58, 181)(59, 192)(60, 187)(61, 175)(62, 173)(63, 188)(64, 191)(65, 143)(66, 159)(67, 140)(68, 160)(69, 144)(70, 156)(71, 154)(72, 139)(73, 133)(74, 142)(75, 141)(76, 158)(77, 134)(78, 129)(79, 153)(80, 135)(81, 150)(82, 151)(83, 138)(84, 157)(85, 146)(86, 137)(87, 136)(88, 148)(89, 132)(90, 155)(91, 145)(92, 149)(93, 131)(94, 130)(95, 152)(96, 147) MAP : A3.99 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.3 * x.2^2 * x.3^-1 * x.2^-2, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 164)(34, 180)(35, 162)(36, 170)(37, 186)(38, 178)(39, 177)(40, 166)(41, 167)(42, 175)(43, 188)(44, 191)(45, 181)(46, 185)(47, 192)(48, 187)(49, 165)(50, 171)(51, 161)(52, 172)(53, 168)(54, 176)(55, 173)(56, 163)(57, 179)(58, 182)(59, 169)(60, 183)(61, 190)(62, 184)(63, 189)(64, 174)(65, 144)(66, 141)(67, 143)(68, 158)(69, 139)(70, 135)(71, 134)(72, 140)(73, 138)(74, 137)(75, 133)(76, 136)(77, 130)(78, 148)(79, 131)(80, 129)(81, 160)(82, 157)(83, 159)(84, 142)(85, 155)(86, 151)(87, 150)(88, 156)(89, 154)(90, 153)(91, 149)(92, 152)(93, 146)(94, 132)(95, 147)(96, 145) MAP : A3.100 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.3 * x.2^2 * x.3^-1 * x.2^-2, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 175)(34, 191)(35, 172)(36, 192)(37, 176)(38, 188)(39, 186)(40, 171)(41, 165)(42, 174)(43, 173)(44, 190)(45, 166)(46, 161)(47, 185)(48, 167)(49, 182)(50, 183)(51, 170)(52, 189)(53, 178)(54, 169)(55, 168)(56, 180)(57, 164)(58, 187)(59, 177)(60, 181)(61, 163)(62, 162)(63, 184)(64, 179)(65, 130)(66, 129)(67, 134)(68, 133)(69, 132)(70, 131)(71, 147)(72, 154)(73, 156)(74, 140)(75, 148)(76, 138)(77, 145)(78, 155)(79, 150)(80, 146)(81, 141)(82, 144)(83, 135)(84, 139)(85, 158)(86, 143)(87, 159)(88, 153)(89, 152)(90, 136)(91, 142)(92, 137)(93, 160)(94, 149)(95, 151)(96, 157) MAP : A3.101 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 163)(34, 169)(35, 185)(36, 165)(37, 168)(38, 186)(39, 184)(40, 179)(41, 170)(42, 177)(43, 180)(44, 190)(45, 187)(46, 178)(47, 183)(48, 191)(49, 162)(50, 166)(51, 164)(52, 167)(53, 161)(54, 172)(55, 173)(56, 171)(57, 181)(58, 174)(59, 175)(60, 189)(61, 176)(62, 192)(63, 188)(64, 182)(65, 130)(66, 134)(67, 132)(68, 135)(69, 129)(70, 140)(71, 141)(72, 139)(73, 149)(74, 142)(75, 143)(76, 157)(77, 144)(78, 160)(79, 156)(80, 150)(81, 131)(82, 137)(83, 153)(84, 133)(85, 136)(86, 154)(87, 152)(88, 147)(89, 138)(90, 145)(91, 148)(92, 158)(93, 155)(94, 146)(95, 151)(96, 159) MAP : A3.102 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 163)(34, 169)(35, 185)(36, 165)(37, 168)(38, 186)(39, 184)(40, 179)(41, 170)(42, 177)(43, 180)(44, 190)(45, 187)(46, 178)(47, 183)(48, 191)(49, 162)(50, 166)(51, 164)(52, 167)(53, 161)(54, 172)(55, 173)(56, 171)(57, 181)(58, 174)(59, 175)(60, 189)(61, 176)(62, 192)(63, 188)(64, 182)(65, 140)(66, 157)(67, 141)(68, 144)(69, 134)(70, 155)(71, 150)(72, 156)(73, 139)(74, 159)(75, 158)(76, 148)(77, 154)(78, 151)(79, 146)(80, 145)(81, 135)(82, 136)(83, 142)(84, 130)(85, 143)(86, 131)(87, 153)(88, 138)(89, 160)(90, 132)(91, 129)(92, 137)(93, 133)(94, 149)(95, 147)(96, 152) MAP : A3.103 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 163)(34, 169)(35, 185)(36, 165)(37, 168)(38, 186)(39, 184)(40, 179)(41, 170)(42, 177)(43, 180)(44, 190)(45, 187)(46, 178)(47, 183)(48, 191)(49, 162)(50, 166)(51, 164)(52, 167)(53, 161)(54, 172)(55, 173)(56, 171)(57, 181)(58, 174)(59, 175)(60, 189)(61, 176)(62, 192)(63, 188)(64, 182)(65, 155)(66, 148)(67, 150)(68, 154)(69, 157)(70, 133)(71, 145)(72, 146)(73, 156)(74, 152)(75, 137)(76, 129)(77, 131)(78, 147)(79, 149)(80, 132)(81, 144)(82, 143)(83, 159)(84, 140)(85, 158)(86, 135)(87, 142)(88, 160)(89, 151)(90, 141)(91, 134)(92, 136)(93, 130)(94, 139)(95, 138)(96, 153) MAP : A3.104 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 168)(34, 163)(35, 162)(36, 185)(37, 167)(38, 169)(39, 165)(40, 161)(41, 166)(42, 181)(43, 179)(44, 186)(45, 184)(46, 177)(47, 180)(48, 187)(49, 174)(50, 192)(51, 171)(52, 175)(53, 170)(54, 191)(55, 188)(56, 173)(57, 164)(58, 172)(59, 176)(60, 183)(61, 190)(62, 189)(63, 182)(64, 178)(65, 131)(66, 137)(67, 153)(68, 133)(69, 136)(70, 154)(71, 152)(72, 147)(73, 138)(74, 145)(75, 148)(76, 158)(77, 155)(78, 146)(79, 151)(80, 159)(81, 130)(82, 134)(83, 132)(84, 135)(85, 129)(86, 140)(87, 141)(88, 139)(89, 149)(90, 142)(91, 143)(92, 157)(93, 144)(94, 160)(95, 156)(96, 150) MAP : A3.105 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2)^2, x.3^-1 * x.2^-1 * x.3^3 * x.2^-1, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 182)(34, 183)(35, 170)(36, 189)(37, 178)(38, 169)(39, 168)(40, 180)(41, 164)(42, 187)(43, 177)(44, 181)(45, 163)(46, 162)(47, 184)(48, 179)(49, 175)(50, 191)(51, 172)(52, 192)(53, 176)(54, 188)(55, 186)(56, 171)(57, 165)(58, 174)(59, 173)(60, 190)(61, 166)(62, 161)(63, 185)(64, 167)(65, 143)(66, 159)(67, 140)(68, 160)(69, 144)(70, 156)(71, 154)(72, 139)(73, 133)(74, 142)(75, 141)(76, 158)(77, 134)(78, 129)(79, 153)(80, 135)(81, 150)(82, 151)(83, 138)(84, 157)(85, 146)(86, 137)(87, 136)(88, 148)(89, 132)(90, 155)(91, 145)(92, 149)(93, 131)(94, 130)(95, 152)(96, 147) MAP : A3.106 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-2 * x.3 * x.2^-2 * x.3^-1, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 162)(34, 166)(35, 164)(36, 167)(37, 161)(38, 172)(39, 173)(40, 171)(41, 181)(42, 174)(43, 175)(44, 189)(45, 176)(46, 192)(47, 188)(48, 182)(49, 163)(50, 169)(51, 185)(52, 165)(53, 168)(54, 186)(55, 184)(56, 179)(57, 170)(58, 177)(59, 180)(60, 190)(61, 187)(62, 178)(63, 183)(64, 191)(65, 132)(66, 149)(67, 138)(68, 129)(69, 139)(70, 145)(71, 147)(72, 153)(73, 142)(74, 131)(75, 133)(76, 146)(77, 148)(78, 137)(79, 152)(80, 151)(81, 134)(82, 140)(83, 135)(84, 141)(85, 130)(86, 157)(87, 144)(88, 143)(89, 136)(90, 160)(91, 156)(92, 155)(93, 150)(94, 159)(95, 158)(96, 154) MAP : A3.107 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.2 * x.3^-1 * x.2^-2 * x.3 * x.2, x.3^-1 * x.2^-1 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 162)(34, 161)(35, 166)(36, 165)(37, 164)(38, 163)(39, 179)(40, 186)(41, 188)(42, 172)(43, 180)(44, 170)(45, 177)(46, 187)(47, 182)(48, 178)(49, 173)(50, 176)(51, 167)(52, 171)(53, 190)(54, 175)(55, 191)(56, 185)(57, 184)(58, 168)(59, 174)(60, 169)(61, 192)(62, 181)(63, 183)(64, 189)(65, 133)(66, 139)(67, 129)(68, 140)(69, 136)(70, 144)(71, 141)(72, 131)(73, 147)(74, 150)(75, 137)(76, 151)(77, 158)(78, 152)(79, 157)(80, 142)(81, 132)(82, 148)(83, 130)(84, 138)(85, 154)(86, 146)(87, 145)(88, 134)(89, 135)(90, 143)(91, 156)(92, 159)(93, 149)(94, 153)(95, 160)(96, 155) MAP : A3.108 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2)^2, x.3^-1 * x.2^-1 * x.3^3 * x.2^-1, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 165)(34, 171)(35, 161)(36, 172)(37, 168)(38, 176)(39, 173)(40, 163)(41, 179)(42, 182)(43, 169)(44, 183)(45, 190)(46, 184)(47, 189)(48, 174)(49, 164)(50, 180)(51, 162)(52, 170)(53, 186)(54, 178)(55, 177)(56, 166)(57, 167)(58, 175)(59, 188)(60, 191)(61, 181)(62, 185)(63, 192)(64, 187)(65, 132)(66, 148)(67, 130)(68, 138)(69, 154)(70, 146)(71, 145)(72, 134)(73, 135)(74, 143)(75, 156)(76, 159)(77, 149)(78, 153)(79, 160)(80, 155)(81, 133)(82, 139)(83, 129)(84, 140)(85, 136)(86, 144)(87, 141)(88, 131)(89, 147)(90, 150)(91, 137)(92, 151)(93, 158)(94, 152)(95, 157)(96, 142) MAP : A3.109 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.2 * x.3^-1 * x.2^-2 * x.3 * x.2, x.3^-1 * x.2^-1 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 162)(34, 161)(35, 166)(36, 165)(37, 164)(38, 163)(39, 179)(40, 186)(41, 188)(42, 172)(43, 180)(44, 170)(45, 177)(46, 187)(47, 182)(48, 178)(49, 173)(50, 176)(51, 167)(52, 171)(53, 190)(54, 175)(55, 191)(56, 185)(57, 184)(58, 168)(59, 174)(60, 169)(61, 192)(62, 181)(63, 183)(64, 189)(65, 158)(66, 142)(67, 141)(68, 137)(69, 153)(70, 157)(71, 160)(72, 135)(73, 134)(74, 131)(75, 152)(76, 147)(77, 155)(78, 154)(79, 145)(80, 149)(81, 139)(82, 133)(83, 144)(84, 136)(85, 140)(86, 129)(87, 130)(88, 143)(89, 159)(90, 151)(91, 138)(92, 150)(93, 132)(94, 156)(95, 146)(96, 148) MAP : A3.110 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 164)(34, 181)(35, 170)(36, 161)(37, 171)(38, 177)(39, 179)(40, 185)(41, 174)(42, 163)(43, 165)(44, 178)(45, 180)(46, 169)(47, 184)(48, 183)(49, 166)(50, 172)(51, 167)(52, 173)(53, 162)(54, 189)(55, 176)(56, 175)(57, 168)(58, 192)(59, 188)(60, 187)(61, 182)(62, 191)(63, 190)(64, 186)(65, 146)(66, 150)(67, 148)(68, 151)(69, 145)(70, 156)(71, 157)(72, 155)(73, 133)(74, 158)(75, 159)(76, 141)(77, 160)(78, 144)(79, 140)(80, 134)(81, 147)(82, 153)(83, 137)(84, 149)(85, 152)(86, 138)(87, 136)(88, 131)(89, 154)(90, 129)(91, 132)(92, 142)(93, 139)(94, 130)(95, 135)(96, 143) MAP : A3.111 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 164)(34, 181)(35, 170)(36, 161)(37, 171)(38, 177)(39, 179)(40, 185)(41, 174)(42, 163)(43, 165)(44, 178)(45, 180)(46, 169)(47, 184)(48, 183)(49, 166)(50, 172)(51, 167)(52, 173)(53, 162)(54, 189)(55, 176)(56, 175)(57, 168)(58, 192)(59, 188)(60, 187)(61, 182)(62, 191)(63, 190)(64, 186)(65, 149)(66, 145)(67, 129)(68, 147)(69, 132)(70, 146)(71, 148)(72, 133)(73, 130)(74, 137)(75, 152)(76, 150)(77, 151)(78, 154)(79, 155)(80, 157)(81, 138)(82, 142)(83, 136)(84, 139)(85, 153)(86, 160)(87, 143)(88, 135)(89, 131)(90, 134)(91, 141)(92, 159)(93, 156)(94, 140)(95, 144)(96, 158) MAP : A3.112 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 164)(34, 181)(35, 170)(36, 161)(37, 171)(38, 177)(39, 179)(40, 185)(41, 174)(42, 163)(43, 165)(44, 178)(45, 180)(46, 169)(47, 184)(48, 183)(49, 166)(50, 172)(51, 167)(52, 173)(53, 162)(54, 189)(55, 176)(56, 175)(57, 168)(58, 192)(59, 188)(60, 187)(61, 182)(62, 191)(63, 190)(64, 186)(65, 154)(66, 158)(67, 152)(68, 155)(69, 137)(70, 144)(71, 159)(72, 151)(73, 147)(74, 150)(75, 157)(76, 143)(77, 140)(78, 156)(79, 160)(80, 142)(81, 133)(82, 129)(83, 145)(84, 131)(85, 148)(86, 130)(87, 132)(88, 149)(89, 146)(90, 153)(91, 136)(92, 134)(93, 135)(94, 138)(95, 139)(96, 141) MAP : A3.113 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-2 * x.3 * x.2^-2 * x.3^-1, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 165)(34, 161)(35, 177)(36, 163)(37, 180)(38, 162)(39, 164)(40, 181)(41, 178)(42, 185)(43, 168)(44, 166)(45, 167)(46, 170)(47, 171)(48, 173)(49, 186)(50, 190)(51, 184)(52, 187)(53, 169)(54, 176)(55, 191)(56, 183)(57, 179)(58, 182)(59, 189)(60, 175)(61, 172)(62, 188)(63, 192)(64, 174)(65, 132)(66, 149)(67, 138)(68, 129)(69, 139)(70, 145)(71, 147)(72, 153)(73, 142)(74, 131)(75, 133)(76, 146)(77, 148)(78, 137)(79, 152)(80, 151)(81, 134)(82, 140)(83, 135)(84, 141)(85, 130)(86, 157)(87, 144)(88, 143)(89, 136)(90, 160)(91, 156)(92, 155)(93, 150)(94, 159)(95, 158)(96, 154) MAP : A3.114 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 168)(34, 163)(35, 162)(36, 185)(37, 167)(38, 169)(39, 165)(40, 161)(41, 166)(42, 181)(43, 179)(44, 186)(45, 184)(46, 177)(47, 180)(48, 187)(49, 174)(50, 192)(51, 171)(52, 175)(53, 170)(54, 191)(55, 188)(56, 173)(57, 164)(58, 172)(59, 176)(60, 183)(61, 190)(62, 189)(63, 182)(64, 178)(65, 146)(66, 150)(67, 148)(68, 151)(69, 145)(70, 156)(71, 157)(72, 155)(73, 133)(74, 158)(75, 159)(76, 141)(77, 160)(78, 144)(79, 140)(80, 134)(81, 147)(82, 153)(83, 137)(84, 149)(85, 152)(86, 138)(87, 136)(88, 131)(89, 154)(90, 129)(91, 132)(92, 142)(93, 139)(94, 130)(95, 135)(96, 143) MAP : A3.115 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 168)(34, 163)(35, 162)(36, 185)(37, 167)(38, 169)(39, 165)(40, 161)(41, 166)(42, 181)(43, 179)(44, 186)(45, 184)(46, 177)(47, 180)(48, 187)(49, 174)(50, 192)(51, 171)(52, 175)(53, 170)(54, 191)(55, 188)(56, 173)(57, 164)(58, 172)(59, 176)(60, 183)(61, 190)(62, 189)(63, 182)(64, 178)(65, 149)(66, 145)(67, 129)(68, 147)(69, 132)(70, 146)(71, 148)(72, 133)(73, 130)(74, 137)(75, 152)(76, 150)(77, 151)(78, 154)(79, 155)(80, 157)(81, 138)(82, 142)(83, 136)(84, 139)(85, 153)(86, 160)(87, 143)(88, 135)(89, 131)(90, 134)(91, 141)(92, 159)(93, 156)(94, 140)(95, 144)(96, 158) MAP : A3.116 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 168)(34, 163)(35, 162)(36, 185)(37, 167)(38, 169)(39, 165)(40, 161)(41, 166)(42, 181)(43, 179)(44, 186)(45, 184)(46, 177)(47, 180)(48, 187)(49, 174)(50, 192)(51, 171)(52, 175)(53, 170)(54, 191)(55, 188)(56, 173)(57, 164)(58, 172)(59, 176)(60, 183)(61, 190)(62, 189)(63, 182)(64, 178)(65, 154)(66, 158)(67, 152)(68, 155)(69, 137)(70, 144)(71, 159)(72, 151)(73, 147)(74, 150)(75, 157)(76, 143)(77, 140)(78, 156)(79, 160)(80, 142)(81, 133)(82, 129)(83, 145)(84, 131)(85, 148)(86, 130)(87, 132)(88, 149)(89, 146)(90, 153)(91, 136)(92, 134)(93, 135)(94, 138)(95, 139)(96, 141) MAP : A3.117 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 163)(34, 169)(35, 185)(36, 165)(37, 168)(38, 186)(39, 184)(40, 179)(41, 170)(42, 177)(43, 180)(44, 190)(45, 187)(46, 178)(47, 183)(48, 191)(49, 162)(50, 166)(51, 164)(52, 167)(53, 161)(54, 172)(55, 173)(56, 171)(57, 181)(58, 174)(59, 175)(60, 189)(61, 176)(62, 192)(63, 188)(64, 182)(65, 133)(66, 129)(67, 145)(68, 131)(69, 148)(70, 130)(71, 132)(72, 149)(73, 146)(74, 153)(75, 136)(76, 134)(77, 135)(78, 138)(79, 139)(80, 141)(81, 154)(82, 158)(83, 152)(84, 155)(85, 137)(86, 144)(87, 159)(88, 151)(89, 147)(90, 150)(91, 157)(92, 143)(93, 140)(94, 156)(95, 160)(96, 142) MAP : A3.118 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 181)(34, 177)(35, 161)(36, 179)(37, 164)(38, 178)(39, 180)(40, 165)(41, 162)(42, 169)(43, 184)(44, 182)(45, 183)(46, 186)(47, 187)(48, 189)(49, 170)(50, 174)(51, 168)(52, 171)(53, 185)(54, 192)(55, 175)(56, 167)(57, 163)(58, 166)(59, 173)(60, 191)(61, 188)(62, 172)(63, 176)(64, 190)(65, 130)(66, 134)(67, 132)(68, 135)(69, 129)(70, 140)(71, 141)(72, 139)(73, 149)(74, 142)(75, 143)(76, 157)(77, 144)(78, 160)(79, 156)(80, 150)(81, 131)(82, 137)(83, 153)(84, 133)(85, 136)(86, 154)(87, 152)(88, 147)(89, 138)(90, 145)(91, 148)(92, 158)(93, 155)(94, 146)(95, 151)(96, 159) MAP : A3.119 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 181)(34, 177)(35, 161)(36, 179)(37, 164)(38, 178)(39, 180)(40, 165)(41, 162)(42, 169)(43, 184)(44, 182)(45, 183)(46, 186)(47, 187)(48, 189)(49, 170)(50, 174)(51, 168)(52, 171)(53, 185)(54, 192)(55, 175)(56, 167)(57, 163)(58, 166)(59, 173)(60, 191)(61, 188)(62, 172)(63, 176)(64, 190)(65, 140)(66, 157)(67, 141)(68, 144)(69, 134)(70, 155)(71, 150)(72, 156)(73, 139)(74, 159)(75, 158)(76, 148)(77, 154)(78, 151)(79, 146)(80, 145)(81, 135)(82, 136)(83, 142)(84, 130)(85, 143)(86, 131)(87, 153)(88, 138)(89, 160)(90, 132)(91, 129)(92, 137)(93, 133)(94, 149)(95, 147)(96, 152) MAP : A3.120 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2)^2, x.3^-1 * x.2^-1 * x.3^3 * x.2^-1, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 190)(34, 174)(35, 173)(36, 169)(37, 185)(38, 189)(39, 192)(40, 167)(41, 166)(42, 163)(43, 184)(44, 179)(45, 187)(46, 186)(47, 177)(48, 181)(49, 171)(50, 165)(51, 176)(52, 168)(53, 172)(54, 161)(55, 162)(56, 175)(57, 191)(58, 183)(59, 170)(60, 182)(61, 164)(62, 188)(63, 178)(64, 180)(65, 132)(66, 148)(67, 130)(68, 138)(69, 154)(70, 146)(71, 145)(72, 134)(73, 135)(74, 143)(75, 156)(76, 159)(77, 149)(78, 153)(79, 160)(80, 155)(81, 133)(82, 139)(83, 129)(84, 140)(85, 136)(86, 144)(87, 141)(88, 131)(89, 147)(90, 150)(91, 137)(92, 151)(93, 158)(94, 152)(95, 157)(96, 142) MAP : A3.121 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.2 * x.3^-1 * x.2^-2 * x.3 * x.2, x.3^-1 * x.2^-1 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 162)(34, 161)(35, 166)(36, 165)(37, 164)(38, 163)(39, 179)(40, 186)(41, 188)(42, 172)(43, 180)(44, 170)(45, 177)(46, 187)(47, 182)(48, 178)(49, 173)(50, 176)(51, 167)(52, 171)(53, 190)(54, 175)(55, 191)(56, 185)(57, 184)(58, 168)(59, 174)(60, 169)(61, 192)(62, 181)(63, 183)(64, 189)(65, 150)(66, 151)(67, 138)(68, 157)(69, 146)(70, 137)(71, 136)(72, 148)(73, 132)(74, 155)(75, 145)(76, 149)(77, 131)(78, 130)(79, 152)(80, 147)(81, 143)(82, 159)(83, 140)(84, 160)(85, 144)(86, 156)(87, 154)(88, 139)(89, 133)(90, 142)(91, 141)(92, 158)(93, 134)(94, 129)(95, 153)(96, 135) MAP : A3.122 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 164)(34, 181)(35, 170)(36, 161)(37, 171)(38, 177)(39, 179)(40, 185)(41, 174)(42, 163)(43, 165)(44, 178)(45, 180)(46, 169)(47, 184)(48, 183)(49, 166)(50, 172)(51, 167)(52, 173)(53, 162)(54, 189)(55, 176)(56, 175)(57, 168)(58, 192)(59, 188)(60, 187)(61, 182)(62, 191)(63, 190)(64, 186)(65, 131)(66, 137)(67, 153)(68, 133)(69, 136)(70, 154)(71, 152)(72, 147)(73, 138)(74, 145)(75, 148)(76, 158)(77, 155)(78, 146)(79, 151)(80, 159)(81, 130)(82, 134)(83, 132)(84, 135)(85, 129)(86, 140)(87, 141)(88, 139)(89, 149)(90, 142)(91, 143)(92, 157)(93, 144)(94, 160)(95, 156)(96, 150) MAP : A3.123 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-2 * x.3 * x.2^-2 * x.3^-1, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 172)(34, 189)(35, 173)(36, 176)(37, 166)(38, 187)(39, 182)(40, 188)(41, 171)(42, 191)(43, 190)(44, 180)(45, 186)(46, 183)(47, 178)(48, 177)(49, 167)(50, 168)(51, 174)(52, 162)(53, 175)(54, 163)(55, 185)(56, 170)(57, 192)(58, 164)(59, 161)(60, 169)(61, 165)(62, 181)(63, 179)(64, 184)(65, 136)(66, 131)(67, 130)(68, 153)(69, 135)(70, 137)(71, 133)(72, 129)(73, 134)(74, 149)(75, 147)(76, 154)(77, 152)(78, 145)(79, 148)(80, 155)(81, 142)(82, 160)(83, 139)(84, 143)(85, 138)(86, 159)(87, 156)(88, 141)(89, 132)(90, 140)(91, 144)(92, 151)(93, 158)(94, 157)(95, 150)(96, 146) MAP : A3.124 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-2 * x.3 * x.2^-2 * x.3^-1, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 187)(34, 180)(35, 182)(36, 186)(37, 189)(38, 165)(39, 177)(40, 178)(41, 188)(42, 184)(43, 169)(44, 161)(45, 163)(46, 179)(47, 181)(48, 164)(49, 176)(50, 175)(51, 191)(52, 172)(53, 190)(54, 167)(55, 174)(56, 192)(57, 183)(58, 173)(59, 166)(60, 168)(61, 162)(62, 171)(63, 170)(64, 185)(65, 132)(66, 149)(67, 138)(68, 129)(69, 139)(70, 145)(71, 147)(72, 153)(73, 142)(74, 131)(75, 133)(76, 146)(77, 148)(78, 137)(79, 152)(80, 151)(81, 134)(82, 140)(83, 135)(84, 141)(85, 130)(86, 157)(87, 144)(88, 143)(89, 136)(90, 160)(91, 156)(92, 155)(93, 150)(94, 159)(95, 158)(96, 154) MAP : A3.125 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-2 * x.3 * x.2^-2 * x.3^-1, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 187)(34, 180)(35, 182)(36, 186)(37, 189)(38, 165)(39, 177)(40, 178)(41, 188)(42, 184)(43, 169)(44, 161)(45, 163)(46, 179)(47, 181)(48, 164)(49, 176)(50, 175)(51, 191)(52, 172)(53, 190)(54, 167)(55, 174)(56, 192)(57, 183)(58, 173)(59, 166)(60, 168)(61, 162)(62, 171)(63, 170)(64, 185)(65, 136)(66, 131)(67, 130)(68, 153)(69, 135)(70, 137)(71, 133)(72, 129)(73, 134)(74, 149)(75, 147)(76, 154)(77, 152)(78, 145)(79, 148)(80, 155)(81, 142)(82, 160)(83, 139)(84, 143)(85, 138)(86, 159)(87, 156)(88, 141)(89, 132)(90, 140)(91, 144)(92, 151)(93, 158)(94, 157)(95, 150)(96, 146) MAP : A3.126 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 8, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.2 * x.3^-1 * x.2^-2 * x.3 * x.2, x.3^-1 * x.2^-1 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 162)(34, 161)(35, 166)(36, 165)(37, 164)(38, 163)(39, 179)(40, 186)(41, 188)(42, 172)(43, 180)(44, 170)(45, 177)(46, 187)(47, 182)(48, 178)(49, 173)(50, 176)(51, 167)(52, 171)(53, 190)(54, 175)(55, 191)(56, 185)(57, 184)(58, 168)(59, 174)(60, 169)(61, 192)(62, 181)(63, 183)(64, 189)(65, 131)(66, 147)(67, 136)(68, 145)(69, 129)(70, 152)(71, 153)(72, 133)(73, 139)(74, 148)(75, 130)(76, 132)(77, 135)(78, 144)(79, 154)(80, 134)(81, 151)(82, 150)(83, 137)(84, 146)(85, 157)(86, 138)(87, 140)(88, 142)(89, 158)(90, 149)(91, 160)(92, 155)(93, 143)(94, 141)(95, 156)(96, 159) MAP : A3.127 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-2 * x.3 * x.2^-2 * x.3^-1, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 165)(34, 161)(35, 177)(36, 163)(37, 180)(38, 162)(39, 164)(40, 181)(41, 178)(42, 185)(43, 168)(44, 166)(45, 167)(46, 170)(47, 171)(48, 173)(49, 186)(50, 190)(51, 184)(52, 187)(53, 169)(54, 176)(55, 191)(56, 183)(57, 179)(58, 182)(59, 189)(60, 175)(61, 172)(62, 188)(63, 192)(64, 174)(65, 136)(66, 131)(67, 130)(68, 153)(69, 135)(70, 137)(71, 133)(72, 129)(73, 134)(74, 149)(75, 147)(76, 154)(77, 152)(78, 145)(79, 148)(80, 155)(81, 142)(82, 160)(83, 139)(84, 143)(85, 138)(86, 159)(87, 156)(88, 141)(89, 132)(90, 140)(91, 144)(92, 151)(93, 158)(94, 157)(95, 150)(96, 146) MAP : A3.128 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.43. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.3 * x.2^2 * x.3^-1 * x.2^-2, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 164)(34, 180)(35, 162)(36, 170)(37, 186)(38, 178)(39, 177)(40, 166)(41, 167)(42, 175)(43, 188)(44, 191)(45, 181)(46, 185)(47, 192)(48, 187)(49, 165)(50, 171)(51, 161)(52, 172)(53, 168)(54, 176)(55, 173)(56, 163)(57, 179)(58, 182)(59, 169)(60, 183)(61, 190)(62, 184)(63, 189)(64, 174)(65, 130)(66, 129)(67, 134)(68, 133)(69, 132)(70, 131)(71, 147)(72, 154)(73, 156)(74, 140)(75, 148)(76, 138)(77, 145)(78, 155)(79, 150)(80, 146)(81, 141)(82, 144)(83, 135)(84, 139)(85, 158)(86, 143)(87, 159)(88, 153)(89, 152)(90, 136)(91, 142)(92, 137)(93, 160)(94, 149)(95, 151)(96, 157) MAP : A3.129 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-2 * x.3 * x.2^-2 * x.3^-1, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 172)(34, 189)(35, 173)(36, 176)(37, 166)(38, 187)(39, 182)(40, 188)(41, 171)(42, 191)(43, 190)(44, 180)(45, 186)(46, 183)(47, 178)(48, 177)(49, 167)(50, 168)(51, 174)(52, 162)(53, 175)(54, 163)(55, 185)(56, 170)(57, 192)(58, 164)(59, 161)(60, 169)(61, 165)(62, 181)(63, 179)(64, 184)(65, 132)(66, 149)(67, 138)(68, 129)(69, 139)(70, 145)(71, 147)(72, 153)(73, 142)(74, 131)(75, 133)(76, 146)(77, 148)(78, 137)(79, 152)(80, 151)(81, 134)(82, 140)(83, 135)(84, 141)(85, 130)(86, 157)(87, 144)(88, 143)(89, 136)(90, 160)(91, 156)(92, 155)(93, 150)(94, 159)(95, 158)(96, 154) MAP : A3.130 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 181)(34, 177)(35, 161)(36, 179)(37, 164)(38, 178)(39, 180)(40, 165)(41, 162)(42, 169)(43, 184)(44, 182)(45, 183)(46, 186)(47, 187)(48, 189)(49, 170)(50, 174)(51, 168)(52, 171)(53, 185)(54, 192)(55, 175)(56, 167)(57, 163)(58, 166)(59, 173)(60, 191)(61, 188)(62, 172)(63, 176)(64, 190)(65, 133)(66, 129)(67, 145)(68, 131)(69, 148)(70, 130)(71, 132)(72, 149)(73, 146)(74, 153)(75, 136)(76, 134)(77, 135)(78, 138)(79, 139)(80, 141)(81, 154)(82, 158)(83, 152)(84, 155)(85, 137)(86, 144)(87, 159)(88, 151)(89, 147)(90, 150)(91, 157)(92, 143)(93, 140)(94, 156)(95, 160)(96, 142) MAP : A3.131 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^4, (u.1 * u.2^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-2 * x.3 * x.2^-2 * x.3^-1, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 162)(34, 166)(35, 164)(36, 167)(37, 161)(38, 172)(39, 173)(40, 171)(41, 181)(42, 174)(43, 175)(44, 189)(45, 176)(46, 192)(47, 188)(48, 182)(49, 163)(50, 169)(51, 185)(52, 165)(53, 168)(54, 186)(55, 184)(56, 179)(57, 170)(58, 177)(59, 180)(60, 190)(61, 187)(62, 178)(63, 183)(64, 191)(65, 136)(66, 131)(67, 130)(68, 153)(69, 135)(70, 137)(71, 133)(72, 129)(73, 134)(74, 149)(75, 147)(76, 154)(77, 152)(78, 145)(79, 148)(80, 155)(81, 142)(82, 160)(83, 139)(84, 143)(85, 138)(86, 159)(87, 156)(88, 141)(89, 132)(90, 140)(91, 144)(92, 151)(93, 158)(94, 157)(95, 150)(96, 146) MAP : A3.132 NOTES : type II, reflexible, isomorphic to DBar({4,8}), isomorphic to A3.48. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 8 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^4, (u.3 * u.1^-1)^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3^-1 * x.2^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^8 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 16, 8) #DARTS : 192 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96)(97, 129, 161)(98, 130, 162)(99, 131, 163)(100, 132, 164)(101, 133, 165)(102, 134, 166)(103, 135, 167)(104, 136, 168)(105, 137, 169)(106, 138, 170)(107, 139, 171)(108, 140, 172)(109, 141, 173)(110, 142, 174)(111, 143, 175)(112, 144, 176)(113, 145, 177)(114, 146, 178)(115, 147, 179)(116, 148, 180)(117, 149, 181)(118, 150, 182)(119, 151, 183)(120, 152, 184)(121, 153, 185)(122, 154, 186)(123, 155, 187)(124, 156, 188)(125, 157, 189)(126, 158, 190)(127, 159, 191)(128, 160, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 181)(34, 177)(35, 161)(36, 179)(37, 164)(38, 178)(39, 180)(40, 165)(41, 162)(42, 169)(43, 184)(44, 182)(45, 183)(46, 186)(47, 187)(48, 189)(49, 170)(50, 174)(51, 168)(52, 171)(53, 185)(54, 192)(55, 175)(56, 167)(57, 163)(58, 166)(59, 173)(60, 191)(61, 188)(62, 172)(63, 176)(64, 190)(65, 155)(66, 148)(67, 150)(68, 154)(69, 157)(70, 133)(71, 145)(72, 146)(73, 156)(74, 152)(75, 137)(76, 129)(77, 131)(78, 147)(79, 149)(80, 132)(81, 144)(82, 143)(83, 159)(84, 140)(85, 158)(86, 135)(87, 142)(88, 160)(89, 151)(90, 141)(91, 134)(92, 136)(93, 130)(94, 139)(95, 138)(96, 153) MAP : A3.133 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 12, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^3, x.3^-1 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2^-1, x.3^-3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 24, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 249)(51, 241)(52, 245)(53, 244)(54, 250)(55, 266)(56, 251)(57, 242)(58, 246)(59, 248)(60, 264)(61, 282)(62, 265)(63, 280)(64, 277)(65, 263)(66, 262)(67, 270)(68, 286)(69, 269)(70, 258)(71, 257)(72, 252)(73, 254)(74, 247)(75, 279)(76, 285)(77, 261)(78, 259)(79, 278)(80, 274)(81, 288)(82, 272)(83, 287)(84, 283)(85, 256)(86, 271)(87, 267)(88, 255)(89, 284)(90, 253)(91, 276)(92, 281)(93, 268)(94, 260)(95, 275)(96, 273)(97, 239)(98, 236)(99, 240)(100, 208)(101, 235)(102, 205)(103, 198)(104, 228)(105, 224)(106, 223)(107, 207)(108, 203)(109, 199)(110, 194)(111, 204)(112, 221)(113, 218)(114, 202)(115, 217)(116, 211)(117, 234)(118, 201)(119, 195)(120, 233)(121, 212)(122, 219)(123, 209)(124, 213)(125, 196)(126, 193)(127, 210)(128, 214)(129, 226)(130, 229)(131, 230)(132, 231)(133, 225)(134, 232)(135, 200)(136, 227)(137, 237)(138, 220)(139, 238)(140, 206)(141, 216)(142, 197)(143, 222)(144, 215) MAP : A3.134 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 12, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^3, x.3^-1 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2^-1, x.3^-3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 24, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 249)(51, 241)(52, 245)(53, 244)(54, 250)(55, 266)(56, 251)(57, 242)(58, 246)(59, 248)(60, 264)(61, 282)(62, 265)(63, 280)(64, 277)(65, 263)(66, 262)(67, 270)(68, 286)(69, 269)(70, 258)(71, 257)(72, 252)(73, 254)(74, 247)(75, 279)(76, 285)(77, 261)(78, 259)(79, 278)(80, 274)(81, 288)(82, 272)(83, 287)(84, 283)(85, 256)(86, 271)(87, 267)(88, 255)(89, 284)(90, 253)(91, 276)(92, 281)(93, 268)(94, 260)(95, 275)(96, 273)(97, 197)(98, 193)(99, 200)(100, 216)(101, 194)(102, 195)(103, 196)(104, 198)(105, 232)(106, 229)(107, 213)(108, 210)(109, 201)(110, 203)(111, 209)(112, 211)(113, 238)(114, 222)(115, 231)(116, 237)(117, 206)(118, 215)(119, 221)(120, 199)(121, 230)(122, 226)(123, 220)(124, 223)(125, 214)(126, 204)(127, 219)(128, 212)(129, 235)(130, 239)(131, 228)(132, 233)(133, 236)(134, 240)(135, 208)(136, 205)(137, 227)(138, 225)(139, 234)(140, 202)(141, 224)(142, 207)(143, 218)(144, 217) MAP : A3.135 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 12, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^3, x.3^-1 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2^-1, x.3^-3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 24, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 249)(51, 241)(52, 245)(53, 244)(54, 250)(55, 266)(56, 251)(57, 242)(58, 246)(59, 248)(60, 264)(61, 282)(62, 265)(63, 280)(64, 277)(65, 263)(66, 262)(67, 270)(68, 286)(69, 269)(70, 258)(71, 257)(72, 252)(73, 254)(74, 247)(75, 279)(76, 285)(77, 261)(78, 259)(79, 278)(80, 274)(81, 288)(82, 272)(83, 287)(84, 283)(85, 256)(86, 271)(87, 267)(88, 255)(89, 284)(90, 253)(91, 276)(92, 281)(93, 268)(94, 260)(95, 275)(96, 273)(97, 222)(98, 206)(99, 215)(100, 221)(101, 238)(102, 199)(103, 205)(104, 231)(105, 214)(106, 210)(107, 204)(108, 207)(109, 198)(110, 236)(111, 203)(112, 196)(113, 219)(114, 223)(115, 212)(116, 217)(117, 220)(118, 224)(119, 240)(120, 237)(121, 211)(122, 209)(123, 218)(124, 234)(125, 208)(126, 239)(127, 202)(128, 201)(129, 229)(130, 225)(131, 232)(132, 200)(133, 226)(134, 227)(135, 228)(136, 230)(137, 216)(138, 213)(139, 197)(140, 194)(141, 233)(142, 235)(143, 193)(144, 195) MAP : A3.136 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 12, 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.2 * x.3^-1)^3, x.3 * x.2^3 * x.3^-1 * x.2^-3, (x.1 * x.2^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 24, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 244)(50, 243)(51, 251)(52, 252)(53, 249)(54, 241)(55, 245)(56, 250)(57, 255)(58, 256)(59, 269)(60, 262)(61, 242)(62, 248)(63, 263)(64, 270)(65, 260)(66, 259)(67, 267)(68, 268)(69, 265)(70, 257)(71, 261)(72, 266)(73, 271)(74, 272)(75, 285)(76, 278)(77, 258)(78, 264)(79, 279)(80, 286)(81, 276)(82, 275)(83, 283)(84, 284)(85, 281)(86, 273)(87, 277)(88, 282)(89, 287)(90, 288)(91, 253)(92, 246)(93, 274)(94, 280)(95, 247)(96, 254)(97, 195)(98, 201)(99, 193)(100, 197)(101, 196)(102, 202)(103, 218)(104, 203)(105, 194)(106, 198)(107, 200)(108, 216)(109, 234)(110, 217)(111, 232)(112, 229)(113, 215)(114, 214)(115, 222)(116, 238)(117, 221)(118, 210)(119, 209)(120, 204)(121, 206)(122, 199)(123, 231)(124, 237)(125, 213)(126, 211)(127, 230)(128, 226)(129, 240)(130, 224)(131, 239)(132, 235)(133, 208)(134, 223)(135, 219)(136, 207)(137, 236)(138, 205)(139, 228)(140, 233)(141, 220)(142, 212)(143, 227)(144, 225) MAP : A3.137 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 12, 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.2 * x.3^-1)^3, x.3 * x.2^3 * x.3^-1 * x.2^-3, (x.1 * x.2^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 24, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 260)(50, 259)(51, 267)(52, 268)(53, 265)(54, 257)(55, 261)(56, 266)(57, 271)(58, 272)(59, 285)(60, 278)(61, 258)(62, 264)(63, 279)(64, 286)(65, 276)(66, 275)(67, 283)(68, 284)(69, 281)(70, 273)(71, 277)(72, 282)(73, 287)(74, 288)(75, 253)(76, 246)(77, 274)(78, 280)(79, 247)(80, 254)(81, 244)(82, 243)(83, 251)(84, 252)(85, 249)(86, 241)(87, 245)(88, 250)(89, 255)(90, 256)(91, 269)(92, 262)(93, 242)(94, 248)(95, 263)(96, 270)(97, 232)(98, 216)(99, 229)(100, 226)(101, 200)(102, 213)(103, 210)(104, 197)(105, 225)(106, 227)(107, 230)(108, 231)(109, 209)(110, 214)(111, 237)(112, 220)(113, 205)(114, 199)(115, 236)(116, 239)(117, 198)(118, 206)(119, 222)(120, 194)(121, 235)(122, 228)(123, 240)(124, 208)(125, 238)(126, 215)(127, 224)(128, 223)(129, 201)(130, 196)(131, 202)(132, 218)(133, 195)(134, 203)(135, 204)(136, 193)(137, 234)(138, 233)(139, 217)(140, 211)(141, 207)(142, 221)(143, 212)(144, 219) MAP : A3.138 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 12 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^3, (u.3 * u.1^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2)^2, (x.1 * x.2^-1)^3, x.2^-1 * x.3^4 * x.2^-1 * x.3^-2, x.3^2 * x.2^2 * x.3 * x.2 * x.3 * x.2^2, (x.3 * x.1^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 24, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 245)(50, 241)(51, 248)(52, 264)(53, 242)(54, 243)(55, 244)(56, 246)(57, 280)(58, 277)(59, 261)(60, 258)(61, 249)(62, 251)(63, 257)(64, 259)(65, 286)(66, 270)(67, 279)(68, 285)(69, 254)(70, 263)(71, 269)(72, 247)(73, 278)(74, 274)(75, 268)(76, 271)(77, 262)(78, 252)(79, 267)(80, 260)(81, 283)(82, 287)(83, 276)(84, 281)(85, 284)(86, 288)(87, 256)(88, 253)(89, 275)(90, 273)(91, 282)(92, 250)(93, 272)(94, 255)(95, 266)(96, 265)(97, 230)(98, 237)(99, 226)(100, 225)(101, 231)(102, 220)(103, 223)(104, 238)(105, 229)(106, 232)(107, 227)(108, 228)(109, 219)(110, 224)(111, 233)(112, 234)(113, 198)(114, 205)(115, 194)(116, 193)(117, 199)(118, 236)(119, 239)(120, 206)(121, 197)(122, 200)(123, 195)(124, 196)(125, 235)(126, 240)(127, 201)(128, 202)(129, 214)(130, 221)(131, 210)(132, 209)(133, 215)(134, 204)(135, 207)(136, 222)(137, 213)(138, 216)(139, 211)(140, 212)(141, 203)(142, 208)(143, 217)(144, 218) MAP : A3.139 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 12, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^3, x.3^-1 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2^-1, x.3^-3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 24, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 249)(51, 241)(52, 245)(53, 244)(54, 250)(55, 266)(56, 251)(57, 242)(58, 246)(59, 248)(60, 264)(61, 282)(62, 265)(63, 280)(64, 277)(65, 263)(66, 262)(67, 270)(68, 286)(69, 269)(70, 258)(71, 257)(72, 252)(73, 254)(74, 247)(75, 279)(76, 285)(77, 261)(78, 259)(79, 278)(80, 274)(81, 288)(82, 272)(83, 287)(84, 283)(85, 256)(86, 271)(87, 267)(88, 255)(89, 284)(90, 253)(91, 276)(92, 281)(93, 268)(94, 260)(95, 275)(96, 273)(97, 194)(98, 197)(99, 198)(100, 199)(101, 193)(102, 200)(103, 216)(104, 195)(105, 205)(106, 236)(107, 206)(108, 222)(109, 232)(110, 213)(111, 238)(112, 231)(113, 207)(114, 204)(115, 208)(116, 224)(117, 203)(118, 221)(119, 214)(120, 196)(121, 240)(122, 239)(123, 223)(124, 219)(125, 215)(126, 210)(127, 220)(128, 237)(129, 234)(130, 218)(131, 233)(132, 227)(133, 202)(134, 217)(135, 211)(136, 201)(137, 228)(138, 235)(139, 225)(140, 229)(141, 212)(142, 209)(143, 226)(144, 230) MAP : A3.140 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 12 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^3, (u.3 * u.1^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2)^2, (x.1 * x.2^-1)^3, x.2^-1 * x.3^4 * x.2^-1 * x.3^-2, x.3^2 * x.2^2 * x.3 * x.2 * x.3 * x.2^2, (x.3 * x.1^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 24, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 242)(50, 245)(51, 246)(52, 247)(53, 241)(54, 248)(55, 264)(56, 243)(57, 253)(58, 284)(59, 254)(60, 270)(61, 280)(62, 261)(63, 286)(64, 279)(65, 255)(66, 252)(67, 256)(68, 272)(69, 251)(70, 269)(71, 262)(72, 244)(73, 288)(74, 287)(75, 271)(76, 267)(77, 263)(78, 258)(79, 268)(80, 285)(81, 282)(82, 266)(83, 281)(84, 275)(85, 250)(86, 265)(87, 259)(88, 249)(89, 276)(90, 283)(91, 273)(92, 277)(93, 260)(94, 257)(95, 274)(96, 278)(97, 212)(98, 211)(99, 219)(100, 220)(101, 217)(102, 209)(103, 213)(104, 218)(105, 223)(106, 224)(107, 237)(108, 230)(109, 210)(110, 216)(111, 231)(112, 238)(113, 228)(114, 227)(115, 235)(116, 236)(117, 233)(118, 225)(119, 229)(120, 234)(121, 239)(122, 240)(123, 205)(124, 198)(125, 226)(126, 232)(127, 199)(128, 206)(129, 196)(130, 195)(131, 203)(132, 204)(133, 201)(134, 193)(135, 197)(136, 202)(137, 207)(138, 208)(139, 221)(140, 214)(141, 194)(142, 200)(143, 215)(144, 222) MAP : A3.141 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 12 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^3, (u.3 * u.1^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2)^2, (x.1 * x.2^-1)^3, x.2^-1 * x.3^4 * x.2^-1 * x.3^-2, x.3^2 * x.2^2 * x.3 * x.2 * x.3 * x.2^2, (x.3 * x.1^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 24, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 242)(50, 245)(51, 246)(52, 247)(53, 241)(54, 248)(55, 264)(56, 243)(57, 253)(58, 284)(59, 254)(60, 270)(61, 280)(62, 261)(63, 286)(64, 279)(65, 255)(66, 252)(67, 256)(68, 272)(69, 251)(70, 269)(71, 262)(72, 244)(73, 288)(74, 287)(75, 271)(76, 267)(77, 263)(78, 258)(79, 268)(80, 285)(81, 282)(82, 266)(83, 281)(84, 275)(85, 250)(86, 265)(87, 259)(88, 249)(89, 276)(90, 283)(91, 273)(92, 277)(93, 260)(94, 257)(95, 274)(96, 278)(97, 198)(98, 205)(99, 194)(100, 193)(101, 199)(102, 236)(103, 239)(104, 206)(105, 197)(106, 200)(107, 195)(108, 196)(109, 235)(110, 240)(111, 201)(112, 202)(113, 214)(114, 221)(115, 210)(116, 209)(117, 215)(118, 204)(119, 207)(120, 222)(121, 213)(122, 216)(123, 211)(124, 212)(125, 203)(126, 208)(127, 217)(128, 218)(129, 230)(130, 237)(131, 226)(132, 225)(133, 231)(134, 220)(135, 223)(136, 238)(137, 229)(138, 232)(139, 227)(140, 228)(141, 219)(142, 224)(143, 233)(144, 234) MAP : A3.142 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 12 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.1 * u.2^-1)^3, (u.3 * u.1^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2)^2, (x.1 * x.2^-1)^3, x.2^-1 * x.3^4 * x.2^-1 * x.3^-2, x.3^2 * x.2^2 * x.3 * x.2 * x.3 * x.2^2, (x.3 * x.1^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 24, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 245)(50, 241)(51, 248)(52, 264)(53, 242)(54, 243)(55, 244)(56, 246)(57, 280)(58, 277)(59, 261)(60, 258)(61, 249)(62, 251)(63, 257)(64, 259)(65, 286)(66, 270)(67, 279)(68, 285)(69, 254)(70, 263)(71, 269)(72, 247)(73, 278)(74, 274)(75, 268)(76, 271)(77, 262)(78, 252)(79, 267)(80, 260)(81, 283)(82, 287)(83, 276)(84, 281)(85, 284)(86, 288)(87, 256)(88, 253)(89, 275)(90, 273)(91, 282)(92, 250)(93, 272)(94, 255)(95, 266)(96, 265)(97, 196)(98, 195)(99, 203)(100, 204)(101, 201)(102, 193)(103, 197)(104, 202)(105, 207)(106, 208)(107, 221)(108, 214)(109, 194)(110, 200)(111, 215)(112, 222)(113, 212)(114, 211)(115, 219)(116, 220)(117, 217)(118, 209)(119, 213)(120, 218)(121, 223)(122, 224)(123, 237)(124, 230)(125, 210)(126, 216)(127, 231)(128, 238)(129, 228)(130, 227)(131, 235)(132, 236)(133, 233)(134, 225)(135, 229)(136, 234)(137, 239)(138, 240)(139, 205)(140, 198)(141, 226)(142, 232)(143, 199)(144, 206) MAP : A3.143 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 12, 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.2 * x.3^-1)^3, x.3 * x.2^3 * x.3^-1 * x.2^-3, (x.1 * x.2^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 24, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 278)(50, 285)(51, 274)(52, 273)(53, 279)(54, 268)(55, 271)(56, 286)(57, 277)(58, 280)(59, 275)(60, 276)(61, 267)(62, 272)(63, 281)(64, 282)(65, 246)(66, 253)(67, 242)(68, 241)(69, 247)(70, 284)(71, 287)(72, 254)(73, 245)(74, 248)(75, 243)(76, 244)(77, 283)(78, 288)(79, 249)(80, 250)(81, 262)(82, 269)(83, 258)(84, 257)(85, 263)(86, 252)(87, 255)(88, 270)(89, 261)(90, 264)(91, 259)(92, 260)(93, 251)(94, 256)(95, 265)(96, 266)(97, 232)(98, 216)(99, 229)(100, 226)(101, 200)(102, 213)(103, 210)(104, 197)(105, 225)(106, 227)(107, 230)(108, 231)(109, 209)(110, 214)(111, 237)(112, 220)(113, 205)(114, 199)(115, 236)(116, 239)(117, 198)(118, 206)(119, 222)(120, 194)(121, 235)(122, 228)(123, 240)(124, 208)(125, 238)(126, 215)(127, 224)(128, 223)(129, 201)(130, 196)(131, 202)(132, 218)(133, 195)(134, 203)(135, 204)(136, 193)(137, 234)(138, 233)(139, 217)(140, 211)(141, 207)(142, 221)(143, 212)(144, 219) MAP : A3.144 NOTES : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A3.25. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 12, 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.2 * x.3^-1)^3, x.3 * x.2^3 * x.3^-1 * x.2^-3, (x.1 * x.2^-1)^12 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (4, 24, 6) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 253)(51, 242)(52, 241)(53, 247)(54, 284)(55, 287)(56, 254)(57, 245)(58, 248)(59, 243)(60, 244)(61, 283)(62, 288)(63, 249)(64, 250)(65, 262)(66, 269)(67, 258)(68, 257)(69, 263)(70, 252)(71, 255)(72, 270)(73, 261)(74, 264)(75, 259)(76, 260)(77, 251)(78, 256)(79, 265)(80, 266)(81, 278)(82, 285)(83, 274)(84, 273)(85, 279)(86, 268)(87, 271)(88, 286)(89, 277)(90, 280)(91, 275)(92, 276)(93, 267)(94, 272)(95, 281)(96, 282)(97, 195)(98, 201)(99, 193)(100, 197)(101, 196)(102, 202)(103, 218)(104, 203)(105, 194)(106, 198)(107, 200)(108, 216)(109, 234)(110, 217)(111, 232)(112, 229)(113, 215)(114, 214)(115, 222)(116, 238)(117, 221)(118, 210)(119, 209)(120, 204)(121, 206)(122, 199)(123, 231)(124, 237)(125, 213)(126, 211)(127, 230)(128, 226)(129, 240)(130, 224)(131, 239)(132, 235)(133, 208)(134, 223)(135, 219)(136, 207)(137, 236)(138, 205)(139, 228)(140, 233)(141, 220)(142, 212)(143, 227)(144, 225) MAP : A3.145 NOTES : type I, reflexible, isomorphic to TDual({3,7}), representative. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^3, u.2^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2)^3, x.2^7, x.1 * x.2^-2 * x.1 * x.2 * x.1 * x.2^-2 * x.1 * x.2^-3 * x.1 * x.2^-3 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 6, 7) #DARTS : 504 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168)(169, 472)(170, 469)(171, 360)(172, 467)(173, 374)(174, 465)(175, 466)(176, 375)(177, 486)(178, 487)(179, 484)(180, 382)(181, 482)(182, 389)(183, 392)(184, 481)(185, 413)(186, 416)(187, 430)(188, 357)(189, 359)(190, 372)(191, 355)(192, 358)(193, 415)(194, 414)(195, 383)(196, 400)(197, 380)(198, 384)(199, 381)(200, 387)(201, 411)(202, 428)(203, 426)(204, 431)(205, 427)(206, 495)(207, 494)(208, 444)(209, 412)(210, 395)(211, 397)(212, 394)(213, 464)(214, 403)(215, 396)(216, 461)(217, 410)(218, 409)(219, 393)(220, 425)(221, 401)(222, 442)(223, 441)(224, 402)(225, 349)(226, 352)(227, 342)(228, 453)(229, 455)(230, 468)(231, 451)(232, 454)(233, 440)(234, 437)(235, 456)(236, 435)(237, 470)(238, 433)(239, 434)(240, 471)(241, 347)(242, 340)(243, 338)(244, 343)(245, 339)(246, 399)(247, 398)(248, 356)(249, 422)(250, 423)(251, 420)(252, 502)(253, 418)(254, 485)(255, 488)(256, 417)(257, 346)(258, 345)(259, 361)(260, 337)(261, 377)(262, 354)(263, 353)(264, 378)(265, 351)(266, 350)(267, 503)(268, 368)(269, 500)(270, 504)(271, 501)(272, 483)(273, 348)(274, 363)(275, 365)(276, 362)(277, 432)(278, 379)(279, 364)(280, 429)(281, 474)(282, 473)(283, 489)(284, 457)(285, 497)(286, 450)(287, 449)(288, 498)(289, 475)(290, 460)(291, 458)(292, 463)(293, 459)(294, 367)(295, 366)(296, 452)(297, 476)(298, 491)(299, 493)(300, 490)(301, 344)(302, 499)(303, 492)(304, 341)(305, 477)(306, 480)(307, 462)(308, 445)(309, 447)(310, 436)(311, 443)(312, 446)(313, 479)(314, 478)(315, 407)(316, 496)(317, 404)(318, 408)(319, 405)(320, 419)(321, 376)(322, 373)(323, 448)(324, 371)(325, 438)(326, 369)(327, 370)(328, 439)(329, 390)(330, 391)(331, 388)(332, 406)(333, 386)(334, 421)(335, 424)(336, 385) MAP : A3.146 NOTES : type I, reflexible, isomorphic to TDual({3,7}), isomorphic to A3.145. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^3, u.2^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2)^3, x.2^7, x.1 * x.2^-2 * x.1 * x.2 * x.1 * x.2^-2 * x.1 * x.2^-3 * x.1 * x.2^-3 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 6, 7) #DARTS : 504 R = (1, 169, 337)(2, 170, 338)(3, 171, 339)(4, 172, 340)(5, 173, 341)(6, 174, 342)(7, 175, 343)(8, 176, 344)(9, 177, 345)(10, 178, 346)(11, 179, 347)(12, 180, 348)(13, 181, 349)(14, 182, 350)(15, 183, 351)(16, 184, 352)(17, 185, 353)(18, 186, 354)(19, 187, 355)(20, 188, 356)(21, 189, 357)(22, 190, 358)(23, 191, 359)(24, 192, 360)(25, 193, 361)(26, 194, 362)(27, 195, 363)(28, 196, 364)(29, 197, 365)(30, 198, 366)(31, 199, 367)(32, 200, 368)(33, 201, 369)(34, 202, 370)(35, 203, 371)(36, 204, 372)(37, 205, 373)(38, 206, 374)(39, 207, 375)(40, 208, 376)(41, 209, 377)(42, 210, 378)(43, 211, 379)(44, 212, 380)(45, 213, 381)(46, 214, 382)(47, 215, 383)(48, 216, 384)(49, 217, 385)(50, 218, 386)(51, 219, 387)(52, 220, 388)(53, 221, 389)(54, 222, 390)(55, 223, 391)(56, 224, 392)(57, 225, 393)(58, 226, 394)(59, 227, 395)(60, 228, 396)(61, 229, 397)(62, 230, 398)(63, 231, 399)(64, 232, 400)(65, 233, 401)(66, 234, 402)(67, 235, 403)(68, 236, 404)(69, 237, 405)(70, 238, 406)(71, 239, 407)(72, 240, 408)(73, 241, 409)(74, 242, 410)(75, 243, 411)(76, 244, 412)(77, 245, 413)(78, 246, 414)(79, 247, 415)(80, 248, 416)(81, 249, 417)(82, 250, 418)(83, 251, 419)(84, 252, 420)(85, 253, 421)(86, 254, 422)(87, 255, 423)(88, 256, 424)(89, 257, 425)(90, 258, 426)(91, 259, 427)(92, 260, 428)(93, 261, 429)(94, 262, 430)(95, 263, 431)(96, 264, 432)(97, 265, 433)(98, 266, 434)(99, 267, 435)(100, 268, 436)(101, 269, 437)(102, 270, 438)(103, 271, 439)(104, 272, 440)(105, 273, 441)(106, 274, 442)(107, 275, 443)(108, 276, 444)(109, 277, 445)(110, 278, 446)(111, 279, 447)(112, 280, 448)(113, 281, 449)(114, 282, 450)(115, 283, 451)(116, 284, 452)(117, 285, 453)(118, 286, 454)(119, 287, 455)(120, 288, 456)(121, 289, 457)(122, 290, 458)(123, 291, 459)(124, 292, 460)(125, 293, 461)(126, 294, 462)(127, 295, 463)(128, 296, 464)(129, 297, 465)(130, 298, 466)(131, 299, 467)(132, 300, 468)(133, 301, 469)(134, 302, 470)(135, 303, 471)(136, 304, 472)(137, 305, 473)(138, 306, 474)(139, 307, 475)(140, 308, 476)(141, 309, 477)(142, 310, 478)(143, 311, 479)(144, 312, 480)(145, 313, 481)(146, 314, 482)(147, 315, 483)(148, 316, 484)(149, 317, 485)(150, 318, 486)(151, 319, 487)(152, 320, 488)(153, 321, 489)(154, 322, 490)(155, 323, 491)(156, 324, 492)(157, 325, 493)(158, 326, 494)(159, 327, 495)(160, 328, 496)(161, 329, 497)(162, 330, 498)(163, 331, 499)(164, 332, 500)(165, 333, 501)(166, 334, 502)(167, 335, 503)(168, 336, 504) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168)(169, 428)(170, 411)(171, 413)(172, 410)(173, 472)(174, 395)(175, 412)(176, 469)(177, 426)(178, 425)(179, 409)(180, 441)(181, 393)(182, 434)(183, 433)(184, 394)(185, 431)(186, 430)(187, 359)(188, 416)(189, 356)(190, 360)(191, 357)(192, 339)(193, 427)(194, 444)(195, 442)(196, 447)(197, 443)(198, 463)(199, 462)(200, 436)(201, 494)(202, 495)(203, 492)(204, 358)(205, 490)(206, 341)(207, 344)(208, 489)(209, 429)(210, 432)(211, 446)(212, 365)(213, 367)(214, 348)(215, 363)(216, 366)(217, 504)(218, 501)(219, 368)(220, 499)(221, 350)(222, 497)(223, 498)(224, 351)(225, 387)(226, 380)(227, 378)(228, 383)(229, 379)(230, 415)(231, 414)(232, 364)(233, 389)(234, 392)(235, 382)(236, 485)(237, 487)(238, 500)(239, 483)(240, 486)(241, 386)(242, 385)(243, 369)(244, 377)(245, 353)(246, 362)(247, 361)(248, 354)(249, 424)(250, 421)(251, 488)(252, 419)(253, 502)(254, 417)(255, 418)(256, 503)(257, 388)(258, 371)(259, 373)(260, 370)(261, 448)(262, 355)(263, 372)(264, 445)(265, 406)(266, 407)(267, 404)(268, 478)(269, 402)(270, 493)(271, 496)(272, 401)(273, 391)(274, 390)(275, 479)(276, 376)(277, 476)(278, 480)(279, 477)(280, 491)(281, 455)(282, 454)(283, 399)(284, 464)(285, 396)(286, 400)(287, 397)(288, 403)(289, 452)(290, 459)(291, 461)(292, 458)(293, 384)(294, 475)(295, 460)(296, 381)(297, 342)(298, 343)(299, 340)(300, 398)(301, 338)(302, 405)(303, 408)(304, 337)(305, 450)(306, 449)(307, 457)(308, 465)(309, 473)(310, 482)(311, 481)(312, 474)(313, 352)(314, 349)(315, 440)(316, 347)(317, 422)(318, 345)(319, 346)(320, 423)(321, 451)(322, 468)(323, 466)(324, 471)(325, 467)(326, 375)(327, 374)(328, 484)(329, 453)(330, 456)(331, 470)(332, 437)(333, 439)(334, 420)(335, 435)(336, 438) MAP : A3.147 NOTES : type I, reflexible, isomorphic to TDual({3,8}), representative. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.3 * x.2^-1)^3, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 284)(50, 276)(51, 260)(52, 254)(53, 272)(54, 261)(55, 277)(56, 252)(57, 273)(58, 257)(59, 248)(60, 281)(61, 275)(62, 288)(63, 258)(64, 262)(65, 253)(66, 246)(67, 283)(68, 271)(69, 255)(70, 249)(71, 241)(72, 243)(73, 242)(74, 270)(75, 269)(76, 266)(77, 247)(78, 274)(79, 264)(80, 282)(81, 256)(82, 268)(83, 250)(84, 285)(85, 267)(86, 286)(87, 244)(88, 245)(89, 251)(90, 280)(91, 278)(92, 287)(93, 265)(94, 259)(95, 263)(96, 279)(97, 198)(98, 202)(99, 193)(100, 201)(101, 205)(102, 195)(103, 238)(104, 208)(105, 232)(106, 229)(107, 222)(108, 199)(109, 226)(110, 219)(111, 225)(112, 228)(113, 223)(114, 221)(115, 207)(116, 224)(117, 218)(118, 239)(119, 203)(120, 217)(121, 240)(122, 237)(123, 236)(124, 235)(125, 234)(126, 215)(127, 230)(128, 233)(129, 211)(130, 197)(131, 214)(132, 200)(133, 194)(134, 209)(135, 220)(136, 196)(137, 212)(138, 210)(139, 231)(140, 206)(141, 213)(142, 204)(143, 227)(144, 216) MAP : A3.148 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.3 * x.2^-1)^3, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 263)(50, 265)(51, 264)(52, 279)(53, 280)(54, 258)(55, 269)(56, 251)(57, 262)(58, 275)(59, 281)(60, 248)(61, 257)(62, 244)(63, 261)(64, 273)(65, 250)(66, 255)(67, 286)(68, 243)(69, 246)(70, 256)(71, 287)(72, 271)(73, 285)(74, 268)(75, 277)(76, 274)(77, 267)(78, 266)(79, 260)(80, 245)(81, 249)(82, 270)(83, 253)(84, 242)(85, 247)(86, 283)(87, 288)(88, 282)(89, 252)(90, 272)(91, 259)(92, 241)(93, 276)(94, 278)(95, 284)(96, 254)(97, 198)(98, 202)(99, 193)(100, 201)(101, 205)(102, 195)(103, 238)(104, 208)(105, 232)(106, 229)(107, 222)(108, 199)(109, 226)(110, 219)(111, 225)(112, 228)(113, 223)(114, 221)(115, 207)(116, 224)(117, 218)(118, 239)(119, 203)(120, 217)(121, 240)(122, 237)(123, 236)(124, 235)(125, 234)(126, 215)(127, 230)(128, 233)(129, 211)(130, 197)(131, 214)(132, 200)(133, 194)(134, 209)(135, 220)(136, 196)(137, 212)(138, 210)(139, 231)(140, 206)(141, 213)(142, 204)(143, 227)(144, 216) MAP : A3.149 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.3 * x.2^-1)^3, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 284)(50, 276)(51, 260)(52, 254)(53, 272)(54, 261)(55, 277)(56, 252)(57, 273)(58, 257)(59, 248)(60, 281)(61, 275)(62, 288)(63, 258)(64, 262)(65, 253)(66, 246)(67, 283)(68, 271)(69, 255)(70, 249)(71, 241)(72, 243)(73, 242)(74, 270)(75, 269)(76, 266)(77, 247)(78, 274)(79, 264)(80, 282)(81, 256)(82, 268)(83, 250)(84, 285)(85, 267)(86, 286)(87, 244)(88, 245)(89, 251)(90, 280)(91, 278)(92, 287)(93, 265)(94, 259)(95, 263)(96, 279)(97, 195)(98, 229)(99, 198)(100, 232)(101, 226)(102, 193)(103, 204)(104, 228)(105, 196)(106, 194)(107, 215)(108, 238)(109, 197)(110, 236)(111, 211)(112, 200)(113, 230)(114, 234)(115, 225)(116, 233)(117, 237)(118, 227)(119, 222)(120, 240)(121, 216)(122, 213)(123, 206)(124, 231)(125, 210)(126, 203)(127, 209)(128, 212)(129, 207)(130, 205)(131, 239)(132, 208)(133, 202)(134, 223)(135, 235)(136, 201)(137, 224)(138, 221)(139, 220)(140, 219)(141, 218)(142, 199)(143, 214)(144, 217) MAP : A3.150 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^3, u.2^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2^-1)^3, x.2^8, x.2^2 * x.1 * x.2^-1 * x.1 * x.2^2 * x.1 * x.2^3 * x.1, (x.2^2 * x.1 * x.2^-3 * x.1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288) L = (1, 4)(2, 8)(3, 5)(6, 34)(7, 37)(9, 18)(10, 81)(11, 82)(12, 33)(13, 17)(14, 21)(15, 85)(16, 53)(19, 30)(20, 29)(22, 63)(23, 58)(24, 25)(26, 48)(27, 64)(28, 59)(31, 32)(35, 39)(36, 44)(38, 40)(41, 43)(42, 45)(46, 47)(49, 80)(50, 96)(51, 75)(52, 79)(54, 76)(55, 70)(56, 74)(57, 94)(60, 71)(61, 89)(62, 93)(65, 91)(66, 95)(67, 92)(68, 86)(69, 90)(72, 87)(73, 83)(77, 88)(78, 84)(97, 202)(98, 203)(99, 265)(100, 270)(101, 207)(102, 260)(103, 264)(104, 269)(105, 253)(106, 261)(107, 257)(108, 259)(109, 254)(110, 249)(111, 258)(112, 242)(113, 204)(114, 198)(115, 231)(116, 236)(117, 199)(118, 232)(119, 227)(120, 230)(121, 235)(122, 237)(123, 233)(124, 228)(125, 234)(126, 239)(127, 238)(128, 218)(129, 272)(130, 288)(131, 267)(132, 271)(133, 208)(134, 268)(135, 262)(136, 266)(137, 286)(138, 215)(139, 220)(140, 263)(141, 281)(142, 285)(143, 214)(144, 219)(145, 205)(146, 201)(147, 222)(148, 221)(149, 206)(150, 255)(151, 250)(152, 217)(153, 216)(154, 240)(155, 256)(156, 251)(157, 212)(158, 211)(159, 224)(160, 223)(161, 196)(162, 200)(163, 197)(164, 193)(165, 195)(166, 226)(167, 229)(168, 194)(169, 210)(170, 273)(171, 274)(172, 225)(173, 209)(174, 213)(175, 277)(176, 245)(177, 283)(178, 287)(179, 284)(180, 278)(181, 282)(182, 247)(183, 252)(184, 279)(185, 275)(186, 248)(187, 243)(188, 246)(189, 280)(190, 276)(191, 244)(192, 241) MAP : A3.151 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.3 * x.2^-1)^3, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 245)(50, 241)(51, 268)(52, 257)(53, 259)(54, 244)(55, 243)(56, 246)(57, 277)(58, 251)(59, 258)(60, 261)(61, 252)(62, 253)(63, 288)(64, 269)(65, 248)(66, 279)(67, 242)(68, 266)(69, 254)(70, 247)(71, 280)(72, 274)(73, 263)(74, 249)(75, 271)(76, 262)(77, 264)(78, 273)(79, 270)(80, 283)(81, 267)(82, 256)(83, 281)(84, 284)(85, 260)(86, 285)(87, 250)(88, 286)(89, 255)(90, 278)(91, 276)(92, 272)(93, 287)(94, 265)(95, 282)(96, 275)(97, 195)(98, 229)(99, 198)(100, 232)(101, 226)(102, 193)(103, 204)(104, 228)(105, 196)(106, 194)(107, 215)(108, 238)(109, 197)(110, 236)(111, 211)(112, 200)(113, 230)(114, 234)(115, 225)(116, 233)(117, 237)(118, 227)(119, 222)(120, 240)(121, 216)(122, 213)(123, 206)(124, 231)(125, 210)(126, 203)(127, 209)(128, 212)(129, 207)(130, 205)(131, 239)(132, 208)(133, 202)(134, 223)(135, 235)(136, 201)(137, 224)(138, 221)(139, 220)(140, 219)(141, 218)(142, 199)(143, 214)(144, 217) MAP : A3.152 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.3^-1 * x.2)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 277)(51, 246)(52, 280)(53, 274)(54, 241)(55, 252)(56, 276)(57, 244)(58, 242)(59, 263)(60, 286)(61, 245)(62, 284)(63, 259)(64, 248)(65, 278)(66, 282)(67, 273)(68, 281)(69, 285)(70, 275)(71, 270)(72, 288)(73, 264)(74, 261)(75, 254)(76, 279)(77, 258)(78, 251)(79, 257)(80, 260)(81, 255)(82, 253)(83, 287)(84, 256)(85, 250)(86, 271)(87, 283)(88, 249)(89, 272)(90, 269)(91, 268)(92, 267)(93, 266)(94, 247)(95, 262)(96, 265)(97, 194)(98, 211)(99, 199)(100, 198)(101, 193)(102, 200)(103, 214)(104, 209)(105, 218)(106, 231)(107, 202)(108, 205)(109, 206)(110, 213)(111, 233)(112, 226)(113, 196)(114, 203)(115, 197)(116, 229)(117, 204)(118, 220)(119, 217)(120, 221)(121, 238)(122, 212)(123, 225)(124, 195)(125, 208)(126, 223)(127, 219)(128, 236)(129, 222)(130, 216)(131, 240)(132, 235)(133, 201)(134, 234)(135, 210)(136, 215)(137, 227)(138, 239)(139, 224)(140, 228)(141, 230)(142, 232)(143, 237)(144, 207) MAP : A3.153 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.3^-1 * x.2)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 277)(51, 246)(52, 280)(53, 274)(54, 241)(55, 252)(56, 276)(57, 244)(58, 242)(59, 263)(60, 286)(61, 245)(62, 284)(63, 259)(64, 248)(65, 278)(66, 282)(67, 273)(68, 281)(69, 285)(70, 275)(71, 270)(72, 288)(73, 264)(74, 261)(75, 254)(76, 279)(77, 258)(78, 251)(79, 257)(80, 260)(81, 255)(82, 253)(83, 287)(84, 256)(85, 250)(86, 271)(87, 283)(88, 249)(89, 272)(90, 269)(91, 268)(92, 267)(93, 266)(94, 247)(95, 262)(96, 265)(97, 197)(98, 193)(99, 220)(100, 209)(101, 211)(102, 196)(103, 195)(104, 198)(105, 229)(106, 203)(107, 210)(108, 213)(109, 204)(110, 205)(111, 240)(112, 221)(113, 200)(114, 231)(115, 194)(116, 218)(117, 206)(118, 199)(119, 232)(120, 226)(121, 215)(122, 201)(123, 223)(124, 214)(125, 216)(126, 225)(127, 222)(128, 235)(129, 219)(130, 208)(131, 233)(132, 236)(133, 212)(134, 237)(135, 202)(136, 238)(137, 207)(138, 230)(139, 228)(140, 224)(141, 239)(142, 217)(143, 234)(144, 227) MAP : A3.154 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.3^-1 * x.2)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 277)(51, 246)(52, 280)(53, 274)(54, 241)(55, 252)(56, 276)(57, 244)(58, 242)(59, 263)(60, 286)(61, 245)(62, 284)(63, 259)(64, 248)(65, 278)(66, 282)(67, 273)(68, 281)(69, 285)(70, 275)(71, 270)(72, 288)(73, 264)(74, 261)(75, 254)(76, 279)(77, 258)(78, 251)(79, 257)(80, 260)(81, 255)(82, 253)(83, 287)(84, 256)(85, 250)(86, 271)(87, 283)(88, 249)(89, 272)(90, 269)(91, 268)(92, 267)(93, 266)(94, 247)(95, 262)(96, 265)(97, 215)(98, 217)(99, 216)(100, 231)(101, 232)(102, 210)(103, 221)(104, 203)(105, 214)(106, 227)(107, 233)(108, 200)(109, 209)(110, 196)(111, 213)(112, 225)(113, 202)(114, 207)(115, 238)(116, 195)(117, 198)(118, 208)(119, 239)(120, 223)(121, 237)(122, 220)(123, 229)(124, 226)(125, 219)(126, 218)(127, 212)(128, 197)(129, 201)(130, 222)(131, 205)(132, 194)(133, 199)(134, 235)(135, 240)(136, 234)(137, 204)(138, 224)(139, 211)(140, 193)(141, 228)(142, 230)(143, 236)(144, 206) MAP : A3.155 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, x.2^3, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^4, x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 277)(51, 246)(52, 280)(53, 274)(54, 241)(55, 252)(56, 276)(57, 244)(58, 242)(59, 263)(60, 286)(61, 245)(62, 284)(63, 259)(64, 248)(65, 278)(66, 282)(67, 273)(68, 281)(69, 285)(70, 275)(71, 270)(72, 288)(73, 264)(74, 261)(75, 254)(76, 279)(77, 258)(78, 251)(79, 257)(80, 260)(81, 255)(82, 253)(83, 287)(84, 256)(85, 250)(86, 271)(87, 283)(88, 249)(89, 272)(90, 269)(91, 268)(92, 267)(93, 266)(94, 247)(95, 262)(96, 265)(97, 199)(98, 201)(99, 200)(100, 215)(101, 216)(102, 194)(103, 205)(104, 235)(105, 198)(106, 211)(107, 217)(108, 232)(109, 193)(110, 228)(111, 197)(112, 209)(113, 234)(114, 239)(115, 222)(116, 227)(117, 230)(118, 240)(119, 223)(120, 207)(121, 221)(122, 204)(123, 213)(124, 210)(125, 203)(126, 202)(127, 196)(128, 229)(129, 233)(130, 206)(131, 237)(132, 226)(133, 231)(134, 219)(135, 224)(136, 218)(137, 236)(138, 208)(139, 195)(140, 225)(141, 212)(142, 214)(143, 220)(144, 238) MAP : A3.156 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.3 * x.2^-1)^3, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 245)(50, 241)(51, 268)(52, 257)(53, 259)(54, 244)(55, 243)(56, 246)(57, 277)(58, 251)(59, 258)(60, 261)(61, 252)(62, 253)(63, 288)(64, 269)(65, 248)(66, 279)(67, 242)(68, 266)(69, 254)(70, 247)(71, 280)(72, 274)(73, 263)(74, 249)(75, 271)(76, 262)(77, 264)(78, 273)(79, 270)(80, 283)(81, 267)(82, 256)(83, 281)(84, 284)(85, 260)(86, 285)(87, 250)(88, 286)(89, 255)(90, 278)(91, 276)(92, 272)(93, 287)(94, 265)(95, 282)(96, 275)(97, 198)(98, 202)(99, 193)(100, 201)(101, 205)(102, 195)(103, 238)(104, 208)(105, 232)(106, 229)(107, 222)(108, 199)(109, 226)(110, 219)(111, 225)(112, 228)(113, 223)(114, 221)(115, 207)(116, 224)(117, 218)(118, 239)(119, 203)(120, 217)(121, 240)(122, 237)(123, 236)(124, 235)(125, 234)(126, 215)(127, 230)(128, 233)(129, 211)(130, 197)(131, 214)(132, 200)(133, 194)(134, 209)(135, 220)(136, 196)(137, 212)(138, 210)(139, 231)(140, 206)(141, 213)(142, 204)(143, 227)(144, 216) MAP : A3.157 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.3 * x.2^-1)^3, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 263)(50, 265)(51, 264)(52, 279)(53, 280)(54, 258)(55, 269)(56, 251)(57, 262)(58, 275)(59, 281)(60, 248)(61, 257)(62, 244)(63, 261)(64, 273)(65, 250)(66, 255)(67, 286)(68, 243)(69, 246)(70, 256)(71, 287)(72, 271)(73, 285)(74, 268)(75, 277)(76, 274)(77, 267)(78, 266)(79, 260)(80, 245)(81, 249)(82, 270)(83, 253)(84, 242)(85, 247)(86, 283)(87, 288)(88, 282)(89, 252)(90, 272)(91, 259)(92, 241)(93, 276)(94, 278)(95, 284)(96, 254)(97, 195)(98, 229)(99, 198)(100, 232)(101, 226)(102, 193)(103, 204)(104, 228)(105, 196)(106, 194)(107, 215)(108, 238)(109, 197)(110, 236)(111, 211)(112, 200)(113, 230)(114, 234)(115, 225)(116, 233)(117, 237)(118, 227)(119, 222)(120, 240)(121, 216)(122, 213)(123, 206)(124, 231)(125, 210)(126, 203)(127, 209)(128, 212)(129, 207)(130, 205)(131, 239)(132, 208)(133, 202)(134, 223)(135, 235)(136, 201)(137, 224)(138, 221)(139, 220)(140, 219)(141, 218)(142, 199)(143, 214)(144, 217) MAP : A3.158 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^3, u.2^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2^-1)^3, x.2^8, x.2^2 * x.1 * x.2^-1 * x.1 * x.2^2 * x.1 * x.2^3 * x.1, (x.2^2 * x.1 * x.2^-3 * x.1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 97, 193)(2, 98, 194)(3, 99, 195)(4, 100, 196)(5, 101, 197)(6, 102, 198)(7, 103, 199)(8, 104, 200)(9, 105, 201)(10, 106, 202)(11, 107, 203)(12, 108, 204)(13, 109, 205)(14, 110, 206)(15, 111, 207)(16, 112, 208)(17, 113, 209)(18, 114, 210)(19, 115, 211)(20, 116, 212)(21, 117, 213)(22, 118, 214)(23, 119, 215)(24, 120, 216)(25, 121, 217)(26, 122, 218)(27, 123, 219)(28, 124, 220)(29, 125, 221)(30, 126, 222)(31, 127, 223)(32, 128, 224)(33, 129, 225)(34, 130, 226)(35, 131, 227)(36, 132, 228)(37, 133, 229)(38, 134, 230)(39, 135, 231)(40, 136, 232)(41, 137, 233)(42, 138, 234)(43, 139, 235)(44, 140, 236)(45, 141, 237)(46, 142, 238)(47, 143, 239)(48, 144, 240)(49, 145, 241)(50, 146, 242)(51, 147, 243)(52, 148, 244)(53, 149, 245)(54, 150, 246)(55, 151, 247)(56, 152, 248)(57, 153, 249)(58, 154, 250)(59, 155, 251)(60, 156, 252)(61, 157, 253)(62, 158, 254)(63, 159, 255)(64, 160, 256)(65, 161, 257)(66, 162, 258)(67, 163, 259)(68, 164, 260)(69, 165, 261)(70, 166, 262)(71, 167, 263)(72, 168, 264)(73, 169, 265)(74, 170, 266)(75, 171, 267)(76, 172, 268)(77, 173, 269)(78, 174, 270)(79, 175, 271)(80, 176, 272)(81, 177, 273)(82, 178, 274)(83, 179, 275)(84, 180, 276)(85, 181, 277)(86, 182, 278)(87, 183, 279)(88, 184, 280)(89, 185, 281)(90, 186, 282)(91, 187, 283)(92, 188, 284)(93, 189, 285)(94, 190, 286)(95, 191, 287)(96, 192, 288) L = (1, 4)(2, 8)(3, 5)(6, 34)(7, 37)(9, 18)(10, 81)(11, 82)(12, 33)(13, 17)(14, 21)(15, 85)(16, 53)(19, 30)(20, 29)(22, 63)(23, 58)(24, 25)(26, 48)(27, 64)(28, 59)(31, 32)(35, 39)(36, 44)(38, 40)(41, 43)(42, 45)(46, 47)(49, 80)(50, 96)(51, 75)(52, 79)(54, 76)(55, 70)(56, 74)(57, 94)(60, 71)(61, 89)(62, 93)(65, 91)(66, 95)(67, 92)(68, 86)(69, 90)(72, 87)(73, 83)(77, 88)(78, 84)(97, 195)(98, 196)(99, 198)(100, 199)(101, 200)(102, 202)(103, 203)(104, 204)(105, 236)(106, 265)(107, 270)(108, 207)(109, 231)(110, 230)(111, 269)(112, 253)(113, 197)(114, 193)(115, 226)(116, 229)(117, 194)(118, 273)(119, 274)(120, 225)(121, 228)(122, 275)(123, 276)(124, 277)(125, 227)(126, 232)(127, 280)(128, 281)(129, 206)(130, 205)(131, 287)(132, 282)(133, 201)(134, 272)(135, 288)(136, 283)(137, 278)(138, 267)(139, 271)(140, 208)(141, 284)(142, 279)(143, 266)(144, 286)(145, 211)(146, 212)(147, 214)(148, 215)(149, 216)(150, 218)(151, 219)(152, 220)(153, 268)(154, 233)(155, 238)(156, 223)(157, 263)(158, 262)(159, 237)(160, 285)(161, 213)(162, 209)(163, 258)(164, 261)(165, 210)(166, 241)(167, 242)(168, 257)(169, 260)(170, 243)(171, 244)(172, 245)(173, 259)(174, 264)(175, 248)(176, 249)(177, 222)(178, 221)(179, 255)(180, 250)(181, 217)(182, 240)(183, 256)(184, 251)(185, 246)(186, 235)(187, 239)(188, 224)(189, 252)(190, 247)(191, 234)(192, 254) MAP : A3.159 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, x.2^3, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^4, x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 250)(51, 241)(52, 249)(53, 253)(54, 243)(55, 286)(56, 256)(57, 280)(58, 277)(59, 270)(60, 247)(61, 274)(62, 267)(63, 273)(64, 276)(65, 271)(66, 269)(67, 255)(68, 272)(69, 266)(70, 287)(71, 251)(72, 265)(73, 288)(74, 285)(75, 284)(76, 283)(77, 282)(78, 263)(79, 278)(80, 281)(81, 259)(82, 245)(83, 262)(84, 248)(85, 242)(86, 257)(87, 268)(88, 244)(89, 260)(90, 258)(91, 279)(92, 254)(93, 261)(94, 252)(95, 275)(96, 264)(97, 205)(98, 198)(99, 235)(100, 223)(101, 207)(102, 201)(103, 193)(104, 195)(105, 194)(106, 222)(107, 221)(108, 218)(109, 199)(110, 226)(111, 216)(112, 234)(113, 208)(114, 220)(115, 202)(116, 237)(117, 219)(118, 238)(119, 196)(120, 197)(121, 203)(122, 232)(123, 230)(124, 239)(125, 217)(126, 211)(127, 215)(128, 231)(129, 236)(130, 228)(131, 212)(132, 206)(133, 224)(134, 213)(135, 229)(136, 204)(137, 225)(138, 209)(139, 200)(140, 233)(141, 227)(142, 240)(143, 210)(144, 214) MAP : A3.160 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, x.2^3, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^4, x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 250)(51, 241)(52, 249)(53, 253)(54, 243)(55, 286)(56, 256)(57, 280)(58, 277)(59, 270)(60, 247)(61, 274)(62, 267)(63, 273)(64, 276)(65, 271)(66, 269)(67, 255)(68, 272)(69, 266)(70, 287)(71, 251)(72, 265)(73, 288)(74, 285)(75, 284)(76, 283)(77, 282)(78, 263)(79, 278)(80, 281)(81, 259)(82, 245)(83, 262)(84, 248)(85, 242)(86, 257)(87, 268)(88, 244)(89, 260)(90, 258)(91, 279)(92, 254)(93, 261)(94, 252)(95, 275)(96, 264)(97, 203)(98, 240)(99, 217)(100, 220)(101, 196)(102, 221)(103, 234)(104, 222)(105, 239)(106, 214)(107, 212)(108, 208)(109, 223)(110, 201)(111, 218)(112, 211)(113, 229)(114, 225)(115, 204)(116, 193)(117, 195)(118, 228)(119, 227)(120, 230)(121, 213)(122, 235)(123, 194)(124, 197)(125, 236)(126, 237)(127, 224)(128, 205)(129, 232)(130, 215)(131, 226)(132, 202)(133, 238)(134, 231)(135, 216)(136, 210)(137, 199)(138, 233)(139, 207)(140, 198)(141, 200)(142, 209)(143, 206)(144, 219) MAP : A3.161 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, x.2^3, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^4, x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 250)(51, 241)(52, 249)(53, 253)(54, 243)(55, 286)(56, 256)(57, 280)(58, 277)(59, 270)(60, 247)(61, 274)(62, 267)(63, 273)(64, 276)(65, 271)(66, 269)(67, 255)(68, 272)(69, 266)(70, 287)(71, 251)(72, 265)(73, 288)(74, 285)(75, 284)(76, 283)(77, 282)(78, 263)(79, 278)(80, 281)(81, 259)(82, 245)(83, 262)(84, 248)(85, 242)(86, 257)(87, 268)(88, 244)(89, 260)(90, 258)(91, 279)(92, 254)(93, 261)(94, 252)(95, 275)(96, 264)(97, 213)(98, 209)(99, 236)(100, 225)(101, 227)(102, 212)(103, 211)(104, 214)(105, 197)(106, 219)(107, 226)(108, 229)(109, 220)(110, 221)(111, 208)(112, 237)(113, 216)(114, 199)(115, 210)(116, 234)(117, 222)(118, 215)(119, 200)(120, 194)(121, 231)(122, 217)(123, 239)(124, 230)(125, 232)(126, 193)(127, 238)(128, 203)(129, 235)(130, 224)(131, 201)(132, 204)(133, 228)(134, 205)(135, 218)(136, 206)(137, 223)(138, 198)(139, 196)(140, 240)(141, 207)(142, 233)(143, 202)(144, 195) MAP : A3.162 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, x.2^3, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^4, x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 250)(51, 241)(52, 249)(53, 253)(54, 243)(55, 286)(56, 256)(57, 280)(58, 277)(59, 270)(60, 247)(61, 274)(62, 267)(63, 273)(64, 276)(65, 271)(66, 269)(67, 255)(68, 272)(69, 266)(70, 287)(71, 251)(72, 265)(73, 288)(74, 285)(75, 284)(76, 283)(77, 282)(78, 263)(79, 278)(80, 281)(81, 259)(82, 245)(83, 262)(84, 248)(85, 242)(86, 257)(87, 268)(88, 244)(89, 260)(90, 258)(91, 279)(92, 254)(93, 261)(94, 252)(95, 275)(96, 264)(97, 200)(98, 231)(99, 194)(100, 218)(101, 206)(102, 199)(103, 232)(104, 226)(105, 215)(106, 201)(107, 223)(108, 214)(109, 216)(110, 225)(111, 222)(112, 235)(113, 219)(114, 208)(115, 233)(116, 236)(117, 212)(118, 237)(119, 202)(120, 238)(121, 207)(122, 230)(123, 228)(124, 224)(125, 239)(126, 217)(127, 234)(128, 227)(129, 197)(130, 193)(131, 220)(132, 209)(133, 211)(134, 196)(135, 195)(136, 198)(137, 229)(138, 203)(139, 210)(140, 213)(141, 204)(142, 205)(143, 240)(144, 221) MAP : A3.163 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.3 * x.2^-1)^3, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 242)(50, 259)(51, 247)(52, 246)(53, 241)(54, 248)(55, 262)(56, 257)(57, 266)(58, 279)(59, 250)(60, 253)(61, 254)(62, 261)(63, 281)(64, 274)(65, 244)(66, 251)(67, 245)(68, 277)(69, 252)(70, 268)(71, 265)(72, 269)(73, 286)(74, 260)(75, 273)(76, 243)(77, 256)(78, 271)(79, 267)(80, 284)(81, 270)(82, 264)(83, 288)(84, 283)(85, 249)(86, 282)(87, 258)(88, 263)(89, 275)(90, 287)(91, 272)(92, 276)(93, 278)(94, 280)(95, 285)(96, 255)(97, 198)(98, 202)(99, 193)(100, 201)(101, 205)(102, 195)(103, 238)(104, 208)(105, 232)(106, 229)(107, 222)(108, 199)(109, 226)(110, 219)(111, 225)(112, 228)(113, 223)(114, 221)(115, 207)(116, 224)(117, 218)(118, 239)(119, 203)(120, 217)(121, 240)(122, 237)(123, 236)(124, 235)(125, 234)(126, 215)(127, 230)(128, 233)(129, 211)(130, 197)(131, 214)(132, 200)(133, 194)(134, 209)(135, 220)(136, 196)(137, 212)(138, 210)(139, 231)(140, 206)(141, 213)(142, 204)(143, 227)(144, 216) MAP : A3.164 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.3^-1 * x.2)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 250)(51, 241)(52, 249)(53, 253)(54, 243)(55, 286)(56, 256)(57, 280)(58, 277)(59, 270)(60, 247)(61, 274)(62, 267)(63, 273)(64, 276)(65, 271)(66, 269)(67, 255)(68, 272)(69, 266)(70, 287)(71, 251)(72, 265)(73, 288)(74, 285)(75, 284)(76, 283)(77, 282)(78, 263)(79, 278)(80, 281)(81, 259)(82, 245)(83, 262)(84, 248)(85, 242)(86, 257)(87, 268)(88, 244)(89, 260)(90, 258)(91, 279)(92, 254)(93, 261)(94, 252)(95, 275)(96, 264)(97, 215)(98, 217)(99, 216)(100, 231)(101, 232)(102, 210)(103, 221)(104, 203)(105, 214)(106, 227)(107, 233)(108, 200)(109, 209)(110, 196)(111, 213)(112, 225)(113, 202)(114, 207)(115, 238)(116, 195)(117, 198)(118, 208)(119, 239)(120, 223)(121, 237)(122, 220)(123, 229)(124, 226)(125, 219)(126, 218)(127, 212)(128, 197)(129, 201)(130, 222)(131, 205)(132, 194)(133, 199)(134, 235)(135, 240)(136, 234)(137, 204)(138, 224)(139, 211)(140, 193)(141, 228)(142, 230)(143, 236)(144, 206) MAP : A3.165 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.3^-1 * x.2)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 250)(51, 241)(52, 249)(53, 253)(54, 243)(55, 286)(56, 256)(57, 280)(58, 277)(59, 270)(60, 247)(61, 274)(62, 267)(63, 273)(64, 276)(65, 271)(66, 269)(67, 255)(68, 272)(69, 266)(70, 287)(71, 251)(72, 265)(73, 288)(74, 285)(75, 284)(76, 283)(77, 282)(78, 263)(79, 278)(80, 281)(81, 259)(82, 245)(83, 262)(84, 248)(85, 242)(86, 257)(87, 268)(88, 244)(89, 260)(90, 258)(91, 279)(92, 254)(93, 261)(94, 252)(95, 275)(96, 264)(97, 236)(98, 228)(99, 212)(100, 206)(101, 224)(102, 213)(103, 229)(104, 204)(105, 225)(106, 209)(107, 200)(108, 233)(109, 227)(110, 240)(111, 210)(112, 214)(113, 205)(114, 198)(115, 235)(116, 223)(117, 207)(118, 201)(119, 193)(120, 195)(121, 194)(122, 222)(123, 221)(124, 218)(125, 199)(126, 226)(127, 216)(128, 234)(129, 208)(130, 220)(131, 202)(132, 237)(133, 219)(134, 238)(135, 196)(136, 197)(137, 203)(138, 232)(139, 230)(140, 239)(141, 217)(142, 211)(143, 215)(144, 231) MAP : A3.166 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.3 * x.2^-1)^3, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 242)(50, 259)(51, 247)(52, 246)(53, 241)(54, 248)(55, 262)(56, 257)(57, 266)(58, 279)(59, 250)(60, 253)(61, 254)(62, 261)(63, 281)(64, 274)(65, 244)(66, 251)(67, 245)(68, 277)(69, 252)(70, 268)(71, 265)(72, 269)(73, 286)(74, 260)(75, 273)(76, 243)(77, 256)(78, 271)(79, 267)(80, 284)(81, 270)(82, 264)(83, 288)(84, 283)(85, 249)(86, 282)(87, 258)(88, 263)(89, 275)(90, 287)(91, 272)(92, 276)(93, 278)(94, 280)(95, 285)(96, 255)(97, 195)(98, 229)(99, 198)(100, 232)(101, 226)(102, 193)(103, 204)(104, 228)(105, 196)(106, 194)(107, 215)(108, 238)(109, 197)(110, 236)(111, 211)(112, 200)(113, 230)(114, 234)(115, 225)(116, 233)(117, 237)(118, 227)(119, 222)(120, 240)(121, 216)(122, 213)(123, 206)(124, 231)(125, 210)(126, 203)(127, 209)(128, 212)(129, 207)(130, 205)(131, 239)(132, 208)(133, 202)(134, 223)(135, 235)(136, 201)(137, 224)(138, 221)(139, 220)(140, 219)(141, 218)(142, 199)(143, 214)(144, 217) MAP : A3.167 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, x.2^3, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^4, x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 277)(51, 246)(52, 280)(53, 274)(54, 241)(55, 252)(56, 276)(57, 244)(58, 242)(59, 263)(60, 286)(61, 245)(62, 284)(63, 259)(64, 248)(65, 278)(66, 282)(67, 273)(68, 281)(69, 285)(70, 275)(71, 270)(72, 288)(73, 264)(74, 261)(75, 254)(76, 279)(77, 258)(78, 251)(79, 257)(80, 260)(81, 255)(82, 253)(83, 287)(84, 256)(85, 250)(86, 271)(87, 283)(88, 249)(89, 272)(90, 269)(91, 268)(92, 267)(93, 266)(94, 247)(95, 262)(96, 265)(97, 222)(98, 216)(99, 240)(100, 235)(101, 201)(102, 234)(103, 210)(104, 215)(105, 227)(106, 239)(107, 224)(108, 228)(109, 230)(110, 232)(111, 237)(112, 207)(113, 194)(114, 211)(115, 199)(116, 198)(117, 193)(118, 200)(119, 214)(120, 209)(121, 218)(122, 231)(123, 202)(124, 205)(125, 206)(126, 213)(127, 233)(128, 226)(129, 196)(130, 203)(131, 197)(132, 229)(133, 204)(134, 220)(135, 217)(136, 221)(137, 238)(138, 212)(139, 225)(140, 195)(141, 208)(142, 223)(143, 219)(144, 236) MAP : A3.168 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, x.2^3, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^4, x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 277)(51, 246)(52, 280)(53, 274)(54, 241)(55, 252)(56, 276)(57, 244)(58, 242)(59, 263)(60, 286)(61, 245)(62, 284)(63, 259)(64, 248)(65, 278)(66, 282)(67, 273)(68, 281)(69, 285)(70, 275)(71, 270)(72, 288)(73, 264)(74, 261)(75, 254)(76, 279)(77, 258)(78, 251)(79, 257)(80, 260)(81, 255)(82, 253)(83, 287)(84, 256)(85, 250)(86, 271)(87, 283)(88, 249)(89, 272)(90, 269)(91, 268)(92, 267)(93, 266)(94, 247)(95, 262)(96, 265)(97, 226)(98, 195)(99, 231)(100, 230)(101, 225)(102, 232)(103, 198)(104, 193)(105, 202)(106, 215)(107, 234)(108, 237)(109, 238)(110, 197)(111, 217)(112, 210)(113, 228)(114, 235)(115, 229)(116, 213)(117, 236)(118, 204)(119, 201)(120, 205)(121, 222)(122, 196)(123, 209)(124, 227)(125, 240)(126, 207)(127, 203)(128, 220)(129, 206)(130, 200)(131, 224)(132, 219)(133, 233)(134, 218)(135, 194)(136, 199)(137, 211)(138, 223)(139, 208)(140, 212)(141, 214)(142, 216)(143, 221)(144, 239) MAP : A3.169 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.3^-1 * x.2)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 250)(51, 241)(52, 249)(53, 253)(54, 243)(55, 286)(56, 256)(57, 280)(58, 277)(59, 270)(60, 247)(61, 274)(62, 267)(63, 273)(64, 276)(65, 271)(66, 269)(67, 255)(68, 272)(69, 266)(70, 287)(71, 251)(72, 265)(73, 288)(74, 285)(75, 284)(76, 283)(77, 282)(78, 263)(79, 278)(80, 281)(81, 259)(82, 245)(83, 262)(84, 248)(85, 242)(86, 257)(87, 268)(88, 244)(89, 260)(90, 258)(91, 279)(92, 254)(93, 261)(94, 252)(95, 275)(96, 264)(97, 197)(98, 193)(99, 220)(100, 209)(101, 211)(102, 196)(103, 195)(104, 198)(105, 229)(106, 203)(107, 210)(108, 213)(109, 204)(110, 205)(111, 240)(112, 221)(113, 200)(114, 231)(115, 194)(116, 218)(117, 206)(118, 199)(119, 232)(120, 226)(121, 215)(122, 201)(123, 223)(124, 214)(125, 216)(126, 225)(127, 222)(128, 235)(129, 219)(130, 208)(131, 233)(132, 236)(133, 212)(134, 237)(135, 202)(136, 238)(137, 207)(138, 230)(139, 228)(140, 224)(141, 239)(142, 217)(143, 234)(144, 227) MAP : A3.170 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, x.2^3, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^4, x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 277)(51, 246)(52, 280)(53, 274)(54, 241)(55, 252)(56, 276)(57, 244)(58, 242)(59, 263)(60, 286)(61, 245)(62, 284)(63, 259)(64, 248)(65, 278)(66, 282)(67, 273)(68, 281)(69, 285)(70, 275)(71, 270)(72, 288)(73, 264)(74, 261)(75, 254)(76, 279)(77, 258)(78, 251)(79, 257)(80, 260)(81, 255)(82, 253)(83, 287)(84, 256)(85, 250)(86, 271)(87, 283)(88, 249)(89, 272)(90, 269)(91, 268)(92, 267)(93, 266)(94, 247)(95, 262)(96, 265)(97, 212)(98, 219)(99, 213)(100, 197)(101, 220)(102, 236)(103, 233)(104, 237)(105, 206)(106, 228)(107, 193)(108, 211)(109, 224)(110, 239)(111, 235)(112, 204)(113, 238)(114, 232)(115, 208)(116, 203)(117, 217)(118, 202)(119, 226)(120, 231)(121, 195)(122, 207)(123, 240)(124, 196)(125, 198)(126, 200)(127, 205)(128, 223)(129, 210)(130, 227)(131, 215)(132, 214)(133, 209)(134, 216)(135, 230)(136, 225)(137, 234)(138, 199)(139, 218)(140, 221)(141, 222)(142, 229)(143, 201)(144, 194) MAP : A3.171 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.3^-1 * x.2)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 243)(50, 277)(51, 246)(52, 280)(53, 274)(54, 241)(55, 252)(56, 276)(57, 244)(58, 242)(59, 263)(60, 286)(61, 245)(62, 284)(63, 259)(64, 248)(65, 278)(66, 282)(67, 273)(68, 281)(69, 285)(70, 275)(71, 270)(72, 288)(73, 264)(74, 261)(75, 254)(76, 279)(77, 258)(78, 251)(79, 257)(80, 260)(81, 255)(82, 253)(83, 287)(84, 256)(85, 250)(86, 271)(87, 283)(88, 249)(89, 272)(90, 269)(91, 268)(92, 267)(93, 266)(94, 247)(95, 262)(96, 265)(97, 236)(98, 228)(99, 212)(100, 206)(101, 224)(102, 213)(103, 229)(104, 204)(105, 225)(106, 209)(107, 200)(108, 233)(109, 227)(110, 240)(111, 210)(112, 214)(113, 205)(114, 198)(115, 235)(116, 223)(117, 207)(118, 201)(119, 193)(120, 195)(121, 194)(122, 222)(123, 221)(124, 218)(125, 199)(126, 226)(127, 216)(128, 234)(129, 208)(130, 220)(131, 202)(132, 237)(133, 219)(134, 238)(135, 196)(136, 197)(137, 203)(138, 232)(139, 230)(140, 239)(141, 217)(142, 211)(143, 215)(144, 231) MAP : A3.172 NOTES : type I, reflexible, isomorphic to TDual({3,8}), isomorphic to A3.147. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.3^-1 * x.2)^3, (x.1 * x.2^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 8) #DARTS : 288 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144)(145, 193, 241)(146, 194, 242)(147, 195, 243)(148, 196, 244)(149, 197, 245)(150, 198, 246)(151, 199, 247)(152, 200, 248)(153, 201, 249)(154, 202, 250)(155, 203, 251)(156, 204, 252)(157, 205, 253)(158, 206, 254)(159, 207, 255)(160, 208, 256)(161, 209, 257)(162, 210, 258)(163, 211, 259)(164, 212, 260)(165, 213, 261)(166, 214, 262)(167, 215, 263)(168, 216, 264)(169, 217, 265)(170, 218, 266)(171, 219, 267)(172, 220, 268)(173, 221, 269)(174, 222, 270)(175, 223, 271)(176, 224, 272)(177, 225, 273)(178, 226, 274)(179, 227, 275)(180, 228, 276)(181, 229, 277)(182, 230, 278)(183, 231, 279)(184, 232, 280)(185, 233, 281)(186, 234, 282)(187, 235, 283)(188, 236, 284)(189, 237, 285)(190, 238, 286)(191, 239, 287)(192, 240, 288) L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 246)(50, 250)(51, 241)(52, 249)(53, 253)(54, 243)(55, 286)(56, 256)(57, 280)(58, 277)(59, 270)(60, 247)(61, 274)(62, 267)(63, 273)(64, 276)(65, 271)(66, 269)(67, 255)(68, 272)(69, 266)(70, 287)(71, 251)(72, 265)(73, 288)(74, 285)(75, 284)(76, 283)(77, 282)(78, 263)(79, 278)(80, 281)(81, 259)(82, 245)(83, 262)(84, 248)(85, 242)(86, 257)(87, 268)(88, 244)(89, 260)(90, 258)(91, 279)(92, 254)(93, 261)(94, 252)(95, 275)(96, 264)(97, 194)(98, 211)(99, 199)(100, 198)(101, 193)(102, 200)(103, 214)(104, 209)(105, 218)(106, 231)(107, 202)(108, 205)(109, 206)(110, 213)(111, 233)(112, 226)(113, 196)(114, 203)(115, 197)(116, 229)(117, 204)(118, 220)(119, 217)(120, 221)(121, 238)(122, 212)(123, 225)(124, 195)(125, 208)(126, 223)(127, 219)(128, 236)(129, 222)(130, 216)(131, 240)(132, 235)(133, 201)(134, 234)(135, 210)(136, 215)(137, 227)(138, 239)(139, 224)(140, 228)(141, 230)(142, 232)(143, 237)(144, 207) MAP : A3.173 NOTES : type I, reflexible, isomorphic to TDual({3,12}), representative. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 3, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2 * x.3 * x.2^-2 * x.3, x.2^6, (x.3 * x.1^-1)^3, (x.2 * x.3^-1)^3, (x.1 * x.2^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 12) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 131)(26, 134)(27, 121)(28, 135)(29, 136)(30, 122)(31, 124)(32, 125)(33, 139)(34, 142)(35, 129)(36, 143)(37, 144)(38, 130)(39, 132)(40, 133)(41, 123)(42, 126)(43, 137)(44, 127)(45, 128)(46, 138)(47, 140)(48, 141)(49, 98)(50, 101)(51, 103)(52, 107)(53, 97)(54, 111)(55, 114)(56, 119)(57, 108)(58, 116)(59, 109)(60, 110)(61, 100)(62, 105)(63, 117)(64, 106)(65, 104)(66, 99)(67, 118)(68, 112)(69, 102)(70, 120)(71, 113)(72, 115) MAP : A3.174 NOTES : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A3.173. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 6 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2 * x.3^-2 * x.2 * x.3, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 12) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 122)(26, 125)(27, 127)(28, 131)(29, 121)(30, 135)(31, 138)(32, 143)(33, 132)(34, 140)(35, 133)(36, 134)(37, 124)(38, 129)(39, 141)(40, 130)(41, 128)(42, 123)(43, 142)(44, 136)(45, 126)(46, 144)(47, 137)(48, 139)(49, 107)(50, 110)(51, 97)(52, 111)(53, 112)(54, 98)(55, 100)(56, 101)(57, 115)(58, 118)(59, 105)(60, 119)(61, 120)(62, 106)(63, 108)(64, 109)(65, 99)(66, 102)(67, 113)(68, 103)(69, 104)(70, 114)(71, 116)(72, 117) MAP : A3.175 NOTES : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A3.173. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 6 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2 * x.3^-2 * x.2 * x.3, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 12) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 125)(26, 121)(27, 138)(28, 133)(29, 122)(30, 141)(31, 123)(32, 137)(33, 134)(34, 136)(35, 124)(36, 129)(37, 131)(38, 132)(39, 126)(40, 140)(41, 143)(42, 127)(43, 144)(44, 130)(45, 135)(46, 139)(47, 128)(48, 142)(49, 99)(50, 102)(51, 113)(52, 103)(53, 104)(54, 114)(55, 116)(56, 117)(57, 107)(58, 110)(59, 97)(60, 111)(61, 112)(62, 98)(63, 100)(64, 101)(65, 115)(66, 118)(67, 105)(68, 119)(69, 120)(70, 106)(71, 108)(72, 109) MAP : A3.176 NOTES : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A3.173. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 6, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^3, x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1, (x.2^2 * x.3^-1 * x.2)^3 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 12) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 122)(26, 125)(27, 127)(28, 131)(29, 121)(30, 135)(31, 138)(32, 143)(33, 132)(34, 140)(35, 133)(36, 134)(37, 124)(38, 129)(39, 141)(40, 130)(41, 128)(42, 123)(43, 142)(44, 136)(45, 126)(46, 144)(47, 137)(48, 139)(49, 102)(50, 104)(51, 116)(52, 97)(53, 99)(54, 100)(55, 118)(56, 108)(57, 111)(58, 119)(59, 112)(60, 98)(61, 103)(62, 107)(63, 120)(64, 110)(65, 117)(66, 113)(67, 106)(68, 101)(69, 114)(70, 109)(71, 115)(72, 105) MAP : A3.177 NOTES : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A3.173. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 6, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^3, x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1, (x.2^2 * x.3^-1 * x.2)^3 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 12) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 125)(26, 121)(27, 138)(28, 133)(29, 122)(30, 141)(31, 123)(32, 137)(33, 134)(34, 136)(35, 124)(36, 129)(37, 131)(38, 132)(39, 126)(40, 140)(41, 143)(42, 127)(43, 144)(44, 130)(45, 135)(46, 139)(47, 128)(48, 142)(49, 100)(50, 108)(51, 101)(52, 102)(53, 116)(54, 97)(55, 109)(56, 98)(57, 120)(58, 115)(59, 110)(60, 104)(61, 118)(62, 112)(63, 105)(64, 107)(65, 114)(66, 117)(67, 119)(68, 99)(69, 113)(70, 103)(71, 106)(72, 111) MAP : A3.178 NOTES : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A3.173. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 12, 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^3, u.2^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2^-1)^3, x.2^-1 * x.1 * x.2^3 * x.1 * x.2^-2, x.2^12 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 6, 12) #DARTS : 144 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144) L = (1, 3)(2, 9)(4, 5)(6, 10)(7, 26)(8, 11)(12, 24)(13, 42)(14, 25)(15, 40)(16, 37)(17, 23)(18, 22)(19, 30)(20, 46)(21, 29)(27, 39)(28, 45)(31, 38)(32, 34)(33, 48)(35, 47)(36, 43)(41, 44)(49, 144)(50, 128)(51, 143)(52, 139)(53, 112)(54, 127)(55, 123)(56, 111)(57, 140)(58, 109)(59, 132)(60, 137)(61, 124)(62, 116)(63, 131)(64, 129)(65, 99)(66, 105)(67, 97)(68, 101)(69, 100)(70, 106)(71, 122)(72, 107)(73, 98)(74, 102)(75, 104)(76, 120)(77, 138)(78, 121)(79, 136)(80, 133)(81, 119)(82, 118)(83, 126)(84, 142)(85, 125)(86, 114)(87, 113)(88, 108)(89, 110)(90, 103)(91, 135)(92, 141)(93, 117)(94, 115)(95, 134)(96, 130) MAP : A3.179 NOTES : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A3.173. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 12, 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^3, u.2^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2^-1)^3, x.2^-1 * x.1 * x.2^3 * x.1 * x.2^-2, x.2^12 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 6, 12) #DARTS : 144 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144) L = (1, 3)(2, 9)(4, 5)(6, 10)(7, 26)(8, 11)(12, 24)(13, 42)(14, 25)(15, 40)(16, 37)(17, 23)(18, 22)(19, 30)(20, 46)(21, 29)(27, 39)(28, 45)(31, 38)(32, 34)(33, 48)(35, 47)(36, 43)(41, 44)(49, 115)(50, 121)(51, 113)(52, 117)(53, 116)(54, 122)(55, 138)(56, 123)(57, 114)(58, 118)(59, 120)(60, 136)(61, 106)(62, 137)(63, 104)(64, 101)(65, 135)(66, 134)(67, 142)(68, 110)(69, 141)(70, 130)(71, 129)(72, 124)(73, 126)(74, 119)(75, 103)(76, 109)(77, 133)(78, 131)(79, 102)(80, 98)(81, 112)(82, 144)(83, 111)(84, 107)(85, 128)(86, 143)(87, 139)(88, 127)(89, 108)(90, 125)(91, 100)(92, 105)(93, 140)(94, 132)(95, 99)(96, 97) MAP : A3.180 NOTES : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A3.173. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 12, 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^3, u.2^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2^-1)^3, x.2^-1 * x.1 * x.2^3 * x.1 * x.2^-2, x.2^12 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 6, 12) #DARTS : 144 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144) L = (1, 3)(2, 9)(4, 5)(6, 10)(7, 26)(8, 11)(12, 24)(13, 42)(14, 25)(15, 40)(16, 37)(17, 23)(18, 22)(19, 30)(20, 46)(21, 29)(27, 39)(28, 45)(31, 38)(32, 34)(33, 48)(35, 47)(36, 43)(41, 44)(49, 102)(50, 109)(51, 98)(52, 97)(53, 103)(54, 140)(55, 143)(56, 110)(57, 101)(58, 104)(59, 99)(60, 100)(61, 139)(62, 144)(63, 105)(64, 106)(65, 118)(66, 125)(67, 114)(68, 113)(69, 119)(70, 108)(71, 111)(72, 126)(73, 117)(74, 120)(75, 115)(76, 116)(77, 107)(78, 112)(79, 121)(80, 122)(81, 134)(82, 141)(83, 130)(84, 129)(85, 135)(86, 124)(87, 127)(88, 142)(89, 133)(90, 136)(91, 131)(92, 132)(93, 123)(94, 128)(95, 137)(96, 138) MAP : A3.181 NOTES : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A3.173. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 3, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.2 * u.3^-1)^3, (u.1 * u.2^-1)^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2 * x.3 * x.2^-2 * x.3, x.2^6, (x.3 * x.1^-1)^3, (x.2 * x.3^-1)^3, (x.1 * x.2^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 6, 12) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 123)(26, 126)(27, 137)(28, 127)(29, 128)(30, 138)(31, 140)(32, 141)(33, 131)(34, 134)(35, 121)(36, 135)(37, 136)(38, 122)(39, 124)(40, 125)(41, 139)(42, 142)(43, 129)(44, 143)(45, 144)(46, 130)(47, 132)(48, 133)(49, 101)(50, 97)(51, 114)(52, 109)(53, 98)(54, 117)(55, 99)(56, 113)(57, 110)(58, 112)(59, 100)(60, 105)(61, 107)(62, 108)(63, 102)(64, 116)(65, 119)(66, 103)(67, 120)(68, 106)(69, 111)(70, 115)(71, 104)(72, 118) MAP : A3.182 NOTES : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A3.173. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 12, 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^3, u.2^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2^-1)^3, x.2^-1 * x.1 * x.2^3 * x.1 * x.2^-2, x.2^12 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 6, 12) #DARTS : 144 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144) L = (1, 3)(2, 9)(4, 5)(6, 10)(7, 26)(8, 11)(12, 24)(13, 42)(14, 25)(15, 40)(16, 37)(17, 23)(18, 22)(19, 30)(20, 46)(21, 29)(27, 39)(28, 45)(31, 38)(32, 34)(33, 48)(35, 47)(36, 43)(41, 44)(49, 100)(50, 99)(51, 107)(52, 108)(53, 105)(54, 97)(55, 101)(56, 106)(57, 111)(58, 112)(59, 125)(60, 118)(61, 98)(62, 104)(63, 119)(64, 126)(65, 116)(66, 115)(67, 123)(68, 124)(69, 121)(70, 113)(71, 117)(72, 122)(73, 127)(74, 128)(75, 141)(76, 134)(77, 114)(78, 120)(79, 135)(80, 142)(81, 132)(82, 131)(83, 139)(84, 140)(85, 137)(86, 129)(87, 133)(88, 138)(89, 143)(90, 144)(91, 109)(92, 102)(93, 130)(94, 136)(95, 103)(96, 110) MAP : A3.183 NOTES : type I, reflexible, isomorphic to TDual({4,6}), representative. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^6, u.3^6, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^2 > CTG (small) : <24, 13> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2^-1)^2, x.3^-3 * x.2^-3, x.3^-3 * x.2^3, x.2^-3 * x.3^3, (x.3 * x.2^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 8, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 66)(26, 49)(27, 68)(28, 51)(29, 70)(30, 53)(31, 72)(32, 55)(33, 50)(34, 57)(35, 52)(36, 59)(37, 54)(38, 61)(39, 56)(40, 63)(41, 58)(42, 65)(43, 60)(44, 67)(45, 62)(46, 69)(47, 64)(48, 71)(97, 136)(98, 132)(99, 135)(100, 125)(101, 143)(102, 130)(103, 141)(104, 124)(105, 133)(106, 127)(107, 129)(108, 144)(109, 140)(110, 128)(111, 122)(112, 126)(113, 123)(114, 142)(115, 134)(116, 138)(117, 121)(118, 131)(119, 139)(120, 137) MAP : A3.184 NOTES : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A3.183. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(3, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^3, (u.3 * u.1 * u.4^-1 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, x.4 * x.2 * x.4^-1 * x.1, (x.4 * x.3^-1)^3, (x.2 * x.1)^3, (x.3 * x.1 * x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.3, x.1, x.4) LOCAL TYPE : (6, 8, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 40)(26, 48)(27, 32)(28, 31)(29, 36)(30, 44)(33, 47)(34, 45)(35, 46)(37, 43)(38, 41)(39, 42)(49, 98)(50, 99)(51, 97)(52, 114)(53, 103)(54, 101)(55, 102)(56, 109)(57, 100)(58, 108)(59, 116)(60, 115)(61, 118)(62, 119)(63, 117)(64, 110)(65, 107)(66, 105)(67, 106)(68, 113)(69, 120)(70, 104)(71, 112)(72, 111)(121, 141)(122, 142)(123, 143)(124, 144)(125, 129)(126, 130)(127, 131)(128, 132)(133, 137)(134, 138)(135, 139)(136, 140) MAP : A3.185 NOTES : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A3.183. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 4 ] UNIGROUP : < u.1, u.2 | u.1^2, u.2^6, (u.1 * u.2^-1)^4 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2 | x.1^2, x.2^6, x.2^-1 * x.1 * x.2^3 * x.1 * x.2^-2, (x.1 * x.2^-1)^4, x.2^-1 * x.1 * x.2^-2 * x.1 * x.2 * x.1 * x.2 * x.1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 8, 8) #DARTS : 144 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144) L = (1, 13)(2, 8)(3, 9)(4, 38)(5, 15)(6, 36)(7, 11)(10, 22)(12, 18)(14, 48)(16, 46)(17, 31)(19, 29)(20, 32)(21, 27)(23, 25)(24, 28)(26, 44)(30, 42)(33, 45)(34, 40)(35, 41)(37, 47)(39, 43)(49, 98)(50, 105)(51, 100)(52, 107)(53, 102)(54, 109)(55, 136)(56, 135)(57, 106)(58, 113)(59, 108)(60, 115)(61, 110)(62, 117)(63, 128)(64, 127)(65, 114)(66, 97)(67, 116)(68, 99)(69, 118)(70, 101)(71, 144)(72, 143)(73, 138)(74, 121)(75, 140)(76, 123)(77, 142)(78, 125)(79, 120)(80, 119)(81, 122)(82, 129)(83, 124)(84, 131)(85, 126)(86, 133)(87, 112)(88, 111)(89, 130)(90, 137)(91, 132)(92, 139)(93, 134)(94, 141)(95, 104)(96, 103) MAP : A3.186 NOTES : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A3.183. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^6, u.3^6, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^2 > CTG (small) : <24, 13> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2^-1)^2, x.3^-3 * x.2^-3, x.3^-3 * x.2^3, x.2^-3 * x.3^3, (x.3 * x.2^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 8, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 50)(26, 57)(27, 52)(28, 59)(29, 54)(30, 61)(31, 56)(32, 63)(33, 58)(34, 65)(35, 60)(36, 67)(37, 62)(38, 69)(39, 64)(40, 71)(41, 66)(42, 49)(43, 68)(44, 51)(45, 70)(46, 53)(47, 72)(48, 55)(97, 141)(98, 135)(99, 137)(100, 128)(101, 124)(102, 136)(103, 130)(104, 134)(105, 131)(106, 126)(107, 142)(108, 122)(109, 129)(110, 139)(111, 123)(112, 121)(113, 144)(114, 140)(115, 143)(116, 133)(117, 127)(118, 138)(119, 125)(120, 132) MAP : A3.187 NOTES : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A3.183. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^3, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^3, (x.3^-1 * x.2^-1)^2, (x.3 * x.1^-1)^3, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 8, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 122)(26, 135)(27, 128)(28, 121)(29, 127)(30, 132)(31, 138)(32, 130)(33, 140)(34, 137)(35, 129)(36, 143)(37, 126)(38, 131)(39, 124)(40, 125)(41, 123)(42, 136)(43, 142)(44, 134)(45, 144)(46, 141)(47, 133)(48, 139)(49, 119)(50, 116)(51, 98)(52, 114)(53, 106)(54, 103)(55, 120)(56, 105)(57, 118)(58, 115)(59, 108)(60, 117)(61, 100)(62, 97)(63, 113)(64, 111)(65, 112)(66, 109)(67, 101)(68, 99)(69, 107)(70, 104)(71, 110)(72, 102) MAP : A3.188 NOTES : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A3.183. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 3, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^3, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1, x.3^4, (x.3^-2 * x.2^-1)^2, x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1, (x.3^-1 * x.2 * x.3^-1)^2, x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 8, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 122)(26, 135)(27, 128)(28, 121)(29, 127)(30, 132)(31, 138)(32, 130)(33, 140)(34, 137)(35, 129)(36, 143)(37, 126)(38, 131)(39, 124)(40, 125)(41, 123)(42, 136)(43, 142)(44, 134)(45, 144)(46, 141)(47, 133)(48, 139)(49, 107)(50, 104)(51, 110)(52, 102)(53, 118)(54, 115)(55, 108)(56, 117)(57, 106)(58, 103)(59, 120)(60, 105)(61, 112)(62, 109)(63, 101)(64, 99)(65, 100)(66, 97)(67, 113)(68, 111)(69, 119)(70, 116)(71, 98)(72, 114) MAP : A3.189 NOTES : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A3.183. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^3, (u.3 * u.1^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, (x.3^-1 * x.2^-1)^2, (x.1 * x.2^-1)^3, (x.3 * x.1^-1)^4, (x.2 * x.3^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (6, 8, 8) #DARTS : 144 R = (1, 25, 49)(2, 26, 50)(3, 27, 51)(4, 28, 52)(5, 29, 53)(6, 30, 54)(7, 31, 55)(8, 32, 56)(9, 33, 57)(10, 34, 58)(11, 35, 59)(12, 36, 60)(13, 37, 61)(14, 38, 62)(15, 39, 63)(16, 40, 64)(17, 41, 65)(18, 42, 66)(19, 43, 67)(20, 44, 68)(21, 45, 69)(22, 46, 70)(23, 47, 71)(24, 48, 72)(73, 97, 121)(74, 98, 122)(75, 99, 123)(76, 100, 124)(77, 101, 125)(78, 102, 126)(79, 103, 127)(80, 104, 128)(81, 105, 129)(82, 106, 130)(83, 107, 131)(84, 108, 132)(85, 109, 133)(86, 110, 134)(87, 111, 135)(88, 112, 136)(89, 113, 137)(90, 114, 138)(91, 115, 139)(92, 116, 140)(93, 117, 141)(94, 118, 142)(95, 119, 143)(96, 120, 144) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 134)(26, 123)(27, 140)(28, 133)(29, 139)(30, 144)(31, 126)(32, 142)(33, 128)(34, 125)(35, 141)(36, 131)(37, 138)(38, 143)(39, 136)(40, 137)(41, 135)(42, 124)(43, 130)(44, 122)(45, 132)(46, 129)(47, 121)(48, 127)(49, 107)(50, 104)(51, 110)(52, 102)(53, 118)(54, 115)(55, 108)(56, 117)(57, 106)(58, 103)(59, 120)(60, 105)(61, 112)(62, 109)(63, 101)(64, 99)(65, 100)(66, 97)(67, 113)(68, 111)(69, 119)(70, 116)(71, 98)(72, 114) MAP : A3.190 NOTES : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A3.183. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 4 ] UNIGROUP : < u.1, u.2 | u.1^2, u.2^6, (u.1 * u.2^-1)^4 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2 | x.1^2, x.2^6, x.2^-1 * x.1 * x.2^3 * x.1 * x.2^-2, (x.1 * x.2^-1)^4, x.2^-1 * x.1 * x.2^-2 * x.1 * x.2 * x.1 * x.2 * x.1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (6, 8, 8) #DARTS : 144 R = (1, 49, 97)(2, 50, 98)(3, 51, 99)(4, 52, 100)(5, 53, 101)(6, 54, 102)(7, 55, 103)(8, 56, 104)(9, 57, 105)(10, 58, 106)(11, 59, 107)(12, 60, 108)(13, 61, 109)(14, 62, 110)(15, 63, 111)(16, 64, 112)(17, 65, 113)(18, 66, 114)(19, 67, 115)(20, 68, 116)(21, 69, 117)(22, 70, 118)(23, 71, 119)(24, 72, 120)(25, 73, 121)(26, 74, 122)(27, 75, 123)(28, 76, 124)(29, 77, 125)(30, 78, 126)(31, 79, 127)(32, 80, 128)(33, 81, 129)(34, 82, 130)(35, 83, 131)(36, 84, 132)(37, 85, 133)(38, 86, 134)(39, 87, 135)(40, 88, 136)(41, 89, 137)(42, 90, 138)(43, 91, 139)(44, 92, 140)(45, 93, 141)(46, 94, 142)(47, 95, 143)(48, 96, 144) L = (1, 4)(2, 5)(3, 40)(6, 7)(8, 45)(9, 24)(10, 19)(11, 46)(12, 23)(13, 44)(14, 17)(15, 42)(16, 27)(18, 39)(20, 37)(21, 32)(22, 35)(25, 28)(26, 29)(30, 31)(33, 48)(34, 43)(36, 47)(38, 41)(49, 98)(50, 105)(51, 100)(52, 107)(53, 102)(54, 109)(55, 136)(56, 135)(57, 106)(58, 113)(59, 108)(60, 115)(61, 110)(62, 117)(63, 128)(64, 127)(65, 114)(66, 97)(67, 116)(68, 99)(69, 118)(70, 101)(71, 144)(72, 143)(73, 138)(74, 121)(75, 140)(76, 123)(77, 142)(78, 125)(79, 120)(80, 119)(81, 122)(82, 129)(83, 124)(84, 131)(85, 126)(86, 133)(87, 112)(88, 111)(89, 130)(90, 137)(91, 132)(92, 139)(93, 134)(94, 141)(95, 104)(96, 103) MAP : A3.191 NOTES : type I, non-Cayley, reflexible, isomorphic to {3,7}, representative. QUOTIENT : R = Id($) L = Id($) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 3 ], faces: [ 7 ] UNIGROUP : < u.1, u.2 | u.1^2, u.2^3, (u.1 * u.2)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.1^2, x.2^3, (x.1 * x.2)^7, (x.1 * x.2^-1 * x.1 * x.2)^4 > SCHREIER VEC. : (x.1)^3 LOCAL TYPE : (7, 7, 7) #DARTS : 168 R = (1, 18, 3)(2, 17, 20)(4, 33, 23)(5, 9, 19)(6, 50, 95)(7, 49, 94)(8, 10, 36)(11, 34, 22)(12, 39, 157)(13, 35, 159)(14, 103, 140)(15, 102, 155)(16, 52, 158)(21, 72, 25)(24, 69, 26)(27, 38, 160)(28, 133, 67)(29, 135, 142)(30, 148, 65)(31, 131, 66)(32, 134, 143)(37, 156, 104)(40, 163, 101)(41, 80, 62)(42, 77, 63)(43, 136, 60)(44, 75, 118)(45, 150, 58)(46, 73, 125)(47, 74, 128)(48, 151, 57)(51, 92, 119)(53, 90, 116)(54, 165, 120)(55, 168, 117)(56, 89, 123)(59, 64, 79)(61, 78, 76)(68, 110, 130)(70, 93, 115)(71, 96, 132)(81, 127, 146)(82, 126, 145)(83, 111, 129)(84, 144, 161)(85, 108, 113)(86, 112, 154)(87, 109, 153)(88, 91, 114)(97, 124, 147)(98, 139, 164)(99, 141, 162)(100, 138, 167)(105, 122, 149)(106, 121, 152)(107, 137, 166) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168) MAP : A3.192 NOTES : type I, non-Cayley, reflexible, isomorphic to {3,7}, isomorphic to A3.191. QUOTIENT : R = Id($) L = Id($) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 3 ], faces: [ 7 ] UNIGROUP : < u.1, u.2 | u.1^2, u.2^3, (u.1 * u.2)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.1^2, x.2^3, (x.1 * x.2)^7, (x.1 * x.2^-1 * x.1 * x.2)^4 > SCHREIER VEC. : (x.1)^3 LOCAL TYPE : (7, 7, 7) #DARTS : 168 R = (1, 75, 84)(2, 92, 99)(3, 90, 101)(4, 95, 98)(5, 91, 120)(6, 159, 107)(7, 158, 100)(8, 108, 117)(9, 77, 82)(10, 80, 81)(11, 94, 97)(12, 21, 65)(13, 23, 105)(14, 36, 58)(15, 19, 57)(16, 22, 106)(17, 74, 87)(18, 73, 86)(20, 89, 104)(24, 66, 27)(25, 136, 83)(26, 133, 68)(28, 131, 71)(29, 38, 67)(30, 129, 143)(31, 130, 142)(32, 39, 60)(33, 76, 166)(34, 59, 167)(35, 61, 164)(37, 128, 162)(40, 125, 161)(41, 150, 85)(42, 151, 88)(43, 148, 70)(44, 46, 53)(45, 146, 55)(47, 56, 51)(48, 145, 54)(49, 79, 152)(50, 78, 149)(52, 64, 147)(62, 168, 103)(63, 165, 102)(69, 96, 135)(72, 93, 134)(109, 119, 156)(110, 132, 160)(111, 115, 157)(112, 118, 163)(113, 140, 127)(114, 155, 126)(116, 154, 144)(121, 138, 124)(122, 137, 139)(123, 153, 141) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168) MAP : A3.193 NOTES : type I, non-biCayley, reflexible, isomorphic to {3,8}, representative. QUOTIENT : R = Id($) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3, 3 ], faces: [ 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2 * u.1^-1 * u.3)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2 * x.1^-1 * x.3)^4 > SCHREIER VEC. : (x.1)^3 LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 6, 3)(2, 10, 37)(4, 9, 40)(5, 13, 34)(7, 46, 12)(8, 16, 36)(11, 30, 23)(14, 27, 44)(15, 33, 19)(17, 31, 38)(18, 29, 42)(20, 32, 41)(21, 26, 45)(22, 47, 35)(24, 25, 48)(28, 43, 39)(49, 68, 59)(50, 75, 96)(51, 69, 73)(52, 53, 76)(54, 92, 77)(55, 89, 90)(56, 93, 78)(57, 62, 95)(58, 84, 70)(60, 67, 64)(61, 80, 79)(63, 91, 74)(65, 94, 85)(66, 88, 81)(71, 82, 83)(72, 87, 86) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) MAP : A3.194 NOTES : type I, non-biCayley, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = Id($) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3, 3 ], faces: [ 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2 * u.1^-1 * u.3)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2 * x.1^-1 * x.3)^4 > SCHREIER VEC. : (x.1)^3 LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 6, 3)(2, 10, 37)(4, 9, 40)(5, 13, 34)(7, 46, 12)(8, 16, 36)(11, 30, 23)(14, 27, 44)(15, 33, 19)(17, 31, 38)(18, 29, 42)(20, 32, 41)(21, 26, 45)(22, 47, 35)(24, 25, 48)(28, 43, 39)(49, 78, 69)(50, 72, 65)(51, 96, 92)(52, 91, 81)(53, 57, 83)(54, 90, 68)(55, 66, 67)(56, 71, 70)(58, 95, 75)(59, 80, 82)(60, 84, 85)(61, 86, 76)(62, 88, 77)(63, 93, 64)(73, 74, 87)(79, 89, 94) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) MAP : A3.195 NOTES : type I, non-Cayley, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = Id($) L = Id($) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 3 ], faces: [ 8 ] UNIGROUP : < u.1, u.2 | u.1^2, u.2^3, (u.1 * u.2)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.1^2, x.2^3, (x.1 * x.2 * x.1 * x.2^-1)^3, (x.1 * x.2)^8 > SCHREIER VEC. : (x.1)^3 LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 2, 5)(3, 17, 34)(4, 18, 37)(6, 19, 81)(7, 20, 82)(8, 21, 33)(9, 69, 36)(10, 22, 83)(11, 23, 84)(12, 24, 85)(13, 66, 35)(14, 65, 40)(15, 28, 88)(16, 76, 89)(25, 53, 44)(26, 86, 73)(27, 87, 78)(29, 50, 39)(30, 49, 38)(31, 92, 77)(32, 60, 61)(41, 90, 68)(42, 63, 51)(43, 58, 52)(45, 95, 67)(46, 91, 72)(47, 59, 56)(48, 54, 57)(55, 62, 64)(70, 94, 80)(71, 93, 96)(74, 79, 75) L = (1, 4)(2, 8)(3, 5)(6, 34)(7, 37)(9, 18)(10, 81)(11, 82)(12, 33)(13, 17)(14, 21)(15, 85)(16, 53)(19, 30)(20, 29)(22, 63)(23, 58)(24, 25)(26, 48)(27, 64)(28, 59)(31, 32)(35, 39)(36, 44)(38, 40)(41, 43)(42, 45)(46, 47)(49, 80)(50, 96)(51, 75)(52, 79)(54, 76)(55, 70)(56, 74)(57, 94)(60, 71)(61, 89)(62, 93)(65, 91)(66, 95)(67, 92)(68, 86)(69, 90)(72, 87)(73, 83)(77, 88)(78, 84) MAP : A3.196 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 95)(18, 84)(19, 88)(20, 93)(21, 89)(22, 94)(23, 85)(24, 86)(25, 96)(26, 81)(27, 90)(28, 82)(29, 92)(30, 83)(31, 91)(32, 87)(33, 71)(34, 74)(35, 77)(36, 65)(37, 67)(38, 66)(39, 78)(40, 76)(41, 72)(42, 80)(43, 73)(44, 75)(45, 79)(46, 68)(47, 69)(48, 70) MAP : A3.197 NOTES : type I, non-biCayley, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = Id($) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3, 3 ], faces: [ 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2 * u.1^-1 * u.3)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2 * x.1^-1 * x.3)^4 > SCHREIER VEC. : (x.1)^3 LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 6, 3)(2, 10, 37)(4, 9, 40)(5, 13, 34)(7, 46, 12)(8, 16, 36)(11, 30, 23)(14, 27, 44)(15, 33, 19)(17, 31, 38)(18, 29, 42)(20, 32, 41)(21, 26, 45)(22, 47, 35)(24, 25, 48)(28, 43, 39)(49, 82, 56)(50, 51, 87)(52, 86, 74)(53, 81, 62)(54, 88, 55)(57, 58, 71)(59, 90, 79)(60, 93, 70)(61, 94, 72)(63, 73, 78)(64, 66, 91)(65, 84, 75)(67, 85, 89)(68, 69, 92)(76, 83, 80)(77, 96, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) MAP : A3.198 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 95)(18, 84)(19, 88)(20, 93)(21, 89)(22, 94)(23, 85)(24, 86)(25, 96)(26, 81)(27, 90)(28, 82)(29, 92)(30, 83)(31, 91)(32, 87)(33, 76)(34, 67)(35, 80)(36, 72)(37, 74)(38, 69)(39, 75)(40, 71)(41, 65)(42, 77)(43, 68)(44, 78)(45, 70)(46, 73)(47, 66)(48, 79) MAP : A3.199 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 95)(18, 84)(19, 88)(20, 93)(21, 89)(22, 94)(23, 85)(24, 86)(25, 96)(26, 81)(27, 90)(28, 82)(29, 92)(30, 83)(31, 91)(32, 87)(33, 68)(34, 70)(35, 69)(36, 78)(37, 79)(38, 80)(39, 65)(40, 73)(41, 75)(42, 66)(43, 76)(44, 72)(45, 67)(46, 71)(47, 77)(48, 74) MAP : A3.200 NOTES : type I, non-biCayley, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = Id($) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3, 3 ], faces: [ 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2 * u.1^-1 * u.3)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2 * x.1^-1 * x.3)^4 > SCHREIER VEC. : (x.1)^3 LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 3, 6)(2, 37, 10)(4, 40, 9)(5, 34, 13)(7, 12, 46)(8, 36, 16)(11, 23, 30)(14, 44, 27)(15, 19, 33)(17, 38, 31)(18, 42, 29)(20, 41, 32)(21, 45, 26)(22, 35, 47)(24, 48, 25)(28, 39, 43)(49, 59, 68)(50, 96, 75)(51, 73, 69)(52, 76, 53)(54, 77, 92)(55, 90, 89)(56, 78, 93)(57, 95, 62)(58, 70, 84)(60, 64, 67)(61, 79, 80)(63, 74, 91)(65, 85, 94)(66, 81, 88)(71, 83, 82)(72, 86, 87) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) MAP : A3.201 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 95)(18, 84)(19, 88)(20, 93)(21, 89)(22, 94)(23, 85)(24, 86)(25, 96)(26, 81)(27, 90)(28, 82)(29, 92)(30, 83)(31, 91)(32, 87)(33, 73)(34, 79)(35, 66)(36, 75)(37, 70)(38, 77)(39, 72)(40, 68)(41, 78)(42, 69)(43, 71)(44, 65)(45, 74)(46, 76)(47, 80)(48, 67) MAP : A3.202 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 87)(18, 90)(19, 93)(20, 81)(21, 83)(22, 82)(23, 94)(24, 92)(25, 88)(26, 96)(27, 89)(28, 91)(29, 95)(30, 84)(31, 85)(32, 86)(33, 67)(34, 71)(35, 75)(36, 69)(37, 76)(38, 65)(39, 77)(40, 74)(41, 66)(42, 78)(43, 70)(44, 80)(45, 73)(46, 79)(47, 72)(48, 68) MAP : A3.203 NOTES : type I, non-biCayley, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = Id($) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3, 3 ], faces: [ 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2 * u.1^-1 * u.3)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2 * x.1^-1 * x.3)^4 > SCHREIER VEC. : (x.1)^3 LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 6, 3)(2, 10, 37)(4, 9, 40)(5, 13, 34)(7, 46, 12)(8, 16, 36)(11, 30, 23)(14, 27, 44)(15, 33, 19)(17, 31, 38)(18, 29, 42)(20, 32, 41)(21, 26, 45)(22, 47, 35)(24, 25, 48)(28, 43, 39)(49, 55, 61)(50, 57, 54)(51, 56, 91)(52, 71, 79)(53, 72, 63)(58, 67, 78)(59, 73, 77)(60, 88, 74)(62, 84, 82)(64, 65, 90)(66, 95, 76)(68, 83, 93)(69, 86, 75)(70, 96, 94)(80, 85, 87)(81, 89, 92) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) MAP : A3.204 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 93)(18, 94)(19, 89)(20, 83)(21, 91)(22, 87)(23, 95)(24, 96)(25, 90)(26, 84)(27, 82)(28, 86)(29, 88)(30, 85)(31, 92)(32, 81)(33, 71)(34, 74)(35, 77)(36, 65)(37, 67)(38, 66)(39, 78)(40, 76)(41, 72)(42, 80)(43, 73)(44, 75)(45, 79)(46, 68)(47, 69)(48, 70) MAP : A3.205 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 87)(18, 90)(19, 93)(20, 81)(21, 83)(22, 82)(23, 94)(24, 92)(25, 88)(26, 96)(27, 89)(28, 91)(29, 95)(30, 84)(31, 85)(32, 86)(33, 79)(34, 68)(35, 72)(36, 77)(37, 73)(38, 78)(39, 69)(40, 70)(41, 80)(42, 65)(43, 74)(44, 66)(45, 76)(46, 67)(47, 75)(48, 71) MAP : A3.206 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 87)(18, 90)(19, 93)(20, 81)(21, 83)(22, 82)(23, 94)(24, 92)(25, 88)(26, 96)(27, 89)(28, 91)(29, 95)(30, 84)(31, 85)(32, 86)(33, 77)(34, 78)(35, 73)(36, 67)(37, 75)(38, 71)(39, 79)(40, 80)(41, 74)(42, 68)(43, 66)(44, 70)(45, 72)(46, 69)(47, 76)(48, 65) MAP : A3.207 NOTES : type I, non-Cayley, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = Id($) L = Id($) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 3 ], faces: [ 8 ] UNIGROUP : < u.1, u.2 | u.1^2, u.2^3, (u.1 * u.2)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.1^2, x.2^3, (x.1 * x.2 * x.1 * x.2^-1)^3, (x.1 * x.2)^8 > SCHREIER VEC. : (x.1)^3 LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 5, 2)(3, 34, 17)(4, 37, 18)(6, 81, 19)(7, 82, 20)(8, 33, 21)(9, 36, 69)(10, 83, 22)(11, 84, 23)(12, 85, 24)(13, 35, 66)(14, 40, 65)(15, 88, 28)(16, 89, 76)(25, 44, 53)(26, 73, 86)(27, 78, 87)(29, 39, 50)(30, 38, 49)(31, 77, 92)(32, 61, 60)(41, 68, 90)(42, 51, 63)(43, 52, 58)(45, 67, 95)(46, 72, 91)(47, 56, 59)(48, 57, 54)(55, 64, 62)(70, 80, 94)(71, 96, 93)(74, 75, 79) L = (1, 4)(2, 8)(3, 5)(6, 34)(7, 37)(9, 18)(10, 81)(11, 82)(12, 33)(13, 17)(14, 21)(15, 85)(16, 53)(19, 30)(20, 29)(22, 63)(23, 58)(24, 25)(26, 48)(27, 64)(28, 59)(31, 32)(35, 39)(36, 44)(38, 40)(41, 43)(42, 45)(46, 47)(49, 80)(50, 96)(51, 75)(52, 79)(54, 76)(55, 70)(56, 74)(57, 94)(60, 71)(61, 89)(62, 93)(65, 91)(66, 95)(67, 92)(68, 86)(69, 90)(72, 87)(73, 83)(77, 88)(78, 84) MAP : A3.208 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 93)(18, 94)(19, 89)(20, 83)(21, 91)(22, 87)(23, 95)(24, 96)(25, 90)(26, 84)(27, 82)(28, 86)(29, 88)(30, 85)(31, 92)(32, 81)(33, 79)(34, 68)(35, 72)(36, 77)(37, 73)(38, 78)(39, 69)(40, 70)(41, 80)(42, 65)(43, 74)(44, 66)(45, 76)(46, 67)(47, 75)(48, 71) MAP : A3.209 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 96)(18, 91)(19, 84)(20, 90)(21, 94)(22, 92)(23, 86)(24, 93)(25, 83)(26, 89)(27, 85)(28, 95)(29, 81)(30, 82)(31, 87)(32, 88)(33, 67)(34, 71)(35, 75)(36, 69)(37, 76)(38, 65)(39, 77)(40, 74)(41, 66)(42, 78)(43, 70)(44, 80)(45, 73)(46, 79)(47, 72)(48, 68) MAP : A3.210 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 96)(18, 91)(19, 84)(20, 90)(21, 94)(22, 92)(23, 86)(24, 93)(25, 83)(26, 89)(27, 85)(28, 95)(29, 81)(30, 82)(31, 87)(32, 88)(33, 70)(34, 73)(35, 65)(36, 80)(37, 68)(38, 75)(39, 66)(40, 79)(41, 77)(42, 72)(43, 67)(44, 69)(45, 71)(46, 74)(47, 78)(48, 76) MAP : A3.211 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^4, u.2^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2 | x.1^2, x.2^-1 * x.1 * x.2^2 * x.1 * x.2^-1, (x.1 * x.2^-1)^4, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96) L = (1, 2)(3, 6)(4, 5)(7, 19)(8, 26)(9, 28)(10, 12)(11, 20)(13, 17)(14, 27)(15, 22)(16, 18)(21, 30)(23, 31)(24, 25)(29, 32)(33, 68)(34, 84)(35, 66)(36, 74)(37, 90)(38, 82)(39, 81)(40, 70)(41, 71)(42, 79)(43, 92)(44, 95)(45, 85)(46, 89)(47, 96)(48, 91)(49, 69)(50, 75)(51, 65)(52, 76)(53, 72)(54, 80)(55, 77)(56, 67)(57, 83)(58, 86)(59, 73)(60, 87)(61, 94)(62, 88)(63, 93)(64, 78) MAP : A3.212 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 95)(18, 84)(19, 88)(20, 93)(21, 89)(22, 94)(23, 85)(24, 86)(25, 96)(26, 81)(27, 90)(28, 82)(29, 92)(30, 83)(31, 91)(32, 87)(33, 77)(34, 78)(35, 73)(36, 67)(37, 75)(38, 71)(39, 79)(40, 80)(41, 74)(42, 68)(43, 66)(44, 70)(45, 72)(46, 69)(47, 76)(48, 65) MAP : A3.213 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 95)(18, 84)(19, 88)(20, 93)(21, 89)(22, 94)(23, 85)(24, 86)(25, 96)(26, 81)(27, 90)(28, 82)(29, 92)(30, 83)(31, 91)(32, 87)(33, 80)(34, 75)(35, 68)(36, 74)(37, 78)(38, 76)(39, 70)(40, 77)(41, 67)(42, 73)(43, 69)(44, 79)(45, 65)(46, 66)(47, 71)(48, 72) MAP : A3.214 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 93)(18, 94)(19, 89)(20, 83)(21, 91)(22, 87)(23, 95)(24, 96)(25, 90)(26, 84)(27, 82)(28, 86)(29, 88)(30, 85)(31, 92)(32, 81)(33, 67)(34, 71)(35, 75)(36, 69)(37, 76)(38, 65)(39, 77)(40, 74)(41, 66)(42, 78)(43, 70)(44, 80)(45, 73)(46, 79)(47, 72)(48, 68) MAP : A3.215 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 87)(18, 90)(19, 93)(20, 81)(21, 83)(22, 82)(23, 94)(24, 92)(25, 88)(26, 96)(27, 89)(28, 91)(29, 95)(30, 84)(31, 85)(32, 86)(33, 69)(34, 65)(35, 76)(36, 79)(37, 72)(38, 68)(39, 67)(40, 66)(41, 70)(42, 71)(43, 80)(44, 74)(45, 75)(46, 77)(47, 73)(48, 78) MAP : A3.216 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 93)(18, 94)(19, 89)(20, 83)(21, 91)(22, 87)(23, 95)(24, 96)(25, 90)(26, 84)(27, 82)(28, 86)(29, 88)(30, 85)(31, 92)(32, 81)(33, 68)(34, 70)(35, 69)(36, 78)(37, 79)(38, 80)(39, 65)(40, 73)(41, 75)(42, 66)(43, 76)(44, 72)(45, 67)(46, 71)(47, 77)(48, 74) MAP : A3.217 NOTES : type I, non-biCayley, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = Id($) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3, 3 ], faces: [ 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2 * u.1^-1 * u.3)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2 * x.1^-1 * x.3)^4 > SCHREIER VEC. : (x.1)^3 LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 3, 6)(2, 37, 10)(4, 40, 9)(5, 34, 13)(7, 12, 46)(8, 36, 16)(11, 23, 30)(14, 44, 27)(15, 19, 33)(17, 38, 31)(18, 42, 29)(20, 41, 32)(21, 45, 26)(22, 35, 47)(24, 48, 25)(28, 39, 43)(49, 61, 55)(50, 54, 57)(51, 91, 56)(52, 79, 71)(53, 63, 72)(58, 78, 67)(59, 77, 73)(60, 74, 88)(62, 82, 84)(64, 90, 65)(66, 76, 95)(68, 93, 83)(69, 75, 86)(70, 94, 96)(80, 87, 85)(81, 92, 89) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) MAP : A3.218 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 93)(18, 94)(19, 89)(20, 83)(21, 91)(22, 87)(23, 95)(24, 96)(25, 90)(26, 84)(27, 82)(28, 86)(29, 88)(30, 85)(31, 92)(32, 81)(33, 73)(34, 79)(35, 66)(36, 75)(37, 70)(38, 77)(39, 72)(40, 68)(41, 78)(42, 69)(43, 71)(44, 65)(45, 74)(46, 76)(47, 80)(48, 67) MAP : A3.219 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 93)(18, 94)(19, 89)(20, 83)(21, 91)(22, 87)(23, 95)(24, 96)(25, 90)(26, 84)(27, 82)(28, 86)(29, 88)(30, 85)(31, 92)(32, 81)(33, 76)(34, 67)(35, 80)(36, 72)(37, 74)(38, 69)(39, 75)(40, 71)(41, 65)(42, 77)(43, 68)(44, 78)(45, 70)(46, 73)(47, 66)(48, 79) MAP : A3.220 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 93)(18, 94)(19, 89)(20, 83)(21, 91)(22, 87)(23, 95)(24, 96)(25, 90)(26, 84)(27, 82)(28, 86)(29, 88)(30, 85)(31, 92)(32, 81)(33, 74)(34, 76)(35, 78)(36, 66)(37, 71)(38, 72)(39, 80)(40, 67)(41, 69)(42, 75)(43, 79)(44, 77)(45, 68)(46, 70)(47, 65)(48, 73) MAP : A3.221 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 92)(18, 83)(19, 96)(20, 88)(21, 90)(22, 85)(23, 91)(24, 87)(25, 81)(26, 93)(27, 84)(28, 94)(29, 86)(30, 89)(31, 82)(32, 95)(33, 74)(34, 76)(35, 78)(36, 66)(37, 71)(38, 72)(39, 80)(40, 67)(41, 69)(42, 75)(43, 79)(44, 77)(45, 68)(46, 70)(47, 65)(48, 73) MAP : A3.222 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 92)(18, 83)(19, 96)(20, 88)(21, 90)(22, 85)(23, 91)(24, 87)(25, 81)(26, 93)(27, 84)(28, 94)(29, 86)(30, 89)(31, 82)(32, 95)(33, 79)(34, 68)(35, 72)(36, 77)(37, 73)(38, 78)(39, 69)(40, 70)(41, 80)(42, 65)(43, 74)(44, 66)(45, 76)(46, 67)(47, 75)(48, 71) MAP : A3.223 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 92)(18, 83)(19, 96)(20, 88)(21, 90)(22, 85)(23, 91)(24, 87)(25, 81)(26, 93)(27, 84)(28, 94)(29, 86)(30, 89)(31, 82)(32, 95)(33, 77)(34, 78)(35, 73)(36, 67)(37, 75)(38, 71)(39, 79)(40, 80)(41, 74)(42, 68)(43, 66)(44, 70)(45, 72)(46, 69)(47, 76)(48, 65) MAP : A3.224 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 92)(18, 83)(19, 96)(20, 88)(21, 90)(22, 85)(23, 91)(24, 87)(25, 81)(26, 93)(27, 84)(28, 94)(29, 86)(30, 89)(31, 82)(32, 95)(33, 80)(34, 75)(35, 68)(36, 74)(37, 78)(38, 76)(39, 70)(40, 77)(41, 67)(42, 73)(43, 69)(44, 79)(45, 65)(46, 66)(47, 71)(48, 72) MAP : A3.225 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^4, u.2^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2 | x.1^2, x.2^-1 * x.1 * x.2^2 * x.1 * x.2^-1, (x.1 * x.2^-1)^4, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96) L = (1, 2)(3, 6)(4, 5)(7, 19)(8, 26)(9, 28)(10, 12)(11, 20)(13, 17)(14, 27)(15, 22)(16, 18)(21, 30)(23, 31)(24, 25)(29, 32)(33, 78)(34, 94)(35, 93)(36, 89)(37, 73)(38, 77)(39, 80)(40, 87)(41, 86)(42, 83)(43, 72)(44, 67)(45, 75)(46, 74)(47, 65)(48, 69)(49, 91)(50, 85)(51, 96)(52, 88)(53, 92)(54, 81)(55, 82)(56, 95)(57, 79)(58, 71)(59, 90)(60, 70)(61, 84)(62, 76)(63, 66)(64, 68) MAP : A3.226 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^4, u.2^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2 | x.1^2, x.2^-1 * x.1 * x.2^2 * x.1 * x.2^-1, (x.1 * x.2^-1)^4, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96) L = (1, 2)(3, 6)(4, 5)(7, 19)(8, 26)(9, 28)(10, 12)(11, 20)(13, 17)(14, 27)(15, 22)(16, 18)(21, 30)(23, 31)(24, 25)(29, 32)(33, 79)(34, 95)(35, 76)(36, 96)(37, 80)(38, 92)(39, 90)(40, 75)(41, 69)(42, 78)(43, 77)(44, 94)(45, 70)(46, 65)(47, 89)(48, 71)(49, 86)(50, 87)(51, 74)(52, 93)(53, 82)(54, 73)(55, 72)(56, 84)(57, 68)(58, 91)(59, 81)(60, 85)(61, 67)(62, 66)(63, 88)(64, 83) MAP : A3.227 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2^-1)^4, u.2^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2 | x.1^2, x.2^-1 * x.1 * x.2^2 * x.1 * x.2^-1, (x.1 * x.2^-1)^4, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 33, 65)(2, 34, 66)(3, 35, 67)(4, 36, 68)(5, 37, 69)(6, 38, 70)(7, 39, 71)(8, 40, 72)(9, 41, 73)(10, 42, 74)(11, 43, 75)(12, 44, 76)(13, 45, 77)(14, 46, 78)(15, 47, 79)(16, 48, 80)(17, 49, 81)(18, 50, 82)(19, 51, 83)(20, 52, 84)(21, 53, 85)(22, 54, 86)(23, 55, 87)(24, 56, 88)(25, 57, 89)(26, 58, 90)(27, 59, 91)(28, 60, 92)(29, 61, 93)(30, 62, 94)(31, 63, 95)(32, 64, 96) L = (1, 2)(3, 6)(4, 5)(7, 19)(8, 26)(9, 28)(10, 12)(11, 20)(13, 17)(14, 27)(15, 22)(16, 18)(21, 30)(23, 31)(24, 25)(29, 32)(33, 83)(34, 67)(35, 88)(36, 65)(37, 81)(38, 72)(39, 73)(40, 85)(41, 91)(42, 68)(43, 82)(44, 84)(45, 87)(46, 96)(47, 74)(48, 86)(49, 71)(50, 70)(51, 89)(52, 66)(53, 77)(54, 90)(55, 92)(56, 94)(57, 78)(58, 69)(59, 80)(60, 75)(61, 95)(62, 93)(63, 76)(64, 79) MAP : A3.228 NOTES : type I, non-biCayley, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = Id($) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3, 3 ], faces: [ 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2 * u.1^-1 * u.3)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2 * x.1^-1 * x.3)^4 > SCHREIER VEC. : (x.1)^3 LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 3, 6)(2, 37, 10)(4, 40, 9)(5, 34, 13)(7, 12, 46)(8, 36, 16)(11, 23, 30)(14, 44, 27)(15, 19, 33)(17, 38, 31)(18, 42, 29)(20, 41, 32)(21, 45, 26)(22, 35, 47)(24, 48, 25)(28, 39, 43)(49, 69, 78)(50, 65, 72)(51, 92, 96)(52, 81, 91)(53, 83, 57)(54, 68, 90)(55, 67, 66)(56, 70, 71)(58, 75, 95)(59, 82, 80)(60, 85, 84)(61, 76, 86)(62, 77, 88)(63, 64, 93)(73, 87, 74)(79, 94, 89) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) MAP : A3.229 NOTES : type I, non-biCayley, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = Id($) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3, 3 ], faces: [ 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, u.2^3, u.3^3, (u.1 * u.2 * u.1^-1 * u.3)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^3, x.3^3, (x.2 * x.3^-1)^3, (x.1 * x.2 * x.1^-1 * x.3)^4 > SCHREIER VEC. : (x.1)^3 LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 3, 6)(2, 37, 10)(4, 40, 9)(5, 34, 13)(7, 12, 46)(8, 36, 16)(11, 23, 30)(14, 44, 27)(15, 19, 33)(17, 38, 31)(18, 42, 29)(20, 41, 32)(21, 45, 26)(22, 35, 47)(24, 48, 25)(28, 39, 43)(49, 56, 82)(50, 87, 51)(52, 74, 86)(53, 62, 81)(54, 55, 88)(57, 71, 58)(59, 79, 90)(60, 70, 93)(61, 72, 94)(63, 78, 73)(64, 91, 66)(65, 75, 84)(67, 89, 85)(68, 92, 69)(76, 80, 83)(77, 95, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) MAP : A3.230 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 90)(18, 92)(19, 94)(20, 82)(21, 87)(22, 88)(23, 96)(24, 83)(25, 85)(26, 91)(27, 95)(28, 93)(29, 84)(30, 86)(31, 81)(32, 89)(33, 76)(34, 67)(35, 80)(36, 72)(37, 74)(38, 69)(39, 75)(40, 71)(41, 65)(42, 77)(43, 68)(44, 78)(45, 70)(46, 73)(47, 66)(48, 79) MAP : A3.231 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 90)(18, 92)(19, 94)(20, 82)(21, 87)(22, 88)(23, 96)(24, 83)(25, 85)(26, 91)(27, 95)(28, 93)(29, 84)(30, 86)(31, 81)(32, 89)(33, 77)(34, 78)(35, 73)(36, 67)(37, 75)(38, 71)(39, 79)(40, 80)(41, 74)(42, 68)(43, 66)(44, 70)(45, 72)(46, 69)(47, 76)(48, 65) MAP : A3.232 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 90)(18, 92)(19, 94)(20, 82)(21, 87)(22, 88)(23, 96)(24, 83)(25, 85)(26, 91)(27, 95)(28, 93)(29, 84)(30, 86)(31, 81)(32, 89)(33, 80)(34, 75)(35, 68)(36, 74)(37, 78)(38, 76)(39, 70)(40, 77)(41, 67)(42, 73)(43, 69)(44, 79)(45, 65)(46, 66)(47, 71)(48, 72) MAP : A3.233 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 95)(18, 84)(19, 88)(20, 93)(21, 89)(22, 94)(23, 85)(24, 86)(25, 96)(26, 81)(27, 90)(28, 82)(29, 92)(30, 83)(31, 91)(32, 87)(33, 66)(34, 72)(35, 71)(36, 70)(37, 65)(38, 73)(39, 74)(40, 69)(41, 79)(42, 76)(43, 77)(44, 67)(45, 78)(46, 80)(47, 68)(48, 75) MAP : A3.234 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 95)(18, 84)(19, 88)(20, 93)(21, 89)(22, 94)(23, 85)(24, 86)(25, 96)(26, 81)(27, 90)(28, 82)(29, 92)(30, 83)(31, 91)(32, 87)(33, 69)(34, 65)(35, 76)(36, 79)(37, 72)(38, 68)(39, 67)(40, 66)(41, 70)(42, 71)(43, 80)(44, 74)(45, 75)(46, 77)(47, 73)(48, 78) MAP : A3.235 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 84)(18, 86)(19, 85)(20, 94)(21, 95)(22, 96)(23, 81)(24, 89)(25, 91)(26, 82)(27, 92)(28, 88)(29, 83)(30, 87)(31, 93)(32, 90)(33, 69)(34, 65)(35, 76)(36, 79)(37, 72)(38, 68)(39, 67)(40, 66)(41, 70)(42, 71)(43, 80)(44, 74)(45, 75)(46, 77)(47, 73)(48, 78) MAP : A3.236 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 84)(18, 86)(19, 85)(20, 94)(21, 95)(22, 96)(23, 81)(24, 89)(25, 91)(26, 82)(27, 92)(28, 88)(29, 83)(30, 87)(31, 93)(32, 90)(33, 67)(34, 71)(35, 75)(36, 69)(37, 76)(38, 65)(39, 77)(40, 74)(41, 66)(42, 78)(43, 70)(44, 80)(45, 73)(46, 79)(47, 72)(48, 68) MAP : A3.237 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 84)(18, 86)(19, 85)(20, 94)(21, 95)(22, 96)(23, 81)(24, 89)(25, 91)(26, 82)(27, 92)(28, 88)(29, 83)(30, 87)(31, 93)(32, 90)(33, 70)(34, 73)(35, 65)(36, 80)(37, 68)(38, 75)(39, 66)(40, 79)(41, 77)(42, 72)(43, 67)(44, 69)(45, 71)(46, 74)(47, 78)(48, 76) MAP : A3.238 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 84)(18, 86)(19, 85)(20, 94)(21, 95)(22, 96)(23, 81)(24, 89)(25, 91)(26, 82)(27, 92)(28, 88)(29, 83)(30, 87)(31, 93)(32, 90)(33, 74)(34, 76)(35, 78)(36, 66)(37, 71)(38, 72)(39, 80)(40, 67)(41, 69)(42, 75)(43, 79)(44, 77)(45, 68)(46, 70)(47, 65)(48, 73) MAP : A3.239 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 84)(18, 86)(19, 85)(20, 94)(21, 95)(22, 96)(23, 81)(24, 89)(25, 91)(26, 82)(27, 92)(28, 88)(29, 83)(30, 87)(31, 93)(32, 90)(33, 79)(34, 68)(35, 72)(36, 77)(37, 73)(38, 78)(39, 69)(40, 70)(41, 80)(42, 65)(43, 74)(44, 66)(45, 76)(46, 67)(47, 75)(48, 71) MAP : A3.240 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 84)(18, 86)(19, 85)(20, 94)(21, 95)(22, 96)(23, 81)(24, 89)(25, 91)(26, 82)(27, 92)(28, 88)(29, 83)(30, 87)(31, 93)(32, 90)(33, 77)(34, 78)(35, 73)(36, 67)(37, 75)(38, 71)(39, 79)(40, 80)(41, 74)(42, 68)(43, 66)(44, 70)(45, 72)(46, 69)(47, 76)(48, 65) MAP : A3.241 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 84)(18, 86)(19, 85)(20, 94)(21, 95)(22, 96)(23, 81)(24, 89)(25, 91)(26, 82)(27, 92)(28, 88)(29, 83)(30, 87)(31, 93)(32, 90)(33, 80)(34, 75)(35, 68)(36, 74)(37, 78)(38, 76)(39, 70)(40, 77)(41, 67)(42, 73)(43, 69)(44, 79)(45, 65)(46, 66)(47, 71)(48, 72) MAP : A3.242 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 93)(18, 94)(19, 89)(20, 83)(21, 91)(22, 87)(23, 95)(24, 96)(25, 90)(26, 84)(27, 82)(28, 86)(29, 88)(30, 85)(31, 92)(32, 81)(33, 70)(34, 73)(35, 65)(36, 80)(37, 68)(38, 75)(39, 66)(40, 79)(41, 77)(42, 72)(43, 67)(44, 69)(45, 71)(46, 74)(47, 78)(48, 76) MAP : A3.243 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 82)(18, 88)(19, 87)(20, 86)(21, 81)(22, 89)(23, 90)(24, 85)(25, 95)(26, 92)(27, 93)(28, 83)(29, 94)(30, 96)(31, 84)(32, 91)(33, 67)(34, 71)(35, 75)(36, 69)(37, 76)(38, 65)(39, 77)(40, 74)(41, 66)(42, 78)(43, 70)(44, 80)(45, 73)(46, 79)(47, 72)(48, 68) MAP : A3.244 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 82)(18, 88)(19, 87)(20, 86)(21, 81)(22, 89)(23, 90)(24, 85)(25, 95)(26, 92)(27, 93)(28, 83)(29, 94)(30, 96)(31, 84)(32, 91)(33, 70)(34, 73)(35, 65)(36, 80)(37, 68)(38, 75)(39, 66)(40, 79)(41, 77)(42, 72)(43, 67)(44, 69)(45, 71)(46, 74)(47, 78)(48, 76) MAP : A3.245 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 87)(18, 90)(19, 93)(20, 81)(21, 83)(22, 82)(23, 94)(24, 92)(25, 88)(26, 96)(27, 89)(28, 91)(29, 95)(30, 84)(31, 85)(32, 86)(33, 70)(34, 73)(35, 65)(36, 80)(37, 68)(38, 75)(39, 66)(40, 79)(41, 77)(42, 72)(43, 67)(44, 69)(45, 71)(46, 74)(47, 78)(48, 76) MAP : A3.246 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 87)(18, 90)(19, 93)(20, 81)(21, 83)(22, 82)(23, 94)(24, 92)(25, 88)(26, 96)(27, 89)(28, 91)(29, 95)(30, 84)(31, 85)(32, 86)(33, 74)(34, 76)(35, 78)(36, 66)(37, 71)(38, 72)(39, 80)(40, 67)(41, 69)(42, 75)(43, 79)(44, 77)(45, 68)(46, 70)(47, 65)(48, 73) MAP : A3.247 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 82)(18, 88)(19, 87)(20, 86)(21, 81)(22, 89)(23, 90)(24, 85)(25, 95)(26, 92)(27, 93)(28, 83)(29, 94)(30, 96)(31, 84)(32, 91)(33, 73)(34, 79)(35, 66)(36, 75)(37, 70)(38, 77)(39, 72)(40, 68)(41, 78)(42, 69)(43, 71)(44, 65)(45, 74)(46, 76)(47, 80)(48, 67) MAP : A3.248 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 82)(18, 88)(19, 87)(20, 86)(21, 81)(22, 89)(23, 90)(24, 85)(25, 95)(26, 92)(27, 93)(28, 83)(29, 94)(30, 96)(31, 84)(32, 91)(33, 76)(34, 67)(35, 80)(36, 72)(37, 74)(38, 69)(39, 75)(40, 71)(41, 65)(42, 77)(43, 68)(44, 78)(45, 70)(46, 73)(47, 66)(48, 79) MAP : A3.249 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 87)(18, 90)(19, 93)(20, 81)(21, 83)(22, 82)(23, 94)(24, 92)(25, 88)(26, 96)(27, 89)(28, 91)(29, 95)(30, 84)(31, 85)(32, 86)(33, 80)(34, 75)(35, 68)(36, 74)(37, 78)(38, 76)(39, 70)(40, 77)(41, 67)(42, 73)(43, 69)(44, 79)(45, 65)(46, 66)(47, 71)(48, 72) MAP : A3.250 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 89)(18, 95)(19, 82)(20, 91)(21, 86)(22, 93)(23, 88)(24, 84)(25, 94)(26, 85)(27, 87)(28, 81)(29, 90)(30, 92)(31, 96)(32, 83)(33, 66)(34, 72)(35, 71)(36, 70)(37, 65)(38, 73)(39, 74)(40, 69)(41, 79)(42, 76)(43, 77)(44, 67)(45, 78)(46, 80)(47, 68)(48, 75) MAP : A3.251 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 89)(18, 95)(19, 82)(20, 91)(21, 86)(22, 93)(23, 88)(24, 84)(25, 94)(26, 85)(27, 87)(28, 81)(29, 90)(30, 92)(31, 96)(32, 83)(33, 69)(34, 65)(35, 76)(36, 79)(37, 72)(38, 68)(39, 67)(40, 66)(41, 70)(42, 71)(43, 80)(44, 74)(45, 75)(46, 77)(47, 73)(48, 78) MAP : A3.252 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 89)(18, 95)(19, 82)(20, 91)(21, 86)(22, 93)(23, 88)(24, 84)(25, 94)(26, 85)(27, 87)(28, 81)(29, 90)(30, 92)(31, 96)(32, 83)(33, 67)(34, 71)(35, 75)(36, 69)(37, 76)(38, 65)(39, 77)(40, 74)(41, 66)(42, 78)(43, 70)(44, 80)(45, 73)(46, 79)(47, 72)(48, 68) MAP : A3.253 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 89)(18, 95)(19, 82)(20, 91)(21, 86)(22, 93)(23, 88)(24, 84)(25, 94)(26, 85)(27, 87)(28, 81)(29, 90)(30, 92)(31, 96)(32, 83)(33, 70)(34, 73)(35, 65)(36, 80)(37, 68)(38, 75)(39, 66)(40, 79)(41, 77)(42, 72)(43, 67)(44, 69)(45, 71)(46, 74)(47, 78)(48, 76) MAP : A3.254 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 89)(18, 95)(19, 82)(20, 91)(21, 86)(22, 93)(23, 88)(24, 84)(25, 94)(26, 85)(27, 87)(28, 81)(29, 90)(30, 92)(31, 96)(32, 83)(33, 74)(34, 76)(35, 78)(36, 66)(37, 71)(38, 72)(39, 80)(40, 67)(41, 69)(42, 75)(43, 79)(44, 77)(45, 68)(46, 70)(47, 65)(48, 73) MAP : A3.255 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 89)(18, 95)(19, 82)(20, 91)(21, 86)(22, 93)(23, 88)(24, 84)(25, 94)(26, 85)(27, 87)(28, 81)(29, 90)(30, 92)(31, 96)(32, 83)(33, 79)(34, 68)(35, 72)(36, 77)(37, 73)(38, 78)(39, 69)(40, 70)(41, 80)(42, 65)(43, 74)(44, 66)(45, 76)(46, 67)(47, 75)(48, 71) MAP : A3.256 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 89)(18, 95)(19, 82)(20, 91)(21, 86)(22, 93)(23, 88)(24, 84)(25, 94)(26, 85)(27, 87)(28, 81)(29, 90)(30, 92)(31, 96)(32, 83)(33, 77)(34, 78)(35, 73)(36, 67)(37, 75)(38, 71)(39, 79)(40, 80)(41, 74)(42, 68)(43, 66)(44, 70)(45, 72)(46, 69)(47, 76)(48, 65) MAP : A3.257 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 89)(18, 95)(19, 82)(20, 91)(21, 86)(22, 93)(23, 88)(24, 84)(25, 94)(26, 85)(27, 87)(28, 81)(29, 90)(30, 92)(31, 96)(32, 83)(33, 80)(34, 75)(35, 68)(36, 74)(37, 78)(38, 76)(39, 70)(40, 77)(41, 67)(42, 73)(43, 69)(44, 79)(45, 65)(46, 66)(47, 71)(48, 72) MAP : A3.258 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 92)(18, 83)(19, 96)(20, 88)(21, 90)(22, 85)(23, 91)(24, 87)(25, 81)(26, 93)(27, 84)(28, 94)(29, 86)(30, 89)(31, 82)(32, 95)(33, 69)(34, 65)(35, 76)(36, 79)(37, 72)(38, 68)(39, 67)(40, 66)(41, 70)(42, 71)(43, 80)(44, 74)(45, 75)(46, 77)(47, 73)(48, 78) MAP : A3.259 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 92)(18, 83)(19, 96)(20, 88)(21, 90)(22, 85)(23, 91)(24, 87)(25, 81)(26, 93)(27, 84)(28, 94)(29, 86)(30, 89)(31, 82)(32, 95)(33, 67)(34, 71)(35, 75)(36, 69)(37, 76)(38, 65)(39, 77)(40, 74)(41, 66)(42, 78)(43, 70)(44, 80)(45, 73)(46, 79)(47, 72)(48, 68) MAP : A3.260 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 92)(18, 83)(19, 96)(20, 88)(21, 90)(22, 85)(23, 91)(24, 87)(25, 81)(26, 93)(27, 84)(28, 94)(29, 86)(30, 89)(31, 82)(32, 95)(33, 70)(34, 73)(35, 65)(36, 80)(37, 68)(38, 75)(39, 66)(40, 79)(41, 77)(42, 72)(43, 67)(44, 69)(45, 71)(46, 74)(47, 78)(48, 76) MAP : A3.261 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 83)(18, 87)(19, 91)(20, 85)(21, 92)(22, 81)(23, 93)(24, 90)(25, 82)(26, 94)(27, 86)(28, 96)(29, 89)(30, 95)(31, 88)(32, 84)(33, 71)(34, 74)(35, 77)(36, 65)(37, 67)(38, 66)(39, 78)(40, 76)(41, 72)(42, 80)(43, 73)(44, 75)(45, 79)(46, 68)(47, 69)(48, 70) MAP : A3.262 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 83)(18, 87)(19, 91)(20, 85)(21, 92)(22, 81)(23, 93)(24, 90)(25, 82)(26, 94)(27, 86)(28, 96)(29, 89)(30, 95)(31, 88)(32, 84)(33, 73)(34, 79)(35, 66)(36, 75)(37, 70)(38, 77)(39, 72)(40, 68)(41, 78)(42, 69)(43, 71)(44, 65)(45, 74)(46, 76)(47, 80)(48, 67) MAP : A3.263 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 83)(18, 87)(19, 91)(20, 85)(21, 92)(22, 81)(23, 93)(24, 90)(25, 82)(26, 94)(27, 86)(28, 96)(29, 89)(30, 95)(31, 88)(32, 84)(33, 76)(34, 67)(35, 80)(36, 72)(37, 74)(38, 69)(39, 75)(40, 71)(41, 65)(42, 77)(43, 68)(44, 78)(45, 70)(46, 73)(47, 66)(48, 79) MAP : A3.264 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 83)(18, 87)(19, 91)(20, 85)(21, 92)(22, 81)(23, 93)(24, 90)(25, 82)(26, 94)(27, 86)(28, 96)(29, 89)(30, 95)(31, 88)(32, 84)(33, 77)(34, 78)(35, 73)(36, 67)(37, 75)(38, 71)(39, 79)(40, 80)(41, 74)(42, 68)(43, 66)(44, 70)(45, 72)(46, 69)(47, 76)(48, 65) MAP : A3.265 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 90)(18, 92)(19, 94)(20, 82)(21, 87)(22, 88)(23, 96)(24, 83)(25, 85)(26, 91)(27, 95)(28, 93)(29, 84)(30, 86)(31, 81)(32, 89)(33, 66)(34, 72)(35, 71)(36, 70)(37, 65)(38, 73)(39, 74)(40, 69)(41, 79)(42, 76)(43, 77)(44, 67)(45, 78)(46, 80)(47, 68)(48, 75) MAP : A3.266 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 90)(18, 92)(19, 94)(20, 82)(21, 87)(22, 88)(23, 96)(24, 83)(25, 85)(26, 91)(27, 95)(28, 93)(29, 84)(30, 86)(31, 81)(32, 89)(33, 69)(34, 65)(35, 76)(36, 79)(37, 72)(38, 68)(39, 67)(40, 66)(41, 70)(42, 71)(43, 80)(44, 74)(45, 75)(46, 77)(47, 73)(48, 78) MAP : A3.267 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 90)(18, 92)(19, 94)(20, 82)(21, 87)(22, 88)(23, 96)(24, 83)(25, 85)(26, 91)(27, 95)(28, 93)(29, 84)(30, 86)(31, 81)(32, 89)(33, 68)(34, 70)(35, 69)(36, 78)(37, 79)(38, 80)(39, 65)(40, 73)(41, 75)(42, 66)(43, 76)(44, 72)(45, 67)(46, 71)(47, 77)(48, 74) MAP : A3.268 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 90)(18, 92)(19, 94)(20, 82)(21, 87)(22, 88)(23, 96)(24, 83)(25, 85)(26, 91)(27, 95)(28, 93)(29, 84)(30, 86)(31, 81)(32, 89)(33, 71)(34, 74)(35, 77)(36, 65)(37, 67)(38, 66)(39, 78)(40, 76)(41, 72)(42, 80)(43, 73)(44, 75)(45, 79)(46, 68)(47, 69)(48, 70) MAP : A3.269 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 90)(18, 92)(19, 94)(20, 82)(21, 87)(22, 88)(23, 96)(24, 83)(25, 85)(26, 91)(27, 95)(28, 93)(29, 84)(30, 86)(31, 81)(32, 89)(33, 73)(34, 79)(35, 66)(36, 75)(37, 70)(38, 77)(39, 72)(40, 68)(41, 78)(42, 69)(43, 71)(44, 65)(45, 74)(46, 76)(47, 80)(48, 67) MAP : A3.270 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^4, (u.3 * u.1 * u.4^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.4 * x.2, x.4 * x.1 * x.4^-1 * x.1, (x.3 * x.1 * x.4^-1 * x.2)^2, (x.4 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.1, x.4) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 19)(18, 23)(20, 26)(21, 28)(22, 32)(24, 25)(27, 30)(29, 31)(33, 66)(34, 70)(35, 71)(36, 75)(37, 65)(38, 69)(39, 80)(40, 68)(41, 74)(42, 78)(43, 79)(44, 67)(45, 73)(46, 77)(47, 72)(48, 76)(81, 84)(82, 91)(83, 93)(85, 88)(86, 95)(87, 89)(90, 96)(92, 94) MAP : A3.271 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^4, (u.3 * u.1 * u.4^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.4 * x.2, x.4 * x.1 * x.4^-1 * x.1, (x.3 * x.1 * x.4^-1 * x.2)^2, (x.4 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.1, x.4) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 19)(18, 23)(20, 26)(21, 28)(22, 32)(24, 25)(27, 30)(29, 31)(33, 66)(34, 70)(35, 71)(36, 75)(37, 65)(38, 69)(39, 80)(40, 68)(41, 74)(42, 78)(43, 79)(44, 67)(45, 73)(46, 77)(47, 72)(48, 76)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.272 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^4, (u.3 * u.1 * u.4^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.4 * x.2, x.4 * x.1 * x.4^-1 * x.1, (x.3 * x.1 * x.4^-1 * x.2)^2, (x.4 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.1, x.4) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 20)(18, 27)(19, 29)(21, 24)(22, 31)(23, 25)(26, 32)(28, 30)(33, 66)(34, 70)(35, 71)(36, 75)(37, 65)(38, 69)(39, 80)(40, 68)(41, 74)(42, 78)(43, 79)(44, 67)(45, 73)(46, 77)(47, 72)(48, 76)(81, 83)(82, 87)(84, 90)(85, 92)(86, 96)(88, 89)(91, 94)(93, 95) MAP : A3.273 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^4, (u.3 * u.1 * u.4^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.4 * x.2, x.4 * x.1 * x.4^-1 * x.1, (x.3 * x.1 * x.4^-1 * x.2)^2, (x.4 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.1, x.4) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 20)(18, 27)(19, 29)(21, 24)(22, 31)(23, 25)(26, 32)(28, 30)(33, 66)(34, 70)(35, 71)(36, 75)(37, 65)(38, 69)(39, 80)(40, 68)(41, 74)(42, 78)(43, 79)(44, 67)(45, 73)(46, 77)(47, 72)(48, 76)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.274 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^4, (u.3 * u.1 * u.4^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.4 * x.2, x.4 * x.1 * x.4^-1 * x.1, (x.3 * x.1 * x.4^-1 * x.2)^2, (x.4 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.1, x.4) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 66)(34, 70)(35, 71)(36, 75)(37, 65)(38, 69)(39, 80)(40, 68)(41, 74)(42, 78)(43, 79)(44, 67)(45, 73)(46, 77)(47, 72)(48, 76)(81, 83)(82, 87)(84, 90)(85, 92)(86, 96)(88, 89)(91, 94)(93, 95) MAP : A3.275 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^4, (u.3 * u.1 * u.4^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.4 * x.2, x.4 * x.1 * x.4^-1 * x.1, (x.3 * x.1 * x.4^-1 * x.2)^2, (x.4 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.1, x.4) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 66)(34, 70)(35, 71)(36, 75)(37, 65)(38, 69)(39, 80)(40, 68)(41, 74)(42, 78)(43, 79)(44, 67)(45, 73)(46, 77)(47, 72)(48, 76)(81, 84)(82, 91)(83, 93)(85, 88)(86, 95)(87, 89)(90, 96)(92, 94) MAP : A3.276 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^4, (u.3 * u.1 * u.4^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.4 * x.2, x.4 * x.1 * x.4^-1 * x.1, (x.3 * x.1 * x.4^-1 * x.2)^2, (x.4 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.1, x.4) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 19)(18, 23)(20, 26)(21, 28)(22, 32)(24, 25)(27, 30)(29, 31)(33, 69)(34, 65)(35, 76)(36, 72)(37, 70)(38, 66)(39, 67)(40, 79)(41, 77)(42, 73)(43, 68)(44, 80)(45, 78)(46, 74)(47, 75)(48, 71)(81, 84)(82, 91)(83, 93)(85, 88)(86, 95)(87, 89)(90, 96)(92, 94) MAP : A3.277 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^4, (u.3 * u.1 * u.4^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.4 * x.2, x.4 * x.1 * x.4^-1 * x.1, (x.3 * x.1 * x.4^-1 * x.2)^2, (x.4 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.1, x.4) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 19)(18, 23)(20, 26)(21, 28)(22, 32)(24, 25)(27, 30)(29, 31)(33, 69)(34, 65)(35, 76)(36, 72)(37, 70)(38, 66)(39, 67)(40, 79)(41, 77)(42, 73)(43, 68)(44, 80)(45, 78)(46, 74)(47, 75)(48, 71)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.278 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^4, (u.3 * u.1 * u.4^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.4 * x.2, x.4 * x.1 * x.4^-1 * x.1, (x.3 * x.1 * x.4^-1 * x.2)^2, (x.4 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.1, x.4) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 20)(18, 27)(19, 29)(21, 24)(22, 31)(23, 25)(26, 32)(28, 30)(33, 69)(34, 65)(35, 76)(36, 72)(37, 70)(38, 66)(39, 67)(40, 79)(41, 77)(42, 73)(43, 68)(44, 80)(45, 78)(46, 74)(47, 75)(48, 71)(81, 83)(82, 87)(84, 90)(85, 92)(86, 96)(88, 89)(91, 94)(93, 95) MAP : A3.279 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^4, (u.3 * u.1 * u.4^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.4 * x.2, x.4 * x.1 * x.4^-1 * x.1, (x.3 * x.1 * x.4^-1 * x.2)^2, (x.4 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.1, x.4) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 20)(18, 27)(19, 29)(21, 24)(22, 31)(23, 25)(26, 32)(28, 30)(33, 69)(34, 65)(35, 76)(36, 72)(37, 70)(38, 66)(39, 67)(40, 79)(41, 77)(42, 73)(43, 68)(44, 80)(45, 78)(46, 74)(47, 75)(48, 71)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.280 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^4, (u.3 * u.1 * u.4^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.4 * x.2, x.4 * x.1 * x.4^-1 * x.1, (x.3 * x.1 * x.4^-1 * x.2)^2, (x.4 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.1, x.4) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 69)(34, 65)(35, 76)(36, 72)(37, 70)(38, 66)(39, 67)(40, 79)(41, 77)(42, 73)(43, 68)(44, 80)(45, 78)(46, 74)(47, 75)(48, 71)(81, 83)(82, 87)(84, 90)(85, 92)(86, 96)(88, 89)(91, 94)(93, 95) MAP : A3.281 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(3, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^4, (u.3 * u.1 * u.4^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.4 * x.2, x.4 * x.1 * x.4^-1 * x.1, (x.3 * x.1 * x.4^-1 * x.2)^2, (x.4 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.1, x.4) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 69)(34, 65)(35, 76)(36, 72)(37, 70)(38, 66)(39, 67)(40, 79)(41, 77)(42, 73)(43, 68)(44, 80)(45, 78)(46, 74)(47, 75)(48, 71)(81, 84)(82, 91)(83, 93)(85, 88)(86, 95)(87, 89)(90, 96)(92, 94) MAP : A3.282 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 87)(18, 90)(19, 93)(20, 81)(21, 83)(22, 82)(23, 94)(24, 92)(25, 88)(26, 96)(27, 89)(28, 91)(29, 95)(30, 84)(31, 85)(32, 86)(33, 66)(34, 72)(35, 71)(36, 70)(37, 65)(38, 73)(39, 74)(40, 69)(41, 79)(42, 76)(43, 77)(44, 67)(45, 78)(46, 80)(47, 68)(48, 75) MAP : A3.283 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 96)(18, 91)(19, 84)(20, 90)(21, 94)(22, 92)(23, 86)(24, 93)(25, 83)(26, 89)(27, 85)(28, 95)(29, 81)(30, 82)(31, 87)(32, 88)(33, 74)(34, 76)(35, 78)(36, 66)(37, 71)(38, 72)(39, 80)(40, 67)(41, 69)(42, 75)(43, 79)(44, 77)(45, 68)(46, 70)(47, 65)(48, 73) MAP : A3.284 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 96)(18, 91)(19, 84)(20, 90)(21, 94)(22, 92)(23, 86)(24, 93)(25, 83)(26, 89)(27, 85)(28, 95)(29, 81)(30, 82)(31, 87)(32, 88)(33, 79)(34, 68)(35, 72)(36, 77)(37, 73)(38, 78)(39, 69)(40, 70)(41, 80)(42, 65)(43, 74)(44, 66)(45, 76)(46, 67)(47, 75)(48, 71) MAP : A3.285 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 82)(18, 88)(19, 87)(20, 86)(21, 81)(22, 89)(23, 90)(24, 85)(25, 95)(26, 92)(27, 93)(28, 83)(29, 94)(30, 96)(31, 84)(32, 91)(33, 68)(34, 70)(35, 69)(36, 78)(37, 79)(38, 80)(39, 65)(40, 73)(41, 75)(42, 66)(43, 76)(44, 72)(45, 67)(46, 71)(47, 77)(48, 74) MAP : A3.286 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 82)(18, 88)(19, 87)(20, 86)(21, 81)(22, 89)(23, 90)(24, 85)(25, 95)(26, 92)(27, 93)(28, 83)(29, 94)(30, 96)(31, 84)(32, 91)(33, 71)(34, 74)(35, 77)(36, 65)(37, 67)(38, 66)(39, 78)(40, 76)(41, 72)(42, 80)(43, 73)(44, 75)(45, 79)(46, 68)(47, 69)(48, 70) MAP : A3.287 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 83)(18, 87)(19, 91)(20, 85)(21, 92)(22, 81)(23, 93)(24, 90)(25, 82)(26, 94)(27, 86)(28, 96)(29, 89)(30, 95)(31, 88)(32, 84)(33, 69)(34, 65)(35, 76)(36, 79)(37, 72)(38, 68)(39, 67)(40, 66)(41, 70)(42, 71)(43, 80)(44, 74)(45, 75)(46, 77)(47, 73)(48, 78) MAP : A3.288 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 83)(18, 87)(19, 91)(20, 85)(21, 92)(22, 81)(23, 93)(24, 90)(25, 82)(26, 94)(27, 86)(28, 96)(29, 89)(30, 95)(31, 88)(32, 84)(33, 68)(34, 70)(35, 69)(36, 78)(37, 79)(38, 80)(39, 65)(40, 73)(41, 75)(42, 66)(43, 76)(44, 72)(45, 67)(46, 71)(47, 77)(48, 74) MAP : A3.289 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 82)(18, 88)(19, 87)(20, 86)(21, 81)(22, 89)(23, 90)(24, 85)(25, 95)(26, 92)(27, 93)(28, 83)(29, 94)(30, 96)(31, 84)(32, 91)(33, 74)(34, 76)(35, 78)(36, 66)(37, 71)(38, 72)(39, 80)(40, 67)(41, 69)(42, 75)(43, 79)(44, 77)(45, 68)(46, 70)(47, 65)(48, 73) MAP : A3.290 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 82)(18, 88)(19, 87)(20, 86)(21, 81)(22, 89)(23, 90)(24, 85)(25, 95)(26, 92)(27, 93)(28, 83)(29, 94)(30, 96)(31, 84)(32, 91)(33, 79)(34, 68)(35, 72)(36, 77)(37, 73)(38, 78)(39, 69)(40, 70)(41, 80)(42, 65)(43, 74)(44, 66)(45, 76)(46, 67)(47, 75)(48, 71) MAP : A3.291 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 85)(18, 81)(19, 92)(20, 95)(21, 88)(22, 84)(23, 83)(24, 82)(25, 86)(26, 87)(27, 96)(28, 90)(29, 91)(30, 93)(31, 89)(32, 94)(33, 67)(34, 71)(35, 75)(36, 69)(37, 76)(38, 65)(39, 77)(40, 74)(41, 66)(42, 78)(43, 70)(44, 80)(45, 73)(46, 79)(47, 72)(48, 68) MAP : A3.292 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 96)(18, 91)(19, 84)(20, 90)(21, 94)(22, 92)(23, 86)(24, 93)(25, 83)(26, 89)(27, 85)(28, 95)(29, 81)(30, 82)(31, 87)(32, 88)(33, 68)(34, 70)(35, 69)(36, 78)(37, 79)(38, 80)(39, 65)(40, 73)(41, 75)(42, 66)(43, 76)(44, 72)(45, 67)(46, 71)(47, 77)(48, 74) MAP : A3.293 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 96)(18, 91)(19, 84)(20, 90)(21, 94)(22, 92)(23, 86)(24, 93)(25, 83)(26, 89)(27, 85)(28, 95)(29, 81)(30, 82)(31, 87)(32, 88)(33, 71)(34, 74)(35, 77)(36, 65)(37, 67)(38, 66)(39, 78)(40, 76)(41, 72)(42, 80)(43, 73)(44, 75)(45, 79)(46, 68)(47, 69)(48, 70) MAP : A3.294 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 96)(18, 91)(19, 84)(20, 90)(21, 94)(22, 92)(23, 86)(24, 93)(25, 83)(26, 89)(27, 85)(28, 95)(29, 81)(30, 82)(31, 87)(32, 88)(33, 73)(34, 79)(35, 66)(36, 75)(37, 70)(38, 77)(39, 72)(40, 68)(41, 78)(42, 69)(43, 71)(44, 65)(45, 74)(46, 76)(47, 80)(48, 67) MAP : A3.295 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 96)(18, 91)(19, 84)(20, 90)(21, 94)(22, 92)(23, 86)(24, 93)(25, 83)(26, 89)(27, 85)(28, 95)(29, 81)(30, 82)(31, 87)(32, 88)(33, 76)(34, 67)(35, 80)(36, 72)(37, 74)(38, 69)(39, 75)(40, 71)(41, 65)(42, 77)(43, 68)(44, 78)(45, 70)(46, 73)(47, 66)(48, 79) MAP : A3.296 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 86)(18, 89)(19, 81)(20, 96)(21, 84)(22, 91)(23, 82)(24, 95)(25, 93)(26, 88)(27, 83)(28, 85)(29, 87)(30, 90)(31, 94)(32, 92)(33, 68)(34, 70)(35, 69)(36, 78)(37, 79)(38, 80)(39, 65)(40, 73)(41, 75)(42, 66)(43, 76)(44, 72)(45, 67)(46, 71)(47, 77)(48, 74) MAP : A3.297 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 86)(18, 89)(19, 81)(20, 96)(21, 84)(22, 91)(23, 82)(24, 95)(25, 93)(26, 88)(27, 83)(28, 85)(29, 87)(30, 90)(31, 94)(32, 92)(33, 71)(34, 74)(35, 77)(36, 65)(37, 67)(38, 66)(39, 78)(40, 76)(41, 72)(42, 80)(43, 73)(44, 75)(45, 79)(46, 68)(47, 69)(48, 70) MAP : A3.298 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 92)(18, 83)(19, 96)(20, 88)(21, 90)(22, 85)(23, 91)(24, 87)(25, 81)(26, 93)(27, 84)(28, 94)(29, 86)(30, 89)(31, 82)(32, 95)(33, 66)(34, 72)(35, 71)(36, 70)(37, 65)(38, 73)(39, 74)(40, 69)(41, 79)(42, 76)(43, 77)(44, 67)(45, 78)(46, 80)(47, 68)(48, 75) MAP : A3.299 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 83)(18, 87)(19, 91)(20, 85)(21, 92)(22, 81)(23, 93)(24, 90)(25, 82)(26, 94)(27, 86)(28, 96)(29, 89)(30, 95)(31, 88)(32, 84)(33, 66)(34, 72)(35, 71)(36, 70)(37, 65)(38, 73)(39, 74)(40, 69)(41, 79)(42, 76)(43, 77)(44, 67)(45, 78)(46, 80)(47, 68)(48, 75) MAP : A3.300 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 86)(18, 89)(19, 81)(20, 96)(21, 84)(22, 91)(23, 82)(24, 95)(25, 93)(26, 88)(27, 83)(28, 85)(29, 87)(30, 90)(31, 94)(32, 92)(33, 77)(34, 78)(35, 73)(36, 67)(37, 75)(38, 71)(39, 79)(40, 80)(41, 74)(42, 68)(43, 66)(44, 70)(45, 72)(46, 69)(47, 76)(48, 65) MAP : A3.301 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 86)(18, 89)(19, 81)(20, 96)(21, 84)(22, 91)(23, 82)(24, 95)(25, 93)(26, 88)(27, 83)(28, 85)(29, 87)(30, 90)(31, 94)(32, 92)(33, 80)(34, 75)(35, 68)(36, 74)(37, 78)(38, 76)(39, 70)(40, 77)(41, 67)(42, 73)(43, 69)(44, 79)(45, 65)(46, 66)(47, 71)(48, 72) MAP : A3.302 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^2, u.2^8, u.3^8 > CTG (small) : <16, 6> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^2 * x.3^-2, x.2^2 * x.3^6, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 34)(18, 37)(19, 41)(20, 33)(21, 43)(22, 45)(23, 35)(24, 42)(25, 38)(26, 39)(27, 48)(28, 40)(29, 44)(30, 47)(31, 36)(32, 46)(65, 83)(66, 88)(67, 85)(68, 93)(69, 86)(70, 96)(71, 94)(72, 91)(73, 84)(74, 81)(75, 87)(76, 95)(77, 82)(78, 89)(79, 90)(80, 92) MAP : A3.303 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^2, u.2^8, u.3^8 > CTG (small) : <16, 6> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^2 * x.3^-2, x.2^2 * x.3^6, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 43)(18, 48)(19, 45)(20, 37)(21, 46)(22, 40)(23, 38)(24, 35)(25, 44)(26, 41)(27, 47)(28, 39)(29, 42)(30, 33)(31, 34)(32, 36)(65, 86)(66, 87)(67, 96)(68, 88)(69, 92)(70, 95)(71, 84)(72, 94)(73, 82)(74, 85)(75, 89)(76, 81)(77, 91)(78, 93)(79, 83)(80, 90) MAP : A3.304 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^2, u.2^8, u.3^8 > CTG (small) : <16, 6> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^2 * x.3^-2, x.2^2 * x.3^6, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 35)(18, 40)(19, 37)(20, 45)(21, 38)(22, 48)(23, 46)(24, 43)(25, 36)(26, 33)(27, 39)(28, 47)(29, 34)(30, 41)(31, 42)(32, 44)(65, 82)(66, 85)(67, 89)(68, 81)(69, 91)(70, 93)(71, 83)(72, 90)(73, 86)(74, 87)(75, 96)(76, 88)(77, 92)(78, 95)(79, 84)(80, 94) MAP : A3.305 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^2, u.2^8, u.3^8 > CTG (small) : <16, 6> CTG (fp) : < x.1, x.2, x.3 | x.1, x.2^2 * x.3^-2, x.2^2 * x.3^6, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 38)(18, 39)(19, 48)(20, 40)(21, 44)(22, 47)(23, 36)(24, 46)(25, 34)(26, 37)(27, 41)(28, 33)(29, 43)(30, 45)(31, 35)(32, 42)(65, 91)(66, 96)(67, 93)(68, 85)(69, 94)(70, 88)(71, 86)(72, 83)(73, 92)(74, 89)(75, 95)(76, 87)(77, 90)(78, 81)(79, 82)(80, 84) MAP : A3.306 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 83)(18, 87)(19, 91)(20, 85)(21, 92)(22, 81)(23, 93)(24, 90)(25, 82)(26, 94)(27, 86)(28, 96)(29, 89)(30, 95)(31, 88)(32, 84)(33, 80)(34, 75)(35, 68)(36, 74)(37, 78)(38, 76)(39, 70)(40, 77)(41, 67)(42, 73)(43, 69)(44, 79)(45, 65)(46, 66)(47, 71)(48, 72) MAP : A3.307 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 86)(18, 89)(19, 81)(20, 96)(21, 84)(22, 91)(23, 82)(24, 95)(25, 93)(26, 88)(27, 83)(28, 85)(29, 87)(30, 90)(31, 94)(32, 92)(33, 66)(34, 72)(35, 71)(36, 70)(37, 65)(38, 73)(39, 74)(40, 69)(41, 79)(42, 76)(43, 77)(44, 67)(45, 78)(46, 80)(47, 68)(48, 75) MAP : A3.308 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 86)(18, 89)(19, 81)(20, 96)(21, 84)(22, 91)(23, 82)(24, 95)(25, 93)(26, 88)(27, 83)(28, 85)(29, 87)(30, 90)(31, 94)(32, 92)(33, 69)(34, 65)(35, 76)(36, 79)(37, 72)(38, 68)(39, 67)(40, 66)(41, 70)(42, 71)(43, 80)(44, 74)(45, 75)(46, 77)(47, 73)(48, 78) MAP : A3.309 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 85)(18, 81)(19, 92)(20, 95)(21, 88)(22, 84)(23, 83)(24, 82)(25, 86)(26, 87)(27, 96)(28, 90)(29, 91)(30, 93)(31, 89)(32, 94)(33, 73)(34, 79)(35, 66)(36, 75)(37, 70)(38, 77)(39, 72)(40, 68)(41, 78)(42, 69)(43, 71)(44, 65)(45, 74)(46, 76)(47, 80)(48, 67) MAP : A3.310 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 85)(18, 81)(19, 92)(20, 95)(21, 88)(22, 84)(23, 83)(24, 82)(25, 86)(26, 87)(27, 96)(28, 90)(29, 91)(30, 93)(31, 89)(32, 94)(33, 76)(34, 67)(35, 80)(36, 72)(37, 74)(38, 69)(39, 75)(40, 71)(41, 65)(42, 77)(43, 68)(44, 78)(45, 70)(46, 73)(47, 66)(48, 79) MAP : A3.311 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 86)(18, 89)(19, 81)(20, 96)(21, 84)(22, 91)(23, 82)(24, 95)(25, 93)(26, 88)(27, 83)(28, 85)(29, 87)(30, 90)(31, 94)(32, 92)(33, 73)(34, 79)(35, 66)(36, 75)(37, 70)(38, 77)(39, 72)(40, 68)(41, 78)(42, 69)(43, 71)(44, 65)(45, 74)(46, 76)(47, 80)(48, 67) MAP : A3.312 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 86)(18, 89)(19, 81)(20, 96)(21, 84)(22, 91)(23, 82)(24, 95)(25, 93)(26, 88)(27, 83)(28, 85)(29, 87)(30, 90)(31, 94)(32, 92)(33, 76)(34, 67)(35, 80)(36, 72)(37, 74)(38, 69)(39, 75)(40, 71)(41, 65)(42, 77)(43, 68)(44, 78)(45, 70)(46, 73)(47, 66)(48, 79) MAP : A3.313 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 85)(18, 81)(19, 92)(20, 95)(21, 88)(22, 84)(23, 83)(24, 82)(25, 86)(26, 87)(27, 96)(28, 90)(29, 91)(30, 93)(31, 89)(32, 94)(33, 71)(34, 74)(35, 77)(36, 65)(37, 67)(38, 66)(39, 78)(40, 76)(41, 72)(42, 80)(43, 73)(44, 75)(45, 79)(46, 68)(47, 69)(48, 70) MAP : A3.314 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 84)(18, 86)(19, 85)(20, 94)(21, 95)(22, 96)(23, 81)(24, 89)(25, 91)(26, 82)(27, 92)(28, 88)(29, 83)(30, 87)(31, 93)(32, 90)(33, 66)(34, 72)(35, 71)(36, 70)(37, 65)(38, 73)(39, 74)(40, 69)(41, 79)(42, 76)(43, 77)(44, 67)(45, 78)(46, 80)(47, 68)(48, 75) MAP : A3.315 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 85)(18, 81)(19, 92)(20, 95)(21, 88)(22, 84)(23, 83)(24, 82)(25, 86)(26, 87)(27, 96)(28, 90)(29, 91)(30, 93)(31, 89)(32, 94)(33, 68)(34, 70)(35, 69)(36, 78)(37, 79)(38, 80)(39, 65)(40, 73)(41, 75)(42, 66)(43, 76)(44, 72)(45, 67)(46, 71)(47, 77)(48, 74) MAP : A3.316 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 85)(18, 81)(19, 92)(20, 95)(21, 88)(22, 84)(23, 83)(24, 82)(25, 86)(26, 87)(27, 96)(28, 90)(29, 91)(30, 93)(31, 89)(32, 94)(33, 79)(34, 68)(35, 72)(36, 77)(37, 73)(38, 78)(39, 69)(40, 70)(41, 80)(42, 65)(43, 74)(44, 66)(45, 76)(46, 67)(47, 75)(48, 71) MAP : A3.317 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 85)(18, 81)(19, 92)(20, 95)(21, 88)(22, 84)(23, 83)(24, 82)(25, 86)(26, 87)(27, 96)(28, 90)(29, 91)(30, 93)(31, 89)(32, 94)(33, 70)(34, 73)(35, 65)(36, 80)(37, 68)(38, 75)(39, 66)(40, 79)(41, 77)(42, 72)(43, 67)(44, 69)(45, 71)(46, 74)(47, 78)(48, 76) MAP : A3.318 NOTES : type I, reflexible, isomorphic to {3,8}, isomorphic to A3.193. QUOTIENT : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4 ] UNIGROUP : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^4, (u.1 * u.2^-1)^4, (u.2 * u.3^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1, (x.3, x.2), x.3^-3 * x.2 * x.3^-1 * x.2^3, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3) LOCAL TYPE : (8, 8, 8) #DARTS : 96 R = (1, 17, 33)(2, 18, 34)(3, 19, 35)(4, 20, 36)(5, 21, 37)(6, 22, 38)(7, 23, 39)(8, 24, 40)(9, 25, 41)(10, 26, 42)(11, 27, 43)(12, 28, 44)(13, 29, 45)(14, 30, 46)(15, 31, 47)(16, 32, 48)(49, 65, 81)(50, 66, 82)(51, 67, 83)(52, 68, 84)(53, 69, 85)(54, 70, 86)(55, 71, 87)(56, 72, 88)(57, 73, 89)(58, 74, 90)(59, 75, 91)(60, 76, 92)(61, 77, 93)(62, 78, 94)(63, 79, 95)(64, 80, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 85)(18, 81)(19, 92)(20, 95)(21, 88)(22, 84)(23, 83)(24, 82)(25, 86)(26, 87)(27, 96)(28, 90)(29, 91)(30, 93)(31, 89)(32, 94)(33, 74)(34, 76)(35, 78)(36, 66)(37, 71)(38, 72)(39, 80)(40, 67)(41, 69)(42, 75)(43, 79)(44, 77)(45, 68)(46, 70)(47, 65)(48, 73) MAP : A3.319 NOTES : type I, reflexible, isomorphic to Med2({3,7}), representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3, 2 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^2, u.1^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.2^3, (x.1^-1 * x.2^-1)^2, x.1^7, (x.1^-2 * x.2)^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 7, 4) #DARTS : 672 R = (1, 169, 337, 505)(2, 170, 338, 506)(3, 171, 339, 507)(4, 172, 340, 508)(5, 173, 341, 509)(6, 174, 342, 510)(7, 175, 343, 511)(8, 176, 344, 512)(9, 177, 345, 513)(10, 178, 346, 514)(11, 179, 347, 515)(12, 180, 348, 516)(13, 181, 349, 517)(14, 182, 350, 518)(15, 183, 351, 519)(16, 184, 352, 520)(17, 185, 353, 521)(18, 186, 354, 522)(19, 187, 355, 523)(20, 188, 356, 524)(21, 189, 357, 525)(22, 190, 358, 526)(23, 191, 359, 527)(24, 192, 360, 528)(25, 193, 361, 529)(26, 194, 362, 530)(27, 195, 363, 531)(28, 196, 364, 532)(29, 197, 365, 533)(30, 198, 366, 534)(31, 199, 367, 535)(32, 200, 368, 536)(33, 201, 369, 537)(34, 202, 370, 538)(35, 203, 371, 539)(36, 204, 372, 540)(37, 205, 373, 541)(38, 206, 374, 542)(39, 207, 375, 543)(40, 208, 376, 544)(41, 209, 377, 545)(42, 210, 378, 546)(43, 211, 379, 547)(44, 212, 380, 548)(45, 213, 381, 549)(46, 214, 382, 550)(47, 215, 383, 551)(48, 216, 384, 552)(49, 217, 385, 553)(50, 218, 386, 554)(51, 219, 387, 555)(52, 220, 388, 556)(53, 221, 389, 557)(54, 222, 390, 558)(55, 223, 391, 559)(56, 224, 392, 560)(57, 225, 393, 561)(58, 226, 394, 562)(59, 227, 395, 563)(60, 228, 396, 564)(61, 229, 397, 565)(62, 230, 398, 566)(63, 231, 399, 567)(64, 232, 400, 568)(65, 233, 401, 569)(66, 234, 402, 570)(67, 235, 403, 571)(68, 236, 404, 572)(69, 237, 405, 573)(70, 238, 406, 574)(71, 239, 407, 575)(72, 240, 408, 576)(73, 241, 409, 577)(74, 242, 410, 578)(75, 243, 411, 579)(76, 244, 412, 580)(77, 245, 413, 581)(78, 246, 414, 582)(79, 247, 415, 583)(80, 248, 416, 584)(81, 249, 417, 585)(82, 250, 418, 586)(83, 251, 419, 587)(84, 252, 420, 588)(85, 253, 421, 589)(86, 254, 422, 590)(87, 255, 423, 591)(88, 256, 424, 592)(89, 257, 425, 593)(90, 258, 426, 594)(91, 259, 427, 595)(92, 260, 428, 596)(93, 261, 429, 597)(94, 262, 430, 598)(95, 263, 431, 599)(96, 264, 432, 600)(97, 265, 433, 601)(98, 266, 434, 602)(99, 267, 435, 603)(100, 268, 436, 604)(101, 269, 437, 605)(102, 270, 438, 606)(103, 271, 439, 607)(104, 272, 440, 608)(105, 273, 441, 609)(106, 274, 442, 610)(107, 275, 443, 611)(108, 276, 444, 612)(109, 277, 445, 613)(110, 278, 446, 614)(111, 279, 447, 615)(112, 280, 448, 616)(113, 281, 449, 617)(114, 282, 450, 618)(115, 283, 451, 619)(116, 284, 452, 620)(117, 285, 453, 621)(118, 286, 454, 622)(119, 287, 455, 623)(120, 288, 456, 624)(121, 289, 457, 625)(122, 290, 458, 626)(123, 291, 459, 627)(124, 292, 460, 628)(125, 293, 461, 629)(126, 294, 462, 630)(127, 295, 463, 631)(128, 296, 464, 632)(129, 297, 465, 633)(130, 298, 466, 634)(131, 299, 467, 635)(132, 300, 468, 636)(133, 301, 469, 637)(134, 302, 470, 638)(135, 303, 471, 639)(136, 304, 472, 640)(137, 305, 473, 641)(138, 306, 474, 642)(139, 307, 475, 643)(140, 308, 476, 644)(141, 309, 477, 645)(142, 310, 478, 646)(143, 311, 479, 647)(144, 312, 480, 648)(145, 313, 481, 649)(146, 314, 482, 650)(147, 315, 483, 651)(148, 316, 484, 652)(149, 317, 485, 653)(150, 318, 486, 654)(151, 319, 487, 655)(152, 320, 488, 656)(153, 321, 489, 657)(154, 322, 490, 658)(155, 323, 491, 659)(156, 324, 492, 660)(157, 325, 493, 661)(158, 326, 494, 662)(159, 327, 495, 663)(160, 328, 496, 664)(161, 329, 497, 665)(162, 330, 498, 666)(163, 331, 499, 667)(164, 332, 500, 668)(165, 333, 501, 669)(166, 334, 502, 670)(167, 335, 503, 671)(168, 336, 504, 672) L = (1, 173)(2, 176)(3, 190)(4, 325)(5, 327)(6, 308)(7, 323)(8, 326)(9, 240)(10, 237)(11, 328)(12, 235)(13, 310)(14, 233)(15, 234)(16, 311)(17, 171)(18, 188)(19, 186)(20, 191)(21, 187)(22, 263)(23, 262)(24, 204)(25, 230)(26, 231)(27, 228)(28, 286)(29, 226)(30, 293)(31, 296)(32, 225)(33, 170)(34, 169)(35, 177)(36, 185)(37, 193)(38, 202)(39, 201)(40, 194)(41, 175)(42, 174)(43, 287)(44, 184)(45, 284)(46, 288)(47, 285)(48, 291)(49, 172)(50, 179)(51, 181)(52, 178)(53, 272)(54, 195)(55, 180)(56, 269)(57, 314)(58, 313)(59, 297)(60, 329)(61, 281)(62, 322)(63, 321)(64, 282)(65, 315)(66, 332)(67, 330)(68, 335)(69, 331)(70, 183)(71, 182)(72, 324)(73, 316)(74, 299)(75, 301)(76, 298)(77, 192)(78, 283)(79, 300)(80, 189)(81, 317)(82, 320)(83, 334)(84, 253)(85, 255)(86, 236)(87, 251)(88, 254)(89, 319)(90, 318)(91, 247)(92, 304)(93, 244)(94, 248)(95, 245)(96, 227)(97, 224)(98, 221)(99, 256)(100, 219)(101, 238)(102, 217)(103, 218)(104, 239)(105, 214)(106, 215)(107, 212)(108, 246)(109, 210)(110, 229)(111, 232)(112, 209)(113, 312)(114, 309)(115, 208)(116, 307)(117, 222)(118, 305)(119, 306)(120, 223)(121, 294)(122, 295)(123, 292)(124, 198)(125, 290)(126, 213)(127, 216)(128, 289)(129, 277)(130, 280)(131, 270)(132, 205)(133, 207)(134, 220)(135, 203)(136, 206)(137, 279)(138, 278)(139, 199)(140, 264)(141, 196)(142, 200)(143, 197)(144, 211)(145, 275)(146, 268)(147, 266)(148, 271)(149, 267)(150, 303)(151, 302)(152, 252)(153, 276)(154, 259)(155, 261)(156, 258)(157, 336)(158, 243)(159, 260)(160, 333)(161, 274)(162, 273)(163, 257)(164, 265)(165, 241)(166, 250)(167, 249)(168, 242)(337, 507)(338, 524)(339, 522)(340, 527)(341, 523)(342, 599)(343, 598)(344, 540)(345, 509)(346, 512)(347, 526)(348, 661)(349, 663)(350, 644)(351, 659)(352, 662)(353, 506)(354, 505)(355, 513)(356, 521)(357, 529)(358, 538)(359, 537)(360, 530)(361, 576)(362, 573)(363, 664)(364, 571)(365, 646)(366, 569)(367, 570)(368, 647)(369, 508)(370, 515)(371, 517)(372, 514)(373, 608)(374, 531)(375, 516)(376, 605)(377, 566)(378, 567)(379, 564)(380, 622)(381, 562)(382, 629)(383, 632)(384, 561)(385, 511)(386, 510)(387, 623)(388, 520)(389, 620)(390, 624)(391, 621)(392, 627)(393, 655)(394, 654)(395, 583)(396, 640)(397, 580)(398, 584)(399, 581)(400, 563)(401, 652)(402, 635)(403, 637)(404, 634)(405, 528)(406, 619)(407, 636)(408, 525)(409, 550)(410, 551)(411, 548)(412, 582)(413, 546)(414, 565)(415, 568)(416, 545)(417, 650)(418, 649)(419, 633)(420, 665)(421, 617)(422, 658)(423, 657)(424, 618)(425, 560)(426, 557)(427, 592)(428, 555)(429, 574)(430, 553)(431, 554)(432, 575)(433, 651)(434, 668)(435, 666)(436, 671)(437, 667)(438, 519)(439, 518)(440, 660)(441, 653)(442, 656)(443, 670)(444, 589)(445, 591)(446, 572)(447, 587)(448, 590)(449, 612)(450, 595)(451, 597)(452, 594)(453, 672)(454, 579)(455, 596)(456, 669)(457, 610)(458, 609)(459, 593)(460, 601)(461, 577)(462, 586)(463, 585)(464, 578)(465, 615)(466, 614)(467, 535)(468, 600)(469, 532)(470, 536)(471, 533)(472, 547)(473, 611)(474, 604)(475, 602)(476, 607)(477, 603)(478, 639)(479, 638)(480, 588)(481, 630)(482, 631)(483, 628)(484, 534)(485, 626)(486, 549)(487, 552)(488, 625)(489, 613)(490, 616)(491, 606)(492, 541)(493, 543)(494, 556)(495, 539)(496, 542)(497, 648)(498, 645)(499, 544)(500, 643)(501, 558)(502, 641)(503, 642)(504, 559) MAP : A3.320 NOTES : type I, reflexible, isomorphic to Med2({3,7}), isomorphic to A3.319. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 2 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^2, u.2^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.1^3, (x.1^-1 * x.2^-1)^2, x.2^7, (x.1 * x.2^-2)^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 7, 4) #DARTS : 672 R = (1, 169, 337, 505)(2, 170, 338, 506)(3, 171, 339, 507)(4, 172, 340, 508)(5, 173, 341, 509)(6, 174, 342, 510)(7, 175, 343, 511)(8, 176, 344, 512)(9, 177, 345, 513)(10, 178, 346, 514)(11, 179, 347, 515)(12, 180, 348, 516)(13, 181, 349, 517)(14, 182, 350, 518)(15, 183, 351, 519)(16, 184, 352, 520)(17, 185, 353, 521)(18, 186, 354, 522)(19, 187, 355, 523)(20, 188, 356, 524)(21, 189, 357, 525)(22, 190, 358, 526)(23, 191, 359, 527)(24, 192, 360, 528)(25, 193, 361, 529)(26, 194, 362, 530)(27, 195, 363, 531)(28, 196, 364, 532)(29, 197, 365, 533)(30, 198, 366, 534)(31, 199, 367, 535)(32, 200, 368, 536)(33, 201, 369, 537)(34, 202, 370, 538)(35, 203, 371, 539)(36, 204, 372, 540)(37, 205, 373, 541)(38, 206, 374, 542)(39, 207, 375, 543)(40, 208, 376, 544)(41, 209, 377, 545)(42, 210, 378, 546)(43, 211, 379, 547)(44, 212, 380, 548)(45, 213, 381, 549)(46, 214, 382, 550)(47, 215, 383, 551)(48, 216, 384, 552)(49, 217, 385, 553)(50, 218, 386, 554)(51, 219, 387, 555)(52, 220, 388, 556)(53, 221, 389, 557)(54, 222, 390, 558)(55, 223, 391, 559)(56, 224, 392, 560)(57, 225, 393, 561)(58, 226, 394, 562)(59, 227, 395, 563)(60, 228, 396, 564)(61, 229, 397, 565)(62, 230, 398, 566)(63, 231, 399, 567)(64, 232, 400, 568)(65, 233, 401, 569)(66, 234, 402, 570)(67, 235, 403, 571)(68, 236, 404, 572)(69, 237, 405, 573)(70, 238, 406, 574)(71, 239, 407, 575)(72, 240, 408, 576)(73, 241, 409, 577)(74, 242, 410, 578)(75, 243, 411, 579)(76, 244, 412, 580)(77, 245, 413, 581)(78, 246, 414, 582)(79, 247, 415, 583)(80, 248, 416, 584)(81, 249, 417, 585)(82, 250, 418, 586)(83, 251, 419, 587)(84, 252, 420, 588)(85, 253, 421, 589)(86, 254, 422, 590)(87, 255, 423, 591)(88, 256, 424, 592)(89, 257, 425, 593)(90, 258, 426, 594)(91, 259, 427, 595)(92, 260, 428, 596)(93, 261, 429, 597)(94, 262, 430, 598)(95, 263, 431, 599)(96, 264, 432, 600)(97, 265, 433, 601)(98, 266, 434, 602)(99, 267, 435, 603)(100, 268, 436, 604)(101, 269, 437, 605)(102, 270, 438, 606)(103, 271, 439, 607)(104, 272, 440, 608)(105, 273, 441, 609)(106, 274, 442, 610)(107, 275, 443, 611)(108, 276, 444, 612)(109, 277, 445, 613)(110, 278, 446, 614)(111, 279, 447, 615)(112, 280, 448, 616)(113, 281, 449, 617)(114, 282, 450, 618)(115, 283, 451, 619)(116, 284, 452, 620)(117, 285, 453, 621)(118, 286, 454, 622)(119, 287, 455, 623)(120, 288, 456, 624)(121, 289, 457, 625)(122, 290, 458, 626)(123, 291, 459, 627)(124, 292, 460, 628)(125, 293, 461, 629)(126, 294, 462, 630)(127, 295, 463, 631)(128, 296, 464, 632)(129, 297, 465, 633)(130, 298, 466, 634)(131, 299, 467, 635)(132, 300, 468, 636)(133, 301, 469, 637)(134, 302, 470, 638)(135, 303, 471, 639)(136, 304, 472, 640)(137, 305, 473, 641)(138, 306, 474, 642)(139, 307, 475, 643)(140, 308, 476, 644)(141, 309, 477, 645)(142, 310, 478, 646)(143, 311, 479, 647)(144, 312, 480, 648)(145, 313, 481, 649)(146, 314, 482, 650)(147, 315, 483, 651)(148, 316, 484, 652)(149, 317, 485, 653)(150, 318, 486, 654)(151, 319, 487, 655)(152, 320, 488, 656)(153, 321, 489, 657)(154, 322, 490, 658)(155, 323, 491, 659)(156, 324, 492, 660)(157, 325, 493, 661)(158, 326, 494, 662)(159, 327, 495, 663)(160, 328, 496, 664)(161, 329, 497, 665)(162, 330, 498, 666)(163, 331, 499, 667)(164, 332, 500, 668)(165, 333, 501, 669)(166, 334, 502, 670)(167, 335, 503, 671)(168, 336, 504, 672) L = (1, 171)(2, 188)(3, 186)(4, 191)(5, 187)(6, 263)(7, 262)(8, 204)(9, 173)(10, 176)(11, 190)(12, 325)(13, 327)(14, 308)(15, 323)(16, 326)(17, 170)(18, 169)(19, 177)(20, 185)(21, 193)(22, 202)(23, 201)(24, 194)(25, 240)(26, 237)(27, 328)(28, 235)(29, 310)(30, 233)(31, 234)(32, 311)(33, 172)(34, 179)(35, 181)(36, 178)(37, 272)(38, 195)(39, 180)(40, 269)(41, 230)(42, 231)(43, 228)(44, 286)(45, 226)(46, 293)(47, 296)(48, 225)(49, 175)(50, 174)(51, 287)(52, 184)(53, 284)(54, 288)(55, 285)(56, 291)(57, 319)(58, 318)(59, 247)(60, 304)(61, 244)(62, 248)(63, 245)(64, 227)(65, 316)(66, 299)(67, 301)(68, 298)(69, 192)(70, 283)(71, 300)(72, 189)(73, 214)(74, 215)(75, 212)(76, 246)(77, 210)(78, 229)(79, 232)(80, 209)(81, 314)(82, 313)(83, 297)(84, 329)(85, 281)(86, 322)(87, 321)(88, 282)(89, 224)(90, 221)(91, 256)(92, 219)(93, 238)(94, 217)(95, 218)(96, 239)(97, 315)(98, 332)(99, 330)(100, 335)(101, 331)(102, 183)(103, 182)(104, 324)(105, 317)(106, 320)(107, 334)(108, 253)(109, 255)(110, 236)(111, 251)(112, 254)(113, 276)(114, 259)(115, 261)(116, 258)(117, 336)(118, 243)(119, 260)(120, 333)(121, 274)(122, 273)(123, 257)(124, 265)(125, 241)(126, 250)(127, 249)(128, 242)(129, 279)(130, 278)(131, 199)(132, 264)(133, 196)(134, 200)(135, 197)(136, 211)(137, 275)(138, 268)(139, 266)(140, 271)(141, 267)(142, 303)(143, 302)(144, 252)(145, 294)(146, 295)(147, 292)(148, 198)(149, 290)(150, 213)(151, 216)(152, 289)(153, 277)(154, 280)(155, 270)(156, 205)(157, 207)(158, 220)(159, 203)(160, 206)(161, 312)(162, 309)(163, 208)(164, 307)(165, 222)(166, 305)(167, 306)(168, 223)(337, 621)(338, 624)(339, 638)(340, 605)(341, 607)(342, 588)(343, 603)(344, 606)(345, 520)(346, 517)(347, 608)(348, 515)(349, 590)(350, 513)(351, 514)(352, 591)(353, 619)(354, 636)(355, 634)(356, 639)(357, 635)(358, 543)(359, 542)(360, 652)(361, 510)(362, 511)(363, 508)(364, 566)(365, 506)(366, 573)(367, 576)(368, 505)(369, 618)(370, 617)(371, 625)(372, 633)(373, 641)(374, 650)(375, 649)(376, 642)(377, 623)(378, 622)(379, 567)(380, 632)(381, 564)(382, 568)(383, 565)(384, 571)(385, 620)(386, 627)(387, 629)(388, 626)(389, 552)(390, 643)(391, 628)(392, 549)(393, 594)(394, 593)(395, 577)(396, 609)(397, 561)(398, 602)(399, 601)(400, 562)(401, 595)(402, 612)(403, 610)(404, 615)(405, 611)(406, 631)(407, 630)(408, 604)(409, 596)(410, 579)(411, 581)(412, 578)(413, 640)(414, 563)(415, 580)(416, 637)(417, 597)(418, 600)(419, 614)(420, 533)(421, 535)(422, 516)(423, 531)(424, 534)(425, 599)(426, 598)(427, 527)(428, 584)(429, 524)(430, 528)(431, 525)(432, 507)(433, 672)(434, 669)(435, 536)(436, 667)(437, 518)(438, 665)(439, 666)(440, 519)(441, 662)(442, 663)(443, 660)(444, 526)(445, 658)(446, 509)(447, 512)(448, 657)(449, 592)(450, 589)(451, 656)(452, 587)(453, 670)(454, 585)(455, 586)(456, 671)(457, 574)(458, 575)(459, 572)(460, 646)(461, 570)(462, 661)(463, 664)(464, 569)(465, 557)(466, 560)(467, 550)(468, 653)(469, 655)(470, 668)(471, 651)(472, 654)(473, 559)(474, 558)(475, 647)(476, 544)(477, 644)(478, 648)(479, 645)(480, 659)(481, 555)(482, 548)(483, 546)(484, 551)(485, 547)(486, 583)(487, 582)(488, 532)(489, 556)(490, 539)(491, 541)(492, 538)(493, 616)(494, 523)(495, 540)(496, 613)(497, 554)(498, 553)(499, 537)(500, 545)(501, 521)(502, 530)(503, 529)(504, 522) MAP : A3.321 NOTES : type I, reflexible, isomorphic to Med2({3,7}), isomorphic to A3.319. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 2 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^2, u.2^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.1^3, (x.1^-1 * x.2^-1)^2, x.2^7, (x.1 * x.2^-2)^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 7, 4) #DARTS : 672 R = (1, 169, 337, 505)(2, 170, 338, 506)(3, 171, 339, 507)(4, 172, 340, 508)(5, 173, 341, 509)(6, 174, 342, 510)(7, 175, 343, 511)(8, 176, 344, 512)(9, 177, 345, 513)(10, 178, 346, 514)(11, 179, 347, 515)(12, 180, 348, 516)(13, 181, 349, 517)(14, 182, 350, 518)(15, 183, 351, 519)(16, 184, 352, 520)(17, 185, 353, 521)(18, 186, 354, 522)(19, 187, 355, 523)(20, 188, 356, 524)(21, 189, 357, 525)(22, 190, 358, 526)(23, 191, 359, 527)(24, 192, 360, 528)(25, 193, 361, 529)(26, 194, 362, 530)(27, 195, 363, 531)(28, 196, 364, 532)(29, 197, 365, 533)(30, 198, 366, 534)(31, 199, 367, 535)(32, 200, 368, 536)(33, 201, 369, 537)(34, 202, 370, 538)(35, 203, 371, 539)(36, 204, 372, 540)(37, 205, 373, 541)(38, 206, 374, 542)(39, 207, 375, 543)(40, 208, 376, 544)(41, 209, 377, 545)(42, 210, 378, 546)(43, 211, 379, 547)(44, 212, 380, 548)(45, 213, 381, 549)(46, 214, 382, 550)(47, 215, 383, 551)(48, 216, 384, 552)(49, 217, 385, 553)(50, 218, 386, 554)(51, 219, 387, 555)(52, 220, 388, 556)(53, 221, 389, 557)(54, 222, 390, 558)(55, 223, 391, 559)(56, 224, 392, 560)(57, 225, 393, 561)(58, 226, 394, 562)(59, 227, 395, 563)(60, 228, 396, 564)(61, 229, 397, 565)(62, 230, 398, 566)(63, 231, 399, 567)(64, 232, 400, 568)(65, 233, 401, 569)(66, 234, 402, 570)(67, 235, 403, 571)(68, 236, 404, 572)(69, 237, 405, 573)(70, 238, 406, 574)(71, 239, 407, 575)(72, 240, 408, 576)(73, 241, 409, 577)(74, 242, 410, 578)(75, 243, 411, 579)(76, 244, 412, 580)(77, 245, 413, 581)(78, 246, 414, 582)(79, 247, 415, 583)(80, 248, 416, 584)(81, 249, 417, 585)(82, 250, 418, 586)(83, 251, 419, 587)(84, 252, 420, 588)(85, 253, 421, 589)(86, 254, 422, 590)(87, 255, 423, 591)(88, 256, 424, 592)(89, 257, 425, 593)(90, 258, 426, 594)(91, 259, 427, 595)(92, 260, 428, 596)(93, 261, 429, 597)(94, 262, 430, 598)(95, 263, 431, 599)(96, 264, 432, 600)(97, 265, 433, 601)(98, 266, 434, 602)(99, 267, 435, 603)(100, 268, 436, 604)(101, 269, 437, 605)(102, 270, 438, 606)(103, 271, 439, 607)(104, 272, 440, 608)(105, 273, 441, 609)(106, 274, 442, 610)(107, 275, 443, 611)(108, 276, 444, 612)(109, 277, 445, 613)(110, 278, 446, 614)(111, 279, 447, 615)(112, 280, 448, 616)(113, 281, 449, 617)(114, 282, 450, 618)(115, 283, 451, 619)(116, 284, 452, 620)(117, 285, 453, 621)(118, 286, 454, 622)(119, 287, 455, 623)(120, 288, 456, 624)(121, 289, 457, 625)(122, 290, 458, 626)(123, 291, 459, 627)(124, 292, 460, 628)(125, 293, 461, 629)(126, 294, 462, 630)(127, 295, 463, 631)(128, 296, 464, 632)(129, 297, 465, 633)(130, 298, 466, 634)(131, 299, 467, 635)(132, 300, 468, 636)(133, 301, 469, 637)(134, 302, 470, 638)(135, 303, 471, 639)(136, 304, 472, 640)(137, 305, 473, 641)(138, 306, 474, 642)(139, 307, 475, 643)(140, 308, 476, 644)(141, 309, 477, 645)(142, 310, 478, 646)(143, 311, 479, 647)(144, 312, 480, 648)(145, 313, 481, 649)(146, 314, 482, 650)(147, 315, 483, 651)(148, 316, 484, 652)(149, 317, 485, 653)(150, 318, 486, 654)(151, 319, 487, 655)(152, 320, 488, 656)(153, 321, 489, 657)(154, 322, 490, 658)(155, 323, 491, 659)(156, 324, 492, 660)(157, 325, 493, 661)(158, 326, 494, 662)(159, 327, 495, 663)(160, 328, 496, 664)(161, 329, 497, 665)(162, 330, 498, 666)(163, 331, 499, 667)(164, 332, 500, 668)(165, 333, 501, 669)(166, 334, 502, 670)(167, 335, 503, 671)(168, 336, 504, 672) L = (1, 171)(2, 188)(3, 186)(4, 191)(5, 187)(6, 263)(7, 262)(8, 204)(9, 173)(10, 176)(11, 190)(12, 325)(13, 327)(14, 308)(15, 323)(16, 326)(17, 170)(18, 169)(19, 177)(20, 185)(21, 193)(22, 202)(23, 201)(24, 194)(25, 240)(26, 237)(27, 328)(28, 235)(29, 310)(30, 233)(31, 234)(32, 311)(33, 172)(34, 179)(35, 181)(36, 178)(37, 272)(38, 195)(39, 180)(40, 269)(41, 230)(42, 231)(43, 228)(44, 286)(45, 226)(46, 293)(47, 296)(48, 225)(49, 175)(50, 174)(51, 287)(52, 184)(53, 284)(54, 288)(55, 285)(56, 291)(57, 319)(58, 318)(59, 247)(60, 304)(61, 244)(62, 248)(63, 245)(64, 227)(65, 316)(66, 299)(67, 301)(68, 298)(69, 192)(70, 283)(71, 300)(72, 189)(73, 214)(74, 215)(75, 212)(76, 246)(77, 210)(78, 229)(79, 232)(80, 209)(81, 314)(82, 313)(83, 297)(84, 329)(85, 281)(86, 322)(87, 321)(88, 282)(89, 224)(90, 221)(91, 256)(92, 219)(93, 238)(94, 217)(95, 218)(96, 239)(97, 315)(98, 332)(99, 330)(100, 335)(101, 331)(102, 183)(103, 182)(104, 324)(105, 317)(106, 320)(107, 334)(108, 253)(109, 255)(110, 236)(111, 251)(112, 254)(113, 276)(114, 259)(115, 261)(116, 258)(117, 336)(118, 243)(119, 260)(120, 333)(121, 274)(122, 273)(123, 257)(124, 265)(125, 241)(126, 250)(127, 249)(128, 242)(129, 279)(130, 278)(131, 199)(132, 264)(133, 196)(134, 200)(135, 197)(136, 211)(137, 275)(138, 268)(139, 266)(140, 271)(141, 267)(142, 303)(143, 302)(144, 252)(145, 294)(146, 295)(147, 292)(148, 198)(149, 290)(150, 213)(151, 216)(152, 289)(153, 277)(154, 280)(155, 270)(156, 205)(157, 207)(158, 220)(159, 203)(160, 206)(161, 312)(162, 309)(163, 208)(164, 307)(165, 222)(166, 305)(167, 306)(168, 223)(337, 509)(338, 512)(339, 526)(340, 661)(341, 663)(342, 644)(343, 659)(344, 662)(345, 576)(346, 573)(347, 664)(348, 571)(349, 646)(350, 569)(351, 570)(352, 647)(353, 507)(354, 524)(355, 522)(356, 527)(357, 523)(358, 599)(359, 598)(360, 540)(361, 566)(362, 567)(363, 564)(364, 622)(365, 562)(366, 629)(367, 632)(368, 561)(369, 506)(370, 505)(371, 513)(372, 521)(373, 529)(374, 538)(375, 537)(376, 530)(377, 511)(378, 510)(379, 623)(380, 520)(381, 620)(382, 624)(383, 621)(384, 627)(385, 508)(386, 515)(387, 517)(388, 514)(389, 608)(390, 531)(391, 516)(392, 605)(393, 650)(394, 649)(395, 633)(396, 665)(397, 617)(398, 658)(399, 657)(400, 618)(401, 651)(402, 668)(403, 666)(404, 671)(405, 667)(406, 519)(407, 518)(408, 660)(409, 652)(410, 635)(411, 637)(412, 634)(413, 528)(414, 619)(415, 636)(416, 525)(417, 653)(418, 656)(419, 670)(420, 589)(421, 591)(422, 572)(423, 587)(424, 590)(425, 655)(426, 654)(427, 583)(428, 640)(429, 580)(430, 584)(431, 581)(432, 563)(433, 560)(434, 557)(435, 592)(436, 555)(437, 574)(438, 553)(439, 554)(440, 575)(441, 550)(442, 551)(443, 548)(444, 582)(445, 546)(446, 565)(447, 568)(448, 545)(449, 648)(450, 645)(451, 544)(452, 643)(453, 558)(454, 641)(455, 642)(456, 559)(457, 630)(458, 631)(459, 628)(460, 534)(461, 626)(462, 549)(463, 552)(464, 625)(465, 613)(466, 616)(467, 606)(468, 541)(469, 543)(470, 556)(471, 539)(472, 542)(473, 615)(474, 614)(475, 535)(476, 600)(477, 532)(478, 536)(479, 533)(480, 547)(481, 611)(482, 604)(483, 602)(484, 607)(485, 603)(486, 639)(487, 638)(488, 588)(489, 612)(490, 595)(491, 597)(492, 594)(493, 672)(494, 579)(495, 596)(496, 669)(497, 610)(498, 609)(499, 593)(500, 601)(501, 577)(502, 586)(503, 585)(504, 578) MAP : A3.322 NOTES : type I, reflexible, isomorphic to Med2({3,7}), isomorphic to A3.319. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3, 2 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^2, u.1^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.2^3, (x.1^-1 * x.2^-1)^2, x.1^7, (x.1^-2 * x.2)^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 7, 4) #DARTS : 672 R = (1, 169, 337, 505)(2, 170, 338, 506)(3, 171, 339, 507)(4, 172, 340, 508)(5, 173, 341, 509)(6, 174, 342, 510)(7, 175, 343, 511)(8, 176, 344, 512)(9, 177, 345, 513)(10, 178, 346, 514)(11, 179, 347, 515)(12, 180, 348, 516)(13, 181, 349, 517)(14, 182, 350, 518)(15, 183, 351, 519)(16, 184, 352, 520)(17, 185, 353, 521)(18, 186, 354, 522)(19, 187, 355, 523)(20, 188, 356, 524)(21, 189, 357, 525)(22, 190, 358, 526)(23, 191, 359, 527)(24, 192, 360, 528)(25, 193, 361, 529)(26, 194, 362, 530)(27, 195, 363, 531)(28, 196, 364, 532)(29, 197, 365, 533)(30, 198, 366, 534)(31, 199, 367, 535)(32, 200, 368, 536)(33, 201, 369, 537)(34, 202, 370, 538)(35, 203, 371, 539)(36, 204, 372, 540)(37, 205, 373, 541)(38, 206, 374, 542)(39, 207, 375, 543)(40, 208, 376, 544)(41, 209, 377, 545)(42, 210, 378, 546)(43, 211, 379, 547)(44, 212, 380, 548)(45, 213, 381, 549)(46, 214, 382, 550)(47, 215, 383, 551)(48, 216, 384, 552)(49, 217, 385, 553)(50, 218, 386, 554)(51, 219, 387, 555)(52, 220, 388, 556)(53, 221, 389, 557)(54, 222, 390, 558)(55, 223, 391, 559)(56, 224, 392, 560)(57, 225, 393, 561)(58, 226, 394, 562)(59, 227, 395, 563)(60, 228, 396, 564)(61, 229, 397, 565)(62, 230, 398, 566)(63, 231, 399, 567)(64, 232, 400, 568)(65, 233, 401, 569)(66, 234, 402, 570)(67, 235, 403, 571)(68, 236, 404, 572)(69, 237, 405, 573)(70, 238, 406, 574)(71, 239, 407, 575)(72, 240, 408, 576)(73, 241, 409, 577)(74, 242, 410, 578)(75, 243, 411, 579)(76, 244, 412, 580)(77, 245, 413, 581)(78, 246, 414, 582)(79, 247, 415, 583)(80, 248, 416, 584)(81, 249, 417, 585)(82, 250, 418, 586)(83, 251, 419, 587)(84, 252, 420, 588)(85, 253, 421, 589)(86, 254, 422, 590)(87, 255, 423, 591)(88, 256, 424, 592)(89, 257, 425, 593)(90, 258, 426, 594)(91, 259, 427, 595)(92, 260, 428, 596)(93, 261, 429, 597)(94, 262, 430, 598)(95, 263, 431, 599)(96, 264, 432, 600)(97, 265, 433, 601)(98, 266, 434, 602)(99, 267, 435, 603)(100, 268, 436, 604)(101, 269, 437, 605)(102, 270, 438, 606)(103, 271, 439, 607)(104, 272, 440, 608)(105, 273, 441, 609)(106, 274, 442, 610)(107, 275, 443, 611)(108, 276, 444, 612)(109, 277, 445, 613)(110, 278, 446, 614)(111, 279, 447, 615)(112, 280, 448, 616)(113, 281, 449, 617)(114, 282, 450, 618)(115, 283, 451, 619)(116, 284, 452, 620)(117, 285, 453, 621)(118, 286, 454, 622)(119, 287, 455, 623)(120, 288, 456, 624)(121, 289, 457, 625)(122, 290, 458, 626)(123, 291, 459, 627)(124, 292, 460, 628)(125, 293, 461, 629)(126, 294, 462, 630)(127, 295, 463, 631)(128, 296, 464, 632)(129, 297, 465, 633)(130, 298, 466, 634)(131, 299, 467, 635)(132, 300, 468, 636)(133, 301, 469, 637)(134, 302, 470, 638)(135, 303, 471, 639)(136, 304, 472, 640)(137, 305, 473, 641)(138, 306, 474, 642)(139, 307, 475, 643)(140, 308, 476, 644)(141, 309, 477, 645)(142, 310, 478, 646)(143, 311, 479, 647)(144, 312, 480, 648)(145, 313, 481, 649)(146, 314, 482, 650)(147, 315, 483, 651)(148, 316, 484, 652)(149, 317, 485, 653)(150, 318, 486, 654)(151, 319, 487, 655)(152, 320, 488, 656)(153, 321, 489, 657)(154, 322, 490, 658)(155, 323, 491, 659)(156, 324, 492, 660)(157, 325, 493, 661)(158, 326, 494, 662)(159, 327, 495, 663)(160, 328, 496, 664)(161, 329, 497, 665)(162, 330, 498, 666)(163, 331, 499, 667)(164, 332, 500, 668)(165, 333, 501, 669)(166, 334, 502, 670)(167, 335, 503, 671)(168, 336, 504, 672) L = (1, 260)(2, 243)(3, 245)(4, 242)(5, 304)(6, 227)(7, 244)(8, 301)(9, 258)(10, 257)(11, 241)(12, 273)(13, 225)(14, 266)(15, 265)(16, 226)(17, 263)(18, 262)(19, 191)(20, 248)(21, 188)(22, 192)(23, 189)(24, 171)(25, 259)(26, 276)(27, 274)(28, 279)(29, 275)(30, 295)(31, 294)(32, 268)(33, 326)(34, 327)(35, 324)(36, 190)(37, 322)(38, 173)(39, 176)(40, 321)(41, 261)(42, 264)(43, 278)(44, 197)(45, 199)(46, 180)(47, 195)(48, 198)(49, 336)(50, 333)(51, 200)(52, 331)(53, 182)(54, 329)(55, 330)(56, 183)(57, 219)(58, 212)(59, 210)(60, 215)(61, 211)(62, 247)(63, 246)(64, 196)(65, 221)(66, 224)(67, 214)(68, 317)(69, 319)(70, 332)(71, 315)(72, 318)(73, 218)(74, 217)(75, 201)(76, 209)(77, 185)(78, 194)(79, 193)(80, 186)(81, 256)(82, 253)(83, 320)(84, 251)(85, 334)(86, 249)(87, 250)(88, 335)(89, 220)(90, 203)(91, 205)(92, 202)(93, 280)(94, 187)(95, 204)(96, 277)(97, 238)(98, 239)(99, 236)(100, 310)(101, 234)(102, 325)(103, 328)(104, 233)(105, 223)(106, 222)(107, 311)(108, 208)(109, 308)(110, 312)(111, 309)(112, 323)(113, 287)(114, 286)(115, 231)(116, 296)(117, 228)(118, 232)(119, 229)(120, 235)(121, 284)(122, 291)(123, 293)(124, 290)(125, 216)(126, 307)(127, 292)(128, 213)(129, 174)(130, 175)(131, 172)(132, 230)(133, 170)(134, 237)(135, 240)(136, 169)(137, 282)(138, 281)(139, 289)(140, 297)(141, 305)(142, 314)(143, 313)(144, 306)(145, 184)(146, 181)(147, 272)(148, 179)(149, 254)(150, 177)(151, 178)(152, 255)(153, 283)(154, 300)(155, 298)(156, 303)(157, 299)(158, 207)(159, 206)(160, 316)(161, 285)(162, 288)(163, 302)(164, 269)(165, 271)(166, 252)(167, 267)(168, 270)(337, 588)(338, 603)(339, 605)(340, 602)(341, 624)(342, 611)(343, 604)(344, 621)(345, 586)(346, 585)(347, 601)(348, 569)(349, 609)(350, 562)(351, 561)(352, 610)(353, 591)(354, 590)(355, 519)(356, 608)(357, 516)(358, 520)(359, 517)(360, 531)(361, 587)(362, 572)(363, 570)(364, 575)(365, 571)(366, 647)(367, 646)(368, 564)(369, 670)(370, 671)(371, 668)(372, 518)(373, 666)(374, 533)(375, 536)(376, 665)(377, 589)(378, 592)(379, 574)(380, 557)(381, 559)(382, 548)(383, 555)(384, 558)(385, 656)(386, 653)(387, 560)(388, 651)(389, 550)(390, 649)(391, 650)(392, 551)(393, 523)(394, 540)(395, 538)(396, 543)(397, 539)(398, 607)(399, 606)(400, 556)(401, 525)(402, 528)(403, 542)(404, 637)(405, 639)(406, 652)(407, 635)(408, 638)(409, 522)(410, 521)(411, 505)(412, 537)(413, 513)(414, 554)(415, 553)(416, 514)(417, 584)(418, 581)(419, 640)(420, 579)(421, 654)(422, 577)(423, 578)(424, 655)(425, 524)(426, 507)(427, 509)(428, 506)(429, 576)(430, 515)(431, 508)(432, 573)(433, 598)(434, 599)(435, 596)(436, 662)(437, 594)(438, 669)(439, 672)(440, 593)(441, 527)(442, 526)(443, 663)(444, 512)(445, 660)(446, 664)(447, 661)(448, 667)(449, 631)(450, 630)(451, 615)(452, 648)(453, 612)(454, 616)(455, 613)(456, 595)(457, 628)(458, 643)(459, 645)(460, 642)(461, 544)(462, 659)(463, 644)(464, 541)(465, 534)(466, 535)(467, 532)(468, 614)(469, 530)(470, 597)(471, 600)(472, 529)(473, 626)(474, 625)(475, 641)(476, 617)(477, 657)(478, 634)(479, 633)(480, 658)(481, 552)(482, 549)(483, 568)(484, 547)(485, 582)(486, 545)(487, 546)(488, 583)(489, 627)(490, 620)(491, 618)(492, 623)(493, 619)(494, 511)(495, 510)(496, 636)(497, 629)(498, 632)(499, 622)(500, 565)(501, 567)(502, 580)(503, 563)(504, 566) MAP : A3.323 NOTES : type I, reflexible, isomorphic to Med2({3,8}), representative. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.2^3, x.4^3, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-1, (x.3 * x.2^-1)^3, x.2 * x.3 * x.4^-1 * x.3^-1 * x.2^-1 * x.3 * x.4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 384 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192)(193, 241, 289, 337)(194, 242, 290, 338)(195, 243, 291, 339)(196, 244, 292, 340)(197, 245, 293, 341)(198, 246, 294, 342)(199, 247, 295, 343)(200, 248, 296, 344)(201, 249, 297, 345)(202, 250, 298, 346)(203, 251, 299, 347)(204, 252, 300, 348)(205, 253, 301, 349)(206, 254, 302, 350)(207, 255, 303, 351)(208, 256, 304, 352)(209, 257, 305, 353)(210, 258, 306, 354)(211, 259, 307, 355)(212, 260, 308, 356)(213, 261, 309, 357)(214, 262, 310, 358)(215, 263, 311, 359)(216, 264, 312, 360)(217, 265, 313, 361)(218, 266, 314, 362)(219, 267, 315, 363)(220, 268, 316, 364)(221, 269, 317, 365)(222, 270, 318, 366)(223, 271, 319, 367)(224, 272, 320, 368)(225, 273, 321, 369)(226, 274, 322, 370)(227, 275, 323, 371)(228, 276, 324, 372)(229, 277, 325, 373)(230, 278, 326, 374)(231, 279, 327, 375)(232, 280, 328, 376)(233, 281, 329, 377)(234, 282, 330, 378)(235, 283, 331, 379)(236, 284, 332, 380)(237, 285, 333, 381)(238, 286, 334, 382)(239, 287, 335, 383)(240, 288, 336, 384) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 102)(50, 106)(51, 97)(52, 105)(53, 109)(54, 99)(55, 142)(56, 112)(57, 136)(58, 133)(59, 126)(60, 103)(61, 130)(62, 123)(63, 129)(64, 132)(65, 127)(66, 125)(67, 111)(68, 128)(69, 122)(70, 143)(71, 107)(72, 121)(73, 144)(74, 141)(75, 140)(76, 139)(77, 138)(78, 119)(79, 134)(80, 137)(81, 115)(82, 101)(83, 118)(84, 104)(85, 98)(86, 113)(87, 124)(88, 100)(89, 116)(90, 114)(91, 135)(92, 110)(93, 117)(94, 108)(95, 131)(96, 120)(145, 284)(146, 276)(147, 260)(148, 254)(149, 272)(150, 261)(151, 277)(152, 252)(153, 273)(154, 257)(155, 248)(156, 281)(157, 275)(158, 288)(159, 258)(160, 262)(161, 253)(162, 246)(163, 283)(164, 271)(165, 255)(166, 249)(167, 241)(168, 243)(169, 242)(170, 270)(171, 269)(172, 266)(173, 247)(174, 274)(175, 264)(176, 282)(177, 256)(178, 268)(179, 250)(180, 285)(181, 267)(182, 286)(183, 244)(184, 245)(185, 251)(186, 280)(187, 278)(188, 287)(189, 265)(190, 259)(191, 263)(192, 279)(289, 366)(290, 360)(291, 384)(292, 379)(293, 345)(294, 378)(295, 354)(296, 359)(297, 371)(298, 383)(299, 368)(300, 372)(301, 374)(302, 376)(303, 381)(304, 351)(305, 338)(306, 355)(307, 343)(308, 342)(309, 337)(310, 344)(311, 358)(312, 353)(313, 362)(314, 375)(315, 346)(316, 349)(317, 350)(318, 357)(319, 377)(320, 370)(321, 340)(322, 347)(323, 341)(324, 373)(325, 348)(326, 364)(327, 361)(328, 365)(329, 382)(330, 356)(331, 369)(332, 339)(333, 352)(334, 367)(335, 363)(336, 380) MAP : A3.324 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A3.323. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.2^3, x.4^3, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-1, (x.3 * x.2^-1)^3, x.2 * x.3 * x.4^-1 * x.3^-1 * x.2^-1 * x.3 * x.4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 384 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192)(193, 241, 289, 337)(194, 242, 290, 338)(195, 243, 291, 339)(196, 244, 292, 340)(197, 245, 293, 341)(198, 246, 294, 342)(199, 247, 295, 343)(200, 248, 296, 344)(201, 249, 297, 345)(202, 250, 298, 346)(203, 251, 299, 347)(204, 252, 300, 348)(205, 253, 301, 349)(206, 254, 302, 350)(207, 255, 303, 351)(208, 256, 304, 352)(209, 257, 305, 353)(210, 258, 306, 354)(211, 259, 307, 355)(212, 260, 308, 356)(213, 261, 309, 357)(214, 262, 310, 358)(215, 263, 311, 359)(216, 264, 312, 360)(217, 265, 313, 361)(218, 266, 314, 362)(219, 267, 315, 363)(220, 268, 316, 364)(221, 269, 317, 365)(222, 270, 318, 366)(223, 271, 319, 367)(224, 272, 320, 368)(225, 273, 321, 369)(226, 274, 322, 370)(227, 275, 323, 371)(228, 276, 324, 372)(229, 277, 325, 373)(230, 278, 326, 374)(231, 279, 327, 375)(232, 280, 328, 376)(233, 281, 329, 377)(234, 282, 330, 378)(235, 283, 331, 379)(236, 284, 332, 380)(237, 285, 333, 381)(238, 286, 334, 382)(239, 287, 335, 383)(240, 288, 336, 384) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 102)(50, 106)(51, 97)(52, 105)(53, 109)(54, 99)(55, 142)(56, 112)(57, 136)(58, 133)(59, 126)(60, 103)(61, 130)(62, 123)(63, 129)(64, 132)(65, 127)(66, 125)(67, 111)(68, 128)(69, 122)(70, 143)(71, 107)(72, 121)(73, 144)(74, 141)(75, 140)(76, 139)(77, 138)(78, 119)(79, 134)(80, 137)(81, 115)(82, 101)(83, 118)(84, 104)(85, 98)(86, 113)(87, 124)(88, 100)(89, 116)(90, 114)(91, 135)(92, 110)(93, 117)(94, 108)(95, 131)(96, 120)(145, 245)(146, 241)(147, 268)(148, 257)(149, 259)(150, 244)(151, 243)(152, 246)(153, 277)(154, 251)(155, 258)(156, 261)(157, 252)(158, 253)(159, 288)(160, 269)(161, 248)(162, 279)(163, 242)(164, 266)(165, 254)(166, 247)(167, 280)(168, 274)(169, 263)(170, 249)(171, 271)(172, 262)(173, 264)(174, 273)(175, 270)(176, 283)(177, 267)(178, 256)(179, 281)(180, 284)(181, 260)(182, 285)(183, 250)(184, 286)(185, 255)(186, 278)(187, 276)(188, 272)(189, 287)(190, 265)(191, 282)(192, 275)(289, 373)(290, 369)(291, 348)(292, 337)(293, 339)(294, 372)(295, 371)(296, 374)(297, 357)(298, 379)(299, 338)(300, 341)(301, 380)(302, 381)(303, 368)(304, 349)(305, 376)(306, 359)(307, 370)(308, 346)(309, 382)(310, 375)(311, 360)(312, 354)(313, 343)(314, 377)(315, 351)(316, 342)(317, 344)(318, 353)(319, 350)(320, 363)(321, 347)(322, 384)(323, 361)(324, 364)(325, 340)(326, 365)(327, 378)(328, 366)(329, 383)(330, 358)(331, 356)(332, 352)(333, 367)(334, 345)(335, 362)(336, 355) MAP : A3.325 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A3.323. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.2^3, x.4^3, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-1, (x.3 * x.2^-1)^3, x.2 * x.3 * x.4^-1 * x.3^-1 * x.2^-1 * x.3 * x.4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 384 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192)(193, 241, 289, 337)(194, 242, 290, 338)(195, 243, 291, 339)(196, 244, 292, 340)(197, 245, 293, 341)(198, 246, 294, 342)(199, 247, 295, 343)(200, 248, 296, 344)(201, 249, 297, 345)(202, 250, 298, 346)(203, 251, 299, 347)(204, 252, 300, 348)(205, 253, 301, 349)(206, 254, 302, 350)(207, 255, 303, 351)(208, 256, 304, 352)(209, 257, 305, 353)(210, 258, 306, 354)(211, 259, 307, 355)(212, 260, 308, 356)(213, 261, 309, 357)(214, 262, 310, 358)(215, 263, 311, 359)(216, 264, 312, 360)(217, 265, 313, 361)(218, 266, 314, 362)(219, 267, 315, 363)(220, 268, 316, 364)(221, 269, 317, 365)(222, 270, 318, 366)(223, 271, 319, 367)(224, 272, 320, 368)(225, 273, 321, 369)(226, 274, 322, 370)(227, 275, 323, 371)(228, 276, 324, 372)(229, 277, 325, 373)(230, 278, 326, 374)(231, 279, 327, 375)(232, 280, 328, 376)(233, 281, 329, 377)(234, 282, 330, 378)(235, 283, 331, 379)(236, 284, 332, 380)(237, 285, 333, 381)(238, 286, 334, 382)(239, 287, 335, 383)(240, 288, 336, 384) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 99)(50, 133)(51, 102)(52, 136)(53, 130)(54, 97)(55, 108)(56, 132)(57, 100)(58, 98)(59, 119)(60, 142)(61, 101)(62, 140)(63, 115)(64, 104)(65, 134)(66, 138)(67, 129)(68, 137)(69, 141)(70, 131)(71, 126)(72, 144)(73, 120)(74, 117)(75, 110)(76, 135)(77, 114)(78, 107)(79, 113)(80, 116)(81, 111)(82, 109)(83, 143)(84, 112)(85, 106)(86, 127)(87, 139)(88, 105)(89, 128)(90, 125)(91, 124)(92, 123)(93, 122)(94, 103)(95, 118)(96, 121)(145, 284)(146, 276)(147, 260)(148, 254)(149, 272)(150, 261)(151, 277)(152, 252)(153, 273)(154, 257)(155, 248)(156, 281)(157, 275)(158, 288)(159, 258)(160, 262)(161, 253)(162, 246)(163, 283)(164, 271)(165, 255)(166, 249)(167, 241)(168, 243)(169, 242)(170, 270)(171, 269)(172, 266)(173, 247)(174, 274)(175, 264)(176, 282)(177, 256)(178, 268)(179, 250)(180, 285)(181, 267)(182, 286)(183, 244)(184, 245)(185, 251)(186, 280)(187, 278)(188, 287)(189, 265)(190, 259)(191, 263)(192, 279)(289, 347)(290, 384)(291, 361)(292, 364)(293, 340)(294, 365)(295, 378)(296, 366)(297, 383)(298, 358)(299, 356)(300, 352)(301, 367)(302, 345)(303, 362)(304, 355)(305, 373)(306, 369)(307, 348)(308, 337)(309, 339)(310, 372)(311, 371)(312, 374)(313, 357)(314, 379)(315, 338)(316, 341)(317, 380)(318, 381)(319, 368)(320, 349)(321, 376)(322, 359)(323, 370)(324, 346)(325, 382)(326, 375)(327, 360)(328, 354)(329, 343)(330, 377)(331, 351)(332, 342)(333, 344)(334, 353)(335, 350)(336, 363) MAP : A3.326 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A3.323. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.2^3, x.4^3, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-1, (x.3 * x.2^-1)^3, x.2 * x.3 * x.4^-1 * x.3^-1 * x.2^-1 * x.3 * x.4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 384 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192)(193, 241, 289, 337)(194, 242, 290, 338)(195, 243, 291, 339)(196, 244, 292, 340)(197, 245, 293, 341)(198, 246, 294, 342)(199, 247, 295, 343)(200, 248, 296, 344)(201, 249, 297, 345)(202, 250, 298, 346)(203, 251, 299, 347)(204, 252, 300, 348)(205, 253, 301, 349)(206, 254, 302, 350)(207, 255, 303, 351)(208, 256, 304, 352)(209, 257, 305, 353)(210, 258, 306, 354)(211, 259, 307, 355)(212, 260, 308, 356)(213, 261, 309, 357)(214, 262, 310, 358)(215, 263, 311, 359)(216, 264, 312, 360)(217, 265, 313, 361)(218, 266, 314, 362)(219, 267, 315, 363)(220, 268, 316, 364)(221, 269, 317, 365)(222, 270, 318, 366)(223, 271, 319, 367)(224, 272, 320, 368)(225, 273, 321, 369)(226, 274, 322, 370)(227, 275, 323, 371)(228, 276, 324, 372)(229, 277, 325, 373)(230, 278, 326, 374)(231, 279, 327, 375)(232, 280, 328, 376)(233, 281, 329, 377)(234, 282, 330, 378)(235, 283, 331, 379)(236, 284, 332, 380)(237, 285, 333, 381)(238, 286, 334, 382)(239, 287, 335, 383)(240, 288, 336, 384) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 99)(50, 133)(51, 102)(52, 136)(53, 130)(54, 97)(55, 108)(56, 132)(57, 100)(58, 98)(59, 119)(60, 142)(61, 101)(62, 140)(63, 115)(64, 104)(65, 134)(66, 138)(67, 129)(68, 137)(69, 141)(70, 131)(71, 126)(72, 144)(73, 120)(74, 117)(75, 110)(76, 135)(77, 114)(78, 107)(79, 113)(80, 116)(81, 111)(82, 109)(83, 143)(84, 112)(85, 106)(86, 127)(87, 139)(88, 105)(89, 128)(90, 125)(91, 124)(92, 123)(93, 122)(94, 103)(95, 118)(96, 121)(145, 245)(146, 241)(147, 268)(148, 257)(149, 259)(150, 244)(151, 243)(152, 246)(153, 277)(154, 251)(155, 258)(156, 261)(157, 252)(158, 253)(159, 288)(160, 269)(161, 248)(162, 279)(163, 242)(164, 266)(165, 254)(166, 247)(167, 280)(168, 274)(169, 263)(170, 249)(171, 271)(172, 262)(173, 264)(174, 273)(175, 270)(176, 283)(177, 267)(178, 256)(179, 281)(180, 284)(181, 260)(182, 285)(183, 250)(184, 286)(185, 255)(186, 278)(187, 276)(188, 272)(189, 287)(190, 265)(191, 282)(192, 275)(289, 346)(290, 351)(291, 382)(292, 339)(293, 342)(294, 352)(295, 383)(296, 367)(297, 381)(298, 364)(299, 373)(300, 370)(301, 363)(302, 362)(303, 356)(304, 341)(305, 345)(306, 366)(307, 349)(308, 338)(309, 343)(310, 379)(311, 384)(312, 378)(313, 348)(314, 368)(315, 355)(316, 337)(317, 372)(318, 374)(319, 380)(320, 350)(321, 359)(322, 361)(323, 360)(324, 375)(325, 376)(326, 354)(327, 365)(328, 347)(329, 358)(330, 371)(331, 377)(332, 344)(333, 353)(334, 340)(335, 357)(336, 369) MAP : A3.327 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A3.323. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.2^3, x.4^3, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-1, (x.3 * x.2^-1)^3, x.2 * x.3 * x.4^-1 * x.3^-1 * x.2^-1 * x.3 * x.4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 384 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192)(193, 241, 289, 337)(194, 242, 290, 338)(195, 243, 291, 339)(196, 244, 292, 340)(197, 245, 293, 341)(198, 246, 294, 342)(199, 247, 295, 343)(200, 248, 296, 344)(201, 249, 297, 345)(202, 250, 298, 346)(203, 251, 299, 347)(204, 252, 300, 348)(205, 253, 301, 349)(206, 254, 302, 350)(207, 255, 303, 351)(208, 256, 304, 352)(209, 257, 305, 353)(210, 258, 306, 354)(211, 259, 307, 355)(212, 260, 308, 356)(213, 261, 309, 357)(214, 262, 310, 358)(215, 263, 311, 359)(216, 264, 312, 360)(217, 265, 313, 361)(218, 266, 314, 362)(219, 267, 315, 363)(220, 268, 316, 364)(221, 269, 317, 365)(222, 270, 318, 366)(223, 271, 319, 367)(224, 272, 320, 368)(225, 273, 321, 369)(226, 274, 322, 370)(227, 275, 323, 371)(228, 276, 324, 372)(229, 277, 325, 373)(230, 278, 326, 374)(231, 279, 327, 375)(232, 280, 328, 376)(233, 281, 329, 377)(234, 282, 330, 378)(235, 283, 331, 379)(236, 284, 332, 380)(237, 285, 333, 381)(238, 286, 334, 382)(239, 287, 335, 383)(240, 288, 336, 384) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 102)(50, 106)(51, 97)(52, 105)(53, 109)(54, 99)(55, 142)(56, 112)(57, 136)(58, 133)(59, 126)(60, 103)(61, 130)(62, 123)(63, 129)(64, 132)(65, 127)(66, 125)(67, 111)(68, 128)(69, 122)(70, 143)(71, 107)(72, 121)(73, 144)(74, 141)(75, 140)(76, 139)(77, 138)(78, 119)(79, 134)(80, 137)(81, 115)(82, 101)(83, 118)(84, 104)(85, 98)(86, 113)(87, 124)(88, 100)(89, 116)(90, 114)(91, 135)(92, 110)(93, 117)(94, 108)(95, 131)(96, 120)(145, 242)(146, 259)(147, 247)(148, 246)(149, 241)(150, 248)(151, 262)(152, 257)(153, 266)(154, 279)(155, 250)(156, 253)(157, 254)(158, 261)(159, 281)(160, 274)(161, 244)(162, 251)(163, 245)(164, 277)(165, 252)(166, 268)(167, 265)(168, 269)(169, 286)(170, 260)(171, 273)(172, 243)(173, 256)(174, 271)(175, 267)(176, 284)(177, 270)(178, 264)(179, 288)(180, 283)(181, 249)(182, 282)(183, 258)(184, 263)(185, 275)(186, 287)(187, 272)(188, 276)(189, 278)(190, 280)(191, 285)(192, 255)(289, 370)(290, 339)(291, 375)(292, 374)(293, 369)(294, 376)(295, 342)(296, 337)(297, 346)(298, 359)(299, 378)(300, 381)(301, 382)(302, 341)(303, 361)(304, 354)(305, 372)(306, 379)(307, 373)(308, 357)(309, 380)(310, 348)(311, 345)(312, 349)(313, 366)(314, 340)(315, 353)(316, 371)(317, 384)(318, 351)(319, 347)(320, 364)(321, 350)(322, 344)(323, 368)(324, 363)(325, 377)(326, 362)(327, 338)(328, 343)(329, 355)(330, 367)(331, 352)(332, 356)(333, 358)(334, 360)(335, 365)(336, 383) MAP : A3.328 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A3.323. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.1^3, (x.2 * x.1)^2, x.2^8, (x.2^2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 384 R = (1, 97, 193, 289)(2, 98, 194, 290)(3, 99, 195, 291)(4, 100, 196, 292)(5, 101, 197, 293)(6, 102, 198, 294)(7, 103, 199, 295)(8, 104, 200, 296)(9, 105, 201, 297)(10, 106, 202, 298)(11, 107, 203, 299)(12, 108, 204, 300)(13, 109, 205, 301)(14, 110, 206, 302)(15, 111, 207, 303)(16, 112, 208, 304)(17, 113, 209, 305)(18, 114, 210, 306)(19, 115, 211, 307)(20, 116, 212, 308)(21, 117, 213, 309)(22, 118, 214, 310)(23, 119, 215, 311)(24, 120, 216, 312)(25, 121, 217, 313)(26, 122, 218, 314)(27, 123, 219, 315)(28, 124, 220, 316)(29, 125, 221, 317)(30, 126, 222, 318)(31, 127, 223, 319)(32, 128, 224, 320)(33, 129, 225, 321)(34, 130, 226, 322)(35, 131, 227, 323)(36, 132, 228, 324)(37, 133, 229, 325)(38, 134, 230, 326)(39, 135, 231, 327)(40, 136, 232, 328)(41, 137, 233, 329)(42, 138, 234, 330)(43, 139, 235, 331)(44, 140, 236, 332)(45, 141, 237, 333)(46, 142, 238, 334)(47, 143, 239, 335)(48, 144, 240, 336)(49, 145, 241, 337)(50, 146, 242, 338)(51, 147, 243, 339)(52, 148, 244, 340)(53, 149, 245, 341)(54, 150, 246, 342)(55, 151, 247, 343)(56, 152, 248, 344)(57, 153, 249, 345)(58, 154, 250, 346)(59, 155, 251, 347)(60, 156, 252, 348)(61, 157, 253, 349)(62, 158, 254, 350)(63, 159, 255, 351)(64, 160, 256, 352)(65, 161, 257, 353)(66, 162, 258, 354)(67, 163, 259, 355)(68, 164, 260, 356)(69, 165, 261, 357)(70, 166, 262, 358)(71, 167, 263, 359)(72, 168, 264, 360)(73, 169, 265, 361)(74, 170, 266, 362)(75, 171, 267, 363)(76, 172, 268, 364)(77, 173, 269, 365)(78, 174, 270, 366)(79, 175, 271, 367)(80, 176, 272, 368)(81, 177, 273, 369)(82, 178, 274, 370)(83, 179, 275, 371)(84, 180, 276, 372)(85, 181, 277, 373)(86, 182, 278, 374)(87, 183, 279, 375)(88, 184, 280, 376)(89, 185, 281, 377)(90, 186, 282, 378)(91, 187, 283, 379)(92, 188, 284, 380)(93, 189, 285, 381)(94, 190, 286, 382)(95, 191, 287, 383)(96, 192, 288, 384) L = (1, 98)(2, 101)(3, 113)(4, 114)(5, 97)(6, 115)(7, 116)(8, 117)(9, 165)(10, 118)(11, 119)(12, 120)(13, 162)(14, 161)(15, 124)(16, 172)(17, 130)(18, 133)(19, 177)(20, 178)(21, 129)(22, 179)(23, 180)(24, 181)(25, 149)(26, 182)(27, 183)(28, 184)(29, 146)(30, 145)(31, 188)(32, 156)(33, 104)(34, 99)(35, 109)(36, 105)(37, 100)(38, 126)(39, 125)(40, 110)(41, 186)(42, 159)(43, 154)(44, 121)(45, 191)(46, 187)(47, 155)(48, 150)(49, 134)(50, 135)(51, 138)(52, 139)(53, 140)(54, 153)(55, 158)(56, 143)(57, 144)(58, 148)(59, 152)(60, 157)(61, 128)(62, 160)(63, 147)(64, 151)(65, 136)(66, 131)(67, 141)(68, 137)(69, 132)(70, 190)(71, 189)(72, 142)(73, 122)(74, 175)(75, 170)(76, 185)(77, 127)(78, 123)(79, 171)(80, 166)(81, 102)(82, 103)(83, 106)(84, 107)(85, 108)(86, 169)(87, 174)(88, 111)(89, 112)(90, 164)(91, 168)(92, 173)(93, 192)(94, 176)(95, 163)(96, 167)(193, 291)(194, 292)(195, 294)(196, 295)(197, 296)(198, 298)(199, 299)(200, 300)(201, 332)(202, 361)(203, 366)(204, 303)(205, 327)(206, 326)(207, 365)(208, 349)(209, 293)(210, 289)(211, 322)(212, 325)(213, 290)(214, 369)(215, 370)(216, 321)(217, 324)(218, 371)(219, 372)(220, 373)(221, 323)(222, 328)(223, 376)(224, 377)(225, 302)(226, 301)(227, 383)(228, 378)(229, 297)(230, 368)(231, 384)(232, 379)(233, 374)(234, 363)(235, 367)(236, 304)(237, 380)(238, 375)(239, 362)(240, 382)(241, 307)(242, 308)(243, 310)(244, 311)(245, 312)(246, 314)(247, 315)(248, 316)(249, 364)(250, 329)(251, 334)(252, 319)(253, 359)(254, 358)(255, 333)(256, 381)(257, 309)(258, 305)(259, 354)(260, 357)(261, 306)(262, 337)(263, 338)(264, 353)(265, 356)(266, 339)(267, 340)(268, 341)(269, 355)(270, 360)(271, 344)(272, 345)(273, 318)(274, 317)(275, 351)(276, 346)(277, 313)(278, 336)(279, 352)(280, 347)(281, 342)(282, 331)(283, 335)(284, 320)(285, 348)(286, 343)(287, 330)(288, 350) MAP : A3.329 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A3.323. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.1^3, (x.2 * x.1)^2, x.2^8, (x.2^2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 384 R = (1, 97, 193, 289)(2, 98, 194, 290)(3, 99, 195, 291)(4, 100, 196, 292)(5, 101, 197, 293)(6, 102, 198, 294)(7, 103, 199, 295)(8, 104, 200, 296)(9, 105, 201, 297)(10, 106, 202, 298)(11, 107, 203, 299)(12, 108, 204, 300)(13, 109, 205, 301)(14, 110, 206, 302)(15, 111, 207, 303)(16, 112, 208, 304)(17, 113, 209, 305)(18, 114, 210, 306)(19, 115, 211, 307)(20, 116, 212, 308)(21, 117, 213, 309)(22, 118, 214, 310)(23, 119, 215, 311)(24, 120, 216, 312)(25, 121, 217, 313)(26, 122, 218, 314)(27, 123, 219, 315)(28, 124, 220, 316)(29, 125, 221, 317)(30, 126, 222, 318)(31, 127, 223, 319)(32, 128, 224, 320)(33, 129, 225, 321)(34, 130, 226, 322)(35, 131, 227, 323)(36, 132, 228, 324)(37, 133, 229, 325)(38, 134, 230, 326)(39, 135, 231, 327)(40, 136, 232, 328)(41, 137, 233, 329)(42, 138, 234, 330)(43, 139, 235, 331)(44, 140, 236, 332)(45, 141, 237, 333)(46, 142, 238, 334)(47, 143, 239, 335)(48, 144, 240, 336)(49, 145, 241, 337)(50, 146, 242, 338)(51, 147, 243, 339)(52, 148, 244, 340)(53, 149, 245, 341)(54, 150, 246, 342)(55, 151, 247, 343)(56, 152, 248, 344)(57, 153, 249, 345)(58, 154, 250, 346)(59, 155, 251, 347)(60, 156, 252, 348)(61, 157, 253, 349)(62, 158, 254, 350)(63, 159, 255, 351)(64, 160, 256, 352)(65, 161, 257, 353)(66, 162, 258, 354)(67, 163, 259, 355)(68, 164, 260, 356)(69, 165, 261, 357)(70, 166, 262, 358)(71, 167, 263, 359)(72, 168, 264, 360)(73, 169, 265, 361)(74, 170, 266, 362)(75, 171, 267, 363)(76, 172, 268, 364)(77, 173, 269, 365)(78, 174, 270, 366)(79, 175, 271, 367)(80, 176, 272, 368)(81, 177, 273, 369)(82, 178, 274, 370)(83, 179, 275, 371)(84, 180, 276, 372)(85, 181, 277, 373)(86, 182, 278, 374)(87, 183, 279, 375)(88, 184, 280, 376)(89, 185, 281, 377)(90, 186, 282, 378)(91, 187, 283, 379)(92, 188, 284, 380)(93, 189, 285, 381)(94, 190, 286, 382)(95, 191, 287, 383)(96, 192, 288, 384) L = (1, 98)(2, 101)(3, 113)(4, 114)(5, 97)(6, 115)(7, 116)(8, 117)(9, 165)(10, 118)(11, 119)(12, 120)(13, 162)(14, 161)(15, 124)(16, 172)(17, 130)(18, 133)(19, 177)(20, 178)(21, 129)(22, 179)(23, 180)(24, 181)(25, 149)(26, 182)(27, 183)(28, 184)(29, 146)(30, 145)(31, 188)(32, 156)(33, 104)(34, 99)(35, 109)(36, 105)(37, 100)(38, 126)(39, 125)(40, 110)(41, 186)(42, 159)(43, 154)(44, 121)(45, 191)(46, 187)(47, 155)(48, 150)(49, 134)(50, 135)(51, 138)(52, 139)(53, 140)(54, 153)(55, 158)(56, 143)(57, 144)(58, 148)(59, 152)(60, 157)(61, 128)(62, 160)(63, 147)(64, 151)(65, 136)(66, 131)(67, 141)(68, 137)(69, 132)(70, 190)(71, 189)(72, 142)(73, 122)(74, 175)(75, 170)(76, 185)(77, 127)(78, 123)(79, 171)(80, 166)(81, 102)(82, 103)(83, 106)(84, 107)(85, 108)(86, 169)(87, 174)(88, 111)(89, 112)(90, 164)(91, 168)(92, 173)(93, 192)(94, 176)(95, 163)(96, 167)(193, 349)(194, 345)(195, 366)(196, 365)(197, 350)(198, 303)(199, 298)(200, 361)(201, 360)(202, 384)(203, 304)(204, 299)(205, 356)(206, 355)(207, 368)(208, 367)(209, 340)(210, 344)(211, 341)(212, 337)(213, 339)(214, 370)(215, 373)(216, 338)(217, 354)(218, 321)(219, 322)(220, 369)(221, 353)(222, 357)(223, 325)(224, 293)(225, 331)(226, 335)(227, 332)(228, 326)(229, 330)(230, 295)(231, 300)(232, 327)(233, 323)(234, 296)(235, 291)(236, 294)(237, 328)(238, 324)(239, 292)(240, 289)(241, 346)(242, 347)(243, 313)(244, 318)(245, 351)(246, 308)(247, 312)(248, 317)(249, 301)(250, 309)(251, 305)(252, 307)(253, 302)(254, 297)(255, 306)(256, 290)(257, 348)(258, 342)(259, 375)(260, 380)(261, 343)(262, 376)(263, 371)(264, 374)(265, 379)(266, 381)(267, 377)(268, 372)(269, 378)(270, 383)(271, 382)(272, 362)(273, 320)(274, 336)(275, 315)(276, 319)(277, 352)(278, 316)(279, 310)(280, 314)(281, 334)(282, 359)(283, 364)(284, 311)(285, 329)(286, 333)(287, 358)(288, 363) MAP : A3.330 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A3.323. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.2^3, x.4^3, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-1, (x.3 * x.2^-1)^3, x.2 * x.3 * x.4^-1 * x.3^-1 * x.2^-1 * x.3 * x.4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 384 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192)(193, 241, 289, 337)(194, 242, 290, 338)(195, 243, 291, 339)(196, 244, 292, 340)(197, 245, 293, 341)(198, 246, 294, 342)(199, 247, 295, 343)(200, 248, 296, 344)(201, 249, 297, 345)(202, 250, 298, 346)(203, 251, 299, 347)(204, 252, 300, 348)(205, 253, 301, 349)(206, 254, 302, 350)(207, 255, 303, 351)(208, 256, 304, 352)(209, 257, 305, 353)(210, 258, 306, 354)(211, 259, 307, 355)(212, 260, 308, 356)(213, 261, 309, 357)(214, 262, 310, 358)(215, 263, 311, 359)(216, 264, 312, 360)(217, 265, 313, 361)(218, 266, 314, 362)(219, 267, 315, 363)(220, 268, 316, 364)(221, 269, 317, 365)(222, 270, 318, 366)(223, 271, 319, 367)(224, 272, 320, 368)(225, 273, 321, 369)(226, 274, 322, 370)(227, 275, 323, 371)(228, 276, 324, 372)(229, 277, 325, 373)(230, 278, 326, 374)(231, 279, 327, 375)(232, 280, 328, 376)(233, 281, 329, 377)(234, 282, 330, 378)(235, 283, 331, 379)(236, 284, 332, 380)(237, 285, 333, 381)(238, 286, 334, 382)(239, 287, 335, 383)(240, 288, 336, 384) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 102)(50, 106)(51, 97)(52, 105)(53, 109)(54, 99)(55, 142)(56, 112)(57, 136)(58, 133)(59, 126)(60, 103)(61, 130)(62, 123)(63, 129)(64, 132)(65, 127)(66, 125)(67, 111)(68, 128)(69, 122)(70, 143)(71, 107)(72, 121)(73, 144)(74, 141)(75, 140)(76, 139)(77, 138)(78, 119)(79, 134)(80, 137)(81, 115)(82, 101)(83, 118)(84, 104)(85, 98)(86, 113)(87, 124)(88, 100)(89, 116)(90, 114)(91, 135)(92, 110)(93, 117)(94, 108)(95, 131)(96, 120)(145, 263)(146, 265)(147, 264)(148, 279)(149, 280)(150, 258)(151, 269)(152, 251)(153, 262)(154, 275)(155, 281)(156, 248)(157, 257)(158, 244)(159, 261)(160, 273)(161, 250)(162, 255)(163, 286)(164, 243)(165, 246)(166, 256)(167, 287)(168, 271)(169, 285)(170, 268)(171, 277)(172, 274)(173, 267)(174, 266)(175, 260)(176, 245)(177, 249)(178, 270)(179, 253)(180, 242)(181, 247)(182, 283)(183, 288)(184, 282)(185, 252)(186, 272)(187, 259)(188, 241)(189, 276)(190, 278)(191, 284)(192, 254)(289, 363)(290, 352)(291, 377)(292, 380)(293, 356)(294, 381)(295, 346)(296, 382)(297, 351)(298, 374)(299, 372)(300, 368)(301, 383)(302, 361)(303, 378)(304, 371)(305, 341)(306, 337)(307, 364)(308, 353)(309, 355)(310, 340)(311, 339)(312, 342)(313, 373)(314, 347)(315, 354)(316, 357)(317, 348)(318, 349)(319, 384)(320, 365)(321, 344)(322, 375)(323, 338)(324, 362)(325, 350)(326, 343)(327, 376)(328, 370)(329, 359)(330, 345)(331, 367)(332, 358)(333, 360)(334, 369)(335, 366)(336, 379) MAP : A3.331 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A3.323. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 3, 2 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.2^3, (x.1^-1 * x.2^-1)^2, x.1^8, (x.1^2 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 384 R = (1, 97, 193, 289)(2, 98, 194, 290)(3, 99, 195, 291)(4, 100, 196, 292)(5, 101, 197, 293)(6, 102, 198, 294)(7, 103, 199, 295)(8, 104, 200, 296)(9, 105, 201, 297)(10, 106, 202, 298)(11, 107, 203, 299)(12, 108, 204, 300)(13, 109, 205, 301)(14, 110, 206, 302)(15, 111, 207, 303)(16, 112, 208, 304)(17, 113, 209, 305)(18, 114, 210, 306)(19, 115, 211, 307)(20, 116, 212, 308)(21, 117, 213, 309)(22, 118, 214, 310)(23, 119, 215, 311)(24, 120, 216, 312)(25, 121, 217, 313)(26, 122, 218, 314)(27, 123, 219, 315)(28, 124, 220, 316)(29, 125, 221, 317)(30, 126, 222, 318)(31, 127, 223, 319)(32, 128, 224, 320)(33, 129, 225, 321)(34, 130, 226, 322)(35, 131, 227, 323)(36, 132, 228, 324)(37, 133, 229, 325)(38, 134, 230, 326)(39, 135, 231, 327)(40, 136, 232, 328)(41, 137, 233, 329)(42, 138, 234, 330)(43, 139, 235, 331)(44, 140, 236, 332)(45, 141, 237, 333)(46, 142, 238, 334)(47, 143, 239, 335)(48, 144, 240, 336)(49, 145, 241, 337)(50, 146, 242, 338)(51, 147, 243, 339)(52, 148, 244, 340)(53, 149, 245, 341)(54, 150, 246, 342)(55, 151, 247, 343)(56, 152, 248, 344)(57, 153, 249, 345)(58, 154, 250, 346)(59, 155, 251, 347)(60, 156, 252, 348)(61, 157, 253, 349)(62, 158, 254, 350)(63, 159, 255, 351)(64, 160, 256, 352)(65, 161, 257, 353)(66, 162, 258, 354)(67, 163, 259, 355)(68, 164, 260, 356)(69, 165, 261, 357)(70, 166, 262, 358)(71, 167, 263, 359)(72, 168, 264, 360)(73, 169, 265, 361)(74, 170, 266, 362)(75, 171, 267, 363)(76, 172, 268, 364)(77, 173, 269, 365)(78, 174, 270, 366)(79, 175, 271, 367)(80, 176, 272, 368)(81, 177, 273, 369)(82, 178, 274, 370)(83, 179, 275, 371)(84, 180, 276, 372)(85, 181, 277, 373)(86, 182, 278, 374)(87, 183, 279, 375)(88, 184, 280, 376)(89, 185, 281, 377)(90, 186, 282, 378)(91, 187, 283, 379)(92, 188, 284, 380)(93, 189, 285, 381)(94, 190, 286, 382)(95, 191, 287, 383)(96, 192, 288, 384) L = (1, 99)(2, 100)(3, 102)(4, 103)(5, 104)(6, 106)(7, 107)(8, 108)(9, 140)(10, 169)(11, 174)(12, 111)(13, 135)(14, 134)(15, 173)(16, 157)(17, 101)(18, 97)(19, 130)(20, 133)(21, 98)(22, 177)(23, 178)(24, 129)(25, 132)(26, 179)(27, 180)(28, 181)(29, 131)(30, 136)(31, 184)(32, 185)(33, 110)(34, 109)(35, 191)(36, 186)(37, 105)(38, 176)(39, 192)(40, 187)(41, 182)(42, 171)(43, 175)(44, 112)(45, 188)(46, 183)(47, 170)(48, 190)(49, 115)(50, 116)(51, 118)(52, 119)(53, 120)(54, 122)(55, 123)(56, 124)(57, 172)(58, 137)(59, 142)(60, 127)(61, 167)(62, 166)(63, 141)(64, 189)(65, 117)(66, 113)(67, 162)(68, 165)(69, 114)(70, 145)(71, 146)(72, 161)(73, 164)(74, 147)(75, 148)(76, 149)(77, 163)(78, 168)(79, 152)(80, 153)(81, 126)(82, 125)(83, 159)(84, 154)(85, 121)(86, 144)(87, 160)(88, 155)(89, 150)(90, 139)(91, 143)(92, 128)(93, 156)(94, 151)(95, 138)(96, 158)(193, 290)(194, 293)(195, 305)(196, 306)(197, 289)(198, 307)(199, 308)(200, 309)(201, 357)(202, 310)(203, 311)(204, 312)(205, 354)(206, 353)(207, 316)(208, 364)(209, 322)(210, 325)(211, 369)(212, 370)(213, 321)(214, 371)(215, 372)(216, 373)(217, 341)(218, 374)(219, 375)(220, 376)(221, 338)(222, 337)(223, 380)(224, 348)(225, 296)(226, 291)(227, 301)(228, 297)(229, 292)(230, 318)(231, 317)(232, 302)(233, 378)(234, 351)(235, 346)(236, 313)(237, 383)(238, 379)(239, 347)(240, 342)(241, 326)(242, 327)(243, 330)(244, 331)(245, 332)(246, 345)(247, 350)(248, 335)(249, 336)(250, 340)(251, 344)(252, 349)(253, 320)(254, 352)(255, 339)(256, 343)(257, 328)(258, 323)(259, 333)(260, 329)(261, 324)(262, 382)(263, 381)(264, 334)(265, 314)(266, 367)(267, 362)(268, 377)(269, 319)(270, 315)(271, 363)(272, 358)(273, 294)(274, 295)(275, 298)(276, 299)(277, 300)(278, 361)(279, 366)(280, 303)(281, 304)(282, 356)(283, 360)(284, 365)(285, 384)(286, 368)(287, 355)(288, 359) MAP : A3.332 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A3.323. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 3, 2 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.2^3, (x.1^-1 * x.2^-1)^2, x.1^8, (x.1^2 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 384 R = (1, 97, 193, 289)(2, 98, 194, 290)(3, 99, 195, 291)(4, 100, 196, 292)(5, 101, 197, 293)(6, 102, 198, 294)(7, 103, 199, 295)(8, 104, 200, 296)(9, 105, 201, 297)(10, 106, 202, 298)(11, 107, 203, 299)(12, 108, 204, 300)(13, 109, 205, 301)(14, 110, 206, 302)(15, 111, 207, 303)(16, 112, 208, 304)(17, 113, 209, 305)(18, 114, 210, 306)(19, 115, 211, 307)(20, 116, 212, 308)(21, 117, 213, 309)(22, 118, 214, 310)(23, 119, 215, 311)(24, 120, 216, 312)(25, 121, 217, 313)(26, 122, 218, 314)(27, 123, 219, 315)(28, 124, 220, 316)(29, 125, 221, 317)(30, 126, 222, 318)(31, 127, 223, 319)(32, 128, 224, 320)(33, 129, 225, 321)(34, 130, 226, 322)(35, 131, 227, 323)(36, 132, 228, 324)(37, 133, 229, 325)(38, 134, 230, 326)(39, 135, 231, 327)(40, 136, 232, 328)(41, 137, 233, 329)(42, 138, 234, 330)(43, 139, 235, 331)(44, 140, 236, 332)(45, 141, 237, 333)(46, 142, 238, 334)(47, 143, 239, 335)(48, 144, 240, 336)(49, 145, 241, 337)(50, 146, 242, 338)(51, 147, 243, 339)(52, 148, 244, 340)(53, 149, 245, 341)(54, 150, 246, 342)(55, 151, 247, 343)(56, 152, 248, 344)(57, 153, 249, 345)(58, 154, 250, 346)(59, 155, 251, 347)(60, 156, 252, 348)(61, 157, 253, 349)(62, 158, 254, 350)(63, 159, 255, 351)(64, 160, 256, 352)(65, 161, 257, 353)(66, 162, 258, 354)(67, 163, 259, 355)(68, 164, 260, 356)(69, 165, 261, 357)(70, 166, 262, 358)(71, 167, 263, 359)(72, 168, 264, 360)(73, 169, 265, 361)(74, 170, 266, 362)(75, 171, 267, 363)(76, 172, 268, 364)(77, 173, 269, 365)(78, 174, 270, 366)(79, 175, 271, 367)(80, 176, 272, 368)(81, 177, 273, 369)(82, 178, 274, 370)(83, 179, 275, 371)(84, 180, 276, 372)(85, 181, 277, 373)(86, 182, 278, 374)(87, 183, 279, 375)(88, 184, 280, 376)(89, 185, 281, 377)(90, 186, 282, 378)(91, 187, 283, 379)(92, 188, 284, 380)(93, 189, 285, 381)(94, 190, 286, 382)(95, 191, 287, 383)(96, 192, 288, 384) L = (1, 106)(2, 107)(3, 169)(4, 174)(5, 111)(6, 164)(7, 168)(8, 173)(9, 157)(10, 165)(11, 161)(12, 163)(13, 158)(14, 153)(15, 162)(16, 146)(17, 108)(18, 102)(19, 135)(20, 140)(21, 103)(22, 136)(23, 131)(24, 134)(25, 139)(26, 141)(27, 137)(28, 132)(29, 138)(30, 143)(31, 142)(32, 122)(33, 176)(34, 192)(35, 171)(36, 175)(37, 112)(38, 172)(39, 166)(40, 170)(41, 190)(42, 119)(43, 124)(44, 167)(45, 185)(46, 189)(47, 118)(48, 123)(49, 109)(50, 105)(51, 126)(52, 125)(53, 110)(54, 159)(55, 154)(56, 121)(57, 120)(58, 144)(59, 160)(60, 155)(61, 116)(62, 115)(63, 128)(64, 127)(65, 100)(66, 104)(67, 101)(68, 97)(69, 99)(70, 130)(71, 133)(72, 98)(73, 114)(74, 177)(75, 178)(76, 129)(77, 113)(78, 117)(79, 181)(80, 149)(81, 187)(82, 191)(83, 188)(84, 182)(85, 186)(86, 151)(87, 156)(88, 183)(89, 179)(90, 152)(91, 147)(92, 150)(93, 184)(94, 180)(95, 148)(96, 145)(193, 384)(194, 304)(195, 379)(196, 383)(197, 368)(198, 380)(199, 374)(200, 378)(201, 302)(202, 343)(203, 348)(204, 375)(205, 297)(206, 301)(207, 342)(208, 347)(209, 299)(210, 303)(211, 300)(212, 294)(213, 298)(214, 327)(215, 332)(216, 295)(217, 291)(218, 328)(219, 323)(220, 326)(221, 296)(222, 292)(223, 324)(224, 321)(225, 362)(226, 363)(227, 377)(228, 382)(229, 367)(230, 372)(231, 376)(232, 381)(233, 333)(234, 373)(235, 369)(236, 371)(237, 334)(238, 329)(239, 370)(240, 322)(241, 356)(242, 360)(243, 357)(244, 353)(245, 355)(246, 306)(247, 309)(248, 354)(249, 338)(250, 289)(251, 290)(252, 305)(253, 337)(254, 341)(255, 293)(256, 325)(257, 365)(258, 361)(259, 350)(260, 349)(261, 366)(262, 335)(263, 330)(264, 345)(265, 344)(266, 320)(267, 336)(268, 331)(269, 340)(270, 339)(271, 352)(272, 351)(273, 364)(274, 358)(275, 311)(276, 316)(277, 359)(278, 312)(279, 307)(280, 310)(281, 315)(282, 317)(283, 313)(284, 308)(285, 314)(286, 319)(287, 318)(288, 346) MAP : A3.333 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A3.323. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.2^3, x.4^3, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-1, (x.3 * x.2^-1)^3, x.2 * x.3 * x.4^-1 * x.3^-1 * x.2^-1 * x.3 * x.4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 384 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192)(193, 241, 289, 337)(194, 242, 290, 338)(195, 243, 291, 339)(196, 244, 292, 340)(197, 245, 293, 341)(198, 246, 294, 342)(199, 247, 295, 343)(200, 248, 296, 344)(201, 249, 297, 345)(202, 250, 298, 346)(203, 251, 299, 347)(204, 252, 300, 348)(205, 253, 301, 349)(206, 254, 302, 350)(207, 255, 303, 351)(208, 256, 304, 352)(209, 257, 305, 353)(210, 258, 306, 354)(211, 259, 307, 355)(212, 260, 308, 356)(213, 261, 309, 357)(214, 262, 310, 358)(215, 263, 311, 359)(216, 264, 312, 360)(217, 265, 313, 361)(218, 266, 314, 362)(219, 267, 315, 363)(220, 268, 316, 364)(221, 269, 317, 365)(222, 270, 318, 366)(223, 271, 319, 367)(224, 272, 320, 368)(225, 273, 321, 369)(226, 274, 322, 370)(227, 275, 323, 371)(228, 276, 324, 372)(229, 277, 325, 373)(230, 278, 326, 374)(231, 279, 327, 375)(232, 280, 328, 376)(233, 281, 329, 377)(234, 282, 330, 378)(235, 283, 331, 379)(236, 284, 332, 380)(237, 285, 333, 381)(238, 286, 334, 382)(239, 287, 335, 383)(240, 288, 336, 384) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 99)(50, 133)(51, 102)(52, 136)(53, 130)(54, 97)(55, 108)(56, 132)(57, 100)(58, 98)(59, 119)(60, 142)(61, 101)(62, 140)(63, 115)(64, 104)(65, 134)(66, 138)(67, 129)(68, 137)(69, 141)(70, 131)(71, 126)(72, 144)(73, 120)(74, 117)(75, 110)(76, 135)(77, 114)(78, 107)(79, 113)(80, 116)(81, 111)(82, 109)(83, 143)(84, 112)(85, 106)(86, 127)(87, 139)(88, 105)(89, 128)(90, 125)(91, 124)(92, 123)(93, 122)(94, 103)(95, 118)(96, 121)(145, 242)(146, 259)(147, 247)(148, 246)(149, 241)(150, 248)(151, 262)(152, 257)(153, 266)(154, 279)(155, 250)(156, 253)(157, 254)(158, 261)(159, 281)(160, 274)(161, 244)(162, 251)(163, 245)(164, 277)(165, 252)(166, 268)(167, 265)(168, 269)(169, 286)(170, 260)(171, 273)(172, 243)(173, 256)(174, 271)(175, 267)(176, 284)(177, 270)(178, 264)(179, 288)(180, 283)(181, 249)(182, 282)(183, 258)(184, 263)(185, 275)(186, 287)(187, 272)(188, 276)(189, 278)(190, 280)(191, 285)(192, 255)(289, 349)(290, 342)(291, 379)(292, 367)(293, 351)(294, 345)(295, 337)(296, 339)(297, 338)(298, 366)(299, 365)(300, 362)(301, 343)(302, 370)(303, 360)(304, 378)(305, 352)(306, 364)(307, 346)(308, 381)(309, 363)(310, 382)(311, 340)(312, 341)(313, 347)(314, 376)(315, 374)(316, 383)(317, 361)(318, 355)(319, 359)(320, 375)(321, 380)(322, 372)(323, 356)(324, 350)(325, 368)(326, 357)(327, 373)(328, 348)(329, 369)(330, 353)(331, 344)(332, 377)(333, 371)(334, 384)(335, 354)(336, 358) MAP : A3.334 NOTES : type I, reflexible, isomorphic to Med2({3,8}), isomorphic to A3.323. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.2^3, x.4^3, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-1, (x.3 * x.2^-1)^3, x.2 * x.3 * x.4^-1 * x.3^-1 * x.2^-1 * x.3 * x.4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 8, 4) #DARTS : 384 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192)(193, 241, 289, 337)(194, 242, 290, 338)(195, 243, 291, 339)(196, 244, 292, 340)(197, 245, 293, 341)(198, 246, 294, 342)(199, 247, 295, 343)(200, 248, 296, 344)(201, 249, 297, 345)(202, 250, 298, 346)(203, 251, 299, 347)(204, 252, 300, 348)(205, 253, 301, 349)(206, 254, 302, 350)(207, 255, 303, 351)(208, 256, 304, 352)(209, 257, 305, 353)(210, 258, 306, 354)(211, 259, 307, 355)(212, 260, 308, 356)(213, 261, 309, 357)(214, 262, 310, 358)(215, 263, 311, 359)(216, 264, 312, 360)(217, 265, 313, 361)(218, 266, 314, 362)(219, 267, 315, 363)(220, 268, 316, 364)(221, 269, 317, 365)(222, 270, 318, 366)(223, 271, 319, 367)(224, 272, 320, 368)(225, 273, 321, 369)(226, 274, 322, 370)(227, 275, 323, 371)(228, 276, 324, 372)(229, 277, 325, 373)(230, 278, 326, 374)(231, 279, 327, 375)(232, 280, 328, 376)(233, 281, 329, 377)(234, 282, 330, 378)(235, 283, 331, 379)(236, 284, 332, 380)(237, 285, 333, 381)(238, 286, 334, 382)(239, 287, 335, 383)(240, 288, 336, 384) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 99)(50, 133)(51, 102)(52, 136)(53, 130)(54, 97)(55, 108)(56, 132)(57, 100)(58, 98)(59, 119)(60, 142)(61, 101)(62, 140)(63, 115)(64, 104)(65, 134)(66, 138)(67, 129)(68, 137)(69, 141)(70, 131)(71, 126)(72, 144)(73, 120)(74, 117)(75, 110)(76, 135)(77, 114)(78, 107)(79, 113)(80, 116)(81, 111)(82, 109)(83, 143)(84, 112)(85, 106)(86, 127)(87, 139)(88, 105)(89, 128)(90, 125)(91, 124)(92, 123)(93, 122)(94, 103)(95, 118)(96, 121)(145, 263)(146, 265)(147, 264)(148, 279)(149, 280)(150, 258)(151, 269)(152, 251)(153, 262)(154, 275)(155, 281)(156, 248)(157, 257)(158, 244)(159, 261)(160, 273)(161, 250)(162, 255)(163, 286)(164, 243)(165, 246)(166, 256)(167, 287)(168, 271)(169, 285)(170, 268)(171, 277)(172, 274)(173, 267)(174, 266)(175, 260)(176, 245)(177, 249)(178, 270)(179, 253)(180, 242)(181, 247)(182, 283)(183, 288)(184, 282)(185, 252)(186, 272)(187, 259)(188, 241)(189, 276)(190, 278)(191, 284)(192, 254)(289, 350)(290, 344)(291, 368)(292, 363)(293, 377)(294, 362)(295, 338)(296, 343)(297, 355)(298, 367)(299, 352)(300, 356)(301, 358)(302, 360)(303, 365)(304, 383)(305, 370)(306, 339)(307, 375)(308, 374)(309, 369)(310, 376)(311, 342)(312, 337)(313, 346)(314, 359)(315, 378)(316, 381)(317, 382)(318, 341)(319, 361)(320, 354)(321, 372)(322, 379)(323, 373)(324, 357)(325, 380)(326, 348)(327, 345)(328, 349)(329, 366)(330, 340)(331, 353)(332, 371)(333, 384)(334, 351)(335, 347)(336, 364) MAP : A3.335 NOTES : type I, reflexible, isomorphic to Med2({3,12}), representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 12, 2 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^2, u.2^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2 | x.1^3, (x.1^-1 * x.2^-1)^2, x.2^-2 * x.1 * x.2^3 * x.1^-1 * x.2^-1, (x.1^-1 * x.2^5)^2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 12, 4) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 50)(2, 53)(3, 54)(4, 55)(5, 49)(6, 56)(7, 72)(8, 51)(9, 61)(10, 92)(11, 62)(12, 78)(13, 88)(14, 69)(15, 94)(16, 87)(17, 63)(18, 60)(19, 64)(20, 80)(21, 59)(22, 77)(23, 70)(24, 52)(25, 96)(26, 95)(27, 79)(28, 75)(29, 71)(30, 66)(31, 76)(32, 93)(33, 90)(34, 74)(35, 89)(36, 83)(37, 58)(38, 73)(39, 67)(40, 57)(41, 84)(42, 91)(43, 81)(44, 85)(45, 68)(46, 65)(47, 82)(48, 86)(97, 182)(98, 189)(99, 178)(100, 177)(101, 183)(102, 172)(103, 175)(104, 190)(105, 181)(106, 184)(107, 179)(108, 180)(109, 171)(110, 176)(111, 185)(112, 186)(113, 150)(114, 157)(115, 146)(116, 145)(117, 151)(118, 188)(119, 191)(120, 158)(121, 149)(122, 152)(123, 147)(124, 148)(125, 187)(126, 192)(127, 153)(128, 154)(129, 166)(130, 173)(131, 162)(132, 161)(133, 167)(134, 156)(135, 159)(136, 174)(137, 165)(138, 168)(139, 163)(140, 164)(141, 155)(142, 160)(143, 169)(144, 170) MAP : A3.336 NOTES : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A3.335. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 12, 3, 2 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^2, u.1^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2 | x.2^3, (x.1^-1 * x.2^-1)^2, x.1^-2 * x.2^-1 * x.1^2 * x.2^-1 * x.1^-2, x.2^-2 * x.1^2 * x.2^-1 * x.1 * x.2^-1 * x.1^5 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 12, 4) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 52)(2, 51)(3, 59)(4, 60)(5, 57)(6, 49)(7, 53)(8, 58)(9, 63)(10, 64)(11, 77)(12, 70)(13, 50)(14, 56)(15, 71)(16, 78)(17, 68)(18, 67)(19, 75)(20, 76)(21, 73)(22, 65)(23, 69)(24, 74)(25, 79)(26, 80)(27, 93)(28, 86)(29, 66)(30, 72)(31, 87)(32, 94)(33, 84)(34, 83)(35, 91)(36, 92)(37, 89)(38, 81)(39, 85)(40, 90)(41, 95)(42, 96)(43, 61)(44, 54)(45, 82)(46, 88)(47, 55)(48, 62)(97, 146)(98, 149)(99, 150)(100, 151)(101, 145)(102, 152)(103, 168)(104, 147)(105, 157)(106, 188)(107, 158)(108, 174)(109, 184)(110, 165)(111, 190)(112, 183)(113, 159)(114, 156)(115, 160)(116, 176)(117, 155)(118, 173)(119, 166)(120, 148)(121, 192)(122, 191)(123, 175)(124, 171)(125, 167)(126, 162)(127, 172)(128, 189)(129, 186)(130, 170)(131, 185)(132, 179)(133, 154)(134, 169)(135, 163)(136, 153)(137, 180)(138, 187)(139, 177)(140, 181)(141, 164)(142, 161)(143, 178)(144, 182) MAP : A3.337 NOTES : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A3.335. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 12, 3, 2 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^2, u.1^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2 | x.2^3, (x.1^-1 * x.2^-1)^2, x.1^-2 * x.2^-1 * x.1^2 * x.2^-1 * x.1^-2, x.2^-2 * x.1^2 * x.2^-1 * x.1 * x.2^-1 * x.1^5 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 12, 4) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 68)(2, 67)(3, 75)(4, 76)(5, 73)(6, 65)(7, 69)(8, 74)(9, 79)(10, 80)(11, 93)(12, 86)(13, 66)(14, 72)(15, 87)(16, 94)(17, 84)(18, 83)(19, 91)(20, 92)(21, 89)(22, 81)(23, 85)(24, 90)(25, 95)(26, 96)(27, 61)(28, 54)(29, 82)(30, 88)(31, 55)(32, 62)(33, 52)(34, 51)(35, 59)(36, 60)(37, 57)(38, 49)(39, 53)(40, 58)(41, 63)(42, 64)(43, 77)(44, 70)(45, 50)(46, 56)(47, 71)(48, 78)(97, 149)(98, 145)(99, 152)(100, 168)(101, 146)(102, 147)(103, 148)(104, 150)(105, 184)(106, 181)(107, 165)(108, 162)(109, 153)(110, 155)(111, 161)(112, 163)(113, 190)(114, 174)(115, 183)(116, 189)(117, 158)(118, 167)(119, 173)(120, 151)(121, 182)(122, 178)(123, 172)(124, 175)(125, 166)(126, 156)(127, 171)(128, 164)(129, 187)(130, 191)(131, 180)(132, 185)(133, 188)(134, 192)(135, 160)(136, 157)(137, 179)(138, 177)(139, 186)(140, 154)(141, 176)(142, 159)(143, 170)(144, 169) MAP : A3.338 NOTES : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A3.335. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 12, 2 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^2, u.2^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2 | x.1^3, (x.1^-1 * x.2^-1)^2, x.2^-2 * x.1 * x.2^3 * x.1^-1 * x.2^-1, (x.1^-1 * x.2^5)^2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 12, 4) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 50)(2, 53)(3, 54)(4, 55)(5, 49)(6, 56)(7, 72)(8, 51)(9, 61)(10, 92)(11, 62)(12, 78)(13, 88)(14, 69)(15, 94)(16, 87)(17, 63)(18, 60)(19, 64)(20, 80)(21, 59)(22, 77)(23, 70)(24, 52)(25, 96)(26, 95)(27, 79)(28, 75)(29, 71)(30, 66)(31, 76)(32, 93)(33, 90)(34, 74)(35, 89)(36, 83)(37, 58)(38, 73)(39, 67)(40, 57)(41, 84)(42, 91)(43, 81)(44, 85)(45, 68)(46, 65)(47, 82)(48, 86)(97, 148)(98, 147)(99, 155)(100, 156)(101, 153)(102, 145)(103, 149)(104, 154)(105, 159)(106, 160)(107, 173)(108, 166)(109, 146)(110, 152)(111, 167)(112, 174)(113, 164)(114, 163)(115, 171)(116, 172)(117, 169)(118, 161)(119, 165)(120, 170)(121, 175)(122, 176)(123, 189)(124, 182)(125, 162)(126, 168)(127, 183)(128, 190)(129, 180)(130, 179)(131, 187)(132, 188)(133, 185)(134, 177)(135, 181)(136, 186)(137, 191)(138, 192)(139, 157)(140, 150)(141, 178)(142, 184)(143, 151)(144, 158) MAP : A3.339 NOTES : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A3.335. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 12, 3, 2 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^2, u.1^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2 | x.2^3, (x.1^-1 * x.2^-1)^2, x.1^-2 * x.2^-1 * x.1^2 * x.2^-1 * x.1^-2, x.2^-2 * x.1^2 * x.2^-1 * x.1 * x.2^-1 * x.1^5 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 12, 4) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 54)(2, 61)(3, 50)(4, 49)(5, 55)(6, 92)(7, 95)(8, 62)(9, 53)(10, 56)(11, 51)(12, 52)(13, 91)(14, 96)(15, 57)(16, 58)(17, 70)(18, 77)(19, 66)(20, 65)(21, 71)(22, 60)(23, 63)(24, 78)(25, 69)(26, 72)(27, 67)(28, 68)(29, 59)(30, 64)(31, 73)(32, 74)(33, 86)(34, 93)(35, 82)(36, 81)(37, 87)(38, 76)(39, 79)(40, 94)(41, 85)(42, 88)(43, 83)(44, 84)(45, 75)(46, 80)(47, 89)(48, 90)(97, 149)(98, 145)(99, 152)(100, 168)(101, 146)(102, 147)(103, 148)(104, 150)(105, 184)(106, 181)(107, 165)(108, 162)(109, 153)(110, 155)(111, 161)(112, 163)(113, 190)(114, 174)(115, 183)(116, 189)(117, 158)(118, 167)(119, 173)(120, 151)(121, 182)(122, 178)(123, 172)(124, 175)(125, 166)(126, 156)(127, 171)(128, 164)(129, 187)(130, 191)(131, 180)(132, 185)(133, 188)(134, 192)(135, 160)(136, 157)(137, 179)(138, 177)(139, 186)(140, 154)(141, 176)(142, 159)(143, 170)(144, 169) MAP : A3.340 NOTES : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A3.335. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 12, 2 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^2, u.2^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2 | x.1^3, (x.1^-1 * x.2^-1)^2, x.2^-2 * x.1 * x.2^3 * x.1^-1 * x.2^-1, (x.1^-1 * x.2^5)^2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 12, 4) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 53)(2, 49)(3, 56)(4, 72)(5, 50)(6, 51)(7, 52)(8, 54)(9, 88)(10, 85)(11, 69)(12, 66)(13, 57)(14, 59)(15, 65)(16, 67)(17, 94)(18, 78)(19, 87)(20, 93)(21, 62)(22, 71)(23, 77)(24, 55)(25, 86)(26, 82)(27, 76)(28, 79)(29, 70)(30, 60)(31, 75)(32, 68)(33, 91)(34, 95)(35, 84)(36, 89)(37, 92)(38, 96)(39, 64)(40, 61)(41, 83)(42, 81)(43, 90)(44, 58)(45, 80)(46, 63)(47, 74)(48, 73)(97, 164)(98, 163)(99, 171)(100, 172)(101, 169)(102, 161)(103, 165)(104, 170)(105, 175)(106, 176)(107, 189)(108, 182)(109, 162)(110, 168)(111, 183)(112, 190)(113, 180)(114, 179)(115, 187)(116, 188)(117, 185)(118, 177)(119, 181)(120, 186)(121, 191)(122, 192)(123, 157)(124, 150)(125, 178)(126, 184)(127, 151)(128, 158)(129, 148)(130, 147)(131, 155)(132, 156)(133, 153)(134, 145)(135, 149)(136, 154)(137, 159)(138, 160)(139, 173)(140, 166)(141, 146)(142, 152)(143, 167)(144, 174) MAP : A3.341 NOTES : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A3.335. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 6, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.2^3, x.4^3, x.3 * x.4 * x.3^-1 * x.2^-1, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 12, 4) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 53)(26, 49)(27, 66)(28, 61)(29, 50)(30, 69)(31, 51)(32, 65)(33, 62)(34, 64)(35, 52)(36, 57)(37, 59)(38, 60)(39, 54)(40, 68)(41, 71)(42, 55)(43, 72)(44, 58)(45, 63)(46, 67)(47, 56)(48, 70)(73, 131)(74, 134)(75, 121)(76, 135)(77, 136)(78, 122)(79, 124)(80, 125)(81, 139)(82, 142)(83, 129)(84, 143)(85, 144)(86, 130)(87, 132)(88, 133)(89, 123)(90, 126)(91, 137)(92, 127)(93, 128)(94, 138)(95, 140)(96, 141)(145, 175)(146, 183)(147, 176)(148, 186)(149, 191)(150, 171)(151, 184)(152, 174)(153, 181)(154, 177)(155, 170)(156, 189)(157, 178)(158, 173)(159, 179)(160, 169)(161, 190)(162, 192)(163, 180)(164, 185)(165, 187)(166, 188)(167, 182)(168, 172) MAP : A3.342 NOTES : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A3.335. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 12, 2 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^2, u.2^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2 | x.1^3, (x.1^-1 * x.2^-1)^2, x.2^-2 * x.1 * x.2^3 * x.1^-1 * x.2^-1, (x.1^-1 * x.2^5)^2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 12, 4) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 53)(2, 49)(3, 56)(4, 72)(5, 50)(6, 51)(7, 52)(8, 54)(9, 88)(10, 85)(11, 69)(12, 66)(13, 57)(14, 59)(15, 65)(16, 67)(17, 94)(18, 78)(19, 87)(20, 93)(21, 62)(22, 71)(23, 77)(24, 55)(25, 86)(26, 82)(27, 76)(28, 79)(29, 70)(30, 60)(31, 75)(32, 68)(33, 91)(34, 95)(35, 84)(36, 89)(37, 92)(38, 96)(39, 64)(40, 61)(41, 83)(42, 81)(43, 90)(44, 58)(45, 80)(46, 63)(47, 74)(48, 73)(97, 150)(98, 157)(99, 146)(100, 145)(101, 151)(102, 188)(103, 191)(104, 158)(105, 149)(106, 152)(107, 147)(108, 148)(109, 187)(110, 192)(111, 153)(112, 154)(113, 166)(114, 173)(115, 162)(116, 161)(117, 167)(118, 156)(119, 159)(120, 174)(121, 165)(122, 168)(123, 163)(124, 164)(125, 155)(126, 160)(127, 169)(128, 170)(129, 182)(130, 189)(131, 178)(132, 177)(133, 183)(134, 172)(135, 175)(136, 190)(137, 181)(138, 184)(139, 179)(140, 180)(141, 171)(142, 176)(143, 185)(144, 186) MAP : A3.343 NOTES : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A3.335. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 6, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.2^3, x.4^3, x.3 * x.4 * x.3^-1 * x.2^-1, (x.3 * x.1^-1)^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 12, 4) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 50)(26, 53)(27, 55)(28, 59)(29, 49)(30, 63)(31, 66)(32, 71)(33, 60)(34, 68)(35, 61)(36, 62)(37, 52)(38, 57)(39, 69)(40, 58)(41, 56)(42, 51)(43, 70)(44, 64)(45, 54)(46, 72)(47, 65)(48, 67)(73, 123)(74, 126)(75, 137)(76, 127)(77, 128)(78, 138)(79, 140)(80, 141)(81, 131)(82, 134)(83, 121)(84, 135)(85, 136)(86, 122)(87, 124)(88, 125)(89, 139)(90, 142)(91, 129)(92, 143)(93, 144)(94, 130)(95, 132)(96, 133)(145, 172)(146, 180)(147, 173)(148, 174)(149, 188)(150, 169)(151, 181)(152, 170)(153, 192)(154, 187)(155, 182)(156, 176)(157, 190)(158, 184)(159, 177)(160, 179)(161, 186)(162, 189)(163, 191)(164, 171)(165, 185)(166, 175)(167, 178)(168, 183) MAP : A3.344 NOTES : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A3.335. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 12, 3, 2 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^2, u.1^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2 | x.2^3, (x.1^-1 * x.2^-1)^2, x.1^-2 * x.2^-1 * x.1^2 * x.2^-1 * x.1^-2, x.2^-2 * x.1^2 * x.2^-1 * x.1 * x.2^-1 * x.1^5 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 4, 12, 4) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 86)(2, 93)(3, 82)(4, 81)(5, 87)(6, 76)(7, 79)(8, 94)(9, 85)(10, 88)(11, 83)(12, 84)(13, 75)(14, 80)(15, 89)(16, 90)(17, 54)(18, 61)(19, 50)(20, 49)(21, 55)(22, 92)(23, 95)(24, 62)(25, 53)(26, 56)(27, 51)(28, 52)(29, 91)(30, 96)(31, 57)(32, 58)(33, 70)(34, 77)(35, 66)(36, 65)(37, 71)(38, 60)(39, 63)(40, 78)(41, 69)(42, 72)(43, 67)(44, 68)(45, 59)(46, 64)(47, 73)(48, 74)(97, 146)(98, 149)(99, 150)(100, 151)(101, 145)(102, 152)(103, 168)(104, 147)(105, 157)(106, 188)(107, 158)(108, 174)(109, 184)(110, 165)(111, 190)(112, 183)(113, 159)(114, 156)(115, 160)(116, 176)(117, 155)(118, 173)(119, 166)(120, 148)(121, 192)(122, 191)(123, 175)(124, 171)(125, 167)(126, 162)(127, 172)(128, 189)(129, 186)(130, 170)(131, 185)(132, 179)(133, 154)(134, 169)(135, 163)(136, 153)(137, 180)(138, 187)(139, 177)(140, 181)(141, 164)(142, 161)(143, 178)(144, 182) MAP : A3.345 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 7, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.2^3, x.4^3, x.3 * x.4^-1 * x.3^-1 * x.2^-1, (x.3 * x.1^-1)^7 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 14, 4) #DARTS : 168 R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84)(85, 106, 127, 148)(86, 107, 128, 149)(87, 108, 129, 150)(88, 109, 130, 151)(89, 110, 131, 152)(90, 111, 132, 153)(91, 112, 133, 154)(92, 113, 134, 155)(93, 114, 135, 156)(94, 115, 136, 157)(95, 116, 137, 158)(96, 117, 138, 159)(97, 118, 139, 160)(98, 119, 140, 161)(99, 120, 141, 162)(100, 121, 142, 163)(101, 122, 143, 164)(102, 123, 144, 165)(103, 124, 145, 166)(104, 125, 146, 167)(105, 126, 147, 168) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 47)(23, 43)(24, 53)(25, 57)(26, 44)(27, 58)(28, 46)(29, 52)(30, 59)(31, 55)(32, 54)(33, 45)(34, 50)(35, 61)(36, 49)(37, 60)(38, 63)(39, 48)(40, 62)(41, 56)(42, 51)(64, 126)(65, 116)(66, 119)(67, 125)(68, 118)(69, 112)(70, 107)(71, 124)(72, 120)(73, 109)(74, 113)(75, 121)(76, 114)(77, 123)(78, 108)(79, 115)(80, 111)(81, 110)(82, 122)(83, 106)(84, 117)(127, 166)(128, 162)(129, 151)(130, 155)(131, 163)(132, 156)(133, 165)(134, 150)(135, 157)(136, 153)(137, 152)(138, 164)(139, 148)(140, 159)(141, 168)(142, 158)(143, 161)(144, 167)(145, 160)(146, 154)(147, 149) MAP : A3.346 NOTES : type II, reflexible, isomorphic to A3.345. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 7, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.2^3, x.4^3, x.3 * x.4^-1 * x.3^-1 * x.2^-1, (x.3 * x.1^-1)^7 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 14, 4) #DARTS : 168 R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84)(85, 106, 127, 148)(86, 107, 128, 149)(87, 108, 129, 150)(88, 109, 130, 151)(89, 110, 131, 152)(90, 111, 132, 153)(91, 112, 133, 154)(92, 113, 134, 155)(93, 114, 135, 156)(94, 115, 136, 157)(95, 116, 137, 158)(96, 117, 138, 159)(97, 118, 139, 160)(98, 119, 140, 161)(99, 120, 141, 162)(100, 121, 142, 163)(101, 122, 143, 164)(102, 123, 144, 165)(103, 124, 145, 166)(104, 125, 146, 167)(105, 126, 147, 168) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 47)(23, 43)(24, 53)(25, 57)(26, 44)(27, 58)(28, 46)(29, 52)(30, 59)(31, 55)(32, 54)(33, 45)(34, 50)(35, 61)(36, 49)(37, 60)(38, 63)(39, 48)(40, 62)(41, 56)(42, 51)(64, 109)(65, 111)(66, 114)(67, 121)(68, 119)(69, 124)(70, 122)(71, 107)(72, 110)(73, 117)(74, 112)(75, 106)(76, 123)(77, 120)(78, 118)(79, 126)(80, 113)(81, 108)(82, 116)(83, 115)(84, 125)(127, 158)(128, 160)(129, 163)(130, 149)(131, 168)(132, 152)(133, 150)(134, 156)(135, 159)(136, 166)(137, 161)(138, 155)(139, 151)(140, 148)(141, 167)(142, 154)(143, 162)(144, 157)(145, 165)(146, 164)(147, 153) MAP : A3.347 NOTES : type II, reflexible, isomorphic to A3.345. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 7, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.4^3, x.1 * x.2^-1 * x.3^-1 * x.4^-1, x.3^-1 * x.2^-1 * x.4^-1 * x.3^-1, x.2^2 * x.1^-1 * x.2 * x.1^-1, (x.3 * x.1^-1)^7 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 14, 4) #DARTS : 168 R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84)(85, 106, 127, 148)(86, 107, 128, 149)(87, 108, 129, 150)(88, 109, 130, 151)(89, 110, 131, 152)(90, 111, 132, 153)(91, 112, 133, 154)(92, 113, 134, 155)(93, 114, 135, 156)(94, 115, 136, 157)(95, 116, 137, 158)(96, 117, 138, 159)(97, 118, 139, 160)(98, 119, 140, 161)(99, 120, 141, 162)(100, 121, 142, 163)(101, 122, 143, 164)(102, 123, 144, 165)(103, 124, 145, 166)(104, 125, 146, 167)(105, 126, 147, 168) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 44)(23, 47)(24, 54)(25, 49)(26, 43)(27, 60)(28, 57)(29, 55)(30, 63)(31, 50)(32, 45)(33, 53)(34, 52)(35, 62)(36, 46)(37, 48)(38, 51)(39, 58)(40, 56)(41, 61)(42, 59)(64, 126)(65, 116)(66, 119)(67, 125)(68, 118)(69, 112)(70, 107)(71, 124)(72, 120)(73, 109)(74, 113)(75, 121)(76, 114)(77, 123)(78, 108)(79, 115)(80, 111)(81, 110)(82, 122)(83, 106)(84, 117)(127, 161)(128, 151)(129, 154)(130, 160)(131, 153)(132, 168)(133, 163)(134, 159)(135, 155)(136, 165)(137, 148)(138, 156)(139, 149)(140, 158)(141, 164)(142, 150)(143, 167)(144, 166)(145, 157)(146, 162)(147, 152) MAP : A3.348 NOTES : type II, reflexible, isomorphic to A3.345. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 7, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^3, u.4^3, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.4^3, x.1 * x.2^-1 * x.3^-1 * x.4^-1, x.3^-1 * x.2^-1 * x.4^-1 * x.3^-1, x.2^2 * x.1^-1 * x.2 * x.1^-1, (x.3 * x.1^-1)^7 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (3, 4, 14, 4) #DARTS : 168 R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84)(85, 106, 127, 148)(86, 107, 128, 149)(87, 108, 129, 150)(88, 109, 130, 151)(89, 110, 131, 152)(90, 111, 132, 153)(91, 112, 133, 154)(92, 113, 134, 155)(93, 114, 135, 156)(94, 115, 136, 157)(95, 116, 137, 158)(96, 117, 138, 159)(97, 118, 139, 160)(98, 119, 140, 161)(99, 120, 141, 162)(100, 121, 142, 163)(101, 122, 143, 164)(102, 123, 144, 165)(103, 124, 145, 166)(104, 125, 146, 167)(105, 126, 147, 168) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 44)(23, 47)(24, 54)(25, 49)(26, 43)(27, 60)(28, 57)(29, 55)(30, 63)(31, 50)(32, 45)(33, 53)(34, 52)(35, 62)(36, 46)(37, 48)(38, 51)(39, 58)(40, 56)(41, 61)(42, 59)(64, 109)(65, 111)(66, 114)(67, 121)(68, 119)(69, 124)(70, 122)(71, 107)(72, 110)(73, 117)(74, 112)(75, 106)(76, 123)(77, 120)(78, 118)(79, 126)(80, 113)(81, 108)(82, 116)(83, 115)(84, 125)(127, 150)(128, 157)(129, 153)(130, 152)(131, 164)(132, 148)(133, 159)(134, 168)(135, 158)(136, 161)(137, 167)(138, 160)(139, 154)(140, 149)(141, 166)(142, 162)(143, 151)(144, 155)(145, 163)(146, 156)(147, 165) MAP : A3.349 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 53)(2, 49)(3, 76)(4, 65)(5, 67)(6, 52)(7, 51)(8, 54)(9, 85)(10, 59)(11, 66)(12, 69)(13, 60)(14, 61)(15, 96)(16, 77)(17, 56)(18, 87)(19, 50)(20, 74)(21, 62)(22, 55)(23, 88)(24, 82)(25, 71)(26, 57)(27, 79)(28, 70)(29, 72)(30, 81)(31, 78)(32, 91)(33, 75)(34, 64)(35, 89)(36, 92)(37, 68)(38, 93)(39, 58)(40, 94)(41, 63)(42, 86)(43, 84)(44, 80)(45, 95)(46, 73)(47, 90)(48, 83)(97, 147)(98, 181)(99, 150)(100, 184)(101, 178)(102, 145)(103, 156)(104, 180)(105, 148)(106, 146)(107, 167)(108, 190)(109, 149)(110, 188)(111, 163)(112, 152)(113, 182)(114, 186)(115, 177)(116, 185)(117, 189)(118, 179)(119, 174)(120, 192)(121, 168)(122, 165)(123, 158)(124, 183)(125, 162)(126, 155)(127, 161)(128, 164)(129, 159)(130, 157)(131, 191)(132, 160)(133, 154)(134, 175)(135, 187)(136, 153)(137, 176)(138, 173)(139, 172)(140, 171)(141, 170)(142, 151)(143, 166)(144, 169) MAP : A3.350 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 149)(98, 145)(99, 172)(100, 161)(101, 163)(102, 148)(103, 147)(104, 150)(105, 181)(106, 155)(107, 162)(108, 165)(109, 156)(110, 157)(111, 192)(112, 173)(113, 152)(114, 183)(115, 146)(116, 170)(117, 158)(118, 151)(119, 184)(120, 178)(121, 167)(122, 153)(123, 175)(124, 166)(125, 168)(126, 177)(127, 174)(128, 187)(129, 171)(130, 160)(131, 185)(132, 188)(133, 164)(134, 189)(135, 154)(136, 190)(137, 159)(138, 182)(139, 180)(140, 176)(141, 191)(142, 169)(143, 186)(144, 179) MAP : A3.351 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 50)(2, 67)(3, 55)(4, 54)(5, 49)(6, 56)(7, 70)(8, 65)(9, 74)(10, 87)(11, 58)(12, 61)(13, 62)(14, 69)(15, 89)(16, 82)(17, 52)(18, 59)(19, 53)(20, 85)(21, 60)(22, 76)(23, 73)(24, 77)(25, 94)(26, 68)(27, 81)(28, 51)(29, 64)(30, 79)(31, 75)(32, 92)(33, 78)(34, 72)(35, 96)(36, 91)(37, 57)(38, 90)(39, 66)(40, 71)(41, 83)(42, 95)(43, 80)(44, 84)(45, 86)(46, 88)(47, 93)(48, 63)(97, 150)(98, 154)(99, 145)(100, 153)(101, 157)(102, 147)(103, 190)(104, 160)(105, 184)(106, 181)(107, 174)(108, 151)(109, 178)(110, 171)(111, 177)(112, 180)(113, 175)(114, 173)(115, 159)(116, 176)(117, 170)(118, 191)(119, 155)(120, 169)(121, 192)(122, 189)(123, 188)(124, 187)(125, 186)(126, 167)(127, 182)(128, 185)(129, 163)(130, 149)(131, 166)(132, 152)(133, 146)(134, 161)(135, 172)(136, 148)(137, 164)(138, 162)(139, 183)(140, 158)(141, 165)(142, 156)(143, 179)(144, 168) MAP : A3.352 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 92)(2, 84)(3, 68)(4, 62)(5, 80)(6, 69)(7, 85)(8, 60)(9, 81)(10, 65)(11, 56)(12, 89)(13, 83)(14, 96)(15, 66)(16, 70)(17, 61)(18, 54)(19, 91)(20, 79)(21, 63)(22, 57)(23, 49)(24, 51)(25, 50)(26, 78)(27, 77)(28, 74)(29, 55)(30, 82)(31, 72)(32, 90)(33, 64)(34, 76)(35, 58)(36, 93)(37, 75)(38, 94)(39, 52)(40, 53)(41, 59)(42, 88)(43, 86)(44, 95)(45, 73)(46, 67)(47, 71)(48, 87)(97, 150)(98, 154)(99, 145)(100, 153)(101, 157)(102, 147)(103, 190)(104, 160)(105, 184)(106, 181)(107, 174)(108, 151)(109, 178)(110, 171)(111, 177)(112, 180)(113, 175)(114, 173)(115, 159)(116, 176)(117, 170)(118, 191)(119, 155)(120, 169)(121, 192)(122, 189)(123, 188)(124, 187)(125, 186)(126, 167)(127, 182)(128, 185)(129, 163)(130, 149)(131, 166)(132, 152)(133, 146)(134, 161)(135, 172)(136, 148)(137, 164)(138, 162)(139, 183)(140, 158)(141, 165)(142, 156)(143, 179)(144, 168) MAP : A3.353 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 146)(98, 163)(99, 151)(100, 150)(101, 145)(102, 152)(103, 166)(104, 161)(105, 170)(106, 183)(107, 154)(108, 157)(109, 158)(110, 165)(111, 185)(112, 178)(113, 148)(114, 155)(115, 149)(116, 181)(117, 156)(118, 172)(119, 169)(120, 173)(121, 190)(122, 164)(123, 177)(124, 147)(125, 160)(126, 175)(127, 171)(128, 188)(129, 174)(130, 168)(131, 192)(132, 187)(133, 153)(134, 186)(135, 162)(136, 167)(137, 179)(138, 191)(139, 176)(140, 180)(141, 182)(142, 184)(143, 189)(144, 159) MAP : A3.354 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 188)(98, 180)(99, 164)(100, 158)(101, 176)(102, 165)(103, 181)(104, 156)(105, 177)(106, 161)(107, 152)(108, 185)(109, 179)(110, 192)(111, 162)(112, 166)(113, 157)(114, 150)(115, 187)(116, 175)(117, 159)(118, 153)(119, 145)(120, 147)(121, 146)(122, 174)(123, 173)(124, 170)(125, 151)(126, 178)(127, 168)(128, 186)(129, 160)(130, 172)(131, 154)(132, 189)(133, 171)(134, 190)(135, 148)(136, 149)(137, 155)(138, 184)(139, 182)(140, 191)(141, 169)(142, 163)(143, 167)(144, 183) MAP : A3.355 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 50)(2, 67)(3, 55)(4, 54)(5, 49)(6, 56)(7, 70)(8, 65)(9, 74)(10, 87)(11, 58)(12, 61)(13, 62)(14, 69)(15, 89)(16, 82)(17, 52)(18, 59)(19, 53)(20, 85)(21, 60)(22, 76)(23, 73)(24, 77)(25, 94)(26, 68)(27, 81)(28, 51)(29, 64)(30, 79)(31, 75)(32, 92)(33, 78)(34, 72)(35, 96)(36, 91)(37, 57)(38, 90)(39, 66)(40, 71)(41, 83)(42, 95)(43, 80)(44, 84)(45, 86)(46, 88)(47, 93)(48, 63)(97, 147)(98, 181)(99, 150)(100, 184)(101, 178)(102, 145)(103, 156)(104, 180)(105, 148)(106, 146)(107, 167)(108, 190)(109, 149)(110, 188)(111, 163)(112, 152)(113, 182)(114, 186)(115, 177)(116, 185)(117, 189)(118, 179)(119, 174)(120, 192)(121, 168)(122, 165)(123, 158)(124, 183)(125, 162)(126, 155)(127, 161)(128, 164)(129, 159)(130, 157)(131, 191)(132, 160)(133, 154)(134, 175)(135, 187)(136, 153)(137, 176)(138, 173)(139, 172)(140, 171)(141, 170)(142, 151)(143, 166)(144, 169) MAP : A3.356 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 71)(2, 73)(3, 72)(4, 87)(5, 88)(6, 66)(7, 77)(8, 59)(9, 70)(10, 83)(11, 89)(12, 56)(13, 65)(14, 52)(15, 69)(16, 81)(17, 58)(18, 63)(19, 94)(20, 51)(21, 54)(22, 64)(23, 95)(24, 79)(25, 93)(26, 76)(27, 85)(28, 82)(29, 75)(30, 74)(31, 68)(32, 53)(33, 57)(34, 78)(35, 61)(36, 50)(37, 55)(38, 91)(39, 96)(40, 90)(41, 60)(42, 80)(43, 67)(44, 49)(45, 84)(46, 86)(47, 92)(48, 62)(97, 147)(98, 181)(99, 150)(100, 184)(101, 178)(102, 145)(103, 156)(104, 180)(105, 148)(106, 146)(107, 167)(108, 190)(109, 149)(110, 188)(111, 163)(112, 152)(113, 182)(114, 186)(115, 177)(116, 185)(117, 189)(118, 179)(119, 174)(120, 192)(121, 168)(122, 165)(123, 158)(124, 183)(125, 162)(126, 155)(127, 161)(128, 164)(129, 159)(130, 157)(131, 191)(132, 160)(133, 154)(134, 175)(135, 187)(136, 153)(137, 176)(138, 173)(139, 172)(140, 171)(141, 170)(142, 151)(143, 166)(144, 169) MAP : A3.357 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 92)(2, 84)(3, 68)(4, 62)(5, 80)(6, 69)(7, 85)(8, 60)(9, 81)(10, 65)(11, 56)(12, 89)(13, 83)(14, 96)(15, 66)(16, 70)(17, 61)(18, 54)(19, 91)(20, 79)(21, 63)(22, 57)(23, 49)(24, 51)(25, 50)(26, 78)(27, 77)(28, 74)(29, 55)(30, 82)(31, 72)(32, 90)(33, 64)(34, 76)(35, 58)(36, 93)(37, 75)(38, 94)(39, 52)(40, 53)(41, 59)(42, 88)(43, 86)(44, 95)(45, 73)(46, 67)(47, 71)(48, 87)(97, 147)(98, 181)(99, 150)(100, 184)(101, 178)(102, 145)(103, 156)(104, 180)(105, 148)(106, 146)(107, 167)(108, 190)(109, 149)(110, 188)(111, 163)(112, 152)(113, 182)(114, 186)(115, 177)(116, 185)(117, 189)(118, 179)(119, 174)(120, 192)(121, 168)(122, 165)(123, 158)(124, 183)(125, 162)(126, 155)(127, 161)(128, 164)(129, 159)(130, 157)(131, 191)(132, 160)(133, 154)(134, 175)(135, 187)(136, 153)(137, 176)(138, 173)(139, 172)(140, 171)(141, 170)(142, 151)(143, 166)(144, 169) MAP : A3.358 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 188)(98, 180)(99, 164)(100, 158)(101, 176)(102, 165)(103, 181)(104, 156)(105, 177)(106, 161)(107, 152)(108, 185)(109, 179)(110, 192)(111, 162)(112, 166)(113, 157)(114, 150)(115, 187)(116, 175)(117, 159)(118, 153)(119, 145)(120, 147)(121, 146)(122, 174)(123, 173)(124, 170)(125, 151)(126, 178)(127, 168)(128, 186)(129, 160)(130, 172)(131, 154)(132, 189)(133, 171)(134, 190)(135, 148)(136, 149)(137, 155)(138, 184)(139, 182)(140, 191)(141, 169)(142, 163)(143, 167)(144, 183) MAP : A3.359 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 53)(2, 49)(3, 76)(4, 65)(5, 67)(6, 52)(7, 51)(8, 54)(9, 85)(10, 59)(11, 66)(12, 69)(13, 60)(14, 61)(15, 96)(16, 77)(17, 56)(18, 87)(19, 50)(20, 74)(21, 62)(22, 55)(23, 88)(24, 82)(25, 71)(26, 57)(27, 79)(28, 70)(29, 72)(30, 81)(31, 78)(32, 91)(33, 75)(34, 64)(35, 89)(36, 92)(37, 68)(38, 93)(39, 58)(40, 94)(41, 63)(42, 86)(43, 84)(44, 80)(45, 95)(46, 73)(47, 90)(48, 83)(97, 150)(98, 154)(99, 145)(100, 153)(101, 157)(102, 147)(103, 190)(104, 160)(105, 184)(106, 181)(107, 174)(108, 151)(109, 178)(110, 171)(111, 177)(112, 180)(113, 175)(114, 173)(115, 159)(116, 176)(117, 170)(118, 191)(119, 155)(120, 169)(121, 192)(122, 189)(123, 188)(124, 187)(125, 186)(126, 167)(127, 182)(128, 185)(129, 163)(130, 149)(131, 166)(132, 152)(133, 146)(134, 161)(135, 172)(136, 148)(137, 164)(138, 162)(139, 183)(140, 158)(141, 165)(142, 156)(143, 179)(144, 168) MAP : A3.360 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 167)(98, 169)(99, 168)(100, 183)(101, 184)(102, 162)(103, 173)(104, 155)(105, 166)(106, 179)(107, 185)(108, 152)(109, 161)(110, 148)(111, 165)(112, 177)(113, 154)(114, 159)(115, 190)(116, 147)(117, 150)(118, 160)(119, 191)(120, 175)(121, 189)(122, 172)(123, 181)(124, 178)(125, 171)(126, 170)(127, 164)(128, 149)(129, 153)(130, 174)(131, 157)(132, 146)(133, 151)(134, 187)(135, 192)(136, 186)(137, 156)(138, 176)(139, 163)(140, 145)(141, 180)(142, 182)(143, 188)(144, 158) MAP : A3.361 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 71)(2, 73)(3, 72)(4, 87)(5, 88)(6, 66)(7, 77)(8, 59)(9, 70)(10, 83)(11, 89)(12, 56)(13, 65)(14, 52)(15, 69)(16, 81)(17, 58)(18, 63)(19, 94)(20, 51)(21, 54)(22, 64)(23, 95)(24, 79)(25, 93)(26, 76)(27, 85)(28, 82)(29, 75)(30, 74)(31, 68)(32, 53)(33, 57)(34, 78)(35, 61)(36, 50)(37, 55)(38, 91)(39, 96)(40, 90)(41, 60)(42, 80)(43, 67)(44, 49)(45, 84)(46, 86)(47, 92)(48, 62)(97, 150)(98, 154)(99, 145)(100, 153)(101, 157)(102, 147)(103, 190)(104, 160)(105, 184)(106, 181)(107, 174)(108, 151)(109, 178)(110, 171)(111, 177)(112, 180)(113, 175)(114, 173)(115, 159)(116, 176)(117, 170)(118, 191)(119, 155)(120, 169)(121, 192)(122, 189)(123, 188)(124, 187)(125, 186)(126, 167)(127, 182)(128, 185)(129, 163)(130, 149)(131, 166)(132, 152)(133, 146)(134, 161)(135, 172)(136, 148)(137, 164)(138, 162)(139, 183)(140, 158)(141, 165)(142, 156)(143, 179)(144, 168) MAP : A3.362 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 167)(98, 169)(99, 168)(100, 183)(101, 184)(102, 162)(103, 173)(104, 155)(105, 166)(106, 179)(107, 185)(108, 152)(109, 161)(110, 148)(111, 165)(112, 177)(113, 154)(114, 159)(115, 190)(116, 147)(117, 150)(118, 160)(119, 191)(120, 175)(121, 189)(122, 172)(123, 181)(124, 178)(125, 171)(126, 170)(127, 164)(128, 149)(129, 153)(130, 174)(131, 157)(132, 146)(133, 151)(134, 187)(135, 192)(136, 186)(137, 156)(138, 176)(139, 163)(140, 145)(141, 180)(142, 182)(143, 188)(144, 158) MAP : A3.363 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 149)(98, 145)(99, 172)(100, 161)(101, 163)(102, 148)(103, 147)(104, 150)(105, 181)(106, 155)(107, 162)(108, 165)(109, 156)(110, 157)(111, 192)(112, 173)(113, 152)(114, 183)(115, 146)(116, 170)(117, 158)(118, 151)(119, 184)(120, 178)(121, 167)(122, 153)(123, 175)(124, 166)(125, 168)(126, 177)(127, 174)(128, 187)(129, 171)(130, 160)(131, 185)(132, 188)(133, 164)(134, 189)(135, 154)(136, 190)(137, 159)(138, 182)(139, 180)(140, 176)(141, 191)(142, 169)(143, 186)(144, 179) MAP : A3.364 NOTES : type I, reflexible, isomorphic to A3.349. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1^-1 * u.2^-1)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 146)(98, 163)(99, 151)(100, 150)(101, 145)(102, 152)(103, 166)(104, 161)(105, 170)(106, 183)(107, 154)(108, 157)(109, 158)(110, 165)(111, 185)(112, 178)(113, 148)(114, 155)(115, 149)(116, 181)(117, 156)(118, 172)(119, 169)(120, 173)(121, 190)(122, 164)(123, 177)(124, 147)(125, 160)(126, 175)(127, 171)(128, 188)(129, 174)(130, 168)(131, 192)(132, 187)(133, 153)(134, 186)(135, 162)(136, 167)(137, 179)(138, 191)(139, 176)(140, 180)(141, 182)(142, 184)(143, 189)(144, 159) MAP : A3.365 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, u.3^3, (u.3^-1 * u.1 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^3, x.2 * x.3 * x.1 * x.2 * x.3, x.1 * x.3^-1 * x.2 * x.3^-1 * x.2, (x.3^-1 * x.1 * x.2)^2, (x.3 * x.1)^3 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 6, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 26)(2, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(49, 66)(50, 67)(51, 65)(52, 58)(53, 63)(54, 61)(55, 62)(56, 69)(57, 68)(59, 60)(64, 70)(71, 72)(73, 88)(74, 96)(75, 80)(76, 79)(77, 84)(78, 92)(81, 95)(82, 93)(83, 94)(85, 91)(86, 89)(87, 90) MAP : A3.366 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^6, (u.1^-1 * u.2^-1)^3 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1 * x.2 * x.1^-1 * x.2 * x.1, x.1^6, (x.1^-1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 35)(2, 38)(3, 25)(4, 39)(5, 40)(6, 26)(7, 28)(8, 29)(9, 43)(10, 46)(11, 33)(12, 47)(13, 48)(14, 34)(15, 36)(16, 37)(17, 27)(18, 30)(19, 41)(20, 31)(21, 32)(22, 42)(23, 44)(24, 45)(49, 77)(50, 73)(51, 90)(52, 85)(53, 74)(54, 93)(55, 75)(56, 89)(57, 86)(58, 88)(59, 76)(60, 81)(61, 83)(62, 84)(63, 78)(64, 92)(65, 95)(66, 79)(67, 96)(68, 82)(69, 87)(70, 91)(71, 80)(72, 94) MAP : A3.367 NOTES : type I, reflexible, isomorphic to A3.366. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 6, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^6, (u.1^-1 * u.2^-1)^3 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2 * x.1 * x.2^-1 * x.1 * x.2, x.2^6, (x.1^-1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 29)(2, 25)(3, 42)(4, 37)(5, 26)(6, 45)(7, 27)(8, 41)(9, 38)(10, 40)(11, 28)(12, 33)(13, 35)(14, 36)(15, 30)(16, 44)(17, 47)(18, 31)(19, 48)(20, 34)(21, 39)(22, 43)(23, 32)(24, 46)(49, 83)(50, 86)(51, 73)(52, 87)(53, 88)(54, 74)(55, 76)(56, 77)(57, 91)(58, 94)(59, 81)(60, 95)(61, 96)(62, 82)(63, 84)(64, 85)(65, 75)(66, 78)(67, 89)(68, 79)(69, 80)(70, 90)(71, 92)(72, 93) MAP : A3.368 NOTES : type I, chiral, isomorphic to A3.365. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, u.3^3, (u.3^-1 * u.1 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^3, x.1 * x.2 * x.3 * x.1 * x.3, x.1 * x.3^-1 * x.1 * x.3^-1 * x.2, (x.3^-1 * x.1 * x.2)^2, (x.3 * x.2)^3 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 6, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 26)(2, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(49, 64)(50, 72)(51, 56)(52, 55)(53, 60)(54, 68)(57, 71)(58, 69)(59, 70)(61, 67)(62, 65)(63, 66)(73, 83)(74, 81)(75, 82)(76, 89)(77, 94)(78, 95)(79, 93)(80, 86)(84, 90)(85, 96)(87, 88)(91, 92) MAP : A3.369 NOTES : type I, reflexible, isomorphic to A3.366. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 6, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^6, (u.1^-1 * u.2^-1)^3 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2 * x.1 * x.2^-1 * x.1 * x.2, x.2^6, (x.1^-1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 26)(2, 29)(3, 31)(4, 35)(5, 25)(6, 39)(7, 42)(8, 47)(9, 36)(10, 44)(11, 37)(12, 38)(13, 28)(14, 33)(15, 45)(16, 34)(17, 32)(18, 27)(19, 46)(20, 40)(21, 30)(22, 48)(23, 41)(24, 43)(49, 75)(50, 78)(51, 89)(52, 79)(53, 80)(54, 90)(55, 92)(56, 93)(57, 83)(58, 86)(59, 73)(60, 87)(61, 88)(62, 74)(63, 76)(64, 77)(65, 91)(66, 94)(67, 81)(68, 95)(69, 96)(70, 82)(71, 84)(72, 85) MAP : A3.370 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, u.3^3, (u.3^-1 * u.1 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^3, x.3 * x.1 * x.3^-1 * x.2, (x.3^-1 * x.1 * x.2)^2, (x.2 * x.1)^3 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 6, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 26)(2, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(49, 64)(50, 72)(51, 56)(52, 55)(53, 60)(54, 68)(57, 71)(58, 69)(59, 70)(61, 67)(62, 65)(63, 66)(73, 85)(74, 86)(75, 87)(76, 88)(77, 89)(78, 90)(79, 91)(80, 92)(81, 93)(82, 94)(83, 95)(84, 96) MAP : A3.371 NOTES : type I, reflexible, isomorphic to A3.370. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 8)(2, 5)(3, 4)(6, 7) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.3^3, u.4^3, (u.2 * u.3^-1 * u.1^-1)^2, (u.1 * u.2^-1 * u.4^-1)^2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^3, x.4^3, x.2 * x.3 * x.4^-1, x.2^3, x.3^-1 * x.4 * x.3 * x.2, x.4^-1 * x.3 * x.4 * x.2^-1, x.2 * x.3^-1 * x.1^-1 * x.3^-1 * x.4^-1 * x.1^-1, (x.1 * x.4^-1 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1) LOCAL TYPE : (3, 6, 6, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 51)(14, 49)(15, 50)(16, 57)(17, 56)(18, 52)(19, 60)(20, 59)(21, 54)(22, 55)(23, 53)(24, 58)(25, 41)(26, 42)(27, 43)(28, 44)(29, 45)(30, 46)(31, 47)(32, 48)(33, 37)(34, 38)(35, 39)(36, 40)(61, 80)(62, 76)(63, 84)(64, 83)(65, 78)(66, 79)(67, 77)(68, 82)(69, 75)(70, 73)(71, 74)(72, 81) MAP : A3.372 NOTES : type I, reflexible, isomorphic to A3.370. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 8)(2, 5)(3, 4)(6, 7) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.3^3, u.4^3, (u.2 * u.3^-1 * u.1^-1)^2, (u.1 * u.2^-1 * u.4^-1)^2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^3, x.4^3, x.2 * x.3 * x.4^-1, x.2^3, x.3^-1 * x.4 * x.3 * x.2, x.4^-1 * x.3 * x.4 * x.2^-1, x.2 * x.3^-1 * x.1^-1 * x.3^-1 * x.4^-1 * x.1^-1, (x.1 * x.4^-1 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1) LOCAL TYPE : (3, 6, 6, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 50)(14, 51)(15, 49)(16, 54)(17, 59)(18, 57)(19, 58)(20, 53)(21, 52)(22, 60)(23, 56)(24, 55)(25, 43)(26, 41)(27, 42)(28, 37)(29, 48)(30, 44)(31, 40)(32, 39)(33, 46)(34, 47)(35, 45)(36, 38)(61, 82)(62, 83)(63, 81)(64, 74)(65, 79)(66, 77)(67, 78)(68, 73)(69, 84)(70, 80)(71, 76)(72, 75) MAP : A3.373 NOTES : type I, reflexible, isomorphic to A3.366. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^6, (u.1^-1 * u.2^-1)^3 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1 * x.2 * x.1^-1 * x.2 * x.1, x.1^6, (x.1^-1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 27)(2, 30)(3, 41)(4, 31)(5, 32)(6, 42)(7, 44)(8, 45)(9, 35)(10, 38)(11, 25)(12, 39)(13, 40)(14, 26)(15, 28)(16, 29)(17, 43)(18, 46)(19, 33)(20, 47)(21, 48)(22, 34)(23, 36)(24, 37)(49, 74)(50, 77)(51, 79)(52, 83)(53, 73)(54, 87)(55, 90)(56, 95)(57, 84)(58, 92)(59, 85)(60, 86)(61, 76)(62, 81)(63, 93)(64, 82)(65, 80)(66, 75)(67, 94)(68, 88)(69, 78)(70, 96)(71, 89)(72, 91) MAP : A3.374 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^3, u.1^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2 | x.2^3, x.1^-2 * x.2^-1 * x.1 * x.2, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.1^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 7, 6) #DARTS : 84 R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84) L = (1, 42)(2, 32)(3, 35)(4, 41)(5, 34)(6, 28)(7, 23)(8, 40)(9, 36)(10, 25)(11, 29)(12, 37)(13, 30)(14, 39)(15, 24)(16, 31)(17, 27)(18, 26)(19, 38)(20, 22)(21, 33)(43, 65)(44, 68)(45, 75)(46, 70)(47, 64)(48, 81)(49, 78)(50, 76)(51, 84)(52, 71)(53, 66)(54, 74)(55, 73)(56, 83)(57, 67)(58, 69)(59, 72)(60, 79)(61, 77)(62, 82)(63, 80) MAP : A3.375 NOTES : type I, chiral, isomorphic to A3.374. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^3, u.2^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2 | x.1^3, x.2 * x.1^-1 * x.2^-2 * x.1, (x.1^-1 * x.2^-1)^3, x.2^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 7, 6) #DARTS : 84 R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84) L = (1, 26)(2, 22)(3, 32)(4, 36)(5, 23)(6, 37)(7, 25)(8, 31)(9, 38)(10, 34)(11, 33)(12, 24)(13, 29)(14, 40)(15, 28)(16, 39)(17, 42)(18, 27)(19, 41)(20, 35)(21, 30)(43, 84)(44, 74)(45, 77)(46, 83)(47, 76)(48, 70)(49, 65)(50, 82)(51, 78)(52, 67)(53, 71)(54, 79)(55, 72)(56, 81)(57, 66)(58, 73)(59, 69)(60, 68)(61, 80)(62, 64)(63, 75) MAP : A3.376 NOTES : type I, chiral, isomorphic to A3.374. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^3, u.2^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2 | x.1^3, x.2 * x.1^-1 * x.2^-2 * x.1, (x.1^-1 * x.2^-1)^3, x.2^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 7, 6) #DARTS : 84 R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84) L = (1, 26)(2, 22)(3, 32)(4, 36)(5, 23)(6, 37)(7, 25)(8, 31)(9, 38)(10, 34)(11, 33)(12, 24)(13, 29)(14, 40)(15, 28)(16, 39)(17, 42)(18, 27)(19, 41)(20, 35)(21, 30)(43, 67)(44, 69)(45, 72)(46, 79)(47, 77)(48, 82)(49, 80)(50, 65)(51, 68)(52, 75)(53, 70)(54, 64)(55, 81)(56, 78)(57, 76)(58, 84)(59, 71)(60, 66)(61, 74)(62, 73)(63, 83) MAP : A3.377 NOTES : type I, chiral, isomorphic to A3.374. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^3, u.1^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2 | x.2^3, x.1^-2 * x.2 * x.1 * x.2^-1, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.1^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 7, 6) #DARTS : 84 R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84) L = (1, 25)(2, 27)(3, 30)(4, 37)(5, 35)(6, 40)(7, 38)(8, 23)(9, 26)(10, 33)(11, 28)(12, 22)(13, 39)(14, 36)(15, 34)(16, 42)(17, 29)(18, 24)(19, 32)(20, 31)(21, 41)(43, 68)(44, 64)(45, 74)(46, 78)(47, 65)(48, 79)(49, 67)(50, 73)(51, 80)(52, 76)(53, 75)(54, 66)(55, 71)(56, 82)(57, 70)(58, 81)(59, 84)(60, 69)(61, 83)(62, 77)(63, 72) MAP : A3.378 NOTES : type I, chiral, isomorphic to A3.374. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^3, u.2^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2 | x.1^3, x.2^2 * x.1^-1 * x.2^-1 * x.1, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.2^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 7, 6) #DARTS : 84 R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84) L = (1, 23)(2, 26)(3, 33)(4, 28)(5, 22)(6, 39)(7, 36)(8, 34)(9, 42)(10, 29)(11, 24)(12, 32)(13, 31)(14, 41)(15, 25)(16, 27)(17, 30)(18, 37)(19, 35)(20, 40)(21, 38)(43, 67)(44, 69)(45, 72)(46, 79)(47, 77)(48, 82)(49, 80)(50, 65)(51, 68)(52, 75)(53, 70)(54, 64)(55, 81)(56, 78)(57, 76)(58, 84)(59, 71)(60, 66)(61, 74)(62, 73)(63, 83) MAP : A3.379 NOTES : type I, chiral, isomorphic to A3.374. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^3, u.1^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2 | x.2^3, x.1^-2 * x.2 * x.1 * x.2^-1, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.1^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 7, 6) #DARTS : 84 R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84) L = (1, 42)(2, 32)(3, 35)(4, 41)(5, 34)(6, 28)(7, 23)(8, 40)(9, 36)(10, 25)(11, 29)(12, 37)(13, 30)(14, 39)(15, 24)(16, 31)(17, 27)(18, 26)(19, 38)(20, 22)(21, 33)(43, 68)(44, 64)(45, 74)(46, 78)(47, 65)(48, 79)(49, 67)(50, 73)(51, 80)(52, 76)(53, 75)(54, 66)(55, 71)(56, 82)(57, 70)(58, 81)(59, 84)(60, 69)(61, 83)(62, 77)(63, 72) MAP : A3.380 NOTES : type I, chiral, isomorphic to A3.374. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, (u.1^-1 * u.2^-1)^3, u.1^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2 | x.2^3, x.1^-2 * x.2^-1 * x.1 * x.2, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.1^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 7, 6) #DARTS : 84 R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84) L = (1, 25)(2, 27)(3, 30)(4, 37)(5, 35)(6, 40)(7, 38)(8, 23)(9, 26)(10, 33)(11, 28)(12, 22)(13, 39)(14, 36)(15, 34)(16, 42)(17, 29)(18, 24)(19, 32)(20, 31)(21, 41)(43, 65)(44, 68)(45, 75)(46, 70)(47, 64)(48, 81)(49, 78)(50, 76)(51, 84)(52, 71)(53, 66)(54, 74)(55, 73)(56, 83)(57, 67)(58, 69)(59, 72)(60, 79)(61, 77)(62, 82)(63, 80) MAP : A3.381 NOTES : type I, chiral, isomorphic to A3.374. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, (u.1^-1 * u.2^-1)^3, u.2^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2 | x.1^3, x.2^2 * x.1^-1 * x.2^-1 * x.1, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.2^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 6, 7, 6) #DARTS : 84 R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84) L = (1, 23)(2, 26)(3, 33)(4, 28)(5, 22)(6, 39)(7, 36)(8, 34)(9, 42)(10, 29)(11, 24)(12, 32)(13, 31)(14, 41)(15, 25)(16, 27)(17, 30)(18, 37)(19, 35)(20, 40)(21, 38)(43, 84)(44, 74)(45, 77)(46, 83)(47, 76)(48, 70)(49, 65)(50, 82)(51, 78)(52, 67)(53, 71)(54, 79)(55, 72)(56, 81)(57, 66)(58, 73)(59, 69)(60, 68)(61, 80)(62, 64)(63, 75) MAP : A3.382 NOTES : type I, non-Cayley, reflexible, isomorphic to Med({3,7}), representative. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 3, 7 ] UNIGROUP : < u.1, u.2 | u.2^2, (u.1 * u.2)^3, u.1^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.2^2, (x.1 * x.2)^3, x.1^7, (x.2 * x.1^-3)^4 > SCHREIER VEC. : (x.1, x.1^-1)^2 LOCAL TYPE : (3, 7, 3, 7) #DARTS : 336 R = (1, 187, 19, 169)(2, 204, 36, 170)(3, 202, 34, 171)(4, 207, 39, 172)(5, 203, 35, 173)(6, 271, 103, 174)(7, 270, 102, 175)(8, 220, 52, 176)(9, 189, 21, 177)(10, 192, 24, 178)(11, 206, 38, 179)(12, 301, 133, 180)(13, 303, 135, 181)(14, 316, 148, 182)(15, 299, 131, 183)(16, 302, 134, 184)(17, 186, 18, 185)(20, 201, 33, 188)(22, 218, 50, 190)(23, 217, 49, 191)(25, 248, 80, 193)(26, 245, 77, 194)(27, 304, 136, 195)(28, 243, 75, 196)(29, 318, 150, 197)(30, 241, 73, 198)(31, 242, 74, 199)(32, 319, 151, 200)(37, 240, 72, 205)(40, 237, 69, 208)(41, 262, 94, 209)(42, 263, 95, 210)(43, 260, 92, 211)(44, 326, 158, 212)(45, 258, 90, 213)(46, 333, 165, 214)(47, 336, 168, 215)(48, 257, 89, 216)(51, 327, 159, 219)(53, 324, 156, 221)(54, 328, 160, 222)(55, 325, 157, 223)(56, 331, 163, 224)(57, 295, 127, 225)(58, 294, 126, 226)(59, 279, 111, 227)(60, 312, 144, 228)(61, 276, 108, 229)(62, 280, 112, 230)(63, 277, 109, 231)(64, 259, 91, 232)(65, 292, 124, 233)(66, 307, 139, 234)(67, 309, 141, 235)(68, 306, 138, 236)(70, 323, 155, 238)(71, 308, 140, 239)(76, 278, 110, 244)(78, 261, 93, 246)(79, 264, 96, 247)(81, 290, 122, 249)(82, 289, 121, 250)(83, 305, 137, 251)(84, 281, 113, 252)(85, 321, 153, 253)(86, 298, 130, 254)(87, 297, 129, 255)(88, 322, 154, 256)(97, 291, 123, 265)(98, 284, 116, 266)(99, 282, 114, 267)(100, 287, 119, 268)(101, 283, 115, 269)(104, 300, 132, 272)(105, 293, 125, 273)(106, 296, 128, 274)(107, 286, 118, 275)(117, 288, 120, 285)(142, 311, 143, 310)(145, 334, 166, 313)(146, 335, 167, 314)(147, 332, 164, 315)(149, 330, 162, 317)(152, 329, 161, 320) L = (1, 173)(2, 176)(3, 190)(4, 325)(5, 327)(6, 308)(7, 323)(8, 326)(9, 240)(10, 237)(11, 328)(12, 235)(13, 310)(14, 233)(15, 234)(16, 311)(17, 171)(18, 188)(19, 186)(20, 191)(21, 187)(22, 263)(23, 262)(24, 204)(25, 230)(26, 231)(27, 228)(28, 286)(29, 226)(30, 293)(31, 296)(32, 225)(33, 170)(34, 169)(35, 177)(36, 185)(37, 193)(38, 202)(39, 201)(40, 194)(41, 175)(42, 174)(43, 287)(44, 184)(45, 284)(46, 288)(47, 285)(48, 291)(49, 172)(50, 179)(51, 181)(52, 178)(53, 272)(54, 195)(55, 180)(56, 269)(57, 314)(58, 313)(59, 297)(60, 329)(61, 281)(62, 322)(63, 321)(64, 282)(65, 315)(66, 332)(67, 330)(68, 335)(69, 331)(70, 183)(71, 182)(72, 324)(73, 316)(74, 299)(75, 301)(76, 298)(77, 192)(78, 283)(79, 300)(80, 189)(81, 317)(82, 320)(83, 334)(84, 253)(85, 255)(86, 236)(87, 251)(88, 254)(89, 319)(90, 318)(91, 247)(92, 304)(93, 244)(94, 248)(95, 245)(96, 227)(97, 224)(98, 221)(99, 256)(100, 219)(101, 238)(102, 217)(103, 218)(104, 239)(105, 214)(106, 215)(107, 212)(108, 246)(109, 210)(110, 229)(111, 232)(112, 209)(113, 312)(114, 309)(115, 208)(116, 307)(117, 222)(118, 305)(119, 306)(120, 223)(121, 294)(122, 295)(123, 292)(124, 198)(125, 290)(126, 213)(127, 216)(128, 289)(129, 277)(130, 280)(131, 270)(132, 205)(133, 207)(134, 220)(135, 203)(136, 206)(137, 279)(138, 278)(139, 199)(140, 264)(141, 196)(142, 200)(143, 197)(144, 211)(145, 275)(146, 268)(147, 266)(148, 271)(149, 267)(150, 303)(151, 302)(152, 252)(153, 276)(154, 259)(155, 261)(156, 258)(157, 336)(158, 243)(159, 260)(160, 333)(161, 274)(162, 273)(163, 257)(164, 265)(165, 241)(166, 250)(167, 249)(168, 242) MAP : A3.383 NOTES : type I, non-Cayley, reflexible, isomorphic to Med({3,7}), isomorphic to A3.382. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 7, 3 ] UNIGROUP : < u.1, u.2 | u.2^2, u.1^3, (u.1 * u.2)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.2^2, x.1^3, (x.2 * x.1^-1)^7, (x.2 * x.1 * x.2 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.1^-1)^2 LOCAL TYPE : (3, 7, 3, 7) #DARTS : 336 R = (1, 239, 71, 169)(2, 238, 70, 170)(3, 223, 55, 171)(4, 256, 88, 172)(5, 220, 52, 173)(6, 224, 56, 174)(7, 221, 53, 175)(8, 203, 35, 176)(9, 236, 68, 177)(10, 251, 83, 178)(11, 253, 85, 179)(12, 250, 82, 180)(13, 320, 152, 181)(14, 267, 99, 182)(15, 252, 84, 183)(16, 317, 149, 184)(17, 310, 142, 185)(18, 311, 143, 186)(19, 308, 140, 187)(20, 222, 54, 188)(21, 306, 138, 189)(22, 205, 37, 190)(23, 208, 40, 191)(24, 305, 137, 192)(25, 234, 66, 193)(26, 233, 65, 194)(27, 249, 81, 195)(28, 225, 57, 196)(29, 265, 97, 197)(30, 242, 74, 198)(31, 241, 73, 199)(32, 266, 98, 200)(33, 328, 160, 201)(34, 325, 157, 202)(36, 323, 155, 204)(38, 321, 153, 206)(39, 322, 154, 207)(41, 235, 67, 209)(42, 228, 60, 210)(43, 226, 58, 211)(44, 231, 63, 212)(45, 227, 59, 213)(46, 287, 119, 214)(47, 286, 118, 215)(48, 244, 76, 216)(49, 237, 69, 217)(50, 240, 72, 218)(51, 230, 62, 219)(61, 232, 64, 229)(75, 295, 127, 243)(77, 292, 124, 245)(78, 296, 128, 246)(79, 293, 125, 247)(80, 307, 139, 248)(86, 255, 87, 254)(89, 278, 110, 257)(90, 279, 111, 258)(91, 276, 108, 259)(92, 294, 126, 260)(93, 274, 106, 261)(94, 309, 141, 262)(95, 312, 144, 263)(96, 273, 105, 264)(100, 333, 165, 268)(101, 335, 167, 269)(102, 324, 156, 270)(103, 331, 163, 271)(104, 334, 166, 272)(107, 336, 168, 275)(109, 326, 158, 277)(112, 327, 159, 280)(113, 299, 131, 281)(114, 316, 148, 282)(115, 314, 146, 283)(116, 319, 151, 284)(117, 315, 147, 285)(120, 332, 164, 288)(121, 301, 133, 289)(122, 304, 136, 290)(123, 318, 150, 291)(129, 298, 130, 297)(132, 313, 145, 300)(134, 330, 162, 302)(135, 329, 161, 303) L = (1, 171)(2, 188)(3, 186)(4, 191)(5, 187)(6, 263)(7, 262)(8, 204)(9, 173)(10, 176)(11, 190)(12, 325)(13, 327)(14, 308)(15, 323)(16, 326)(17, 170)(18, 169)(19, 177)(20, 185)(21, 193)(22, 202)(23, 201)(24, 194)(25, 240)(26, 237)(27, 328)(28, 235)(29, 310)(30, 233)(31, 234)(32, 311)(33, 172)(34, 179)(35, 181)(36, 178)(37, 272)(38, 195)(39, 180)(40, 269)(41, 230)(42, 231)(43, 228)(44, 286)(45, 226)(46, 293)(47, 296)(48, 225)(49, 175)(50, 174)(51, 287)(52, 184)(53, 284)(54, 288)(55, 285)(56, 291)(57, 319)(58, 318)(59, 247)(60, 304)(61, 244)(62, 248)(63, 245)(64, 227)(65, 316)(66, 299)(67, 301)(68, 298)(69, 192)(70, 283)(71, 300)(72, 189)(73, 214)(74, 215)(75, 212)(76, 246)(77, 210)(78, 229)(79, 232)(80, 209)(81, 314)(82, 313)(83, 297)(84, 329)(85, 281)(86, 322)(87, 321)(88, 282)(89, 224)(90, 221)(91, 256)(92, 219)(93, 238)(94, 217)(95, 218)(96, 239)(97, 315)(98, 332)(99, 330)(100, 335)(101, 331)(102, 183)(103, 182)(104, 324)(105, 317)(106, 320)(107, 334)(108, 253)(109, 255)(110, 236)(111, 251)(112, 254)(113, 276)(114, 259)(115, 261)(116, 258)(117, 336)(118, 243)(119, 260)(120, 333)(121, 274)(122, 273)(123, 257)(124, 265)(125, 241)(126, 250)(127, 249)(128, 242)(129, 279)(130, 278)(131, 199)(132, 264)(133, 196)(134, 200)(135, 197)(136, 211)(137, 275)(138, 268)(139, 266)(140, 271)(141, 267)(142, 303)(143, 302)(144, 252)(145, 294)(146, 295)(147, 292)(148, 198)(149, 290)(150, 213)(151, 216)(152, 289)(153, 277)(154, 280)(155, 270)(156, 205)(157, 207)(158, 220)(159, 203)(160, 206)(161, 312)(162, 309)(163, 208)(164, 307)(165, 222)(166, 305)(167, 306)(168, 223) MAP : A3.384 NOTES : type I, non-Cayley, reflexible, isomorphic to Med({3,7}), isomorphic to A3.382. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 7, 3 ] UNIGROUP : < u.1, u.2 | u.2^2, u.1^3, (u.1 * u.2)^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.2^2, x.1^3, (x.2 * x.1^-1)^7, (x.2 * x.1 * x.2 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.1^-1)^2 LOCAL TYPE : (3, 7, 3, 7) #DARTS : 336 R = (1, 170, 2, 169)(3, 177, 9, 171)(4, 185, 17, 172)(5, 193, 25, 173)(6, 202, 34, 174)(7, 201, 33, 175)(8, 194, 26, 176)(10, 188, 20, 178)(11, 186, 18, 179)(12, 191, 23, 180)(13, 187, 19, 181)(14, 263, 95, 182)(15, 262, 94, 183)(16, 204, 36, 184)(21, 272, 104, 189)(22, 195, 27, 190)(24, 269, 101, 192)(28, 325, 157, 196)(29, 327, 159, 197)(30, 308, 140, 198)(31, 323, 155, 199)(32, 326, 158, 200)(35, 287, 119, 203)(37, 284, 116, 205)(38, 288, 120, 206)(39, 285, 117, 207)(40, 291, 123, 208)(41, 240, 72, 209)(42, 237, 69, 210)(43, 328, 160, 211)(44, 235, 67, 212)(45, 310, 142, 213)(46, 233, 65, 214)(47, 234, 66, 215)(48, 311, 143, 216)(49, 230, 62, 217)(50, 231, 63, 218)(51, 228, 60, 219)(52, 286, 118, 220)(53, 226, 58, 221)(54, 293, 125, 222)(55, 296, 128, 223)(56, 225, 57, 224)(59, 256, 88, 227)(61, 238, 70, 229)(64, 239, 71, 232)(68, 246, 78, 236)(73, 317, 149, 241)(74, 320, 152, 242)(75, 334, 166, 243)(76, 253, 85, 244)(77, 255, 87, 245)(79, 251, 83, 247)(80, 254, 86, 248)(81, 319, 151, 249)(82, 318, 150, 250)(84, 304, 136, 252)(89, 315, 147, 257)(90, 332, 164, 258)(91, 330, 162, 259)(92, 335, 167, 260)(93, 331, 163, 261)(96, 324, 156, 264)(97, 316, 148, 265)(98, 299, 131, 266)(99, 301, 133, 267)(100, 298, 130, 268)(102, 283, 115, 270)(103, 300, 132, 271)(105, 314, 146, 273)(106, 313, 145, 274)(107, 297, 129, 275)(108, 329, 161, 276)(109, 281, 113, 277)(110, 322, 154, 278)(111, 321, 153, 279)(112, 282, 114, 280)(121, 312, 144, 289)(122, 309, 141, 290)(124, 307, 139, 292)(126, 305, 137, 294)(127, 306, 138, 295)(134, 303, 135, 302)(165, 336, 168, 333) L = (1, 171)(2, 188)(3, 186)(4, 191)(5, 187)(6, 263)(7, 262)(8, 204)(9, 173)(10, 176)(11, 190)(12, 325)(13, 327)(14, 308)(15, 323)(16, 326)(17, 170)(18, 169)(19, 177)(20, 185)(21, 193)(22, 202)(23, 201)(24, 194)(25, 240)(26, 237)(27, 328)(28, 235)(29, 310)(30, 233)(31, 234)(32, 311)(33, 172)(34, 179)(35, 181)(36, 178)(37, 272)(38, 195)(39, 180)(40, 269)(41, 230)(42, 231)(43, 228)(44, 286)(45, 226)(46, 293)(47, 296)(48, 225)(49, 175)(50, 174)(51, 287)(52, 184)(53, 284)(54, 288)(55, 285)(56, 291)(57, 319)(58, 318)(59, 247)(60, 304)(61, 244)(62, 248)(63, 245)(64, 227)(65, 316)(66, 299)(67, 301)(68, 298)(69, 192)(70, 283)(71, 300)(72, 189)(73, 214)(74, 215)(75, 212)(76, 246)(77, 210)(78, 229)(79, 232)(80, 209)(81, 314)(82, 313)(83, 297)(84, 329)(85, 281)(86, 322)(87, 321)(88, 282)(89, 224)(90, 221)(91, 256)(92, 219)(93, 238)(94, 217)(95, 218)(96, 239)(97, 315)(98, 332)(99, 330)(100, 335)(101, 331)(102, 183)(103, 182)(104, 324)(105, 317)(106, 320)(107, 334)(108, 253)(109, 255)(110, 236)(111, 251)(112, 254)(113, 276)(114, 259)(115, 261)(116, 258)(117, 336)(118, 243)(119, 260)(120, 333)(121, 274)(122, 273)(123, 257)(124, 265)(125, 241)(126, 250)(127, 249)(128, 242)(129, 279)(130, 278)(131, 199)(132, 264)(133, 196)(134, 200)(135, 197)(136, 211)(137, 275)(138, 268)(139, 266)(140, 271)(141, 267)(142, 303)(143, 302)(144, 252)(145, 294)(146, 295)(147, 292)(148, 198)(149, 290)(150, 213)(151, 216)(152, 289)(153, 277)(154, 280)(155, 270)(156, 205)(157, 207)(158, 220)(159, 203)(160, 206)(161, 312)(162, 309)(163, 208)(164, 307)(165, 222)(166, 305)(167, 306)(168, 223) MAP : A3.385 NOTES : type I, non-Cayley, reflexible, isomorphic to Med({3,7}), isomorphic to A3.382. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 3, 7 ] UNIGROUP : < u.1, u.2 | u.2^2, (u.1 * u.2)^3, u.1^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.2^2, (x.1 * x.2)^3, x.1^7, (x.2 * x.1^-3)^4 > SCHREIER VEC. : (x.1, x.1^-1)^2 LOCAL TYPE : (3, 7, 3, 7) #DARTS : 336 R = (1, 170, 2, 169)(3, 177, 9, 171)(4, 185, 17, 172)(5, 193, 25, 173)(6, 202, 34, 174)(7, 201, 33, 175)(8, 194, 26, 176)(10, 188, 20, 178)(11, 186, 18, 179)(12, 191, 23, 180)(13, 187, 19, 181)(14, 263, 95, 182)(15, 262, 94, 183)(16, 204, 36, 184)(21, 272, 104, 189)(22, 195, 27, 190)(24, 269, 101, 192)(28, 325, 157, 196)(29, 327, 159, 197)(30, 308, 140, 198)(31, 323, 155, 199)(32, 326, 158, 200)(35, 287, 119, 203)(37, 284, 116, 205)(38, 288, 120, 206)(39, 285, 117, 207)(40, 291, 123, 208)(41, 240, 72, 209)(42, 237, 69, 210)(43, 328, 160, 211)(44, 235, 67, 212)(45, 310, 142, 213)(46, 233, 65, 214)(47, 234, 66, 215)(48, 311, 143, 216)(49, 230, 62, 217)(50, 231, 63, 218)(51, 228, 60, 219)(52, 286, 118, 220)(53, 226, 58, 221)(54, 293, 125, 222)(55, 296, 128, 223)(56, 225, 57, 224)(59, 256, 88, 227)(61, 238, 70, 229)(64, 239, 71, 232)(68, 246, 78, 236)(73, 317, 149, 241)(74, 320, 152, 242)(75, 334, 166, 243)(76, 253, 85, 244)(77, 255, 87, 245)(79, 251, 83, 247)(80, 254, 86, 248)(81, 319, 151, 249)(82, 318, 150, 250)(84, 304, 136, 252)(89, 315, 147, 257)(90, 332, 164, 258)(91, 330, 162, 259)(92, 335, 167, 260)(93, 331, 163, 261)(96, 324, 156, 264)(97, 316, 148, 265)(98, 299, 131, 266)(99, 301, 133, 267)(100, 298, 130, 268)(102, 283, 115, 270)(103, 300, 132, 271)(105, 314, 146, 273)(106, 313, 145, 274)(107, 297, 129, 275)(108, 329, 161, 276)(109, 281, 113, 277)(110, 322, 154, 278)(111, 321, 153, 279)(112, 282, 114, 280)(121, 312, 144, 289)(122, 309, 141, 290)(124, 307, 139, 292)(126, 305, 137, 294)(127, 306, 138, 295)(134, 303, 135, 302)(165, 336, 168, 333) L = (1, 260)(2, 243)(3, 245)(4, 242)(5, 304)(6, 227)(7, 244)(8, 301)(9, 258)(10, 257)(11, 241)(12, 273)(13, 225)(14, 266)(15, 265)(16, 226)(17, 263)(18, 262)(19, 191)(20, 248)(21, 188)(22, 192)(23, 189)(24, 171)(25, 259)(26, 276)(27, 274)(28, 279)(29, 275)(30, 295)(31, 294)(32, 268)(33, 326)(34, 327)(35, 324)(36, 190)(37, 322)(38, 173)(39, 176)(40, 321)(41, 261)(42, 264)(43, 278)(44, 197)(45, 199)(46, 180)(47, 195)(48, 198)(49, 336)(50, 333)(51, 200)(52, 331)(53, 182)(54, 329)(55, 330)(56, 183)(57, 219)(58, 212)(59, 210)(60, 215)(61, 211)(62, 247)(63, 246)(64, 196)(65, 221)(66, 224)(67, 214)(68, 317)(69, 319)(70, 332)(71, 315)(72, 318)(73, 218)(74, 217)(75, 201)(76, 209)(77, 185)(78, 194)(79, 193)(80, 186)(81, 256)(82, 253)(83, 320)(84, 251)(85, 334)(86, 249)(87, 250)(88, 335)(89, 220)(90, 203)(91, 205)(92, 202)(93, 280)(94, 187)(95, 204)(96, 277)(97, 238)(98, 239)(99, 236)(100, 310)(101, 234)(102, 325)(103, 328)(104, 233)(105, 223)(106, 222)(107, 311)(108, 208)(109, 308)(110, 312)(111, 309)(112, 323)(113, 287)(114, 286)(115, 231)(116, 296)(117, 228)(118, 232)(119, 229)(120, 235)(121, 284)(122, 291)(123, 293)(124, 290)(125, 216)(126, 307)(127, 292)(128, 213)(129, 174)(130, 175)(131, 172)(132, 230)(133, 170)(134, 237)(135, 240)(136, 169)(137, 282)(138, 281)(139, 289)(140, 297)(141, 305)(142, 314)(143, 313)(144, 306)(145, 184)(146, 181)(147, 272)(148, 179)(149, 254)(150, 177)(151, 178)(152, 255)(153, 283)(154, 300)(155, 298)(156, 303)(157, 299)(158, 207)(159, 206)(160, 316)(161, 285)(162, 288)(163, 302)(164, 269)(165, 271)(166, 252)(167, 267)(168, 270) MAP : A3.386 NOTES : type I, reflexible, isomorphic to Med({3,8}), representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^3, (u.1^-1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^3, (x.1 * x.2^-1)^3, (x.1^-1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 8, 3, 8) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 151)(98, 153)(99, 152)(100, 167)(101, 168)(102, 146)(103, 157)(104, 187)(105, 150)(106, 163)(107, 169)(108, 184)(109, 145)(110, 180)(111, 149)(112, 161)(113, 186)(114, 191)(115, 174)(116, 179)(117, 182)(118, 192)(119, 175)(120, 159)(121, 173)(122, 156)(123, 165)(124, 162)(125, 155)(126, 154)(127, 148)(128, 181)(129, 185)(130, 158)(131, 189)(132, 178)(133, 183)(134, 171)(135, 176)(136, 170)(137, 188)(138, 160)(139, 147)(140, 177)(141, 164)(142, 166)(143, 172)(144, 190) MAP : A3.387 NOTES : type I, reflexible, isomorphic to Med({3,8}), isomorphic to A3.386. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^3, (u.1^-1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^3, (x.1 * x.2^-1)^3, (x.1^-1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 8, 3, 8) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 164)(98, 171)(99, 165)(100, 149)(101, 172)(102, 188)(103, 185)(104, 189)(105, 158)(106, 180)(107, 145)(108, 163)(109, 176)(110, 191)(111, 187)(112, 156)(113, 190)(114, 184)(115, 160)(116, 155)(117, 169)(118, 154)(119, 178)(120, 183)(121, 147)(122, 159)(123, 192)(124, 148)(125, 150)(126, 152)(127, 157)(128, 175)(129, 162)(130, 179)(131, 167)(132, 166)(133, 161)(134, 168)(135, 182)(136, 177)(137, 186)(138, 151)(139, 170)(140, 173)(141, 174)(142, 181)(143, 153)(144, 146) MAP : A3.388 NOTES : type I, non-Cayley, reflexible, isomorphic to Med({3,8}), isomorphic to A3.386. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 8, 3 ] UNIGROUP : < u.1, u.2 | u.2^2, u.1^3, (u.1 * u.2)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.2^2, x.1^3, (x.2 * x.1 * x.2 * x.1^-1)^3, (x.1 * x.2)^8 > SCHREIER VEC. : (x.1, x.1^-1)^2 LOCAL TYPE : (3, 8, 3, 8) #DARTS : 192 R = (1, 100, 4, 97)(2, 104, 8, 98)(3, 101, 5, 99)(6, 130, 34, 102)(7, 133, 37, 103)(9, 114, 18, 105)(10, 177, 81, 106)(11, 178, 82, 107)(12, 129, 33, 108)(13, 113, 17, 109)(14, 117, 21, 110)(15, 181, 85, 111)(16, 149, 53, 112)(19, 126, 30, 115)(20, 125, 29, 116)(22, 159, 63, 118)(23, 154, 58, 119)(24, 121, 25, 120)(26, 144, 48, 122)(27, 160, 64, 123)(28, 155, 59, 124)(31, 128, 32, 127)(35, 135, 39, 131)(36, 140, 44, 132)(38, 136, 40, 134)(41, 139, 43, 137)(42, 141, 45, 138)(46, 143, 47, 142)(49, 176, 80, 145)(50, 192, 96, 146)(51, 171, 75, 147)(52, 175, 79, 148)(54, 172, 76, 150)(55, 166, 70, 151)(56, 170, 74, 152)(57, 190, 94, 153)(60, 167, 71, 156)(61, 185, 89, 157)(62, 189, 93, 158)(65, 187, 91, 161)(66, 191, 95, 162)(67, 188, 92, 163)(68, 182, 86, 164)(69, 186, 90, 165)(72, 183, 87, 168)(73, 179, 83, 169)(77, 184, 88, 173)(78, 180, 84, 174) L = (1, 98)(2, 101)(3, 113)(4, 114)(5, 97)(6, 115)(7, 116)(8, 117)(9, 165)(10, 118)(11, 119)(12, 120)(13, 162)(14, 161)(15, 124)(16, 172)(17, 130)(18, 133)(19, 177)(20, 178)(21, 129)(22, 179)(23, 180)(24, 181)(25, 149)(26, 182)(27, 183)(28, 184)(29, 146)(30, 145)(31, 188)(32, 156)(33, 104)(34, 99)(35, 109)(36, 105)(37, 100)(38, 126)(39, 125)(40, 110)(41, 186)(42, 159)(43, 154)(44, 121)(45, 191)(46, 187)(47, 155)(48, 150)(49, 134)(50, 135)(51, 138)(52, 139)(53, 140)(54, 153)(55, 158)(56, 143)(57, 144)(58, 148)(59, 152)(60, 157)(61, 128)(62, 160)(63, 147)(64, 151)(65, 136)(66, 131)(67, 141)(68, 137)(69, 132)(70, 190)(71, 189)(72, 142)(73, 122)(74, 175)(75, 170)(76, 185)(77, 127)(78, 123)(79, 171)(80, 166)(81, 102)(82, 103)(83, 106)(84, 107)(85, 108)(86, 169)(87, 174)(88, 111)(89, 112)(90, 164)(91, 168)(92, 173)(93, 192)(94, 176)(95, 163)(96, 167) MAP : A3.389 NOTES : type I, reflexible, isomorphic to Med({3,8}), isomorphic to A3.386. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^3, (u.1^-1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^3, (x.1 * x.2^-1)^3, (x.1^-1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 8, 3, 8) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 157)(98, 150)(99, 187)(100, 175)(101, 159)(102, 153)(103, 145)(104, 147)(105, 146)(106, 174)(107, 173)(108, 170)(109, 151)(110, 178)(111, 168)(112, 186)(113, 160)(114, 172)(115, 154)(116, 189)(117, 171)(118, 190)(119, 148)(120, 149)(121, 155)(122, 184)(123, 182)(124, 191)(125, 169)(126, 163)(127, 167)(128, 183)(129, 188)(130, 180)(131, 164)(132, 158)(133, 176)(134, 165)(135, 181)(136, 156)(137, 177)(138, 161)(139, 152)(140, 185)(141, 179)(142, 192)(143, 162)(144, 166) MAP : A3.390 NOTES : type I, non-Cayley, reflexible, isomorphic to Med({3,8}), isomorphic to A3.386. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 3, 8 ] UNIGROUP : < u.1, u.2 | u.2^2, (u.1 * u.2)^3, u.1^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.2^2, (x.1 * x.2)^3, x.1^8, (x.1^-2 * x.2 * x.1^-1)^3, (x.2 * x.1^3 * x.2 * x.1^-2)^2 > SCHREIER VEC. : (x.1, x.1^-1)^2 LOCAL TYPE : (3, 8, 3, 8) #DARTS : 192 R = (1, 100, 4, 97)(2, 104, 8, 98)(3, 101, 5, 99)(6, 130, 34, 102)(7, 133, 37, 103)(9, 114, 18, 105)(10, 177, 81, 106)(11, 178, 82, 107)(12, 129, 33, 108)(13, 113, 17, 109)(14, 117, 21, 110)(15, 181, 85, 111)(16, 149, 53, 112)(19, 126, 30, 115)(20, 125, 29, 116)(22, 159, 63, 118)(23, 154, 58, 119)(24, 121, 25, 120)(26, 144, 48, 122)(27, 160, 64, 123)(28, 155, 59, 124)(31, 128, 32, 127)(35, 135, 39, 131)(36, 140, 44, 132)(38, 136, 40, 134)(41, 139, 43, 137)(42, 141, 45, 138)(46, 143, 47, 142)(49, 176, 80, 145)(50, 192, 96, 146)(51, 171, 75, 147)(52, 175, 79, 148)(54, 172, 76, 150)(55, 166, 70, 151)(56, 170, 74, 152)(57, 190, 94, 153)(60, 167, 71, 156)(61, 185, 89, 157)(62, 189, 93, 158)(65, 187, 91, 161)(66, 191, 95, 162)(67, 188, 92, 163)(68, 182, 86, 164)(69, 186, 90, 165)(72, 183, 87, 168)(73, 179, 83, 169)(77, 184, 88, 173)(78, 180, 84, 174) L = (1, 106)(2, 107)(3, 169)(4, 174)(5, 111)(6, 164)(7, 168)(8, 173)(9, 157)(10, 165)(11, 161)(12, 163)(13, 158)(14, 153)(15, 162)(16, 146)(17, 108)(18, 102)(19, 135)(20, 140)(21, 103)(22, 136)(23, 131)(24, 134)(25, 139)(26, 141)(27, 137)(28, 132)(29, 138)(30, 143)(31, 142)(32, 122)(33, 176)(34, 192)(35, 171)(36, 175)(37, 112)(38, 172)(39, 166)(40, 170)(41, 190)(42, 119)(43, 124)(44, 167)(45, 185)(46, 189)(47, 118)(48, 123)(49, 109)(50, 105)(51, 126)(52, 125)(53, 110)(54, 159)(55, 154)(56, 121)(57, 120)(58, 144)(59, 160)(60, 155)(61, 116)(62, 115)(63, 128)(64, 127)(65, 100)(66, 104)(67, 101)(68, 97)(69, 99)(70, 130)(71, 133)(72, 98)(73, 114)(74, 177)(75, 178)(76, 129)(77, 113)(78, 117)(79, 181)(80, 149)(81, 187)(82, 191)(83, 188)(84, 182)(85, 186)(86, 151)(87, 156)(88, 183)(89, 179)(90, 152)(91, 147)(92, 150)(93, 184)(94, 180)(95, 148)(96, 145) MAP : A3.391 NOTES : type I, reflexible, isomorphic to Med({3,8}), isomorphic to A3.386. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^3, (u.1^-1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^3, (x.1 * x.2^-1)^3, (x.1^-1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 8, 3, 8) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 178)(98, 147)(99, 183)(100, 182)(101, 177)(102, 184)(103, 150)(104, 145)(105, 154)(106, 167)(107, 186)(108, 189)(109, 190)(110, 149)(111, 169)(112, 162)(113, 180)(114, 187)(115, 181)(116, 165)(117, 188)(118, 156)(119, 153)(120, 157)(121, 174)(122, 148)(123, 161)(124, 179)(125, 192)(126, 159)(127, 155)(128, 172)(129, 158)(130, 152)(131, 176)(132, 171)(133, 185)(134, 170)(135, 146)(136, 151)(137, 163)(138, 175)(139, 160)(140, 164)(141, 166)(142, 168)(143, 173)(144, 191) MAP : A3.392 NOTES : type I, non-Cayley, reflexible, isomorphic to Med({3,8}), isomorphic to A3.386. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 3, 8 ] UNIGROUP : < u.1, u.2 | u.2^2, (u.1 * u.2)^3, u.1^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.2^2, (x.1 * x.2)^3, x.1^8, (x.1^-2 * x.2 * x.1^-1)^3, (x.2 * x.1^3 * x.2 * x.1^-2)^2 > SCHREIER VEC. : (x.1, x.1^-1)^2 LOCAL TYPE : (3, 8, 3, 8) #DARTS : 192 R = (1, 100, 4, 97)(2, 104, 8, 98)(3, 101, 5, 99)(6, 130, 34, 102)(7, 133, 37, 103)(9, 114, 18, 105)(10, 177, 81, 106)(11, 178, 82, 107)(12, 129, 33, 108)(13, 113, 17, 109)(14, 117, 21, 110)(15, 181, 85, 111)(16, 149, 53, 112)(19, 126, 30, 115)(20, 125, 29, 116)(22, 159, 63, 118)(23, 154, 58, 119)(24, 121, 25, 120)(26, 144, 48, 122)(27, 160, 64, 123)(28, 155, 59, 124)(31, 128, 32, 127)(35, 135, 39, 131)(36, 140, 44, 132)(38, 136, 40, 134)(41, 139, 43, 137)(42, 141, 45, 138)(46, 143, 47, 142)(49, 176, 80, 145)(50, 192, 96, 146)(51, 171, 75, 147)(52, 175, 79, 148)(54, 172, 76, 150)(55, 166, 70, 151)(56, 170, 74, 152)(57, 190, 94, 153)(60, 167, 71, 156)(61, 185, 89, 157)(62, 189, 93, 158)(65, 187, 91, 161)(66, 191, 95, 162)(67, 188, 92, 163)(68, 182, 86, 164)(69, 186, 90, 165)(72, 183, 87, 168)(73, 179, 83, 169)(77, 184, 88, 173)(78, 180, 84, 174) L = (1, 99)(2, 100)(3, 102)(4, 103)(5, 104)(6, 106)(7, 107)(8, 108)(9, 140)(10, 169)(11, 174)(12, 111)(13, 135)(14, 134)(15, 173)(16, 157)(17, 101)(18, 97)(19, 130)(20, 133)(21, 98)(22, 177)(23, 178)(24, 129)(25, 132)(26, 179)(27, 180)(28, 181)(29, 131)(30, 136)(31, 184)(32, 185)(33, 110)(34, 109)(35, 191)(36, 186)(37, 105)(38, 176)(39, 192)(40, 187)(41, 182)(42, 171)(43, 175)(44, 112)(45, 188)(46, 183)(47, 170)(48, 190)(49, 115)(50, 116)(51, 118)(52, 119)(53, 120)(54, 122)(55, 123)(56, 124)(57, 172)(58, 137)(59, 142)(60, 127)(61, 167)(62, 166)(63, 141)(64, 189)(65, 117)(66, 113)(67, 162)(68, 165)(69, 114)(70, 145)(71, 146)(72, 161)(73, 164)(74, 147)(75, 148)(76, 149)(77, 163)(78, 168)(79, 152)(80, 153)(81, 126)(82, 125)(83, 159)(84, 154)(85, 121)(86, 144)(87, 160)(88, 155)(89, 150)(90, 139)(91, 143)(92, 128)(93, 156)(94, 151)(95, 138)(96, 158) MAP : A3.393 NOTES : type I, reflexible, isomorphic to Med({3,8}), isomorphic to A3.386. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^3, (u.1^-1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^3, (x.1 * x.2^-1)^3, (x.1^-1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 8, 3, 8) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 152)(98, 183)(99, 146)(100, 170)(101, 158)(102, 151)(103, 184)(104, 178)(105, 167)(106, 153)(107, 175)(108, 166)(109, 168)(110, 177)(111, 174)(112, 187)(113, 171)(114, 160)(115, 185)(116, 188)(117, 164)(118, 189)(119, 154)(120, 190)(121, 159)(122, 182)(123, 180)(124, 176)(125, 191)(126, 169)(127, 186)(128, 179)(129, 149)(130, 145)(131, 172)(132, 161)(133, 163)(134, 148)(135, 147)(136, 150)(137, 181)(138, 155)(139, 162)(140, 165)(141, 156)(142, 157)(143, 192)(144, 173) MAP : A3.394 NOTES : type I, reflexible, isomorphic to Med({3,8}), isomorphic to A3.386. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^3, (u.1^-1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^3, (x.1 * x.2^-1)^3, (x.1^-1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 8, 3, 8) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 165)(98, 161)(99, 188)(100, 177)(101, 179)(102, 164)(103, 163)(104, 166)(105, 149)(106, 171)(107, 178)(108, 181)(109, 172)(110, 173)(111, 160)(112, 189)(113, 168)(114, 151)(115, 162)(116, 186)(117, 174)(118, 167)(119, 152)(120, 146)(121, 183)(122, 169)(123, 191)(124, 182)(125, 184)(126, 145)(127, 190)(128, 155)(129, 187)(130, 176)(131, 153)(132, 156)(133, 180)(134, 157)(135, 170)(136, 158)(137, 175)(138, 150)(139, 148)(140, 192)(141, 159)(142, 185)(143, 154)(144, 147) MAP : A3.395 NOTES : type I, reflexible, isomorphic to Med({3,8}), isomorphic to A3.386. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^3, (u.1^-1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^3, (x.1 * x.2^-1)^3, (x.1^-1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 8, 3, 8) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 155)(98, 192)(99, 169)(100, 172)(101, 148)(102, 173)(103, 186)(104, 174)(105, 191)(106, 166)(107, 164)(108, 160)(109, 175)(110, 153)(111, 170)(112, 163)(113, 181)(114, 177)(115, 156)(116, 145)(117, 147)(118, 180)(119, 179)(120, 182)(121, 165)(122, 187)(123, 146)(124, 149)(125, 188)(126, 189)(127, 176)(128, 157)(129, 184)(130, 167)(131, 178)(132, 154)(133, 190)(134, 183)(135, 168)(136, 162)(137, 151)(138, 185)(139, 159)(140, 150)(141, 152)(142, 161)(143, 158)(144, 171) MAP : A3.396 NOTES : type I, non-Cayley, reflexible, isomorphic to Med({3,8}), isomorphic to A3.386. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 8, 3 ] UNIGROUP : < u.1, u.2 | u.2^2, u.1^3, (u.1 * u.2)^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.2^2, x.1^3, (x.2 * x.1 * x.2 * x.1^-1)^3, (x.1 * x.2)^8 > SCHREIER VEC. : (x.1, x.1^-1)^2 LOCAL TYPE : (3, 8, 3, 8) #DARTS : 192 R = (1, 128, 32, 97)(2, 144, 48, 98)(3, 123, 27, 99)(4, 127, 31, 100)(5, 160, 64, 101)(6, 124, 28, 102)(7, 118, 22, 103)(8, 122, 26, 104)(9, 142, 46, 105)(10, 167, 71, 106)(11, 172, 76, 107)(12, 119, 23, 108)(13, 137, 41, 109)(14, 141, 45, 110)(15, 166, 70, 111)(16, 171, 75, 112)(17, 139, 43, 113)(18, 143, 47, 114)(19, 140, 44, 115)(20, 134, 38, 116)(21, 138, 42, 117)(24, 135, 39, 120)(25, 131, 35, 121)(29, 136, 40, 125)(30, 132, 36, 126)(33, 154, 58, 129)(34, 155, 59, 130)(37, 159, 63, 133)(49, 148, 52, 145)(50, 152, 56, 146)(51, 149, 53, 147)(54, 178, 82, 150)(55, 181, 85, 151)(57, 162, 66, 153)(60, 177, 81, 156)(61, 161, 65, 157)(62, 165, 69, 158)(67, 174, 78, 163)(68, 173, 77, 164)(72, 169, 73, 168)(74, 192, 96, 170)(79, 176, 80, 175)(83, 183, 87, 179)(84, 188, 92, 180)(86, 184, 88, 182)(89, 187, 91, 185)(90, 189, 93, 186)(94, 191, 95, 190) L = (1, 98)(2, 101)(3, 113)(4, 114)(5, 97)(6, 115)(7, 116)(8, 117)(9, 165)(10, 118)(11, 119)(12, 120)(13, 162)(14, 161)(15, 124)(16, 172)(17, 130)(18, 133)(19, 177)(20, 178)(21, 129)(22, 179)(23, 180)(24, 181)(25, 149)(26, 182)(27, 183)(28, 184)(29, 146)(30, 145)(31, 188)(32, 156)(33, 104)(34, 99)(35, 109)(36, 105)(37, 100)(38, 126)(39, 125)(40, 110)(41, 186)(42, 159)(43, 154)(44, 121)(45, 191)(46, 187)(47, 155)(48, 150)(49, 134)(50, 135)(51, 138)(52, 139)(53, 140)(54, 153)(55, 158)(56, 143)(57, 144)(58, 148)(59, 152)(60, 157)(61, 128)(62, 160)(63, 147)(64, 151)(65, 136)(66, 131)(67, 141)(68, 137)(69, 132)(70, 190)(71, 189)(72, 142)(73, 122)(74, 175)(75, 170)(76, 185)(77, 127)(78, 123)(79, 171)(80, 166)(81, 102)(82, 103)(83, 106)(84, 107)(85, 108)(86, 169)(87, 174)(88, 111)(89, 112)(90, 164)(91, 168)(92, 173)(93, 192)(94, 176)(95, 163)(96, 167) MAP : A3.397 NOTES : type I, reflexible, isomorphic to Med({3,8}), isomorphic to A3.386. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^3, (u.1^-1 * u.2^-1)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^3, (x.1 * x.2^-1)^3, (x.1^-1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (3, 8, 3, 8) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 174)(98, 168)(99, 192)(100, 187)(101, 153)(102, 186)(103, 162)(104, 167)(105, 179)(106, 191)(107, 176)(108, 180)(109, 182)(110, 184)(111, 189)(112, 159)(113, 146)(114, 163)(115, 151)(116, 150)(117, 145)(118, 152)(119, 166)(120, 161)(121, 170)(122, 183)(123, 154)(124, 157)(125, 158)(126, 165)(127, 185)(128, 178)(129, 148)(130, 155)(131, 149)(132, 181)(133, 156)(134, 172)(135, 169)(136, 173)(137, 190)(138, 164)(139, 177)(140, 147)(141, 160)(142, 175)(143, 171)(144, 188) MAP : A3.398 NOTES : type I, reflexible, isomorphic to Med2({4,6}), representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 6, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1 * x.2)^2, x.2^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 54)(2, 95)(3, 50)(4, 93)(5, 88)(6, 91)(7, 52)(8, 49)(9, 68)(10, 69)(11, 96)(12, 65)(13, 66)(14, 71)(15, 70)(16, 77)(17, 64)(18, 59)(19, 78)(20, 63)(21, 76)(22, 57)(23, 74)(24, 83)(25, 80)(26, 75)(27, 62)(28, 79)(29, 60)(30, 73)(31, 58)(32, 67)(33, 94)(34, 55)(35, 90)(36, 53)(37, 72)(38, 51)(39, 92)(40, 89)(41, 84)(42, 85)(43, 56)(44, 81)(45, 82)(46, 87)(47, 86)(48, 61)(97, 146)(98, 153)(99, 148)(100, 155)(101, 150)(102, 157)(103, 184)(104, 183)(105, 154)(106, 161)(107, 156)(108, 163)(109, 158)(110, 165)(111, 176)(112, 175)(113, 162)(114, 145)(115, 164)(116, 147)(117, 166)(118, 149)(119, 192)(120, 191)(121, 186)(122, 169)(123, 188)(124, 171)(125, 190)(126, 173)(127, 168)(128, 167)(129, 170)(130, 177)(131, 172)(132, 179)(133, 174)(134, 181)(135, 160)(136, 159)(137, 178)(138, 185)(139, 180)(140, 187)(141, 182)(142, 189)(143, 152)(144, 151) MAP : A3.399 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A3.398. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.1 * x.2^-1 * x.1)^2, x.1^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 50)(2, 57)(3, 52)(4, 59)(5, 54)(6, 61)(7, 88)(8, 87)(9, 58)(10, 65)(11, 60)(12, 67)(13, 62)(14, 69)(15, 80)(16, 79)(17, 66)(18, 49)(19, 68)(20, 51)(21, 70)(22, 53)(23, 96)(24, 95)(25, 90)(26, 73)(27, 92)(28, 75)(29, 94)(30, 77)(31, 72)(32, 71)(33, 74)(34, 81)(35, 76)(36, 83)(37, 78)(38, 85)(39, 64)(40, 63)(41, 82)(42, 89)(43, 84)(44, 91)(45, 86)(46, 93)(47, 56)(48, 55)(97, 147)(98, 166)(99, 151)(100, 162)(101, 145)(102, 192)(103, 149)(104, 190)(105, 175)(106, 156)(107, 173)(108, 176)(109, 171)(110, 154)(111, 169)(112, 172)(113, 157)(114, 152)(115, 153)(116, 182)(117, 159)(118, 180)(119, 155)(120, 146)(121, 179)(122, 174)(123, 183)(124, 170)(125, 177)(126, 160)(127, 181)(128, 158)(129, 167)(130, 188)(131, 165)(132, 168)(133, 163)(134, 186)(135, 161)(136, 164)(137, 189)(138, 184)(139, 185)(140, 150)(141, 191)(142, 148)(143, 187)(144, 178) MAP : A3.400 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 3 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4 * x.1^-1)^3, x.2 * x.3 * x.4^-1 * x.2 * x.4 * x.2^-1 * x.4^-1, x.4 * x.2 * x.4 * x.2 * x.4 * x.2^-1 * x.4 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 174)(26, 175)(27, 173)(28, 190)(29, 171)(30, 169)(31, 170)(32, 177)(33, 176)(34, 184)(35, 192)(36, 191)(37, 186)(38, 187)(39, 185)(40, 178)(41, 183)(42, 181)(43, 182)(44, 189)(45, 188)(46, 172)(47, 180)(48, 179)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 129)(74, 130)(75, 131)(76, 132)(77, 141)(78, 142)(79, 143)(80, 144)(81, 137)(82, 138)(83, 139)(84, 140)(85, 125)(86, 126)(87, 127)(88, 128)(89, 121)(90, 122)(91, 123)(92, 124)(93, 133)(94, 134)(95, 135)(96, 136) MAP : A3.401 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A3.398. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.1 * x.2^-1 * x.1)^2, x.1^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 50)(2, 57)(3, 52)(4, 59)(5, 54)(6, 61)(7, 88)(8, 87)(9, 58)(10, 65)(11, 60)(12, 67)(13, 62)(14, 69)(15, 80)(16, 79)(17, 66)(18, 49)(19, 68)(20, 51)(21, 70)(22, 53)(23, 96)(24, 95)(25, 90)(26, 73)(27, 92)(28, 75)(29, 94)(30, 77)(31, 72)(32, 71)(33, 74)(34, 81)(35, 76)(36, 83)(37, 78)(38, 85)(39, 64)(40, 63)(41, 82)(42, 89)(43, 84)(44, 91)(45, 86)(46, 93)(47, 56)(48, 55)(97, 150)(98, 191)(99, 146)(100, 189)(101, 184)(102, 187)(103, 148)(104, 145)(105, 164)(106, 165)(107, 192)(108, 161)(109, 162)(110, 167)(111, 166)(112, 173)(113, 160)(114, 155)(115, 174)(116, 159)(117, 172)(118, 153)(119, 170)(120, 179)(121, 176)(122, 171)(123, 158)(124, 175)(125, 156)(126, 169)(127, 154)(128, 163)(129, 190)(130, 151)(131, 186)(132, 149)(133, 168)(134, 147)(135, 188)(136, 185)(137, 180)(138, 181)(139, 152)(140, 177)(141, 178)(142, 183)(143, 182)(144, 157) MAP : A3.402 NOTES : type II, reflexible, isomorphic to A3.400. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 3 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^2, (x.1 * x.2)^2, (x.4^-1 * x.2)^2, (x.3 * x.2)^2, (x.3 * x.4^-1)^2, x.3^4, x.3 * x.4 * x.3^-2 * x.4^-1 * x.2, (x.4 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 174)(26, 175)(27, 173)(28, 190)(29, 171)(30, 169)(31, 170)(32, 177)(33, 176)(34, 184)(35, 192)(36, 191)(37, 186)(38, 187)(39, 185)(40, 178)(41, 183)(42, 181)(43, 182)(44, 189)(45, 188)(46, 172)(47, 180)(48, 179)(49, 168)(50, 152)(51, 160)(52, 159)(53, 148)(54, 156)(55, 164)(56, 163)(57, 151)(58, 149)(59, 150)(60, 157)(61, 155)(62, 153)(63, 154)(64, 161)(65, 166)(66, 167)(67, 165)(68, 158)(69, 146)(70, 147)(71, 145)(72, 162)(73, 122)(74, 123)(75, 121)(76, 138)(77, 127)(78, 125)(79, 126)(80, 133)(81, 124)(82, 132)(83, 140)(84, 139)(85, 142)(86, 143)(87, 141)(88, 134)(89, 131)(90, 129)(91, 130)(92, 137)(93, 144)(94, 128)(95, 136)(96, 135) MAP : A3.403 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A3.398. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 6, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1 * x.2)^2, x.2^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 49, 97, 145)(2, 50, 98, 146)(3, 51, 99, 147)(4, 52, 100, 148)(5, 53, 101, 149)(6, 54, 102, 150)(7, 55, 103, 151)(8, 56, 104, 152)(9, 57, 105, 153)(10, 58, 106, 154)(11, 59, 107, 155)(12, 60, 108, 156)(13, 61, 109, 157)(14, 62, 110, 158)(15, 63, 111, 159)(16, 64, 112, 160)(17, 65, 113, 161)(18, 66, 114, 162)(19, 67, 115, 163)(20, 68, 116, 164)(21, 69, 117, 165)(22, 70, 118, 166)(23, 71, 119, 167)(24, 72, 120, 168)(25, 73, 121, 169)(26, 74, 122, 170)(27, 75, 123, 171)(28, 76, 124, 172)(29, 77, 125, 173)(30, 78, 126, 174)(31, 79, 127, 175)(32, 80, 128, 176)(33, 81, 129, 177)(34, 82, 130, 178)(35, 83, 131, 179)(36, 84, 132, 180)(37, 85, 133, 181)(38, 86, 134, 182)(39, 87, 135, 183)(40, 88, 136, 184)(41, 89, 137, 185)(42, 90, 138, 186)(43, 91, 139, 187)(44, 92, 140, 188)(45, 93, 141, 189)(46, 94, 142, 190)(47, 95, 143, 191)(48, 96, 144, 192) L = (1, 51)(2, 70)(3, 55)(4, 66)(5, 49)(6, 96)(7, 53)(8, 94)(9, 79)(10, 60)(11, 77)(12, 80)(13, 75)(14, 58)(15, 73)(16, 76)(17, 61)(18, 56)(19, 57)(20, 86)(21, 63)(22, 84)(23, 59)(24, 50)(25, 83)(26, 78)(27, 87)(28, 74)(29, 81)(30, 64)(31, 85)(32, 62)(33, 71)(34, 92)(35, 69)(36, 72)(37, 67)(38, 90)(39, 65)(40, 68)(41, 93)(42, 88)(43, 89)(44, 54)(45, 95)(46, 52)(47, 91)(48, 82)(97, 146)(98, 153)(99, 148)(100, 155)(101, 150)(102, 157)(103, 184)(104, 183)(105, 154)(106, 161)(107, 156)(108, 163)(109, 158)(110, 165)(111, 176)(112, 175)(113, 162)(114, 145)(115, 164)(116, 147)(117, 166)(118, 149)(119, 192)(120, 191)(121, 186)(122, 169)(123, 188)(124, 171)(125, 190)(126, 173)(127, 168)(128, 167)(129, 170)(130, 177)(131, 172)(132, 179)(133, 174)(134, 181)(135, 160)(136, 159)(137, 178)(138, 185)(139, 180)(140, 187)(141, 182)(142, 189)(143, 152)(144, 151) MAP : A3.404 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.3^3, (x.3 * x.4)^2, x.4 * x.2 * x.4 * x.2^-1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.2^2 * x.3 * x.2^2 * x.3^-1, (x.2^-1 * x.3)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 186)(26, 187)(27, 185)(28, 178)(29, 183)(30, 181)(31, 182)(32, 189)(33, 188)(34, 172)(35, 180)(36, 179)(37, 174)(38, 175)(39, 173)(40, 190)(41, 171)(42, 169)(43, 170)(44, 177)(45, 176)(46, 184)(47, 192)(48, 191)(49, 146)(50, 147)(51, 145)(52, 162)(53, 151)(54, 149)(55, 150)(56, 157)(57, 148)(58, 156)(59, 164)(60, 163)(61, 166)(62, 167)(63, 165)(64, 158)(65, 155)(66, 153)(67, 154)(68, 161)(69, 168)(70, 152)(71, 160)(72, 159)(73, 126)(74, 127)(75, 125)(76, 142)(77, 123)(78, 121)(79, 122)(80, 129)(81, 128)(82, 136)(83, 144)(84, 143)(85, 138)(86, 139)(87, 137)(88, 130)(89, 135)(90, 133)(91, 134)(92, 141)(93, 140)(94, 124)(95, 132)(96, 131) MAP : A3.405 NOTES : type II, reflexible, isomorphic to A3.404. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 3 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.3^3, (x.1 * x.2)^2, (x.4^-1 * x.2)^2, (x.3 * x.4^-1)^2, (x.2 * x.3^-1)^2, (x.4 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 174)(26, 175)(27, 173)(28, 190)(29, 171)(30, 169)(31, 170)(32, 177)(33, 176)(34, 184)(35, 192)(36, 191)(37, 186)(38, 187)(39, 185)(40, 178)(41, 183)(42, 181)(43, 182)(44, 189)(45, 188)(46, 172)(47, 180)(48, 179)(49, 146)(50, 147)(51, 145)(52, 162)(53, 151)(54, 149)(55, 150)(56, 157)(57, 148)(58, 156)(59, 164)(60, 163)(61, 166)(62, 167)(63, 165)(64, 158)(65, 155)(66, 153)(67, 154)(68, 161)(69, 168)(70, 152)(71, 160)(72, 159)(73, 140)(74, 124)(75, 132)(76, 131)(77, 128)(78, 136)(79, 144)(80, 143)(81, 123)(82, 121)(83, 122)(84, 129)(85, 135)(86, 133)(87, 134)(88, 141)(89, 138)(90, 139)(91, 137)(92, 130)(93, 126)(94, 127)(95, 125)(96, 142) MAP : A3.406 NOTES : type II, reflexible, isomorphic to A3.404. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, x.2^3, (x.2 * x.3)^2, (x.3 * x.4)^2, (x.4 * x.1^-1)^2, (x.4 * x.2^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 170)(26, 171)(27, 169)(28, 186)(29, 175)(30, 173)(31, 174)(32, 181)(33, 172)(34, 180)(35, 188)(36, 187)(37, 190)(38, 191)(39, 189)(40, 182)(41, 179)(42, 177)(43, 178)(44, 185)(45, 192)(46, 176)(47, 184)(48, 183)(49, 150)(50, 151)(51, 149)(52, 166)(53, 147)(54, 145)(55, 146)(56, 153)(57, 152)(58, 160)(59, 168)(60, 167)(61, 162)(62, 163)(63, 161)(64, 154)(65, 159)(66, 157)(67, 158)(68, 165)(69, 164)(70, 148)(71, 156)(72, 155)(73, 138)(74, 139)(75, 137)(76, 130)(77, 135)(78, 133)(79, 134)(80, 141)(81, 140)(82, 124)(83, 132)(84, 131)(85, 126)(86, 127)(87, 125)(88, 142)(89, 123)(90, 121)(91, 122)(92, 129)(93, 128)(94, 136)(95, 144)(96, 143) MAP : A3.407 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A3.398. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 3}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^3, x.4 * x.3 * x.2, (x.2^-1 * x.3)^2, x.2^4, x.4^4, (x.3 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 50)(26, 63)(27, 56)(28, 49)(29, 55)(30, 60)(31, 66)(32, 58)(33, 68)(34, 65)(35, 57)(36, 71)(37, 54)(38, 59)(39, 52)(40, 53)(41, 51)(42, 64)(43, 70)(44, 62)(45, 72)(46, 69)(47, 61)(48, 67)(73, 134)(74, 123)(75, 140)(76, 133)(77, 139)(78, 144)(79, 126)(80, 142)(81, 128)(82, 125)(83, 141)(84, 131)(85, 138)(86, 143)(87, 136)(88, 137)(89, 135)(90, 124)(91, 130)(92, 122)(93, 132)(94, 129)(95, 121)(96, 127)(145, 180)(146, 177)(147, 169)(148, 175)(149, 176)(150, 173)(151, 189)(152, 179)(153, 187)(154, 192)(155, 174)(156, 190)(157, 183)(158, 172)(159, 178)(160, 170)(161, 186)(162, 191)(163, 184)(164, 185)(165, 182)(166, 171)(167, 188)(168, 181) MAP : A3.408 NOTES : type II, reflexible, isomorphic to A3.400. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3 * x.2^-1)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.3^4, x.3^2 * x.2 * x.4^-1 * x.3^-1 * x.2^-1, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 170)(26, 171)(27, 169)(28, 186)(29, 175)(30, 173)(31, 174)(32, 181)(33, 172)(34, 180)(35, 188)(36, 187)(37, 190)(38, 191)(39, 189)(40, 182)(41, 179)(42, 177)(43, 178)(44, 185)(45, 192)(46, 176)(47, 184)(48, 183)(49, 158)(50, 159)(51, 157)(52, 150)(53, 163)(54, 161)(55, 162)(56, 145)(57, 160)(58, 168)(59, 152)(60, 151)(61, 154)(62, 155)(63, 153)(64, 146)(65, 167)(66, 165)(67, 166)(68, 149)(69, 156)(70, 164)(71, 148)(72, 147)(73, 127)(74, 125)(75, 126)(76, 133)(77, 122)(78, 123)(79, 121)(80, 138)(81, 142)(82, 143)(83, 141)(84, 134)(85, 124)(86, 132)(87, 140)(88, 139)(89, 144)(90, 128)(91, 136)(92, 135)(93, 131)(94, 129)(95, 130)(96, 137) MAP : A3.409 NOTES : type II, reflexible, isomorphic to A3.400. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^2, (x.3 * x.4)^2, x.4 * x.2 * x.4 * x.2^-1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.3^4, (x.2 * x.3^-1)^3, x.2 * x.4 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 174)(26, 175)(27, 173)(28, 190)(29, 171)(30, 169)(31, 170)(32, 177)(33, 176)(34, 184)(35, 192)(36, 191)(37, 186)(38, 187)(39, 185)(40, 178)(41, 183)(42, 181)(43, 182)(44, 189)(45, 188)(46, 172)(47, 180)(48, 179)(49, 158)(50, 159)(51, 157)(52, 150)(53, 163)(54, 161)(55, 162)(56, 145)(57, 160)(58, 168)(59, 152)(60, 151)(61, 154)(62, 155)(63, 153)(64, 146)(65, 167)(66, 165)(67, 166)(68, 149)(69, 156)(70, 164)(71, 148)(72, 147)(73, 138)(74, 139)(75, 137)(76, 130)(77, 135)(78, 133)(79, 134)(80, 141)(81, 140)(82, 124)(83, 132)(84, 131)(85, 126)(86, 127)(87, 125)(88, 142)(89, 123)(90, 121)(91, 122)(92, 129)(93, 128)(94, 136)(95, 144)(96, 143) MAP : A3.410 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A3.398. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.4^2, (x.1 * x.2)^2, (x.3 * x.4)^2, (x.4 * x.1^-1)^2, x.3^4, x.2 * x.4 * x.2 * x.3^-2, (x.2 * x.3^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 174)(26, 175)(27, 173)(28, 190)(29, 171)(30, 169)(31, 170)(32, 177)(33, 176)(34, 184)(35, 192)(36, 191)(37, 186)(38, 187)(39, 185)(40, 178)(41, 183)(42, 181)(43, 182)(44, 189)(45, 188)(46, 172)(47, 180)(48, 179)(49, 158)(50, 159)(51, 157)(52, 150)(53, 163)(54, 161)(55, 162)(56, 145)(57, 160)(58, 168)(59, 152)(60, 151)(61, 154)(62, 155)(63, 153)(64, 146)(65, 167)(66, 165)(67, 166)(68, 149)(69, 156)(70, 164)(71, 148)(72, 147)(73, 132)(74, 140)(75, 124)(76, 123)(77, 136)(78, 144)(79, 128)(80, 127)(81, 139)(82, 137)(83, 138)(84, 121)(85, 143)(86, 141)(87, 142)(88, 125)(89, 130)(90, 131)(91, 129)(92, 122)(93, 134)(94, 135)(95, 133)(96, 126) MAP : A3.411 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A3.398. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 3 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^2, (x.1 * x.2)^2, x.4 * x.3 * x.4 * x.2, (x.2 * x.3^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 174)(26, 175)(27, 173)(28, 190)(29, 171)(30, 169)(31, 170)(32, 177)(33, 176)(34, 184)(35, 192)(36, 191)(37, 186)(38, 187)(39, 185)(40, 178)(41, 183)(42, 181)(43, 182)(44, 189)(45, 188)(46, 172)(47, 180)(48, 179)(49, 168)(50, 152)(51, 160)(52, 159)(53, 148)(54, 156)(55, 164)(56, 163)(57, 151)(58, 149)(59, 150)(60, 157)(61, 155)(62, 153)(63, 154)(64, 161)(65, 166)(66, 167)(67, 165)(68, 158)(69, 146)(70, 147)(71, 145)(72, 162)(73, 137)(74, 138)(75, 139)(76, 140)(77, 133)(78, 134)(79, 135)(80, 136)(81, 121)(82, 122)(83, 123)(84, 124)(85, 141)(86, 142)(87, 143)(88, 144)(89, 129)(90, 130)(91, 131)(92, 132)(93, 125)(94, 126)(95, 127)(96, 128) MAP : A3.412 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A3.398. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <24, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^2, x.3 * x.4^-1 * x.2^-1, (x.3 * x.1^-1)^2, x.4 * x.2^2 * x.3 * x.4, x.2^6, x.4^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 66)(26, 49)(27, 68)(28, 51)(29, 70)(30, 53)(31, 72)(32, 55)(33, 50)(34, 57)(35, 52)(36, 59)(37, 54)(38, 61)(39, 56)(40, 63)(41, 58)(42, 65)(43, 60)(44, 67)(45, 62)(46, 69)(47, 64)(48, 71)(73, 124)(74, 125)(75, 141)(76, 121)(77, 122)(78, 132)(79, 140)(80, 138)(81, 143)(82, 139)(83, 136)(84, 126)(85, 144)(86, 137)(87, 142)(88, 131)(89, 134)(90, 128)(91, 130)(92, 127)(93, 123)(94, 135)(95, 129)(96, 133)(145, 179)(146, 174)(147, 190)(148, 170)(149, 177)(150, 187)(151, 171)(152, 169)(153, 192)(154, 188)(155, 191)(156, 181)(157, 175)(158, 186)(159, 173)(160, 180)(161, 189)(162, 183)(163, 185)(164, 176)(165, 172)(166, 184)(167, 178)(168, 182) MAP : A3.413 NOTES : type II, reflexible, isomorphic to A3.404. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.3^3, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.4 * x.1^-1)^2, (x.2 * x.3^-1)^2, (x.3 * x.4^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 174)(26, 175)(27, 173)(28, 190)(29, 171)(30, 169)(31, 170)(32, 177)(33, 176)(34, 184)(35, 192)(36, 191)(37, 186)(38, 187)(39, 185)(40, 178)(41, 183)(42, 181)(43, 182)(44, 189)(45, 188)(46, 172)(47, 180)(48, 179)(49, 146)(50, 147)(51, 145)(52, 162)(53, 151)(54, 149)(55, 150)(56, 157)(57, 148)(58, 156)(59, 164)(60, 163)(61, 166)(62, 167)(63, 165)(64, 158)(65, 155)(66, 153)(67, 154)(68, 161)(69, 168)(70, 152)(71, 160)(72, 159)(73, 138)(74, 139)(75, 137)(76, 130)(77, 135)(78, 133)(79, 134)(80, 141)(81, 140)(82, 124)(83, 132)(84, 131)(85, 126)(86, 127)(87, 125)(88, 142)(89, 123)(90, 121)(91, 122)(92, 129)(93, 128)(94, 136)(95, 144)(96, 143) MAP : A3.414 NOTES : type II, reflexible, isomorphic to A3.404. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-2)^2, x.4 * x.2 * x.4 * x.2 * x.4^-1 * x.2, x.3 * x.4 * x.3 * x.4 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 174)(26, 175)(27, 173)(28, 190)(29, 171)(30, 169)(31, 170)(32, 177)(33, 176)(34, 184)(35, 192)(36, 191)(37, 186)(38, 187)(39, 185)(40, 178)(41, 183)(42, 181)(43, 182)(44, 189)(45, 188)(46, 172)(47, 180)(48, 179)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 125)(74, 126)(75, 127)(76, 128)(77, 121)(78, 122)(79, 123)(80, 124)(81, 133)(82, 134)(83, 135)(84, 136)(85, 129)(86, 130)(87, 131)(88, 132)(89, 141)(90, 142)(91, 143)(92, 144)(93, 137)(94, 138)(95, 139)(96, 140) MAP : A3.415 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.4 * x.1 * x.5^-1 * x.2, x.5^-1 * x.1 * x.5 * x.2, x.4 * x.2 * x.1 * x.4 * x.5^-1, (x.5 * x.3^-1)^3, (x.2 * x.1)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 186)(26, 187)(27, 185)(28, 178)(29, 183)(30, 181)(31, 182)(32, 189)(33, 188)(34, 172)(35, 180)(36, 179)(37, 174)(38, 175)(39, 173)(40, 190)(41, 171)(42, 169)(43, 170)(44, 177)(45, 176)(46, 184)(47, 192)(48, 191)(49, 53)(50, 54)(51, 55)(52, 56)(57, 61)(58, 62)(59, 63)(60, 64)(65, 69)(66, 70)(67, 71)(68, 72)(73, 140)(74, 124)(75, 132)(76, 131)(77, 128)(78, 136)(79, 144)(80, 143)(81, 123)(82, 121)(83, 122)(84, 129)(85, 135)(86, 133)(87, 134)(88, 141)(89, 138)(90, 139)(91, 137)(92, 130)(93, 126)(94, 127)(95, 125)(96, 142)(145, 151)(146, 149)(147, 150)(148, 157)(152, 162)(153, 166)(154, 167)(155, 165)(156, 158)(159, 164)(160, 163)(161, 168) MAP : A3.416 NOTES : type II, reflexible, isomorphic to A3.400. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, x.2^3, (x.3 * x.4)^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^3, x.3 * x.2 * x.4 * x.2^-1 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 170)(26, 171)(27, 169)(28, 186)(29, 175)(30, 173)(31, 174)(32, 181)(33, 172)(34, 180)(35, 188)(36, 187)(37, 190)(38, 191)(39, 189)(40, 182)(41, 179)(42, 177)(43, 178)(44, 185)(45, 192)(46, 176)(47, 184)(48, 183)(49, 150)(50, 151)(51, 149)(52, 166)(53, 147)(54, 145)(55, 146)(56, 153)(57, 152)(58, 160)(59, 168)(60, 167)(61, 162)(62, 163)(63, 161)(64, 154)(65, 159)(66, 157)(67, 158)(68, 165)(69, 164)(70, 148)(71, 156)(72, 155)(73, 133)(74, 134)(75, 135)(76, 136)(77, 137)(78, 138)(79, 139)(80, 140)(81, 141)(82, 142)(83, 143)(84, 144)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132) MAP : A3.417 NOTES : type II, reflexible, isomorphic to A3.404. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^3, (x.4 * x.1^-1)^2, (x.2 * x.3^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 170)(26, 171)(27, 169)(28, 186)(29, 175)(30, 173)(31, 174)(32, 181)(33, 172)(34, 180)(35, 188)(36, 187)(37, 190)(38, 191)(39, 189)(40, 182)(41, 179)(42, 177)(43, 178)(44, 185)(45, 192)(46, 176)(47, 184)(48, 183)(49, 164)(50, 148)(51, 156)(52, 155)(53, 152)(54, 160)(55, 168)(56, 167)(57, 147)(58, 145)(59, 146)(60, 153)(61, 159)(62, 157)(63, 158)(64, 165)(65, 162)(66, 163)(67, 161)(68, 154)(69, 150)(70, 151)(71, 149)(72, 166)(73, 126)(74, 127)(75, 125)(76, 142)(77, 123)(78, 121)(79, 122)(80, 129)(81, 128)(82, 136)(83, 144)(84, 143)(85, 138)(86, 139)(87, 137)(88, 130)(89, 135)(90, 133)(91, 134)(92, 141)(93, 140)(94, 124)(95, 132)(96, 131) MAP : A3.418 NOTES : type II, reflexible, isomorphic to A3.415. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, x.4 * x.1 * x.5 * x.2, (x.5 * x.3^-1)^2, x.4 * x.2 * x.4^-1 * x.1, x.5 * x.2 * x.1 * x.5 * x.4^-1, (x.3 * x.4^-1)^3, (x.2 * x.1)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 170)(26, 171)(27, 169)(28, 186)(29, 175)(30, 173)(31, 174)(32, 181)(33, 172)(34, 180)(35, 188)(36, 187)(37, 190)(38, 191)(39, 189)(40, 182)(41, 179)(42, 177)(43, 178)(44, 185)(45, 192)(46, 176)(47, 184)(48, 183)(49, 64)(50, 72)(51, 56)(52, 55)(53, 60)(54, 68)(57, 71)(58, 69)(59, 70)(61, 67)(62, 65)(63, 66)(73, 138)(74, 139)(75, 137)(76, 130)(77, 135)(78, 133)(79, 134)(80, 141)(81, 140)(82, 124)(83, 132)(84, 131)(85, 126)(86, 127)(87, 125)(88, 142)(89, 123)(90, 121)(91, 122)(92, 129)(93, 128)(94, 136)(95, 144)(96, 143)(145, 165)(146, 166)(147, 167)(148, 168)(149, 153)(150, 154)(151, 155)(152, 156)(157, 161)(158, 162)(159, 163)(160, 164) MAP : A3.419 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A3.398. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, (x.2 * x.3^-1)^2, x.3^4, x.3^2 * x.4 * x.2 * x.4^-1, x.2 * x.4 * x.3^-2 * x.4^-1, (x.3 * x.4^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 186)(26, 187)(27, 185)(28, 178)(29, 183)(30, 181)(31, 182)(32, 189)(33, 188)(34, 172)(35, 180)(36, 179)(37, 174)(38, 175)(39, 173)(40, 190)(41, 171)(42, 169)(43, 170)(44, 177)(45, 176)(46, 184)(47, 192)(48, 191)(49, 158)(50, 159)(51, 157)(52, 150)(53, 163)(54, 161)(55, 162)(56, 145)(57, 160)(58, 168)(59, 152)(60, 151)(61, 154)(62, 155)(63, 153)(64, 146)(65, 167)(66, 165)(67, 166)(68, 149)(69, 156)(70, 164)(71, 148)(72, 147)(73, 125)(74, 126)(75, 127)(76, 128)(77, 121)(78, 122)(79, 123)(80, 124)(81, 133)(82, 134)(83, 135)(84, 136)(85, 129)(86, 130)(87, 131)(88, 132)(89, 141)(90, 142)(91, 143)(92, 144)(93, 137)(94, 138)(95, 139)(96, 140) MAP : A3.420 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A3.398. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {6, 6, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 6, 6, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^6, u.4^6 > CTG (small) : <24, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^2, x.3 * x.4^-1 * x.2^-1, (x.3 * x.1^-1)^2, x.4 * x.2^2 * x.3 * x.4, x.2^6, x.4^6 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 50)(26, 57)(27, 52)(28, 59)(29, 54)(30, 61)(31, 56)(32, 63)(33, 58)(34, 65)(35, 60)(36, 67)(37, 62)(38, 69)(39, 64)(40, 71)(41, 66)(42, 49)(43, 68)(44, 51)(45, 70)(46, 53)(47, 72)(48, 55)(73, 124)(74, 125)(75, 141)(76, 121)(77, 122)(78, 132)(79, 140)(80, 138)(81, 143)(82, 139)(83, 136)(84, 126)(85, 144)(86, 137)(87, 142)(88, 131)(89, 134)(90, 128)(91, 130)(92, 127)(93, 123)(94, 135)(95, 129)(96, 133)(145, 171)(146, 190)(147, 182)(148, 186)(149, 169)(150, 179)(151, 187)(152, 185)(153, 184)(154, 180)(155, 183)(156, 173)(157, 191)(158, 178)(159, 189)(160, 172)(161, 181)(162, 175)(163, 177)(164, 192)(165, 188)(166, 176)(167, 170)(168, 174) MAP : A3.421 NOTES : type II, reflexible, isomorphic to A3.404. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 3 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, x.4^3, (x.1 * x.2)^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4 * x.2)^3, (x.4 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 186)(26, 187)(27, 185)(28, 178)(29, 183)(30, 181)(31, 182)(32, 189)(33, 188)(34, 172)(35, 180)(36, 179)(37, 174)(38, 175)(39, 173)(40, 190)(41, 171)(42, 169)(43, 170)(44, 177)(45, 176)(46, 184)(47, 192)(48, 191)(49, 150)(50, 151)(51, 149)(52, 166)(53, 147)(54, 145)(55, 146)(56, 153)(57, 152)(58, 160)(59, 168)(60, 167)(61, 162)(62, 163)(63, 161)(64, 154)(65, 159)(66, 157)(67, 158)(68, 165)(69, 164)(70, 148)(71, 156)(72, 155)(73, 122)(74, 123)(75, 121)(76, 138)(77, 127)(78, 125)(79, 126)(80, 133)(81, 124)(82, 132)(83, 140)(84, 139)(85, 142)(86, 143)(87, 141)(88, 134)(89, 131)(90, 129)(91, 130)(92, 137)(93, 144)(94, 128)(95, 136)(96, 135) MAP : A3.422 NOTES : type II, reflexible, isomorphic to A3.400. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.4 * x.1^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.3 * x.4^-1)^3, x.2 * x.3^2 * x.4 * x.3^-2 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 186)(26, 187)(27, 185)(28, 178)(29, 183)(30, 181)(31, 182)(32, 189)(33, 188)(34, 172)(35, 180)(36, 179)(37, 174)(38, 175)(39, 173)(40, 190)(41, 171)(42, 169)(43, 170)(44, 177)(45, 176)(46, 184)(47, 192)(48, 191)(49, 158)(50, 159)(51, 157)(52, 150)(53, 163)(54, 161)(55, 162)(56, 145)(57, 160)(58, 168)(59, 152)(60, 151)(61, 154)(62, 155)(63, 153)(64, 146)(65, 167)(66, 165)(67, 166)(68, 149)(69, 156)(70, 164)(71, 148)(72, 147)(73, 126)(74, 127)(75, 125)(76, 142)(77, 123)(78, 121)(79, 122)(80, 129)(81, 128)(82, 136)(83, 144)(84, 143)(85, 138)(86, 139)(87, 137)(88, 130)(89, 135)(90, 133)(91, 134)(92, 141)(93, 140)(94, 124)(95, 132)(96, 131) MAP : A3.423 NOTES : type II, reflexible, isomorphic to A3.404. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.2 * x.3)^3, x.4 * x.2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 174)(26, 175)(27, 173)(28, 190)(29, 171)(30, 169)(31, 170)(32, 177)(33, 176)(34, 184)(35, 192)(36, 191)(37, 186)(38, 187)(39, 185)(40, 178)(41, 183)(42, 181)(43, 182)(44, 189)(45, 188)(46, 172)(47, 180)(48, 179)(49, 149)(50, 150)(51, 151)(52, 152)(53, 145)(54, 146)(55, 147)(56, 148)(57, 157)(58, 158)(59, 159)(60, 160)(61, 153)(62, 154)(63, 155)(64, 156)(65, 165)(66, 166)(67, 167)(68, 168)(69, 161)(70, 162)(71, 163)(72, 164)(73, 136)(74, 144)(75, 128)(76, 127)(77, 132)(78, 140)(79, 124)(80, 123)(81, 143)(82, 141)(83, 142)(84, 125)(85, 139)(86, 137)(87, 138)(88, 121)(89, 134)(90, 135)(91, 133)(92, 126)(93, 130)(94, 131)(95, 129)(96, 122) MAP : A3.424 NOTES : type II, reflexible, isomorphic to A3.400. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3)^3, x.4 * x.2 * x.4 * x.2 * x.4^-1 * x.2^-1 * x.4^-1 * x.2^-1, x.2 * x.4^-1 * x.2^-1 * x.4 * x.3 * x.2^-1 * x.4^-1 * x.2^-1 * x.3, x.3 * x.2^-1 * x.4^-1 * x.2^-1 * x.3 * x.2^-1 * x.4 * x.2^-1 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 174)(26, 175)(27, 173)(28, 190)(29, 171)(30, 169)(31, 170)(32, 177)(33, 176)(34, 184)(35, 192)(36, 191)(37, 186)(38, 187)(39, 185)(40, 178)(41, 183)(42, 181)(43, 182)(44, 189)(45, 188)(46, 172)(47, 180)(48, 179)(49, 149)(50, 150)(51, 151)(52, 152)(53, 145)(54, 146)(55, 147)(56, 148)(57, 157)(58, 158)(59, 159)(60, 160)(61, 153)(62, 154)(63, 155)(64, 156)(65, 165)(66, 166)(67, 167)(68, 168)(69, 161)(70, 162)(71, 163)(72, 164)(73, 132)(74, 140)(75, 124)(76, 123)(77, 136)(78, 144)(79, 128)(80, 127)(81, 139)(82, 137)(83, 138)(84, 121)(85, 143)(86, 141)(87, 142)(88, 125)(89, 130)(90, 131)(91, 129)(92, 122)(93, 134)(94, 135)(95, 133)(96, 126) MAP : A3.425 NOTES : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A3.398. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^2, (x.3 * x.4)^2, x.3^-1 * x.2^-1 * x.4 * x.2^-1, (x.4 * x.1^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 170)(26, 171)(27, 169)(28, 186)(29, 175)(30, 173)(31, 174)(32, 181)(33, 172)(34, 180)(35, 188)(36, 187)(37, 190)(38, 191)(39, 189)(40, 182)(41, 179)(42, 177)(43, 178)(44, 185)(45, 192)(46, 176)(47, 184)(48, 183)(49, 158)(50, 159)(51, 157)(52, 150)(53, 163)(54, 161)(55, 162)(56, 145)(57, 160)(58, 168)(59, 152)(60, 151)(61, 154)(62, 155)(63, 153)(64, 146)(65, 167)(66, 165)(67, 166)(68, 149)(69, 156)(70, 164)(71, 148)(72, 147)(73, 141)(74, 142)(75, 143)(76, 144)(77, 129)(78, 130)(79, 131)(80, 132)(81, 125)(82, 126)(83, 127)(84, 128)(85, 137)(86, 138)(87, 139)(88, 140)(89, 133)(90, 134)(91, 135)(92, 136)(93, 121)(94, 122)(95, 123)(96, 124) MAP : A3.426 NOTES : type II, reflexible, isomorphic to A3.400. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, (x.1 * x.2)^2, (x.3 * x.4^-1)^3, x.4 * x.2 * x.4 * x.2 * x.4^-1 * x.2 * x.4^-1 * x.2, x.2 * x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 6) #DARTS : 192 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96)(97, 121, 145, 169)(98, 122, 146, 170)(99, 123, 147, 171)(100, 124, 148, 172)(101, 125, 149, 173)(102, 126, 150, 174)(103, 127, 151, 175)(104, 128, 152, 176)(105, 129, 153, 177)(106, 130, 154, 178)(107, 131, 155, 179)(108, 132, 156, 180)(109, 133, 157, 181)(110, 134, 158, 182)(111, 135, 159, 183)(112, 136, 160, 184)(113, 137, 161, 185)(114, 138, 162, 186)(115, 139, 163, 187)(116, 140, 164, 188)(117, 141, 165, 189)(118, 142, 166, 190)(119, 143, 167, 191)(120, 144, 168, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 186)(26, 187)(27, 185)(28, 178)(29, 183)(30, 181)(31, 182)(32, 189)(33, 188)(34, 172)(35, 180)(36, 179)(37, 174)(38, 175)(39, 173)(40, 190)(41, 171)(42, 169)(43, 170)(44, 177)(45, 176)(46, 184)(47, 192)(48, 191)(49, 150)(50, 151)(51, 149)(52, 166)(53, 147)(54, 145)(55, 146)(56, 153)(57, 152)(58, 160)(59, 168)(60, 167)(61, 162)(62, 163)(63, 161)(64, 154)(65, 159)(66, 157)(67, 158)(68, 165)(69, 164)(70, 148)(71, 156)(72, 155)(73, 125)(74, 126)(75, 127)(76, 128)(77, 121)(78, 122)(79, 123)(80, 124)(81, 133)(82, 134)(83, 135)(84, 136)(85, 129)(86, 130)(87, 131)(88, 132)(89, 141)(90, 142)(91, 143)(92, 144)(93, 137)(94, 138)(95, 139)(96, 140) MAP : A3.427 NOTES : type I, reflexible, isomorphic to Med2({4,8}), representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 44)(2, 61)(3, 45)(4, 48)(5, 38)(6, 59)(7, 54)(8, 60)(9, 43)(10, 63)(11, 62)(12, 52)(13, 58)(14, 55)(15, 50)(16, 49)(17, 39)(18, 40)(19, 46)(20, 34)(21, 47)(22, 35)(23, 57)(24, 42)(25, 64)(26, 36)(27, 33)(28, 41)(29, 37)(30, 53)(31, 51)(32, 56)(65, 99)(66, 105)(67, 121)(68, 101)(69, 104)(70, 122)(71, 120)(72, 115)(73, 106)(74, 113)(75, 116)(76, 126)(77, 123)(78, 114)(79, 119)(80, 127)(81, 98)(82, 102)(83, 100)(84, 103)(85, 97)(86, 108)(87, 109)(88, 107)(89, 117)(90, 110)(91, 111)(92, 125)(93, 112)(94, 128)(95, 124)(96, 118) MAP : A3.428 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 44)(2, 61)(3, 45)(4, 48)(5, 38)(6, 59)(7, 54)(8, 60)(9, 43)(10, 63)(11, 62)(12, 52)(13, 58)(14, 55)(15, 50)(16, 49)(17, 39)(18, 40)(19, 46)(20, 34)(21, 47)(22, 35)(23, 57)(24, 42)(25, 64)(26, 36)(27, 33)(28, 41)(29, 37)(30, 53)(31, 51)(32, 56)(65, 117)(66, 113)(67, 97)(68, 115)(69, 100)(70, 114)(71, 116)(72, 101)(73, 98)(74, 105)(75, 120)(76, 118)(77, 119)(78, 122)(79, 123)(80, 125)(81, 106)(82, 110)(83, 104)(84, 107)(85, 121)(86, 128)(87, 111)(88, 103)(89, 99)(90, 102)(91, 109)(92, 127)(93, 124)(94, 108)(95, 112)(96, 126) MAP : A3.429 NOTES : type I, reflexible, isomorphic to Med2({4,8}), representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2 | (x.1 * x.2)^2, x.2^4, x.1^-1 * x.2^-1 * x.1 * x.2^-1 * x.1^-2, x.2^-2 * x.1 * x.2^-2 * x.1^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 36)(2, 52)(3, 34)(4, 42)(5, 58)(6, 50)(7, 49)(8, 38)(9, 39)(10, 47)(11, 60)(12, 63)(13, 53)(14, 57)(15, 64)(16, 59)(17, 37)(18, 43)(19, 33)(20, 44)(21, 40)(22, 48)(23, 45)(24, 35)(25, 51)(26, 54)(27, 41)(28, 55)(29, 62)(30, 56)(31, 61)(32, 46)(65, 99)(66, 115)(67, 104)(68, 113)(69, 97)(70, 120)(71, 121)(72, 101)(73, 107)(74, 116)(75, 98)(76, 100)(77, 103)(78, 112)(79, 122)(80, 102)(81, 119)(82, 118)(83, 105)(84, 114)(85, 125)(86, 106)(87, 108)(88, 110)(89, 126)(90, 117)(91, 128)(92, 123)(93, 111)(94, 109)(95, 124)(96, 127) MAP : A3.430 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2 | (x.1 * x.2)^2, x.2^4, x.1^-1 * x.2^-1 * x.1 * x.2^-1 * x.1^-2, x.2^-2 * x.1 * x.2^-2 * x.1^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 36)(2, 52)(3, 34)(4, 42)(5, 58)(6, 50)(7, 49)(8, 38)(9, 39)(10, 47)(11, 60)(12, 63)(13, 53)(14, 57)(15, 64)(16, 59)(17, 37)(18, 43)(19, 33)(20, 44)(21, 40)(22, 48)(23, 45)(24, 35)(25, 51)(26, 54)(27, 41)(28, 55)(29, 62)(30, 56)(31, 61)(32, 46)(65, 118)(66, 119)(67, 106)(68, 125)(69, 114)(70, 105)(71, 104)(72, 116)(73, 100)(74, 123)(75, 113)(76, 117)(77, 99)(78, 98)(79, 120)(80, 115)(81, 111)(82, 127)(83, 108)(84, 128)(85, 112)(86, 124)(87, 122)(88, 107)(89, 101)(90, 110)(91, 109)(92, 126)(93, 102)(94, 97)(95, 121)(96, 103) MAP : A3.431 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 34)(2, 38)(3, 36)(4, 39)(5, 33)(6, 44)(7, 45)(8, 43)(9, 53)(10, 46)(11, 47)(12, 61)(13, 48)(14, 64)(15, 60)(16, 54)(17, 35)(18, 41)(19, 57)(20, 37)(21, 40)(22, 58)(23, 56)(24, 51)(25, 42)(26, 49)(27, 52)(28, 62)(29, 59)(30, 50)(31, 55)(32, 63)(65, 117)(66, 113)(67, 97)(68, 115)(69, 100)(70, 114)(71, 116)(72, 101)(73, 98)(74, 105)(75, 120)(76, 118)(77, 119)(78, 122)(79, 123)(80, 125)(81, 106)(82, 110)(83, 104)(84, 107)(85, 121)(86, 128)(87, 111)(88, 103)(89, 99)(90, 102)(91, 109)(92, 127)(93, 124)(94, 108)(95, 112)(96, 126) MAP : A3.432 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 37)(2, 33)(3, 49)(4, 35)(5, 52)(6, 34)(7, 36)(8, 53)(9, 50)(10, 57)(11, 40)(12, 38)(13, 39)(14, 42)(15, 43)(16, 45)(17, 58)(18, 62)(19, 56)(20, 59)(21, 41)(22, 48)(23, 63)(24, 55)(25, 51)(26, 54)(27, 61)(28, 47)(29, 44)(30, 60)(31, 64)(32, 46)(65, 117)(66, 113)(67, 97)(68, 115)(69, 100)(70, 114)(71, 116)(72, 101)(73, 98)(74, 105)(75, 120)(76, 118)(77, 119)(78, 122)(79, 123)(80, 125)(81, 106)(82, 110)(83, 104)(84, 107)(85, 121)(86, 128)(87, 111)(88, 103)(89, 99)(90, 102)(91, 109)(92, 127)(93, 124)(94, 108)(95, 112)(96, 126) MAP : A3.433 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 35)(2, 41)(3, 57)(4, 37)(5, 40)(6, 58)(7, 56)(8, 51)(9, 42)(10, 49)(11, 52)(12, 62)(13, 59)(14, 50)(15, 55)(16, 63)(17, 34)(18, 38)(19, 36)(20, 39)(21, 33)(22, 44)(23, 45)(24, 43)(25, 53)(26, 46)(27, 47)(28, 61)(29, 48)(30, 64)(31, 60)(32, 54)(65, 98)(66, 102)(67, 100)(68, 103)(69, 97)(70, 108)(71, 109)(72, 107)(73, 117)(74, 110)(75, 111)(76, 125)(77, 112)(78, 128)(79, 124)(80, 118)(81, 99)(82, 105)(83, 121)(84, 101)(85, 104)(86, 122)(87, 120)(88, 115)(89, 106)(90, 113)(91, 116)(92, 126)(93, 123)(94, 114)(95, 119)(96, 127) MAP : A3.434 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 85)(50, 81)(51, 92)(52, 88)(53, 86)(54, 82)(55, 83)(56, 95)(57, 93)(58, 89)(59, 84)(60, 96)(61, 94)(62, 90)(63, 91)(64, 87) MAP : A3.435 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 82)(50, 86)(51, 87)(52, 91)(53, 81)(54, 85)(55, 96)(56, 84)(57, 90)(58, 94)(59, 95)(60, 83)(61, 89)(62, 93)(63, 88)(64, 92) MAP : A3.436 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 35)(2, 41)(3, 57)(4, 37)(5, 40)(6, 58)(7, 56)(8, 51)(9, 42)(10, 49)(11, 52)(12, 62)(13, 59)(14, 50)(15, 55)(16, 63)(17, 34)(18, 38)(19, 36)(20, 39)(21, 33)(22, 44)(23, 45)(24, 43)(25, 53)(26, 46)(27, 47)(28, 61)(29, 48)(30, 64)(31, 60)(32, 54)(65, 101)(66, 97)(67, 113)(68, 99)(69, 116)(70, 98)(71, 100)(72, 117)(73, 114)(74, 121)(75, 104)(76, 102)(77, 103)(78, 106)(79, 107)(80, 109)(81, 122)(82, 126)(83, 120)(84, 123)(85, 105)(86, 112)(87, 127)(88, 119)(89, 115)(90, 118)(91, 125)(92, 111)(93, 108)(94, 124)(95, 128)(96, 110) MAP : A3.437 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 53)(2, 49)(3, 33)(4, 51)(5, 36)(6, 50)(7, 52)(8, 37)(9, 34)(10, 41)(11, 56)(12, 54)(13, 55)(14, 58)(15, 59)(16, 61)(17, 42)(18, 46)(19, 40)(20, 43)(21, 57)(22, 64)(23, 47)(24, 39)(25, 35)(26, 38)(27, 45)(28, 63)(29, 60)(30, 44)(31, 48)(32, 62)(65, 98)(66, 102)(67, 100)(68, 103)(69, 97)(70, 108)(71, 109)(72, 107)(73, 117)(74, 110)(75, 111)(76, 125)(77, 112)(78, 128)(79, 124)(80, 118)(81, 99)(82, 105)(83, 121)(84, 101)(85, 104)(86, 122)(87, 120)(88, 115)(89, 106)(90, 113)(91, 116)(92, 126)(93, 123)(94, 114)(95, 119)(96, 127) MAP : A3.438 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2 | (x.1 * x.2)^2, x.2^4, x.1^-1 * x.2^-1 * x.1 * x.2^-1 * x.1^-2, x.2^-2 * x.1 * x.2^-2 * x.1^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 47)(2, 63)(3, 44)(4, 64)(5, 48)(6, 60)(7, 58)(8, 43)(9, 37)(10, 46)(11, 45)(12, 62)(13, 38)(14, 33)(15, 57)(16, 39)(17, 54)(18, 55)(19, 42)(20, 61)(21, 50)(22, 41)(23, 40)(24, 52)(25, 36)(26, 59)(27, 49)(28, 53)(29, 35)(30, 34)(31, 56)(32, 51)(65, 101)(66, 107)(67, 97)(68, 108)(69, 104)(70, 112)(71, 109)(72, 99)(73, 115)(74, 118)(75, 105)(76, 119)(77, 126)(78, 120)(79, 125)(80, 110)(81, 100)(82, 116)(83, 98)(84, 106)(85, 122)(86, 114)(87, 113)(88, 102)(89, 103)(90, 111)(91, 124)(92, 127)(93, 117)(94, 121)(95, 128)(96, 123) MAP : A3.439 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2 | (x.1 * x.2)^2, x.2^4, x.1^-1 * x.2^-1 * x.1 * x.2^-1 * x.1^-2, x.2^-2 * x.1 * x.2^-2 * x.1^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 47)(2, 63)(3, 44)(4, 64)(5, 48)(6, 60)(7, 58)(8, 43)(9, 37)(10, 46)(11, 45)(12, 62)(13, 38)(14, 33)(15, 57)(16, 39)(17, 54)(18, 55)(19, 42)(20, 61)(21, 50)(22, 41)(23, 40)(24, 52)(25, 36)(26, 59)(27, 49)(28, 53)(29, 35)(30, 34)(31, 56)(32, 51)(65, 126)(66, 110)(67, 109)(68, 105)(69, 121)(70, 125)(71, 128)(72, 103)(73, 102)(74, 99)(75, 120)(76, 115)(77, 123)(78, 122)(79, 113)(80, 117)(81, 107)(82, 101)(83, 112)(84, 104)(85, 108)(86, 97)(87, 98)(88, 111)(89, 127)(90, 119)(91, 106)(92, 118)(93, 100)(94, 124)(95, 114)(96, 116) MAP : A3.440 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 53)(2, 49)(3, 33)(4, 51)(5, 36)(6, 50)(7, 52)(8, 37)(9, 34)(10, 41)(11, 56)(12, 54)(13, 55)(14, 58)(15, 59)(16, 61)(17, 42)(18, 46)(19, 40)(20, 43)(21, 57)(22, 64)(23, 47)(24, 39)(25, 35)(26, 38)(27, 45)(28, 63)(29, 60)(30, 44)(31, 48)(32, 62)(65, 101)(66, 97)(67, 113)(68, 99)(69, 116)(70, 98)(71, 100)(72, 117)(73, 114)(74, 121)(75, 104)(76, 102)(77, 103)(78, 106)(79, 107)(80, 109)(81, 122)(82, 126)(83, 120)(84, 123)(85, 105)(86, 112)(87, 127)(88, 119)(89, 115)(90, 118)(91, 125)(92, 111)(93, 108)(94, 124)(95, 128)(96, 110) MAP : A3.441 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 85)(50, 81)(51, 92)(52, 88)(53, 86)(54, 82)(55, 83)(56, 95)(57, 93)(58, 89)(59, 84)(60, 96)(61, 94)(62, 90)(63, 91)(64, 87) MAP : A3.442 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 41)(18, 47)(19, 34)(20, 43)(21, 38)(22, 45)(23, 40)(24, 36)(25, 46)(26, 37)(27, 39)(28, 33)(29, 42)(30, 44)(31, 48)(32, 35)(49, 86)(50, 89)(51, 81)(52, 96)(53, 84)(54, 91)(55, 82)(56, 95)(57, 93)(58, 88)(59, 83)(60, 85)(61, 87)(62, 90)(63, 94)(64, 92)(97, 128)(98, 123)(99, 116)(100, 122)(101, 126)(102, 124)(103, 118)(104, 125)(105, 115)(106, 121)(107, 117)(108, 127)(109, 113)(110, 114)(111, 119)(112, 120) MAP : A3.443 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 44)(18, 35)(19, 48)(20, 40)(21, 42)(22, 37)(23, 43)(24, 39)(25, 33)(26, 45)(27, 36)(28, 46)(29, 38)(30, 41)(31, 34)(32, 47)(49, 86)(50, 89)(51, 81)(52, 96)(53, 84)(54, 91)(55, 82)(56, 95)(57, 93)(58, 88)(59, 83)(60, 85)(61, 87)(62, 90)(63, 94)(64, 92)(97, 114)(98, 120)(99, 119)(100, 118)(101, 113)(102, 121)(103, 122)(104, 117)(105, 127)(106, 124)(107, 125)(108, 115)(109, 126)(110, 128)(111, 116)(112, 123) MAP : A3.444 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 45)(18, 46)(19, 41)(20, 35)(21, 43)(22, 39)(23, 47)(24, 48)(25, 42)(26, 36)(27, 34)(28, 38)(29, 40)(30, 37)(31, 44)(32, 33)(49, 86)(50, 89)(51, 81)(52, 96)(53, 84)(54, 91)(55, 82)(56, 95)(57, 93)(58, 88)(59, 83)(60, 85)(61, 87)(62, 90)(63, 94)(64, 92)(97, 116)(98, 118)(99, 117)(100, 126)(101, 127)(102, 128)(103, 113)(104, 121)(105, 123)(106, 114)(107, 124)(108, 120)(109, 115)(110, 119)(111, 125)(112, 122) MAP : A3.445 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 48)(18, 43)(19, 36)(20, 42)(21, 46)(22, 44)(23, 38)(24, 45)(25, 35)(26, 41)(27, 37)(28, 47)(29, 33)(30, 34)(31, 39)(32, 40)(49, 86)(50, 89)(51, 81)(52, 96)(53, 84)(54, 91)(55, 82)(56, 95)(57, 93)(58, 88)(59, 83)(60, 85)(61, 87)(62, 90)(63, 94)(64, 92)(97, 121)(98, 127)(99, 114)(100, 123)(101, 118)(102, 125)(103, 120)(104, 116)(105, 126)(106, 117)(107, 119)(108, 113)(109, 122)(110, 124)(111, 128)(112, 115) MAP : A3.446 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 34)(18, 40)(19, 39)(20, 38)(21, 33)(22, 41)(23, 42)(24, 37)(25, 47)(26, 44)(27, 45)(28, 35)(29, 46)(30, 48)(31, 36)(32, 43)(49, 84)(50, 86)(51, 85)(52, 94)(53, 95)(54, 96)(55, 81)(56, 89)(57, 91)(58, 82)(59, 92)(60, 88)(61, 83)(62, 87)(63, 93)(64, 90)(97, 115)(98, 119)(99, 123)(100, 117)(101, 124)(102, 113)(103, 125)(104, 122)(105, 114)(106, 126)(107, 118)(108, 128)(109, 121)(110, 127)(111, 120)(112, 116) MAP : A3.447 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 35)(2, 41)(3, 57)(4, 37)(5, 40)(6, 58)(7, 56)(8, 51)(9, 42)(10, 49)(11, 52)(12, 62)(13, 59)(14, 50)(15, 55)(16, 63)(17, 34)(18, 38)(19, 36)(20, 39)(21, 33)(22, 44)(23, 45)(24, 43)(25, 53)(26, 46)(27, 47)(28, 61)(29, 48)(30, 64)(31, 60)(32, 54)(65, 108)(66, 125)(67, 109)(68, 112)(69, 102)(70, 123)(71, 118)(72, 124)(73, 107)(74, 127)(75, 126)(76, 116)(77, 122)(78, 119)(79, 114)(80, 113)(81, 103)(82, 104)(83, 110)(84, 98)(85, 111)(86, 99)(87, 121)(88, 106)(89, 128)(90, 100)(91, 97)(92, 105)(93, 101)(94, 117)(95, 115)(96, 120) MAP : A3.448 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 35)(2, 41)(3, 57)(4, 37)(5, 40)(6, 58)(7, 56)(8, 51)(9, 42)(10, 49)(11, 52)(12, 62)(13, 59)(14, 50)(15, 55)(16, 63)(17, 34)(18, 38)(19, 36)(20, 39)(21, 33)(22, 44)(23, 45)(24, 43)(25, 53)(26, 46)(27, 47)(28, 61)(29, 48)(30, 64)(31, 60)(32, 54)(65, 123)(66, 116)(67, 118)(68, 122)(69, 125)(70, 101)(71, 113)(72, 114)(73, 124)(74, 120)(75, 105)(76, 97)(77, 99)(78, 115)(79, 117)(80, 100)(81, 112)(82, 111)(83, 127)(84, 108)(85, 126)(86, 103)(87, 110)(88, 128)(89, 119)(90, 109)(91, 102)(92, 104)(93, 98)(94, 107)(95, 106)(96, 121) MAP : A3.449 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 85)(50, 81)(51, 92)(52, 88)(53, 86)(54, 82)(55, 83)(56, 95)(57, 93)(58, 89)(59, 84)(60, 96)(61, 94)(62, 90)(63, 91)(64, 87) MAP : A3.450 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-1 * x.2^2 * x.4^-1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.3, x.2^-1), x.3^-2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4 * x.3 * x.2 * x.4^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 84)(50, 91)(51, 93)(52, 81)(53, 88)(54, 95)(55, 89)(56, 85)(57, 87)(58, 96)(59, 82)(60, 94)(61, 83)(62, 92)(63, 86)(64, 90) MAP : A3.451 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 53)(2, 49)(3, 33)(4, 51)(5, 36)(6, 50)(7, 52)(8, 37)(9, 34)(10, 41)(11, 56)(12, 54)(13, 55)(14, 58)(15, 59)(16, 61)(17, 42)(18, 46)(19, 40)(20, 43)(21, 57)(22, 64)(23, 47)(24, 39)(25, 35)(26, 38)(27, 45)(28, 63)(29, 60)(30, 44)(31, 48)(32, 62)(65, 108)(66, 125)(67, 109)(68, 112)(69, 102)(70, 123)(71, 118)(72, 124)(73, 107)(74, 127)(75, 126)(76, 116)(77, 122)(78, 119)(79, 114)(80, 113)(81, 103)(82, 104)(83, 110)(84, 98)(85, 111)(86, 99)(87, 121)(88, 106)(89, 128)(90, 100)(91, 97)(92, 105)(93, 101)(94, 117)(95, 115)(96, 120) MAP : A3.452 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 53)(2, 49)(3, 33)(4, 51)(5, 36)(6, 50)(7, 52)(8, 37)(9, 34)(10, 41)(11, 56)(12, 54)(13, 55)(14, 58)(15, 59)(16, 61)(17, 42)(18, 46)(19, 40)(20, 43)(21, 57)(22, 64)(23, 47)(24, 39)(25, 35)(26, 38)(27, 45)(28, 63)(29, 60)(30, 44)(31, 48)(32, 62)(65, 123)(66, 116)(67, 118)(68, 122)(69, 125)(70, 101)(71, 113)(72, 114)(73, 124)(74, 120)(75, 105)(76, 97)(77, 99)(78, 115)(79, 117)(80, 100)(81, 112)(82, 111)(83, 127)(84, 108)(85, 126)(86, 103)(87, 110)(88, 128)(89, 119)(90, 109)(91, 102)(92, 104)(93, 98)(94, 107)(95, 106)(96, 121) MAP : A3.453 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 82)(50, 86)(51, 87)(52, 91)(53, 81)(54, 85)(55, 96)(56, 84)(57, 90)(58, 94)(59, 95)(60, 83)(61, 89)(62, 93)(63, 88)(64, 92) MAP : A3.454 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 34)(2, 38)(3, 36)(4, 39)(5, 33)(6, 44)(7, 45)(8, 43)(9, 53)(10, 46)(11, 47)(12, 61)(13, 48)(14, 64)(15, 60)(16, 54)(17, 35)(18, 41)(19, 57)(20, 37)(21, 40)(22, 58)(23, 56)(24, 51)(25, 42)(26, 49)(27, 52)(28, 62)(29, 59)(30, 50)(31, 55)(32, 63)(65, 99)(66, 105)(67, 121)(68, 101)(69, 104)(70, 122)(71, 120)(72, 115)(73, 106)(74, 113)(75, 116)(76, 126)(77, 123)(78, 114)(79, 119)(80, 127)(81, 98)(82, 102)(83, 100)(84, 103)(85, 97)(86, 108)(87, 109)(88, 107)(89, 117)(90, 110)(91, 111)(92, 125)(93, 112)(94, 128)(95, 124)(96, 118) MAP : A3.455 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 37)(18, 33)(19, 44)(20, 47)(21, 40)(22, 36)(23, 35)(24, 34)(25, 38)(26, 39)(27, 48)(28, 42)(29, 43)(30, 45)(31, 41)(32, 46)(49, 87)(50, 90)(51, 93)(52, 81)(53, 83)(54, 82)(55, 94)(56, 92)(57, 88)(58, 96)(59, 89)(60, 91)(61, 95)(62, 84)(63, 85)(64, 86)(97, 118)(98, 121)(99, 113)(100, 128)(101, 116)(102, 123)(103, 114)(104, 127)(105, 125)(106, 120)(107, 115)(108, 117)(109, 119)(110, 122)(111, 126)(112, 124) MAP : A3.456 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 35)(18, 39)(19, 43)(20, 37)(21, 44)(22, 33)(23, 45)(24, 42)(25, 34)(26, 46)(27, 38)(28, 48)(29, 41)(30, 47)(31, 40)(32, 36)(49, 87)(50, 90)(51, 93)(52, 81)(53, 83)(54, 82)(55, 94)(56, 92)(57, 88)(58, 96)(59, 89)(60, 91)(61, 95)(62, 84)(63, 85)(64, 86)(97, 128)(98, 123)(99, 116)(100, 122)(101, 126)(102, 124)(103, 118)(104, 125)(105, 115)(106, 121)(107, 117)(108, 127)(109, 113)(110, 114)(111, 119)(112, 120) MAP : A3.457 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 38)(18, 41)(19, 33)(20, 48)(21, 36)(22, 43)(23, 34)(24, 47)(25, 45)(26, 40)(27, 35)(28, 37)(29, 39)(30, 42)(31, 46)(32, 44)(49, 87)(50, 90)(51, 93)(52, 81)(53, 83)(54, 82)(55, 94)(56, 92)(57, 88)(58, 96)(59, 89)(60, 91)(61, 95)(62, 84)(63, 85)(64, 86)(97, 117)(98, 113)(99, 124)(100, 127)(101, 120)(102, 116)(103, 115)(104, 114)(105, 118)(106, 119)(107, 128)(108, 122)(109, 123)(110, 125)(111, 121)(112, 126) MAP : A3.458 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 59)(2, 52)(3, 54)(4, 58)(5, 61)(6, 37)(7, 49)(8, 50)(9, 60)(10, 56)(11, 41)(12, 33)(13, 35)(14, 51)(15, 53)(16, 36)(17, 48)(18, 47)(19, 63)(20, 44)(21, 62)(22, 39)(23, 46)(24, 64)(25, 55)(26, 45)(27, 38)(28, 40)(29, 34)(30, 43)(31, 42)(32, 57)(65, 99)(66, 105)(67, 121)(68, 101)(69, 104)(70, 122)(71, 120)(72, 115)(73, 106)(74, 113)(75, 116)(76, 126)(77, 123)(78, 114)(79, 119)(80, 127)(81, 98)(82, 102)(83, 100)(84, 103)(85, 97)(86, 108)(87, 109)(88, 107)(89, 117)(90, 110)(91, 111)(92, 125)(93, 112)(94, 128)(95, 124)(96, 118) MAP : A3.459 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 59)(2, 52)(3, 54)(4, 58)(5, 61)(6, 37)(7, 49)(8, 50)(9, 60)(10, 56)(11, 41)(12, 33)(13, 35)(14, 51)(15, 53)(16, 36)(17, 48)(18, 47)(19, 63)(20, 44)(21, 62)(22, 39)(23, 46)(24, 64)(25, 55)(26, 45)(27, 38)(28, 40)(29, 34)(30, 43)(31, 42)(32, 57)(65, 117)(66, 113)(67, 97)(68, 115)(69, 100)(70, 114)(71, 116)(72, 101)(73, 98)(74, 105)(75, 120)(76, 118)(77, 119)(78, 122)(79, 123)(80, 125)(81, 106)(82, 110)(83, 104)(84, 107)(85, 121)(86, 128)(87, 111)(88, 103)(89, 99)(90, 102)(91, 109)(92, 127)(93, 124)(94, 108)(95, 112)(96, 126) MAP : A3.460 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 2 ] UNIGROUP : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^8 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 37)(2, 33)(3, 49)(4, 35)(5, 52)(6, 34)(7, 36)(8, 53)(9, 50)(10, 57)(11, 40)(12, 38)(13, 39)(14, 42)(15, 43)(16, 45)(17, 58)(18, 62)(19, 56)(20, 59)(21, 41)(22, 48)(23, 63)(24, 55)(25, 51)(26, 54)(27, 61)(28, 47)(29, 44)(30, 60)(31, 64)(32, 46)(65, 99)(66, 105)(67, 121)(68, 101)(69, 104)(70, 122)(71, 120)(72, 115)(73, 106)(74, 113)(75, 116)(76, 126)(77, 123)(78, 114)(79, 119)(80, 127)(81, 98)(82, 102)(83, 100)(84, 103)(85, 97)(86, 108)(87, 109)(88, 107)(89, 117)(90, 110)(91, 111)(92, 125)(93, 112)(94, 128)(95, 124)(96, 118) MAP : A3.461 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-1 * x.2^2 * x.4^-1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.3, x.2^-1), x.3^-2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4 * x.3 * x.2 * x.4^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 109)(34, 105)(35, 100)(36, 112)(37, 110)(38, 106)(39, 107)(40, 103)(41, 101)(42, 97)(43, 108)(44, 104)(45, 102)(46, 98)(47, 99)(48, 111)(49, 84)(50, 91)(51, 93)(52, 81)(53, 88)(54, 95)(55, 89)(56, 85)(57, 87)(58, 96)(59, 82)(60, 94)(61, 83)(62, 92)(63, 86)(64, 90) MAP : A3.462 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), x.3^2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4^-3 * x.2^-1 * x.4^-1 * x.3^-1 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 84)(50, 91)(51, 93)(52, 81)(53, 88)(54, 95)(55, 89)(56, 85)(57, 87)(58, 96)(59, 82)(60, 94)(61, 83)(62, 92)(63, 86)(64, 90) MAP : A3.463 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), x.3^2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4^-3 * x.2^-1 * x.4^-1 * x.3^-1 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 95)(50, 88)(51, 90)(52, 86)(53, 91)(54, 84)(55, 94)(56, 82)(57, 92)(58, 83)(59, 85)(60, 89)(61, 96)(62, 87)(63, 81)(64, 93) MAP : A3.464 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), x.3^2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4^-3 * x.2^-1 * x.4^-1 * x.3^-1 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.465 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 85)(50, 81)(51, 92)(52, 88)(53, 86)(54, 82)(55, 83)(56, 95)(57, 93)(58, 89)(59, 84)(60, 96)(61, 94)(62, 90)(63, 91)(64, 87) MAP : A3.466 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), x.3^2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4^-3 * x.2^-1 * x.4^-1 * x.3^-1 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 83)(50, 87)(51, 81)(52, 90)(53, 92)(54, 96)(55, 82)(56, 89)(57, 88)(58, 84)(59, 94)(60, 85)(61, 95)(62, 91)(63, 93)(64, 86) MAP : A3.467 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), x.3^2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4^-3 * x.2^-1 * x.4^-1 * x.3^-1 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 96)(50, 92)(51, 86)(52, 93)(53, 87)(54, 83)(55, 85)(56, 94)(57, 91)(58, 95)(59, 89)(60, 82)(61, 84)(62, 88)(63, 90)(64, 81) MAP : A3.468 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), x.3^2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4^-3 * x.2^-1 * x.4^-1 * x.3^-1 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.469 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), x.3^2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4^-3 * x.2^-1 * x.4^-1 * x.3^-1 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 94)(50, 93)(51, 88)(52, 87)(53, 90)(54, 89)(55, 84)(56, 83)(57, 86)(58, 85)(59, 96)(60, 95)(61, 82)(62, 81)(63, 92)(64, 91) MAP : A3.470 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), x.3^2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4^-3 * x.2^-1 * x.4^-1 * x.3^-1 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 83)(50, 87)(51, 81)(52, 90)(53, 92)(54, 96)(55, 82)(56, 89)(57, 88)(58, 84)(59, 94)(60, 85)(61, 95)(62, 91)(63, 93)(64, 86) MAP : A3.471 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), x.3^2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4^-3 * x.2^-1 * x.4^-1 * x.3^-1 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 96)(50, 92)(51, 86)(52, 93)(53, 87)(54, 83)(55, 85)(56, 94)(57, 91)(58, 95)(59, 89)(60, 82)(61, 84)(62, 88)(63, 90)(64, 81) MAP : A3.472 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), x.3^2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4^-3 * x.2^-1 * x.4^-1 * x.3^-1 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 84)(50, 91)(51, 93)(52, 81)(53, 88)(54, 95)(55, 89)(56, 85)(57, 87)(58, 96)(59, 82)(60, 94)(61, 83)(62, 92)(63, 86)(64, 90) MAP : A3.473 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), x.3^2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4^-3 * x.2^-1 * x.4^-1 * x.3^-1 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 95)(50, 88)(51, 90)(52, 86)(53, 91)(54, 84)(55, 94)(56, 82)(57, 92)(58, 83)(59, 85)(60, 89)(61, 96)(62, 87)(63, 81)(64, 93) MAP : A3.474 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, x.2^2 * x.1 * x.2^-2 * x.1^-1, x.2^4 * x.1^-1 * x.2 * x.1^-1 * x.2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 35)(2, 51)(3, 40)(4, 49)(5, 33)(6, 56)(7, 57)(8, 37)(9, 43)(10, 52)(11, 34)(12, 36)(13, 39)(14, 48)(15, 58)(16, 38)(17, 55)(18, 54)(19, 41)(20, 50)(21, 61)(22, 42)(23, 44)(24, 46)(25, 62)(26, 53)(27, 64)(28, 59)(29, 47)(30, 45)(31, 60)(32, 63)(65, 100)(66, 116)(67, 98)(68, 106)(69, 122)(70, 114)(71, 113)(72, 102)(73, 103)(74, 111)(75, 124)(76, 127)(77, 117)(78, 121)(79, 128)(80, 123)(81, 101)(82, 107)(83, 97)(84, 108)(85, 104)(86, 112)(87, 109)(88, 99)(89, 115)(90, 118)(91, 105)(92, 119)(93, 126)(94, 120)(95, 125)(96, 110) MAP : A3.475 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82)(97, 106)(98, 110)(99, 102)(100, 111)(101, 103)(104, 109)(105, 107)(108, 112) MAP : A3.476 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 35)(34, 41)(36, 40)(37, 48)(38, 42)(39, 44)(43, 46)(45, 47)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84)(97, 101)(98, 104)(99, 103)(100, 110)(102, 108)(105, 109)(106, 112)(107, 111) MAP : A3.477 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, x.2^2 * x.1 * x.2^-2 * x.1^-1, x.2^4 * x.1^-1 * x.2 * x.1^-1 * x.2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 62)(2, 46)(3, 45)(4, 41)(5, 57)(6, 61)(7, 64)(8, 39)(9, 38)(10, 35)(11, 56)(12, 51)(13, 59)(14, 58)(15, 49)(16, 53)(17, 43)(18, 37)(19, 48)(20, 40)(21, 44)(22, 33)(23, 34)(24, 47)(25, 63)(26, 55)(27, 42)(28, 54)(29, 36)(30, 60)(31, 50)(32, 52)(65, 111)(66, 127)(67, 108)(68, 128)(69, 112)(70, 124)(71, 122)(72, 107)(73, 101)(74, 110)(75, 109)(76, 126)(77, 102)(78, 97)(79, 121)(80, 103)(81, 118)(82, 119)(83, 106)(84, 125)(85, 114)(86, 105)(87, 104)(88, 116)(89, 100)(90, 123)(91, 113)(92, 117)(93, 99)(94, 98)(95, 120)(96, 115) MAP : A3.478 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), x.3^2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4^-3 * x.2^-1 * x.4^-1 * x.3^-1 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 94)(50, 93)(51, 88)(52, 87)(53, 90)(54, 89)(55, 84)(56, 83)(57, 86)(58, 85)(59, 96)(60, 95)(61, 82)(62, 81)(63, 92)(64, 91) MAP : A3.479 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 37)(34, 40)(35, 39)(36, 46)(38, 44)(41, 45)(42, 48)(43, 47)(49, 96)(50, 84)(51, 92)(52, 91)(53, 83)(54, 87)(55, 81)(56, 89)(57, 95)(58, 85)(59, 93)(60, 90)(61, 82)(62, 88)(63, 94)(64, 86)(97, 104)(98, 108)(99, 100)(101, 107)(102, 111)(103, 105)(106, 109)(110, 112) MAP : A3.480 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 40)(34, 44)(35, 36)(37, 43)(38, 47)(39, 41)(42, 45)(46, 48)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81)(97, 101)(98, 104)(99, 103)(100, 110)(102, 108)(105, 109)(106, 112)(107, 111) MAP : A3.481 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 40)(34, 44)(35, 36)(37, 43)(38, 47)(39, 41)(42, 45)(46, 48)(49, 91)(50, 81)(51, 89)(52, 96)(53, 88)(54, 82)(55, 84)(56, 92)(57, 90)(58, 94)(59, 86)(60, 95)(61, 87)(62, 83)(63, 85)(64, 93)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.482 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81)(97, 99)(98, 105)(100, 104)(101, 112)(102, 106)(103, 108)(107, 110)(109, 111) MAP : A3.483 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84)(97, 104)(98, 108)(99, 100)(101, 107)(102, 111)(103, 105)(106, 109)(110, 112) MAP : A3.484 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 35)(34, 41)(36, 40)(37, 48)(38, 42)(39, 44)(43, 46)(45, 47)(49, 91)(50, 81)(51, 89)(52, 96)(53, 88)(54, 82)(55, 84)(56, 92)(57, 90)(58, 94)(59, 86)(60, 95)(61, 87)(62, 83)(63, 85)(64, 93)(97, 101)(98, 104)(99, 103)(100, 110)(102, 108)(105, 109)(106, 112)(107, 111) MAP : A3.485 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 35)(34, 41)(36, 40)(37, 48)(38, 42)(39, 44)(43, 46)(45, 47)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.486 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 37)(34, 40)(35, 39)(36, 46)(38, 44)(41, 45)(42, 48)(43, 47)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84)(97, 99)(98, 105)(100, 104)(101, 112)(102, 106)(103, 108)(107, 110)(109, 111) MAP : A3.487 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 37)(18, 33)(19, 44)(20, 47)(21, 40)(22, 36)(23, 35)(24, 34)(25, 38)(26, 39)(27, 48)(28, 42)(29, 43)(30, 45)(31, 41)(32, 46)(49, 84)(50, 86)(51, 85)(52, 94)(53, 95)(54, 96)(55, 81)(56, 89)(57, 91)(58, 82)(59, 92)(60, 88)(61, 83)(62, 87)(63, 93)(64, 90)(97, 122)(98, 124)(99, 126)(100, 114)(101, 119)(102, 120)(103, 128)(104, 115)(105, 117)(106, 123)(107, 127)(108, 125)(109, 116)(110, 118)(111, 113)(112, 121) MAP : A3.488 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 35)(18, 39)(19, 43)(20, 37)(21, 44)(22, 33)(23, 45)(24, 42)(25, 34)(26, 46)(27, 38)(28, 48)(29, 41)(30, 47)(31, 40)(32, 36)(49, 84)(50, 86)(51, 85)(52, 94)(53, 95)(54, 96)(55, 81)(56, 89)(57, 91)(58, 82)(59, 92)(60, 88)(61, 83)(62, 87)(63, 93)(64, 90)(97, 114)(98, 120)(99, 119)(100, 118)(101, 113)(102, 121)(103, 122)(104, 117)(105, 127)(106, 124)(107, 125)(108, 115)(109, 126)(110, 128)(111, 116)(112, 123) MAP : A3.489 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 38)(18, 41)(19, 33)(20, 48)(21, 36)(22, 43)(23, 34)(24, 47)(25, 45)(26, 40)(27, 35)(28, 37)(29, 39)(30, 42)(31, 46)(32, 44)(49, 84)(50, 86)(51, 85)(52, 94)(53, 95)(54, 96)(55, 81)(56, 89)(57, 91)(58, 82)(59, 92)(60, 88)(61, 83)(62, 87)(63, 93)(64, 90)(97, 125)(98, 126)(99, 121)(100, 115)(101, 123)(102, 119)(103, 127)(104, 128)(105, 122)(106, 116)(107, 114)(108, 118)(109, 120)(110, 117)(111, 124)(112, 113) MAP : A3.490 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 42)(18, 44)(19, 46)(20, 34)(21, 39)(22, 40)(23, 48)(24, 35)(25, 37)(26, 43)(27, 47)(28, 45)(29, 36)(30, 38)(31, 33)(32, 41)(49, 84)(50, 86)(51, 85)(52, 94)(53, 95)(54, 96)(55, 81)(56, 89)(57, 91)(58, 82)(59, 92)(60, 88)(61, 83)(62, 87)(63, 93)(64, 90)(97, 117)(98, 113)(99, 124)(100, 127)(101, 120)(102, 116)(103, 115)(104, 114)(105, 118)(106, 119)(107, 128)(108, 122)(109, 123)(110, 125)(111, 121)(112, 126) MAP : A3.491 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 47)(18, 36)(19, 40)(20, 45)(21, 41)(22, 46)(23, 37)(24, 38)(25, 48)(26, 33)(27, 42)(28, 34)(29, 44)(30, 35)(31, 43)(32, 39)(49, 84)(50, 86)(51, 85)(52, 94)(53, 95)(54, 96)(55, 81)(56, 89)(57, 91)(58, 82)(59, 92)(60, 88)(61, 83)(62, 87)(63, 93)(64, 90)(97, 128)(98, 123)(99, 116)(100, 122)(101, 126)(102, 124)(103, 118)(104, 125)(105, 115)(106, 121)(107, 117)(108, 127)(109, 113)(110, 114)(111, 119)(112, 120) MAP : A3.492 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 45)(18, 46)(19, 41)(20, 35)(21, 43)(22, 39)(23, 47)(24, 48)(25, 42)(26, 36)(27, 34)(28, 38)(29, 40)(30, 37)(31, 44)(32, 33)(49, 84)(50, 86)(51, 85)(52, 94)(53, 95)(54, 96)(55, 81)(56, 89)(57, 91)(58, 82)(59, 92)(60, 88)(61, 83)(62, 87)(63, 93)(64, 90)(97, 118)(98, 121)(99, 113)(100, 128)(101, 116)(102, 123)(103, 114)(104, 127)(105, 125)(106, 120)(107, 115)(108, 117)(109, 119)(110, 122)(111, 126)(112, 124) MAP : A3.493 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 48)(18, 43)(19, 36)(20, 42)(21, 46)(22, 44)(23, 38)(24, 45)(25, 35)(26, 41)(27, 37)(28, 47)(29, 33)(30, 34)(31, 39)(32, 40)(49, 84)(50, 86)(51, 85)(52, 94)(53, 95)(54, 96)(55, 81)(56, 89)(57, 91)(58, 82)(59, 92)(60, 88)(61, 83)(62, 87)(63, 93)(64, 90)(97, 127)(98, 116)(99, 120)(100, 125)(101, 121)(102, 126)(103, 117)(104, 118)(105, 128)(106, 113)(107, 122)(108, 114)(109, 124)(110, 115)(111, 123)(112, 119) MAP : A3.494 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 34)(18, 40)(19, 39)(20, 38)(21, 33)(22, 41)(23, 42)(24, 37)(25, 47)(26, 44)(27, 45)(28, 35)(29, 46)(30, 48)(31, 36)(32, 43)(49, 87)(50, 90)(51, 93)(52, 81)(53, 83)(54, 82)(55, 94)(56, 92)(57, 88)(58, 96)(59, 89)(60, 91)(61, 95)(62, 84)(63, 85)(64, 86)(97, 127)(98, 116)(99, 120)(100, 125)(101, 121)(102, 126)(103, 117)(104, 118)(105, 128)(106, 113)(107, 122)(108, 114)(109, 124)(110, 115)(111, 123)(112, 119) MAP : A3.495 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, x.5 * x.4^-1 * x.5 * x.4, x.4 * x.5 * x.2 * x.1, x.4^-1 * x.1 * x.4 * x.1, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 119)(20, 123)(21, 113)(22, 117)(23, 128)(24, 116)(25, 122)(26, 126)(27, 127)(28, 115)(29, 121)(30, 125)(31, 120)(32, 124)(33, 36)(34, 43)(35, 45)(37, 40)(38, 47)(39, 41)(42, 48)(44, 46)(49, 83)(50, 87)(51, 81)(52, 90)(53, 92)(54, 96)(55, 82)(56, 89)(57, 88)(58, 84)(59, 94)(60, 85)(61, 95)(62, 91)(63, 93)(64, 86)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.496 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, x.5 * x.4^-1 * x.5 * x.4, x.4 * x.5 * x.2 * x.1, x.4^-1 * x.1 * x.4 * x.1, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 119)(20, 123)(21, 113)(22, 117)(23, 128)(24, 116)(25, 122)(26, 126)(27, 127)(28, 115)(29, 121)(30, 125)(31, 120)(32, 124)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 84)(50, 91)(51, 93)(52, 81)(53, 88)(54, 95)(55, 89)(56, 85)(57, 87)(58, 96)(59, 82)(60, 94)(61, 83)(62, 92)(63, 86)(64, 90)(97, 99)(98, 103)(100, 106)(101, 108)(102, 112)(104, 105)(107, 110)(109, 111) MAP : A3.497 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, x.5 * x.4^-1 * x.5 * x.4, x.4 * x.5 * x.2 * x.1, x.4^-1 * x.1 * x.4 * x.1, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 119)(20, 123)(21, 113)(22, 117)(23, 128)(24, 116)(25, 122)(26, 126)(27, 127)(28, 115)(29, 121)(30, 125)(31, 120)(32, 124)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 96)(50, 92)(51, 86)(52, 93)(53, 87)(54, 83)(55, 85)(56, 94)(57, 91)(58, 95)(59, 89)(60, 82)(61, 84)(62, 88)(63, 90)(64, 81)(97, 100)(98, 107)(99, 109)(101, 104)(102, 111)(103, 105)(106, 112)(108, 110) MAP : A3.498 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 42)(18, 44)(19, 46)(20, 34)(21, 39)(22, 40)(23, 48)(24, 35)(25, 37)(26, 43)(27, 47)(28, 45)(29, 36)(30, 38)(31, 33)(32, 41)(49, 87)(50, 90)(51, 93)(52, 81)(53, 83)(54, 82)(55, 94)(56, 92)(57, 88)(58, 96)(59, 89)(60, 91)(61, 95)(62, 84)(63, 85)(64, 86)(97, 125)(98, 126)(99, 121)(100, 115)(101, 123)(102, 119)(103, 127)(104, 128)(105, 122)(106, 116)(107, 114)(108, 118)(109, 120)(110, 117)(111, 124)(112, 113) MAP : A3.499 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 47)(18, 36)(19, 40)(20, 45)(21, 41)(22, 46)(23, 37)(24, 38)(25, 48)(26, 33)(27, 42)(28, 34)(29, 44)(30, 35)(31, 43)(32, 39)(49, 87)(50, 90)(51, 93)(52, 81)(53, 83)(54, 82)(55, 94)(56, 92)(57, 88)(58, 96)(59, 89)(60, 91)(61, 95)(62, 84)(63, 85)(64, 86)(97, 114)(98, 120)(99, 119)(100, 118)(101, 113)(102, 121)(103, 122)(104, 117)(105, 127)(106, 124)(107, 125)(108, 115)(109, 126)(110, 128)(111, 116)(112, 123) MAP : A3.500 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 35)(34, 41)(36, 40)(37, 48)(38, 42)(39, 44)(43, 46)(45, 47)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91)(97, 101)(98, 104)(99, 103)(100, 110)(102, 108)(105, 109)(106, 112)(107, 111) MAP : A3.501 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 35)(34, 41)(36, 40)(37, 48)(38, 42)(39, 44)(43, 46)(45, 47)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82)(97, 108)(98, 111)(99, 112)(100, 105)(101, 102)(103, 106)(104, 107)(109, 110) MAP : A3.502 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 37)(34, 40)(35, 39)(36, 46)(38, 44)(41, 45)(42, 48)(43, 47)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82)(97, 99)(98, 105)(100, 104)(101, 112)(102, 106)(103, 108)(107, 110)(109, 111) MAP : A3.503 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 37)(34, 40)(35, 39)(36, 46)(38, 44)(41, 45)(42, 48)(43, 47)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91)(97, 106)(98, 110)(99, 102)(100, 111)(101, 103)(104, 109)(105, 107)(108, 112) MAP : A3.504 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 40)(34, 44)(35, 36)(37, 43)(38, 47)(39, 41)(42, 45)(46, 48)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.505 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 40)(34, 44)(35, 36)(37, 43)(38, 47)(39, 41)(42, 45)(46, 48)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91)(97, 110)(98, 99)(100, 101)(102, 105)(103, 104)(106, 107)(108, 109)(111, 112) MAP : A3.506 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91)(97, 104)(98, 108)(99, 100)(101, 107)(102, 111)(103, 105)(106, 109)(110, 112) MAP : A3.507 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82)(97, 111)(98, 101)(99, 109)(100, 106)(102, 104)(103, 110)(105, 112)(107, 108) MAP : A3.508 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 35)(34, 41)(36, 40)(37, 48)(38, 42)(39, 44)(43, 46)(45, 47)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.509 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 35)(34, 41)(36, 40)(37, 48)(38, 42)(39, 44)(43, 46)(45, 47)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91)(97, 110)(98, 99)(100, 101)(102, 105)(103, 104)(106, 107)(108, 109)(111, 112) MAP : A3.510 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 37)(34, 40)(35, 39)(36, 46)(38, 44)(41, 45)(42, 48)(43, 47)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82)(97, 104)(98, 108)(99, 100)(101, 107)(102, 111)(103, 105)(106, 109)(110, 112) MAP : A3.511 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 37)(34, 40)(35, 39)(36, 46)(38, 44)(41, 45)(42, 48)(43, 47)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91)(97, 111)(98, 101)(99, 109)(100, 106)(102, 104)(103, 110)(105, 112)(107, 108) MAP : A3.512 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 40)(34, 44)(35, 36)(37, 43)(38, 47)(39, 41)(42, 45)(46, 48)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91)(97, 101)(98, 104)(99, 103)(100, 110)(102, 108)(105, 109)(106, 112)(107, 111) MAP : A3.513 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 40)(34, 44)(35, 36)(37, 43)(38, 47)(39, 41)(42, 45)(46, 48)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82)(97, 108)(98, 111)(99, 112)(100, 105)(101, 102)(103, 106)(104, 107)(109, 110) MAP : A3.514 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, (x.5 * x.2)^2, x.4^-1 * x.5 * x.2 * x.1, (x.4 * x.2)^2, (x.5 * x.3^-1)^2, x.5 * x.2 * x.4 * x.1, (x.2 * x.4^-1 * x.1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91)(97, 99)(98, 105)(100, 104)(101, 112)(102, 106)(103, 108)(107, 110)(109, 111) MAP : A3.515 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5^-1 * x.1 * x.2, x.4 * x.2 * x.5 * x.1, (x.3 * x.4^-1)^2, x.5 * x.2 * x.1 * x.4, x.4^-1 * x.2 * x.5 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 36)(34, 43)(35, 45)(37, 40)(38, 47)(39, 41)(42, 48)(44, 46)(49, 82)(50, 86)(51, 87)(52, 91)(53, 81)(54, 85)(55, 96)(56, 84)(57, 90)(58, 94)(59, 95)(60, 83)(61, 89)(62, 93)(63, 88)(64, 92)(97, 112)(98, 108)(99, 102)(100, 109)(101, 103)(104, 110)(105, 107)(106, 111) MAP : A3.516 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, x.2^2 * x.1 * x.2^-2 * x.1^-1, x.2^4 * x.1^-1 * x.2 * x.1^-1 * x.2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 37)(2, 43)(3, 33)(4, 44)(5, 40)(6, 48)(7, 45)(8, 35)(9, 51)(10, 54)(11, 41)(12, 55)(13, 62)(14, 56)(15, 61)(16, 46)(17, 36)(18, 52)(19, 34)(20, 42)(21, 58)(22, 50)(23, 49)(24, 38)(25, 39)(26, 47)(27, 60)(28, 63)(29, 53)(30, 57)(31, 64)(32, 59)(65, 111)(66, 127)(67, 108)(68, 128)(69, 112)(70, 124)(71, 122)(72, 107)(73, 101)(74, 110)(75, 109)(76, 126)(77, 102)(78, 97)(79, 121)(80, 103)(81, 118)(82, 119)(83, 106)(84, 125)(85, 114)(86, 105)(87, 104)(88, 116)(89, 100)(90, 123)(91, 113)(92, 117)(93, 99)(94, 98)(95, 120)(96, 115) MAP : A3.517 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 35)(34, 41)(36, 40)(37, 48)(38, 42)(39, 44)(43, 46)(45, 47)(49, 96)(50, 84)(51, 92)(52, 91)(53, 83)(54, 87)(55, 81)(56, 89)(57, 95)(58, 85)(59, 93)(60, 90)(61, 82)(62, 88)(63, 94)(64, 86)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.518 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 37)(34, 40)(35, 39)(36, 46)(38, 44)(41, 45)(42, 48)(43, 47)(49, 91)(50, 81)(51, 89)(52, 96)(53, 88)(54, 82)(55, 84)(56, 92)(57, 90)(58, 94)(59, 86)(60, 95)(61, 87)(62, 83)(63, 85)(64, 93)(97, 99)(98, 105)(100, 104)(101, 112)(102, 106)(103, 108)(107, 110)(109, 111) MAP : A3.519 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.520 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.521 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 95)(50, 85)(51, 93)(52, 90)(53, 82)(54, 88)(55, 94)(56, 86)(57, 96)(58, 84)(59, 92)(60, 91)(61, 83)(62, 87)(63, 81)(64, 89) MAP : A3.522 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.523 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.524 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.525 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 94)(50, 83)(51, 82)(52, 85)(53, 84)(54, 89)(55, 88)(56, 87)(57, 86)(58, 91)(59, 90)(60, 93)(61, 92)(62, 81)(63, 96)(64, 95) MAP : A3.526 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.527 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 37)(34, 40)(35, 39)(36, 46)(38, 44)(41, 45)(42, 48)(43, 47)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81)(97, 104)(98, 108)(99, 100)(101, 107)(102, 111)(103, 105)(106, 109)(110, 112) MAP : A3.528 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 40)(34, 44)(35, 36)(37, 43)(38, 47)(39, 41)(42, 45)(46, 48)(49, 96)(50, 84)(51, 92)(52, 91)(53, 83)(54, 87)(55, 81)(56, 89)(57, 95)(58, 85)(59, 93)(60, 90)(61, 82)(62, 88)(63, 94)(64, 86)(97, 101)(98, 104)(99, 103)(100, 110)(102, 108)(105, 109)(106, 112)(107, 111) MAP : A3.529 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 40)(34, 44)(35, 36)(37, 43)(38, 47)(39, 41)(42, 45)(46, 48)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.530 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 96)(50, 84)(51, 92)(52, 91)(53, 83)(54, 87)(55, 81)(56, 89)(57, 95)(58, 85)(59, 93)(60, 90)(61, 82)(62, 88)(63, 94)(64, 86)(97, 99)(98, 105)(100, 104)(101, 112)(102, 106)(103, 108)(107, 110)(109, 111) MAP : A3.531 NOTES : type II, reflexible, isomorphic to A3.475. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.3 * x.4)^2, x.5^-1 * x.2 * x.4 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.1)^2, x.5^2 * x.4 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 91)(50, 81)(51, 89)(52, 96)(53, 88)(54, 82)(55, 84)(56, 92)(57, 90)(58, 94)(59, 86)(60, 95)(61, 87)(62, 83)(63, 85)(64, 93)(97, 104)(98, 108)(99, 100)(101, 107)(102, 111)(103, 105)(106, 109)(110, 112) MAP : A3.532 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, x.5 * x.4^-1 * x.5 * x.4, x.4 * x.5 * x.2 * x.1, x.4^-1 * x.1 * x.4 * x.1, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 119)(20, 123)(21, 113)(22, 117)(23, 128)(24, 116)(25, 122)(26, 126)(27, 127)(28, 115)(29, 121)(30, 125)(31, 120)(32, 124)(33, 35)(34, 39)(36, 42)(37, 44)(38, 48)(40, 41)(43, 46)(45, 47)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(97, 100)(98, 107)(99, 109)(101, 104)(102, 111)(103, 105)(106, 112)(108, 110) MAP : A3.533 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, x.5 * x.4^-1 * x.5 * x.4, x.4 * x.5 * x.2 * x.1, x.4^-1 * x.1 * x.4 * x.1, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 119)(20, 123)(21, 113)(22, 117)(23, 128)(24, 116)(25, 122)(26, 126)(27, 127)(28, 115)(29, 121)(30, 125)(31, 120)(32, 124)(33, 35)(34, 39)(36, 42)(37, 44)(38, 48)(40, 41)(43, 46)(45, 47)(49, 95)(50, 88)(51, 90)(52, 86)(53, 91)(54, 84)(55, 94)(56, 82)(57, 92)(58, 83)(59, 85)(60, 89)(61, 96)(62, 87)(63, 81)(64, 93)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.534 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, x.5 * x.4^-1 * x.5 * x.4, x.4 * x.5 * x.2 * x.1, x.4^-1 * x.1 * x.4 * x.1, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 119)(20, 123)(21, 113)(22, 117)(23, 128)(24, 116)(25, 122)(26, 126)(27, 127)(28, 115)(29, 121)(30, 125)(31, 120)(32, 124)(33, 36)(34, 43)(35, 45)(37, 40)(38, 47)(39, 41)(42, 48)(44, 46)(49, 94)(50, 93)(51, 88)(52, 87)(53, 90)(54, 89)(55, 84)(56, 83)(57, 86)(58, 85)(59, 96)(60, 95)(61, 82)(62, 81)(63, 92)(64, 91)(97, 99)(98, 103)(100, 106)(101, 108)(102, 112)(104, 105)(107, 110)(109, 111) MAP : A3.535 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.536 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.537 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.538 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, x.5 * x.4^-1 * x.5 * x.4, x.4 * x.5 * x.2 * x.1, x.4^-1 * x.1 * x.4 * x.1, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 113)(19, 124)(20, 120)(21, 118)(22, 114)(23, 115)(24, 127)(25, 125)(26, 121)(27, 116)(28, 128)(29, 126)(30, 122)(31, 123)(32, 119)(33, 35)(34, 39)(36, 42)(37, 44)(38, 48)(40, 41)(43, 46)(45, 47)(49, 94)(50, 93)(51, 88)(52, 87)(53, 90)(54, 89)(55, 84)(56, 83)(57, 86)(58, 85)(59, 96)(60, 95)(61, 82)(62, 81)(63, 92)(64, 91)(97, 100)(98, 107)(99, 109)(101, 104)(102, 111)(103, 105)(106, 112)(108, 110) MAP : A3.539 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, x.5 * x.4^-1 * x.5 * x.4, x.4 * x.5 * x.2 * x.1, x.4^-1 * x.1 * x.4 * x.1, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 113)(19, 124)(20, 120)(21, 118)(22, 114)(23, 115)(24, 127)(25, 125)(26, 121)(27, 116)(28, 128)(29, 126)(30, 122)(31, 123)(32, 119)(33, 35)(34, 39)(36, 42)(37, 44)(38, 48)(40, 41)(43, 46)(45, 47)(49, 84)(50, 91)(51, 93)(52, 81)(53, 88)(54, 95)(55, 89)(56, 85)(57, 87)(58, 96)(59, 82)(60, 94)(61, 83)(62, 92)(63, 86)(64, 90)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.540 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, x.5 * x.4^-1 * x.5 * x.4, x.4 * x.5 * x.2 * x.1, x.4^-1 * x.1 * x.4 * x.1, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 113)(19, 124)(20, 120)(21, 118)(22, 114)(23, 115)(24, 127)(25, 125)(26, 121)(27, 116)(28, 128)(29, 126)(30, 122)(31, 123)(32, 119)(33, 36)(34, 43)(35, 45)(37, 40)(38, 47)(39, 41)(42, 48)(44, 46)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(97, 99)(98, 103)(100, 106)(101, 108)(102, 112)(104, 105)(107, 110)(109, 111) MAP : A3.541 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, x.5 * x.4^-1 * x.5 * x.4, x.4 * x.5 * x.2 * x.1, x.4^-1 * x.1 * x.4 * x.1, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 113)(19, 124)(20, 120)(21, 118)(22, 114)(23, 115)(24, 127)(25, 125)(26, 121)(27, 116)(28, 128)(29, 126)(30, 122)(31, 123)(32, 119)(33, 36)(34, 43)(35, 45)(37, 40)(38, 47)(39, 41)(42, 48)(44, 46)(49, 96)(50, 92)(51, 86)(52, 93)(53, 87)(54, 83)(55, 85)(56, 94)(57, 91)(58, 95)(59, 89)(60, 82)(61, 84)(62, 88)(63, 90)(64, 81)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.542 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, x.5 * x.4^-1 * x.5 * x.4, x.4 * x.5 * x.2 * x.1, x.4^-1 * x.1 * x.4 * x.1, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 113)(19, 124)(20, 120)(21, 118)(22, 114)(23, 115)(24, 127)(25, 125)(26, 121)(27, 116)(28, 128)(29, 126)(30, 122)(31, 123)(32, 119)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 95)(50, 88)(51, 90)(52, 86)(53, 91)(54, 84)(55, 94)(56, 82)(57, 92)(58, 83)(59, 85)(60, 89)(61, 96)(62, 87)(63, 81)(64, 93)(97, 99)(98, 103)(100, 106)(101, 108)(102, 112)(104, 105)(107, 110)(109, 111) MAP : A3.543 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.5 * u.3^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5^2, x.5 * x.4^-1 * x.5 * x.4, x.4 * x.5 * x.2 * x.1, x.4^-1 * x.1 * x.4 * x.1, (x.5 * x.3^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 113)(19, 124)(20, 120)(21, 118)(22, 114)(23, 115)(24, 127)(25, 125)(26, 121)(27, 116)(28, 128)(29, 126)(30, 122)(31, 123)(32, 119)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 83)(50, 87)(51, 81)(52, 90)(53, 92)(54, 96)(55, 82)(56, 89)(57, 88)(58, 84)(59, 94)(60, 85)(61, 95)(62, 91)(63, 93)(64, 86)(97, 100)(98, 107)(99, 109)(101, 104)(102, 111)(103, 105)(106, 112)(108, 110) MAP : A3.544 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5^-1 * x.1 * x.2, x.4 * x.2 * x.5 * x.1, (x.3 * x.4^-1)^2, x.5 * x.2 * x.1 * x.4, x.4^-1 * x.2 * x.5 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 36)(34, 43)(35, 45)(37, 40)(38, 47)(39, 41)(42, 48)(44, 46)(49, 82)(50, 86)(51, 87)(52, 91)(53, 81)(54, 85)(55, 96)(56, 84)(57, 90)(58, 94)(59, 95)(60, 83)(61, 89)(62, 93)(63, 88)(64, 92)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.545 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5^-1 * x.1 * x.2, x.4 * x.2 * x.5 * x.1, (x.3 * x.4^-1)^2, x.5 * x.2 * x.1 * x.4, x.4^-1 * x.2 * x.5 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 36)(34, 43)(35, 45)(37, 40)(38, 47)(39, 41)(42, 48)(44, 46)(49, 85)(50, 81)(51, 92)(52, 88)(53, 86)(54, 82)(55, 83)(56, 95)(57, 93)(58, 89)(59, 84)(60, 96)(61, 94)(62, 90)(63, 91)(64, 87)(97, 110)(98, 109)(99, 104)(100, 103)(101, 106)(102, 105)(107, 112)(108, 111) MAP : A3.546 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5^-1 * x.1 * x.2, x.4 * x.2 * x.5 * x.1, (x.3 * x.4^-1)^2, x.5 * x.2 * x.1 * x.4, x.4^-1 * x.2 * x.5 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 85)(50, 81)(51, 92)(52, 88)(53, 86)(54, 82)(55, 83)(56, 95)(57, 93)(58, 89)(59, 84)(60, 96)(61, 94)(62, 90)(63, 91)(64, 87)(97, 100)(98, 107)(99, 109)(101, 104)(102, 111)(103, 105)(106, 112)(108, 110) MAP : A3.547 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5^-1 * x.1 * x.2, x.4 * x.2 * x.5 * x.1, (x.3 * x.4^-1)^2, x.5 * x.2 * x.1 * x.4, x.4^-1 * x.2 * x.5 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 82)(50, 86)(51, 87)(52, 91)(53, 81)(54, 85)(55, 96)(56, 84)(57, 90)(58, 94)(59, 95)(60, 83)(61, 89)(62, 93)(63, 88)(64, 92)(97, 111)(98, 104)(99, 106)(100, 102)(101, 107)(103, 110)(105, 108)(109, 112) MAP : A3.548 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5^-1 * x.1 * x.2, x.4 * x.2 * x.5 * x.1, (x.3 * x.4^-1)^2, x.5 * x.2 * x.1 * x.4, x.4^-1 * x.2 * x.5 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 35)(34, 39)(36, 42)(37, 44)(38, 48)(40, 41)(43, 46)(45, 47)(49, 85)(50, 81)(51, 92)(52, 88)(53, 86)(54, 82)(55, 83)(56, 95)(57, 93)(58, 89)(59, 84)(60, 96)(61, 94)(62, 90)(63, 91)(64, 87)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.549 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5^-1 * x.1 * x.2, x.4 * x.2 * x.5 * x.1, (x.3 * x.4^-1)^2, x.5 * x.2 * x.1 * x.4, x.4^-1 * x.2 * x.5 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 35)(34, 39)(36, 42)(37, 44)(38, 48)(40, 41)(43, 46)(45, 47)(49, 82)(50, 86)(51, 87)(52, 91)(53, 81)(54, 85)(55, 96)(56, 84)(57, 90)(58, 94)(59, 95)(60, 83)(61, 89)(62, 93)(63, 88)(64, 92)(97, 110)(98, 109)(99, 104)(100, 103)(101, 106)(102, 105)(107, 112)(108, 111) MAP : A3.550 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5^-1 * x.1 * x.2, x.4 * x.2 * x.5 * x.1, (x.3 * x.4^-1)^2, x.5 * x.2 * x.1 * x.4, x.4^-1 * x.2 * x.5 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 82)(50, 86)(51, 87)(52, 91)(53, 81)(54, 85)(55, 96)(56, 84)(57, 90)(58, 94)(59, 95)(60, 83)(61, 89)(62, 93)(63, 88)(64, 92)(97, 99)(98, 103)(100, 106)(101, 108)(102, 112)(104, 105)(107, 110)(109, 111) MAP : A3.551 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5^-1 * x.1 * x.2, x.4 * x.2 * x.5 * x.1, (x.3 * x.4^-1)^2, x.5 * x.2 * x.1 * x.4, x.4^-1 * x.2 * x.5 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 85)(50, 81)(51, 92)(52, 88)(53, 86)(54, 82)(55, 83)(56, 95)(57, 93)(58, 89)(59, 84)(60, 96)(61, 94)(62, 90)(63, 91)(64, 87)(97, 112)(98, 108)(99, 102)(100, 109)(101, 103)(104, 110)(105, 107)(106, 111) MAP : A3.552 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5^-1 * x.1 * x.2, x.4 * x.2 * x.5 * x.1, (x.3 * x.4^-1)^2, x.5 * x.2 * x.1 * x.4, x.4^-1 * x.2 * x.5 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 35)(34, 39)(36, 42)(37, 44)(38, 48)(40, 41)(43, 46)(45, 47)(49, 82)(50, 86)(51, 87)(52, 91)(53, 81)(54, 85)(55, 96)(56, 84)(57, 90)(58, 94)(59, 95)(60, 83)(61, 89)(62, 93)(63, 88)(64, 92)(97, 100)(98, 107)(99, 109)(101, 104)(102, 111)(103, 105)(106, 112)(108, 110) MAP : A3.553 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5^-1 * x.1 * x.2, x.4 * x.2 * x.5 * x.1, (x.3 * x.4^-1)^2, x.5 * x.2 * x.1 * x.4, x.4^-1 * x.2 * x.5 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 35)(34, 39)(36, 42)(37, 44)(38, 48)(40, 41)(43, 46)(45, 47)(49, 85)(50, 81)(51, 92)(52, 88)(53, 86)(54, 82)(55, 83)(56, 95)(57, 93)(58, 89)(59, 84)(60, 96)(61, 94)(62, 90)(63, 91)(64, 87)(97, 111)(98, 104)(99, 106)(100, 102)(101, 107)(103, 110)(105, 108)(109, 112) MAP : A3.554 NOTES : type II, reflexible, isomorphic to A3.495. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, (u.3 * u.4^-1)^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5^-1 * x.1 * x.2, x.4 * x.2 * x.5 * x.1, (x.3 * x.4^-1)^2, x.5 * x.2 * x.1 * x.4, x.4^-1 * x.2 * x.5 * x.1, (x.5 * x.3^-1)^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 36)(34, 43)(35, 45)(37, 40)(38, 47)(39, 41)(42, 48)(44, 46)(49, 85)(50, 81)(51, 92)(52, 88)(53, 86)(54, 82)(55, 83)(56, 95)(57, 93)(58, 89)(59, 84)(60, 96)(61, 94)(62, 90)(63, 91)(64, 87)(97, 99)(98, 103)(100, 106)(101, 108)(102, 112)(104, 105)(107, 110)(109, 111) MAP : A3.555 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.556 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.557 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2)(3, 4) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 2 ] UNIGROUP : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, x.2^2 * x.1 * x.2^-2 * x.1^-1, x.2^4 * x.1^-1 * x.2 * x.1^-1 * x.2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 33, 65, 97)(2, 34, 66, 98)(3, 35, 67, 99)(4, 36, 68, 100)(5, 37, 69, 101)(6, 38, 70, 102)(7, 39, 71, 103)(8, 40, 72, 104)(9, 41, 73, 105)(10, 42, 74, 106)(11, 43, 75, 107)(12, 44, 76, 108)(13, 45, 77, 109)(14, 46, 78, 110)(15, 47, 79, 111)(16, 48, 80, 112)(17, 49, 81, 113)(18, 50, 82, 114)(19, 51, 83, 115)(20, 52, 84, 116)(21, 53, 85, 117)(22, 54, 86, 118)(23, 55, 87, 119)(24, 56, 88, 120)(25, 57, 89, 121)(26, 58, 90, 122)(27, 59, 91, 123)(28, 60, 92, 124)(29, 61, 93, 125)(30, 62, 94, 126)(31, 63, 95, 127)(32, 64, 96, 128) L = (1, 54)(2, 55)(3, 42)(4, 61)(5, 50)(6, 41)(7, 40)(8, 52)(9, 36)(10, 59)(11, 49)(12, 53)(13, 35)(14, 34)(15, 56)(16, 51)(17, 47)(18, 63)(19, 44)(20, 64)(21, 48)(22, 60)(23, 58)(24, 43)(25, 37)(26, 46)(27, 45)(28, 62)(29, 38)(30, 33)(31, 57)(32, 39)(65, 100)(66, 116)(67, 98)(68, 106)(69, 122)(70, 114)(71, 113)(72, 102)(73, 103)(74, 111)(75, 124)(76, 127)(77, 117)(78, 121)(79, 128)(80, 123)(81, 101)(82, 107)(83, 97)(84, 108)(85, 104)(86, 112)(87, 109)(88, 99)(89, 115)(90, 118)(91, 105)(92, 119)(93, 126)(94, 120)(95, 125)(96, 110) MAP : A3.558 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.559 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.560 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.561 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.562 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 107)(34, 97)(35, 105)(36, 112)(37, 104)(38, 98)(39, 100)(40, 108)(41, 106)(42, 110)(43, 102)(44, 111)(45, 103)(46, 99)(47, 101)(48, 109)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.563 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 107)(34, 97)(35, 105)(36, 112)(37, 104)(38, 98)(39, 100)(40, 108)(41, 106)(42, 110)(43, 102)(44, 111)(45, 103)(46, 99)(47, 101)(48, 109)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.564 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 107)(34, 97)(35, 105)(36, 112)(37, 104)(38, 98)(39, 100)(40, 108)(41, 106)(42, 110)(43, 102)(44, 111)(45, 103)(46, 99)(47, 101)(48, 109)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.565 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 107)(34, 97)(35, 105)(36, 112)(37, 104)(38, 98)(39, 100)(40, 108)(41, 106)(42, 110)(43, 102)(44, 111)(45, 103)(46, 99)(47, 101)(48, 109)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.566 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.567 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.568 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.569 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.570 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.571 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.572 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.573 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.574 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.575 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.576 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.577 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.578 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.579 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.580 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.581 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.582 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.583 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.584 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 111)(34, 101)(35, 109)(36, 106)(37, 98)(38, 104)(39, 110)(40, 102)(41, 112)(42, 100)(43, 108)(44, 107)(45, 99)(46, 103)(47, 97)(48, 105)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.585 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 111)(34, 101)(35, 109)(36, 106)(37, 98)(38, 104)(39, 110)(40, 102)(41, 112)(42, 100)(43, 108)(44, 107)(45, 99)(46, 103)(47, 97)(48, 105)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.586 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.587 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 96)(50, 84)(51, 92)(52, 91)(53, 83)(54, 87)(55, 81)(56, 89)(57, 95)(58, 85)(59, 93)(60, 90)(61, 82)(62, 88)(63, 94)(64, 86) MAP : A3.588 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.589 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 91)(50, 81)(51, 89)(52, 96)(53, 88)(54, 82)(55, 84)(56, 92)(57, 90)(58, 94)(59, 86)(60, 95)(61, 87)(62, 83)(63, 85)(64, 93) MAP : A3.590 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.591 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.592 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 110)(34, 99)(35, 98)(36, 101)(37, 100)(38, 105)(39, 104)(40, 103)(41, 102)(42, 107)(43, 106)(44, 109)(45, 108)(46, 97)(47, 112)(48, 111)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.593 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 110)(34, 99)(35, 98)(36, 101)(37, 100)(38, 105)(39, 104)(40, 103)(41, 102)(42, 107)(43, 106)(44, 109)(45, 108)(46, 97)(47, 112)(48, 111)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.594 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.595 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 96)(50, 84)(51, 92)(52, 91)(53, 83)(54, 87)(55, 81)(56, 89)(57, 95)(58, 85)(59, 93)(60, 90)(61, 82)(62, 88)(63, 94)(64, 86) MAP : A3.596 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.597 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 91)(50, 81)(51, 89)(52, 96)(53, 88)(54, 82)(55, 84)(56, 92)(57, 90)(58, 94)(59, 86)(60, 95)(61, 87)(62, 83)(63, 85)(64, 93) MAP : A3.598 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.599 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.600 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 106)(34, 110)(35, 102)(36, 111)(37, 103)(38, 99)(39, 101)(40, 109)(41, 107)(42, 97)(43, 105)(44, 112)(45, 104)(46, 98)(47, 100)(48, 108)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.601 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 106)(34, 110)(35, 102)(36, 111)(37, 103)(38, 99)(39, 101)(40, 109)(41, 107)(42, 97)(43, 105)(44, 112)(45, 104)(46, 98)(47, 100)(48, 108)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.602 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.603 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 96)(50, 84)(51, 92)(52, 91)(53, 83)(54, 87)(55, 81)(56, 89)(57, 95)(58, 85)(59, 93)(60, 90)(61, 82)(62, 88)(63, 94)(64, 86) MAP : A3.604 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.605 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 91)(50, 81)(51, 89)(52, 96)(53, 88)(54, 82)(55, 84)(56, 92)(57, 90)(58, 94)(59, 86)(60, 95)(61, 87)(62, 83)(63, 85)(64, 93) MAP : A3.606 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.607 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.608 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 108)(34, 111)(35, 112)(36, 105)(37, 102)(38, 101)(39, 106)(40, 107)(41, 100)(42, 103)(43, 104)(44, 97)(45, 110)(46, 109)(47, 98)(48, 99)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.609 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^4, (x.2 * x.3)^2, (x.4^-1 * x.3)^2, (x.1 * x.2^-1)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 108)(34, 111)(35, 112)(36, 105)(37, 102)(38, 101)(39, 106)(40, 107)(41, 100)(42, 103)(43, 104)(44, 97)(45, 110)(46, 109)(47, 98)(48, 99)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.610 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81) MAP : A3.611 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 96)(50, 84)(51, 92)(52, 91)(53, 83)(54, 87)(55, 81)(56, 89)(57, 95)(58, 85)(59, 93)(60, 90)(61, 82)(62, 88)(63, 94)(64, 86) MAP : A3.612 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84) MAP : A3.613 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 91)(50, 81)(51, 89)(52, 96)(53, 88)(54, 82)(55, 84)(56, 92)(57, 90)(58, 94)(59, 86)(60, 95)(61, 87)(62, 83)(63, 85)(64, 93) MAP : A3.614 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.615 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.616 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.617 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.618 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.619 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.620 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.621 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.622 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.623 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.624 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.625 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.626 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.627 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.628 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.629 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.4^-1, x.2^-1), (x.3, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.630 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.631 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.632 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.633 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 94)(50, 83)(51, 82)(52, 85)(53, 84)(54, 89)(55, 88)(56, 87)(57, 86)(58, 91)(59, 90)(60, 93)(61, 92)(62, 81)(63, 96)(64, 95) MAP : A3.634 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.635 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.636 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.637 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 92)(50, 95)(51, 96)(52, 89)(53, 86)(54, 85)(55, 90)(56, 91)(57, 84)(58, 87)(59, 88)(60, 81)(61, 94)(62, 93)(63, 82)(64, 83) MAP : A3.638 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.639 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.640 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.641 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 95)(50, 85)(51, 93)(52, 90)(53, 82)(54, 88)(55, 94)(56, 86)(57, 96)(58, 84)(59, 92)(60, 91)(61, 83)(62, 87)(63, 81)(64, 89) MAP : A3.642 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.643 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.644 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.645 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 90)(50, 94)(51, 86)(52, 95)(53, 87)(54, 83)(55, 85)(56, 93)(57, 91)(58, 81)(59, 89)(60, 96)(61, 88)(62, 82)(63, 84)(64, 92) MAP : A3.646 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.647 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.648 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.649 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.650 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 90)(50, 94)(51, 86)(52, 95)(53, 87)(54, 83)(55, 85)(56, 93)(57, 91)(58, 81)(59, 89)(60, 96)(61, 88)(62, 82)(63, 84)(64, 92) MAP : A3.651 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.652 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.653 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.654 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 92)(50, 95)(51, 96)(52, 89)(53, 86)(54, 85)(55, 90)(56, 91)(57, 84)(58, 87)(59, 88)(60, 81)(61, 94)(62, 93)(63, 82)(64, 83) MAP : A3.655 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.656 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.657 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 95)(50, 85)(51, 93)(52, 90)(53, 82)(54, 88)(55, 94)(56, 86)(57, 96)(58, 84)(59, 92)(60, 91)(61, 83)(62, 87)(63, 81)(64, 89) MAP : A3.658 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.659 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.660 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.661 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 90)(50, 94)(51, 86)(52, 95)(53, 87)(54, 83)(55, 85)(56, 93)(57, 91)(58, 81)(59, 89)(60, 96)(61, 88)(62, 82)(63, 84)(64, 92) MAP : A3.662 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.663 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.664 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.665 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.666 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.667 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.668 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.669 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 119)(19, 120)(20, 113)(21, 126)(22, 125)(23, 114)(24, 115)(25, 124)(26, 127)(27, 128)(28, 121)(29, 118)(30, 117)(31, 122)(32, 123)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.670 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.671 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.672 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.673 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.674 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.675 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.676 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.677 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, x.4 * x.2 * x.4^-1 * x.2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 125)(18, 128)(19, 127)(20, 118)(21, 121)(22, 116)(23, 123)(24, 122)(25, 117)(26, 120)(27, 119)(28, 126)(29, 113)(30, 124)(31, 115)(32, 114)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.678 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.679 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.680 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 111)(34, 101)(35, 109)(36, 106)(37, 98)(38, 104)(39, 110)(40, 102)(41, 112)(42, 100)(43, 108)(44, 107)(45, 99)(46, 103)(47, 97)(48, 105)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.681 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 111)(34, 101)(35, 109)(36, 106)(37, 98)(38, 104)(39, 110)(40, 102)(41, 112)(42, 100)(43, 108)(44, 107)(45, 99)(46, 103)(47, 97)(48, 105)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.682 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.683 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.684 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.685 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 121)(19, 113)(20, 120)(21, 128)(22, 122)(23, 124)(24, 116)(25, 114)(26, 118)(27, 126)(28, 119)(29, 127)(30, 123)(31, 125)(32, 117)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.686 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.687 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.688 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 110)(34, 99)(35, 98)(36, 101)(37, 100)(38, 105)(39, 104)(40, 103)(41, 102)(42, 107)(43, 106)(44, 109)(45, 108)(46, 97)(47, 112)(48, 111)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.689 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 110)(34, 99)(35, 98)(36, 101)(37, 100)(38, 105)(39, 104)(40, 103)(41, 102)(42, 107)(43, 106)(44, 109)(45, 108)(46, 97)(47, 112)(48, 111)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.690 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.691 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.692 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.693 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 120)(19, 119)(20, 126)(21, 113)(22, 124)(23, 115)(24, 114)(25, 125)(26, 128)(27, 127)(28, 118)(29, 121)(30, 116)(31, 123)(32, 122)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.694 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.695 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.696 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 106)(34, 110)(35, 102)(36, 111)(37, 103)(38, 99)(39, 101)(40, 109)(41, 107)(42, 97)(43, 105)(44, 112)(45, 104)(46, 98)(47, 100)(48, 108)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.697 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 106)(34, 110)(35, 102)(36, 111)(37, 103)(38, 99)(39, 101)(40, 109)(41, 107)(42, 97)(43, 105)(44, 112)(45, 104)(46, 98)(47, 100)(48, 108)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.698 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.699 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.700 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.701 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.702 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.703 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.704 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 108)(34, 111)(35, 112)(36, 105)(37, 102)(38, 101)(39, 106)(40, 107)(41, 100)(42, 103)(43, 104)(44, 97)(45, 110)(46, 109)(47, 98)(48, 99)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.705 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3 * x.4 * x.2 * x.3 * x.4^-1 * x.2, (x.4 * x.2 * x.4)^2, x.2 * x.4 * x.2 * x.4 * x.3 * x.4^-1 * x.3 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 108)(34, 111)(35, 112)(36, 105)(37, 102)(38, 101)(39, 106)(40, 107)(41, 100)(42, 103)(43, 104)(44, 97)(45, 110)(46, 109)(47, 98)(48, 99)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.706 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.707 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.708 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.709 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 4, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, (x.4^-1, x.3^-1), (x.4^-1, x.2^-1) > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.710 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 119)(20, 123)(21, 113)(22, 117)(23, 128)(24, 116)(25, 122)(26, 126)(27, 127)(28, 115)(29, 121)(30, 125)(31, 120)(32, 124)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 84)(50, 91)(51, 93)(52, 81)(53, 88)(54, 95)(55, 89)(56, 85)(57, 87)(58, 96)(59, 82)(60, 94)(61, 83)(62, 92)(63, 86)(64, 90) MAP : A3.711 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 119)(20, 123)(21, 113)(22, 117)(23, 128)(24, 116)(25, 122)(26, 126)(27, 127)(28, 115)(29, 121)(30, 125)(31, 120)(32, 124)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.712 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 119)(20, 123)(21, 113)(22, 117)(23, 128)(24, 116)(25, 122)(26, 126)(27, 127)(28, 115)(29, 121)(30, 125)(31, 120)(32, 124)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 83)(50, 87)(51, 81)(52, 90)(53, 92)(54, 96)(55, 82)(56, 89)(57, 88)(58, 84)(59, 94)(60, 85)(61, 95)(62, 91)(63, 93)(64, 86) MAP : A3.713 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 119)(20, 123)(21, 113)(22, 117)(23, 128)(24, 116)(25, 122)(26, 126)(27, 127)(28, 115)(29, 121)(30, 125)(31, 120)(32, 124)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.714 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 119)(20, 123)(21, 113)(22, 117)(23, 128)(24, 116)(25, 122)(26, 126)(27, 127)(28, 115)(29, 121)(30, 125)(31, 120)(32, 124)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 83)(50, 87)(51, 81)(52, 90)(53, 92)(54, 96)(55, 82)(56, 89)(57, 88)(58, 84)(59, 94)(60, 85)(61, 95)(62, 91)(63, 93)(64, 86) MAP : A3.715 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 119)(20, 123)(21, 113)(22, 117)(23, 128)(24, 116)(25, 122)(26, 126)(27, 127)(28, 115)(29, 121)(30, 125)(31, 120)(32, 124)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 84)(50, 91)(51, 93)(52, 81)(53, 88)(54, 95)(55, 89)(56, 85)(57, 87)(58, 96)(59, 82)(60, 94)(61, 83)(62, 92)(63, 86)(64, 90) MAP : A3.716 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 113)(19, 124)(20, 120)(21, 118)(22, 114)(23, 115)(24, 127)(25, 125)(26, 121)(27, 116)(28, 128)(29, 126)(30, 122)(31, 123)(32, 119)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 84)(50, 91)(51, 93)(52, 81)(53, 88)(54, 95)(55, 89)(56, 85)(57, 87)(58, 96)(59, 82)(60, 94)(61, 83)(62, 92)(63, 86)(64, 90) MAP : A3.717 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 113)(19, 124)(20, 120)(21, 118)(22, 114)(23, 115)(24, 127)(25, 125)(26, 121)(27, 116)(28, 128)(29, 126)(30, 122)(31, 123)(32, 119)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.718 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 113)(19, 124)(20, 120)(21, 118)(22, 114)(23, 115)(24, 127)(25, 125)(26, 121)(27, 116)(28, 128)(29, 126)(30, 122)(31, 123)(32, 119)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 83)(50, 87)(51, 81)(52, 90)(53, 92)(54, 96)(55, 82)(56, 89)(57, 88)(58, 84)(59, 94)(60, 85)(61, 95)(62, 91)(63, 93)(64, 86) MAP : A3.719 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 113)(19, 124)(20, 120)(21, 118)(22, 114)(23, 115)(24, 127)(25, 125)(26, 121)(27, 116)(28, 128)(29, 126)(30, 122)(31, 123)(32, 119)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.720 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 113)(19, 124)(20, 120)(21, 118)(22, 114)(23, 115)(24, 127)(25, 125)(26, 121)(27, 116)(28, 128)(29, 126)(30, 122)(31, 123)(32, 119)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 83)(50, 87)(51, 81)(52, 90)(53, 92)(54, 96)(55, 82)(56, 89)(57, 88)(58, 84)(59, 94)(60, 85)(61, 95)(62, 91)(63, 93)(64, 86) MAP : A3.721 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 117)(18, 113)(19, 124)(20, 120)(21, 118)(22, 114)(23, 115)(24, 127)(25, 125)(26, 121)(27, 116)(28, 128)(29, 126)(30, 122)(31, 123)(32, 119)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 84)(50, 91)(51, 93)(52, 81)(53, 88)(54, 95)(55, 89)(56, 85)(57, 87)(58, 96)(59, 82)(60, 94)(61, 83)(62, 92)(63, 86)(64, 90) MAP : A3.722 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 82)(50, 86)(51, 87)(52, 91)(53, 81)(54, 85)(55, 96)(56, 84)(57, 90)(58, 94)(59, 95)(60, 83)(61, 89)(62, 93)(63, 88)(64, 92) MAP : A3.723 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 36)(18, 38)(19, 37)(20, 46)(21, 47)(22, 48)(23, 33)(24, 41)(25, 43)(26, 34)(27, 44)(28, 40)(29, 35)(30, 39)(31, 45)(32, 42)(49, 90)(50, 92)(51, 94)(52, 82)(53, 87)(54, 88)(55, 96)(56, 83)(57, 85)(58, 91)(59, 95)(60, 93)(61, 84)(62, 86)(63, 81)(64, 89)(97, 117)(98, 113)(99, 124)(100, 127)(101, 120)(102, 116)(103, 115)(104, 114)(105, 118)(106, 119)(107, 128)(108, 122)(109, 123)(110, 125)(111, 121)(112, 126) MAP : A3.724 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 39)(18, 42)(19, 45)(20, 33)(21, 35)(22, 34)(23, 46)(24, 44)(25, 40)(26, 48)(27, 41)(28, 43)(29, 47)(30, 36)(31, 37)(32, 38)(49, 90)(50, 92)(51, 94)(52, 82)(53, 87)(54, 88)(55, 96)(56, 83)(57, 85)(58, 91)(59, 95)(60, 93)(61, 84)(62, 86)(63, 81)(64, 89)(97, 125)(98, 126)(99, 121)(100, 115)(101, 123)(102, 119)(103, 127)(104, 128)(105, 122)(106, 116)(107, 114)(108, 118)(109, 120)(110, 117)(111, 124)(112, 113) MAP : A3.725 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 41)(18, 47)(19, 34)(20, 43)(21, 38)(22, 45)(23, 40)(24, 36)(25, 46)(26, 37)(27, 39)(28, 33)(29, 42)(30, 44)(31, 48)(32, 35)(49, 90)(50, 92)(51, 94)(52, 82)(53, 87)(54, 88)(55, 96)(56, 83)(57, 85)(58, 91)(59, 95)(60, 93)(61, 84)(62, 86)(63, 81)(64, 89)(97, 114)(98, 120)(99, 119)(100, 118)(101, 113)(102, 121)(103, 122)(104, 117)(105, 127)(106, 124)(107, 125)(108, 115)(109, 126)(110, 128)(111, 116)(112, 123) MAP : A3.726 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 82)(50, 86)(51, 87)(52, 91)(53, 81)(54, 85)(55, 96)(56, 84)(57, 90)(58, 94)(59, 95)(60, 83)(61, 89)(62, 93)(63, 88)(64, 92) MAP : A3.727 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 85)(50, 81)(51, 92)(52, 88)(53, 86)(54, 82)(55, 83)(56, 95)(57, 93)(58, 89)(59, 84)(60, 96)(61, 94)(62, 90)(63, 91)(64, 87) MAP : A3.728 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 82)(50, 86)(51, 87)(52, 91)(53, 81)(54, 85)(55, 96)(56, 84)(57, 90)(58, 94)(59, 95)(60, 83)(61, 89)(62, 93)(63, 88)(64, 92) MAP : A3.729 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 34)(18, 40)(19, 39)(20, 38)(21, 33)(22, 41)(23, 42)(24, 37)(25, 47)(26, 44)(27, 45)(28, 35)(29, 46)(30, 48)(31, 36)(32, 43)(49, 95)(50, 84)(51, 88)(52, 93)(53, 89)(54, 94)(55, 85)(56, 86)(57, 96)(58, 81)(59, 90)(60, 82)(61, 92)(62, 83)(63, 91)(64, 87)(97, 119)(98, 122)(99, 125)(100, 113)(101, 115)(102, 114)(103, 126)(104, 124)(105, 120)(106, 128)(107, 121)(108, 123)(109, 127)(110, 116)(111, 117)(112, 118) MAP : A3.730 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 37)(18, 33)(19, 44)(20, 47)(21, 40)(22, 36)(23, 35)(24, 34)(25, 38)(26, 39)(27, 48)(28, 42)(29, 43)(30, 45)(31, 41)(32, 46)(49, 95)(50, 84)(51, 88)(52, 93)(53, 89)(54, 94)(55, 85)(56, 86)(57, 96)(58, 81)(59, 90)(60, 82)(61, 92)(62, 83)(63, 91)(64, 87)(97, 124)(98, 115)(99, 128)(100, 120)(101, 122)(102, 117)(103, 123)(104, 119)(105, 113)(106, 125)(107, 116)(108, 126)(109, 118)(110, 121)(111, 114)(112, 127) MAP : A3.731 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 85)(50, 81)(51, 92)(52, 88)(53, 86)(54, 82)(55, 83)(56, 95)(57, 93)(58, 89)(59, 84)(60, 96)(61, 94)(62, 90)(63, 91)(64, 87) MAP : A3.732 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 4 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-2 * x.3^2, (x.4 * x.3^-1)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4^4, (x.4, x.2^-1), (x.4 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 82)(50, 86)(51, 87)(52, 91)(53, 81)(54, 85)(55, 96)(56, 84)(57, 90)(58, 94)(59, 95)(60, 83)(61, 89)(62, 93)(63, 88)(64, 92) MAP : A3.733 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 41)(18, 47)(19, 34)(20, 43)(21, 38)(22, 45)(23, 40)(24, 36)(25, 46)(26, 37)(27, 39)(28, 33)(29, 42)(30, 44)(31, 48)(32, 35)(49, 95)(50, 84)(51, 88)(52, 93)(53, 89)(54, 94)(55, 85)(56, 86)(57, 96)(58, 81)(59, 90)(60, 82)(61, 92)(62, 83)(63, 91)(64, 87)(97, 125)(98, 126)(99, 121)(100, 115)(101, 123)(102, 119)(103, 127)(104, 128)(105, 122)(106, 116)(107, 114)(108, 118)(109, 120)(110, 117)(111, 124)(112, 113) MAP : A3.734 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 44)(18, 35)(19, 48)(20, 40)(21, 42)(22, 37)(23, 43)(24, 39)(25, 33)(26, 45)(27, 36)(28, 46)(29, 38)(30, 41)(31, 34)(32, 47)(49, 95)(50, 84)(51, 88)(52, 93)(53, 89)(54, 94)(55, 85)(56, 86)(57, 96)(58, 81)(59, 90)(60, 82)(61, 92)(62, 83)(63, 91)(64, 87)(97, 117)(98, 113)(99, 124)(100, 127)(101, 120)(102, 116)(103, 115)(104, 114)(105, 118)(106, 119)(107, 128)(108, 122)(109, 123)(110, 125)(111, 121)(112, 126) MAP : A3.735 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-1 * x.2^2 * x.4^-1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.3, x.2^-1), x.3^-2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4 * x.3 * x.2 * x.4^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.736 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-1 * x.2^2 * x.4^-1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.3, x.2^-1), x.3^-2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4 * x.3 * x.2 * x.4^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 108)(34, 99)(35, 101)(36, 105)(37, 112)(38, 103)(39, 97)(40, 109)(41, 111)(42, 104)(43, 106)(44, 102)(45, 107)(46, 100)(47, 110)(48, 98)(49, 84)(50, 91)(51, 93)(52, 81)(53, 88)(54, 95)(55, 89)(56, 85)(57, 87)(58, 96)(59, 82)(60, 94)(61, 83)(62, 92)(63, 86)(64, 90) MAP : A3.737 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-1 * x.2^2 * x.4^-1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.3, x.2^-1), x.3^-2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4 * x.3 * x.2 * x.4^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 115)(18, 119)(19, 113)(20, 122)(21, 124)(22, 128)(23, 114)(24, 121)(25, 120)(26, 116)(27, 126)(28, 117)(29, 127)(30, 123)(31, 125)(32, 118)(33, 108)(34, 99)(35, 101)(36, 105)(37, 112)(38, 103)(39, 97)(40, 109)(41, 111)(42, 104)(43, 106)(44, 102)(45, 107)(46, 100)(47, 110)(48, 98)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.738 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-1 * x.2^2 * x.4^-1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.3, x.2^-1), x.3^-2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4 * x.3 * x.2 * x.4^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 83)(50, 87)(51, 81)(52, 90)(53, 92)(54, 96)(55, 82)(56, 89)(57, 88)(58, 84)(59, 94)(60, 85)(61, 95)(62, 91)(63, 93)(64, 86) MAP : A3.739 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-1 * x.2^2 * x.4^-1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.3, x.2^-1), x.3^-2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4 * x.3 * x.2 * x.4^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.740 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-1 * x.2^2 * x.4^-1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.3, x.2^-1), x.3^-2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4 * x.3 * x.2 * x.4^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 107)(34, 111)(35, 105)(36, 98)(37, 100)(38, 104)(39, 106)(40, 97)(41, 112)(42, 108)(43, 102)(44, 109)(45, 103)(46, 99)(47, 101)(48, 110)(49, 83)(50, 87)(51, 81)(52, 90)(53, 92)(54, 96)(55, 82)(56, 89)(57, 88)(58, 84)(59, 94)(60, 85)(61, 95)(62, 91)(63, 93)(64, 86) MAP : A3.741 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-1 * x.2^2 * x.4^-1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.3, x.2^-1), x.3^-2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4 * x.3 * x.2 * x.4^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 116)(18, 123)(19, 125)(20, 113)(21, 120)(22, 127)(23, 121)(24, 117)(25, 119)(26, 128)(27, 114)(28, 126)(29, 115)(30, 124)(31, 118)(32, 122)(33, 107)(34, 111)(35, 105)(36, 98)(37, 100)(38, 104)(39, 106)(40, 97)(41, 112)(42, 108)(43, 102)(44, 109)(45, 103)(46, 99)(47, 101)(48, 110)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.742 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-1 * x.2^2 * x.4^-1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.3, x.2^-1), x.3^-2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4 * x.3 * x.2 * x.4^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 83)(50, 87)(51, 81)(52, 90)(53, 92)(54, 96)(55, 82)(56, 89)(57, 88)(58, 84)(59, 94)(60, 85)(61, 95)(62, 91)(63, 93)(64, 86) MAP : A3.743 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-1 * x.2^2 * x.4^-1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.3, x.2^-1), x.3^-2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4 * x.3 * x.2 * x.4^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 84)(50, 91)(51, 93)(52, 81)(53, 88)(54, 95)(55, 89)(56, 85)(57, 87)(58, 96)(59, 82)(60, 94)(61, 83)(62, 92)(63, 86)(64, 90) MAP : A3.744 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.4^-1 * x.2^2 * x.4^-1, x.4^4, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.3^4, (x.3, x.2^-1), x.3^-2 * x.4 * x.2^-1 * x.4^-1 * x.2^-1, x.4 * x.3 * x.2 * x.4^-1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 109)(34, 105)(35, 100)(36, 112)(37, 110)(38, 106)(39, 107)(40, 103)(41, 101)(42, 97)(43, 108)(44, 104)(45, 102)(46, 98)(47, 99)(48, 111)(49, 83)(50, 87)(51, 81)(52, 90)(53, 92)(54, 96)(55, 82)(56, 89)(57, 88)(58, 84)(59, 94)(60, 85)(61, 95)(62, 91)(63, 93)(64, 86) MAP : A3.745 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 35)(18, 39)(19, 43)(20, 37)(21, 44)(22, 33)(23, 45)(24, 42)(25, 34)(26, 46)(27, 38)(28, 48)(29, 41)(30, 47)(31, 40)(32, 36)(49, 96)(50, 91)(51, 84)(52, 90)(53, 94)(54, 92)(55, 86)(56, 93)(57, 83)(58, 89)(59, 85)(60, 95)(61, 81)(62, 82)(63, 87)(64, 88)(97, 119)(98, 122)(99, 125)(100, 113)(101, 115)(102, 114)(103, 126)(104, 124)(105, 120)(106, 128)(107, 121)(108, 123)(109, 127)(110, 116)(111, 117)(112, 118) MAP : A3.746 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 38)(18, 41)(19, 33)(20, 48)(21, 36)(22, 43)(23, 34)(24, 47)(25, 45)(26, 40)(27, 35)(28, 37)(29, 39)(30, 42)(31, 46)(32, 44)(49, 96)(50, 91)(51, 84)(52, 90)(53, 94)(54, 92)(55, 86)(56, 93)(57, 83)(58, 89)(59, 85)(60, 95)(61, 81)(62, 82)(63, 87)(64, 88)(97, 121)(98, 127)(99, 114)(100, 123)(101, 118)(102, 125)(103, 120)(104, 116)(105, 126)(106, 117)(107, 119)(108, 113)(109, 122)(110, 124)(111, 128)(112, 115) MAP : A3.747 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 36)(18, 38)(19, 37)(20, 46)(21, 47)(22, 48)(23, 33)(24, 41)(25, 43)(26, 34)(27, 44)(28, 40)(29, 35)(30, 39)(31, 45)(32, 42)(49, 96)(50, 91)(51, 84)(52, 90)(53, 94)(54, 92)(55, 86)(56, 93)(57, 83)(58, 89)(59, 85)(60, 95)(61, 81)(62, 82)(63, 87)(64, 88)(97, 127)(98, 116)(99, 120)(100, 125)(101, 121)(102, 126)(103, 117)(104, 118)(105, 128)(106, 113)(107, 122)(108, 114)(109, 124)(110, 115)(111, 123)(112, 119) MAP : A3.748 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 39)(18, 42)(19, 45)(20, 33)(21, 35)(22, 34)(23, 46)(24, 44)(25, 40)(26, 48)(27, 41)(28, 43)(29, 47)(30, 36)(31, 37)(32, 38)(49, 96)(50, 91)(51, 84)(52, 90)(53, 94)(54, 92)(55, 86)(56, 93)(57, 83)(58, 89)(59, 85)(60, 95)(61, 81)(62, 82)(63, 87)(64, 88)(97, 115)(98, 119)(99, 123)(100, 117)(101, 124)(102, 113)(103, 125)(104, 122)(105, 114)(106, 126)(107, 118)(108, 128)(109, 121)(110, 127)(111, 120)(112, 116) MAP : A3.749 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 41)(18, 47)(19, 34)(20, 43)(21, 38)(22, 45)(23, 40)(24, 36)(25, 46)(26, 37)(27, 39)(28, 33)(29, 42)(30, 44)(31, 48)(32, 35)(49, 96)(50, 91)(51, 84)(52, 90)(53, 94)(54, 92)(55, 86)(56, 93)(57, 83)(58, 89)(59, 85)(60, 95)(61, 81)(62, 82)(63, 87)(64, 88)(97, 118)(98, 121)(99, 113)(100, 128)(101, 116)(102, 123)(103, 114)(104, 127)(105, 125)(106, 120)(107, 115)(108, 117)(109, 119)(110, 122)(111, 126)(112, 124) MAP : A3.750 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 44)(18, 35)(19, 48)(20, 40)(21, 42)(22, 37)(23, 43)(24, 39)(25, 33)(26, 45)(27, 36)(28, 46)(29, 38)(30, 41)(31, 34)(32, 47)(49, 96)(50, 91)(51, 84)(52, 90)(53, 94)(54, 92)(55, 86)(56, 93)(57, 83)(58, 89)(59, 85)(60, 95)(61, 81)(62, 82)(63, 87)(64, 88)(97, 122)(98, 124)(99, 126)(100, 114)(101, 119)(102, 120)(103, 128)(104, 115)(105, 117)(106, 123)(107, 127)(108, 125)(109, 116)(110, 118)(111, 113)(112, 121) MAP : A3.751 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 42)(18, 44)(19, 46)(20, 34)(21, 39)(22, 40)(23, 48)(24, 35)(25, 37)(26, 43)(27, 47)(28, 45)(29, 36)(30, 38)(31, 33)(32, 41)(49, 96)(50, 91)(51, 84)(52, 90)(53, 94)(54, 92)(55, 86)(56, 93)(57, 83)(58, 89)(59, 85)(60, 95)(61, 81)(62, 82)(63, 87)(64, 88)(97, 124)(98, 115)(99, 128)(100, 120)(101, 122)(102, 117)(103, 123)(104, 119)(105, 113)(106, 125)(107, 116)(108, 126)(109, 118)(110, 121)(111, 114)(112, 127) MAP : A3.752 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 47)(18, 36)(19, 40)(20, 45)(21, 41)(22, 46)(23, 37)(24, 38)(25, 48)(26, 33)(27, 42)(28, 34)(29, 44)(30, 35)(31, 43)(32, 39)(49, 96)(50, 91)(51, 84)(52, 90)(53, 94)(54, 92)(55, 86)(56, 93)(57, 83)(58, 89)(59, 85)(60, 95)(61, 81)(62, 82)(63, 87)(64, 88)(97, 116)(98, 118)(99, 117)(100, 126)(101, 127)(102, 128)(103, 113)(104, 121)(105, 123)(106, 114)(107, 124)(108, 120)(109, 115)(110, 119)(111, 125)(112, 122) MAP : A3.753 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.4^-1 * x.2^-1 * x.3^-1, x.2 * x.3^-1 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 34)(18, 40)(19, 39)(20, 35)(21, 33)(22, 41)(23, 42)(24, 37)(25, 46)(26, 36)(27, 47)(28, 38)(29, 43)(30, 44)(31, 48)(32, 45)(49, 83)(50, 89)(51, 91)(52, 85)(53, 92)(54, 81)(55, 82)(56, 90)(57, 95)(58, 96)(59, 86)(60, 93)(61, 84)(62, 88)(63, 87)(64, 94)(97, 124)(98, 115)(99, 117)(100, 128)(101, 122)(102, 125)(103, 123)(104, 121)(105, 113)(106, 114)(107, 116)(108, 120)(109, 126)(110, 127)(111, 118)(112, 119) MAP : A3.754 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.4^-1 * x.2^-1 * x.3^-1, x.2 * x.3^-1 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 37)(18, 33)(19, 36)(20, 42)(21, 40)(22, 44)(23, 35)(24, 34)(25, 38)(26, 39)(27, 45)(28, 46)(29, 48)(30, 41)(31, 43)(32, 47)(49, 83)(50, 89)(51, 91)(52, 85)(53, 92)(54, 81)(55, 82)(56, 90)(57, 95)(58, 96)(59, 86)(60, 93)(61, 84)(62, 88)(63, 87)(64, 94)(97, 121)(98, 122)(99, 114)(100, 123)(101, 115)(102, 127)(103, 128)(104, 124)(105, 120)(106, 117)(107, 119)(108, 113)(109, 118)(110, 125)(111, 126)(112, 116) MAP : A3.755 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.4^-1 * x.2^-1 * x.3^-1, x.2 * x.3^-1 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 36)(18, 38)(19, 45)(20, 40)(21, 46)(22, 37)(23, 33)(24, 39)(25, 43)(26, 47)(27, 44)(28, 48)(29, 42)(30, 34)(31, 35)(32, 41)(49, 83)(50, 89)(51, 91)(52, 85)(53, 92)(54, 81)(55, 82)(56, 90)(57, 95)(58, 96)(59, 86)(60, 93)(61, 84)(62, 88)(63, 87)(64, 94)(97, 114)(98, 120)(99, 119)(100, 115)(101, 113)(102, 121)(103, 122)(104, 117)(105, 126)(106, 116)(107, 127)(108, 118)(109, 123)(110, 124)(111, 128)(112, 125) MAP : A3.756 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.4^-1 * x.2^-1 * x.3^-1, x.2 * x.3^-1 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 39)(18, 46)(19, 47)(20, 33)(21, 38)(22, 34)(23, 40)(24, 36)(25, 48)(26, 45)(27, 41)(28, 43)(29, 35)(30, 37)(31, 42)(32, 44)(49, 83)(50, 89)(51, 91)(52, 85)(53, 92)(54, 81)(55, 82)(56, 90)(57, 95)(58, 96)(59, 86)(60, 93)(61, 84)(62, 88)(63, 87)(64, 94)(97, 117)(98, 113)(99, 116)(100, 122)(101, 120)(102, 124)(103, 115)(104, 114)(105, 118)(106, 119)(107, 125)(108, 126)(109, 128)(110, 121)(111, 123)(112, 127) MAP : A3.757 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.4^-1 * x.2^-1 * x.3^-1, x.2 * x.3^-1 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 34)(18, 40)(19, 39)(20, 35)(21, 33)(22, 41)(23, 42)(24, 37)(25, 46)(26, 36)(27, 47)(28, 38)(29, 43)(30, 44)(31, 48)(32, 45)(49, 90)(50, 92)(51, 96)(52, 82)(53, 89)(54, 88)(55, 85)(56, 83)(57, 93)(58, 91)(59, 94)(60, 95)(61, 87)(62, 81)(63, 84)(64, 86)(97, 121)(98, 122)(99, 114)(100, 123)(101, 115)(102, 127)(103, 128)(104, 124)(105, 120)(106, 117)(107, 119)(108, 113)(109, 118)(110, 125)(111, 126)(112, 116) MAP : A3.758 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.4^-1 * x.2^-1 * x.3^-1, x.2 * x.3^-1 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 37)(18, 33)(19, 36)(20, 42)(21, 40)(22, 44)(23, 35)(24, 34)(25, 38)(26, 39)(27, 45)(28, 46)(29, 48)(30, 41)(31, 43)(32, 47)(49, 90)(50, 92)(51, 96)(52, 82)(53, 89)(54, 88)(55, 85)(56, 83)(57, 93)(58, 91)(59, 94)(60, 95)(61, 87)(62, 81)(63, 84)(64, 86)(97, 124)(98, 115)(99, 117)(100, 128)(101, 122)(102, 125)(103, 123)(104, 121)(105, 113)(106, 114)(107, 116)(108, 120)(109, 126)(110, 127)(111, 118)(112, 119) MAP : A3.759 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.4^-1 * x.2^-1 * x.3^-1, x.2 * x.3^-1 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 36)(18, 38)(19, 45)(20, 40)(21, 46)(22, 37)(23, 33)(24, 39)(25, 43)(26, 47)(27, 44)(28, 48)(29, 42)(30, 34)(31, 35)(32, 41)(49, 90)(50, 92)(51, 96)(52, 82)(53, 89)(54, 88)(55, 85)(56, 83)(57, 93)(58, 91)(59, 94)(60, 95)(61, 87)(62, 81)(63, 84)(64, 86)(97, 117)(98, 113)(99, 116)(100, 122)(101, 120)(102, 124)(103, 115)(104, 114)(105, 118)(106, 119)(107, 125)(108, 126)(109, 128)(110, 121)(111, 123)(112, 127) MAP : A3.760 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 4> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.4^-1 * x.2^-1 * x.3^-1, x.2 * x.3^-1 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 39)(18, 46)(19, 47)(20, 33)(21, 38)(22, 34)(23, 40)(24, 36)(25, 48)(26, 45)(27, 41)(28, 43)(29, 35)(30, 37)(31, 42)(32, 44)(49, 90)(50, 92)(51, 96)(52, 82)(53, 89)(54, 88)(55, 85)(56, 83)(57, 93)(58, 91)(59, 94)(60, 95)(61, 87)(62, 81)(63, 84)(64, 86)(97, 114)(98, 120)(99, 119)(100, 115)(101, 113)(102, 121)(103, 122)(104, 117)(105, 126)(106, 116)(107, 127)(108, 118)(109, 123)(110, 124)(111, 128)(112, 125) MAP : A3.761 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 34)(18, 39)(19, 36)(20, 38)(21, 33)(22, 40)(23, 43)(24, 44)(25, 37)(26, 35)(27, 47)(28, 48)(29, 42)(30, 41)(31, 46)(32, 45)(49, 84)(50, 86)(51, 85)(52, 81)(53, 83)(54, 82)(55, 88)(56, 87)(57, 90)(58, 89)(59, 92)(60, 91)(61, 94)(62, 93)(63, 96)(64, 95)(97, 115)(98, 116)(99, 121)(100, 117)(101, 122)(102, 113)(103, 118)(104, 114)(105, 125)(106, 126)(107, 120)(108, 119)(109, 127)(110, 128)(111, 124)(112, 123) MAP : A3.762 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 43)(18, 47)(19, 40)(20, 44)(21, 39)(22, 48)(23, 46)(24, 45)(25, 34)(26, 38)(27, 41)(28, 42)(29, 36)(30, 33)(31, 37)(32, 35)(49, 84)(50, 86)(51, 85)(52, 81)(53, 83)(54, 82)(55, 88)(56, 87)(57, 90)(58, 89)(59, 92)(60, 91)(61, 94)(62, 93)(63, 96)(64, 95)(97, 125)(98, 122)(99, 127)(100, 126)(101, 128)(102, 121)(103, 115)(104, 117)(105, 124)(106, 123)(107, 116)(108, 113)(109, 119)(110, 120)(111, 118)(112, 114) MAP : A3.763 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 46)(18, 41)(19, 48)(20, 45)(21, 47)(22, 42)(23, 37)(24, 35)(25, 43)(26, 44)(27, 33)(28, 36)(29, 40)(30, 39)(31, 34)(32, 38)(49, 84)(50, 86)(51, 85)(52, 81)(53, 83)(54, 82)(55, 88)(56, 87)(57, 90)(58, 89)(59, 92)(60, 91)(61, 94)(62, 93)(63, 96)(64, 95)(97, 124)(98, 128)(99, 119)(100, 123)(101, 120)(102, 127)(103, 125)(104, 126)(105, 118)(106, 114)(107, 122)(108, 121)(109, 113)(110, 116)(111, 115)(112, 117) MAP : A3.764 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 37)(18, 33)(19, 42)(20, 35)(21, 41)(22, 36)(23, 34)(24, 38)(25, 46)(26, 45)(27, 39)(28, 40)(29, 48)(30, 47)(31, 43)(32, 44)(49, 84)(50, 86)(51, 85)(52, 81)(53, 83)(54, 82)(55, 88)(56, 87)(57, 90)(58, 89)(59, 92)(60, 91)(61, 94)(62, 93)(63, 96)(64, 95)(97, 118)(98, 120)(99, 113)(100, 114)(101, 116)(102, 119)(103, 124)(104, 123)(105, 115)(106, 117)(107, 128)(108, 127)(109, 121)(110, 122)(111, 125)(112, 126) MAP : A3.765 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 35)(18, 36)(19, 41)(20, 37)(21, 42)(22, 33)(23, 38)(24, 34)(25, 45)(26, 46)(27, 40)(28, 39)(29, 47)(30, 48)(31, 44)(32, 43)(49, 84)(50, 86)(51, 85)(52, 81)(53, 83)(54, 82)(55, 88)(56, 87)(57, 90)(58, 89)(59, 92)(60, 91)(61, 94)(62, 93)(63, 96)(64, 95)(97, 114)(98, 119)(99, 116)(100, 118)(101, 113)(102, 120)(103, 123)(104, 124)(105, 117)(106, 115)(107, 127)(108, 128)(109, 122)(110, 121)(111, 126)(112, 125) MAP : A3.766 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 45)(18, 42)(19, 47)(20, 46)(21, 48)(22, 41)(23, 35)(24, 37)(25, 44)(26, 43)(27, 36)(28, 33)(29, 39)(30, 40)(31, 38)(32, 34)(49, 84)(50, 86)(51, 85)(52, 81)(53, 83)(54, 82)(55, 88)(56, 87)(57, 90)(58, 89)(59, 92)(60, 91)(61, 94)(62, 93)(63, 96)(64, 95)(97, 123)(98, 127)(99, 120)(100, 124)(101, 119)(102, 128)(103, 126)(104, 125)(105, 114)(106, 118)(107, 121)(108, 122)(109, 116)(110, 113)(111, 117)(112, 115) MAP : A3.767 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 44)(18, 48)(19, 39)(20, 43)(21, 40)(22, 47)(23, 45)(24, 46)(25, 38)(26, 34)(27, 42)(28, 41)(29, 33)(30, 36)(31, 35)(32, 37)(49, 84)(50, 86)(51, 85)(52, 81)(53, 83)(54, 82)(55, 88)(56, 87)(57, 90)(58, 89)(59, 92)(60, 91)(61, 94)(62, 93)(63, 96)(64, 95)(97, 126)(98, 121)(99, 128)(100, 125)(101, 127)(102, 122)(103, 117)(104, 115)(105, 123)(106, 124)(107, 113)(108, 116)(109, 120)(110, 119)(111, 114)(112, 118) MAP : A3.768 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 38)(18, 40)(19, 33)(20, 34)(21, 36)(22, 39)(23, 44)(24, 43)(25, 35)(26, 37)(27, 48)(28, 47)(29, 41)(30, 42)(31, 45)(32, 46)(49, 84)(50, 86)(51, 85)(52, 81)(53, 83)(54, 82)(55, 88)(56, 87)(57, 90)(58, 89)(59, 92)(60, 91)(61, 94)(62, 93)(63, 96)(64, 95)(97, 117)(98, 113)(99, 122)(100, 115)(101, 121)(102, 116)(103, 114)(104, 118)(105, 126)(106, 125)(107, 119)(108, 120)(109, 128)(110, 127)(111, 123)(112, 124) MAP : A3.769 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.770 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 94)(50, 83)(51, 82)(52, 85)(53, 84)(54, 89)(55, 88)(56, 87)(57, 86)(58, 91)(59, 90)(60, 93)(61, 92)(62, 81)(63, 96)(64, 95) MAP : A3.771 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.772 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.773 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.774 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2 * x.3 * x.2 * x.3 * x.2 * x.4 * x.2 * x.4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 120)(18, 124)(19, 116)(20, 115)(21, 123)(22, 127)(23, 121)(24, 113)(25, 119)(26, 125)(27, 117)(28, 114)(29, 122)(30, 128)(31, 118)(32, 126)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 92)(50, 95)(51, 96)(52, 89)(53, 86)(54, 85)(55, 90)(56, 91)(57, 84)(58, 87)(59, 88)(60, 81)(61, 94)(62, 93)(63, 82)(64, 83) MAP : A3.775 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.776 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 4, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.2 * u.3^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.777 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 6> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2 * x.4 * x.3^-1, x.2^2 * x.4^-2, (x.3 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.4^-1, x.4^5 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 34)(18, 37)(19, 41)(20, 33)(21, 43)(22, 45)(23, 35)(24, 42)(25, 38)(26, 39)(27, 48)(28, 40)(29, 44)(30, 47)(31, 36)(32, 46)(49, 88)(50, 86)(51, 84)(52, 83)(53, 87)(54, 82)(55, 85)(56, 81)(57, 96)(58, 94)(59, 92)(60, 91)(61, 95)(62, 90)(63, 93)(64, 89)(97, 124)(98, 121)(99, 127)(100, 119)(101, 122)(102, 113)(103, 114)(104, 116)(105, 123)(106, 128)(107, 125)(108, 117)(109, 126)(110, 120)(111, 118)(112, 115) MAP : A3.778 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 35)(18, 39)(19, 43)(20, 37)(21, 44)(22, 33)(23, 45)(24, 42)(25, 34)(26, 46)(27, 38)(28, 48)(29, 41)(30, 47)(31, 40)(32, 36)(49, 82)(50, 88)(51, 87)(52, 86)(53, 81)(54, 89)(55, 90)(56, 85)(57, 95)(58, 92)(59, 93)(60, 83)(61, 94)(62, 96)(63, 84)(64, 91)(97, 116)(98, 118)(99, 117)(100, 126)(101, 127)(102, 128)(103, 113)(104, 121)(105, 123)(106, 114)(107, 124)(108, 120)(109, 115)(110, 119)(111, 125)(112, 122) MAP : A3.779 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 38)(18, 41)(19, 33)(20, 48)(21, 36)(22, 43)(23, 34)(24, 47)(25, 45)(26, 40)(27, 35)(28, 37)(29, 39)(30, 42)(31, 46)(32, 44)(49, 82)(50, 88)(51, 87)(52, 86)(53, 81)(54, 89)(55, 90)(56, 85)(57, 95)(58, 92)(59, 93)(60, 83)(61, 94)(62, 96)(63, 84)(64, 91)(97, 124)(98, 115)(99, 128)(100, 120)(101, 122)(102, 117)(103, 123)(104, 119)(105, 113)(106, 125)(107, 116)(108, 126)(109, 118)(110, 121)(111, 114)(112, 127) MAP : A3.780 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 36)(18, 38)(19, 37)(20, 46)(21, 47)(22, 48)(23, 33)(24, 41)(25, 43)(26, 34)(27, 44)(28, 40)(29, 35)(30, 39)(31, 45)(32, 42)(49, 82)(50, 88)(51, 87)(52, 86)(53, 81)(54, 89)(55, 90)(56, 85)(57, 95)(58, 92)(59, 93)(60, 83)(61, 94)(62, 96)(63, 84)(64, 91)(97, 115)(98, 119)(99, 123)(100, 117)(101, 124)(102, 113)(103, 125)(104, 122)(105, 114)(106, 126)(107, 118)(108, 128)(109, 121)(110, 127)(111, 120)(112, 116) MAP : A3.781 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 39)(18, 42)(19, 45)(20, 33)(21, 35)(22, 34)(23, 46)(24, 44)(25, 40)(26, 48)(27, 41)(28, 43)(29, 47)(30, 36)(31, 37)(32, 38)(49, 82)(50, 88)(51, 87)(52, 86)(53, 81)(54, 89)(55, 90)(56, 85)(57, 95)(58, 92)(59, 93)(60, 83)(61, 94)(62, 96)(63, 84)(64, 91)(97, 127)(98, 116)(99, 120)(100, 125)(101, 121)(102, 126)(103, 117)(104, 118)(105, 128)(106, 113)(107, 122)(108, 114)(109, 124)(110, 115)(111, 123)(112, 119) MAP : A3.782 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 41)(18, 47)(19, 34)(20, 43)(21, 38)(22, 45)(23, 40)(24, 36)(25, 46)(26, 37)(27, 39)(28, 33)(29, 42)(30, 44)(31, 48)(32, 35)(49, 82)(50, 88)(51, 87)(52, 86)(53, 81)(54, 89)(55, 90)(56, 85)(57, 95)(58, 92)(59, 93)(60, 83)(61, 94)(62, 96)(63, 84)(64, 91)(97, 122)(98, 124)(99, 126)(100, 114)(101, 119)(102, 120)(103, 128)(104, 115)(105, 117)(106, 123)(107, 127)(108, 125)(109, 116)(110, 118)(111, 113)(112, 121) MAP : A3.783 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 44)(18, 35)(19, 48)(20, 40)(21, 42)(22, 37)(23, 43)(24, 39)(25, 33)(26, 45)(27, 36)(28, 46)(29, 38)(30, 41)(31, 34)(32, 47)(49, 82)(50, 88)(51, 87)(52, 86)(53, 81)(54, 89)(55, 90)(56, 85)(57, 95)(58, 92)(59, 93)(60, 83)(61, 94)(62, 96)(63, 84)(64, 91)(97, 118)(98, 121)(99, 113)(100, 128)(101, 116)(102, 123)(103, 114)(104, 127)(105, 125)(106, 120)(107, 115)(108, 117)(109, 119)(110, 122)(111, 126)(112, 124) MAP : A3.784 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 42)(18, 44)(19, 46)(20, 34)(21, 39)(22, 40)(23, 48)(24, 35)(25, 37)(26, 43)(27, 47)(28, 45)(29, 36)(30, 38)(31, 33)(32, 41)(49, 82)(50, 88)(51, 87)(52, 86)(53, 81)(54, 89)(55, 90)(56, 85)(57, 95)(58, 92)(59, 93)(60, 83)(61, 94)(62, 96)(63, 84)(64, 91)(97, 121)(98, 127)(99, 114)(100, 123)(101, 118)(102, 125)(103, 120)(104, 116)(105, 126)(106, 117)(107, 119)(108, 113)(109, 122)(110, 124)(111, 128)(112, 115) MAP : A3.785 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 47)(18, 36)(19, 40)(20, 45)(21, 41)(22, 46)(23, 37)(24, 38)(25, 48)(26, 33)(27, 42)(28, 34)(29, 44)(30, 35)(31, 43)(32, 39)(49, 82)(50, 88)(51, 87)(52, 86)(53, 81)(54, 89)(55, 90)(56, 85)(57, 95)(58, 92)(59, 93)(60, 83)(61, 94)(62, 96)(63, 84)(64, 91)(97, 119)(98, 122)(99, 125)(100, 113)(101, 115)(102, 114)(103, 126)(104, 124)(105, 120)(106, 128)(107, 121)(108, 123)(109, 127)(110, 116)(111, 117)(112, 118) MAP : A3.786 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 35)(18, 39)(19, 43)(20, 37)(21, 44)(22, 33)(23, 45)(24, 42)(25, 34)(26, 46)(27, 38)(28, 48)(29, 41)(30, 47)(31, 40)(32, 36)(49, 85)(50, 81)(51, 92)(52, 95)(53, 88)(54, 84)(55, 83)(56, 82)(57, 86)(58, 87)(59, 96)(60, 90)(61, 91)(62, 93)(63, 89)(64, 94)(97, 121)(98, 127)(99, 114)(100, 123)(101, 118)(102, 125)(103, 120)(104, 116)(105, 126)(106, 117)(107, 119)(108, 113)(109, 122)(110, 124)(111, 128)(112, 115) MAP : A3.787 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 38)(18, 41)(19, 33)(20, 48)(21, 36)(22, 43)(23, 34)(24, 47)(25, 45)(26, 40)(27, 35)(28, 37)(29, 39)(30, 42)(31, 46)(32, 44)(49, 85)(50, 81)(51, 92)(52, 95)(53, 88)(54, 84)(55, 83)(56, 82)(57, 86)(58, 87)(59, 96)(60, 90)(61, 91)(62, 93)(63, 89)(64, 94)(97, 119)(98, 122)(99, 125)(100, 113)(101, 115)(102, 114)(103, 126)(104, 124)(105, 120)(106, 128)(107, 121)(108, 123)(109, 127)(110, 116)(111, 117)(112, 118) MAP : A3.788 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 36)(18, 38)(19, 37)(20, 46)(21, 47)(22, 48)(23, 33)(24, 41)(25, 43)(26, 34)(27, 44)(28, 40)(29, 35)(30, 39)(31, 45)(32, 42)(49, 85)(50, 81)(51, 92)(52, 95)(53, 88)(54, 84)(55, 83)(56, 82)(57, 86)(58, 87)(59, 96)(60, 90)(61, 91)(62, 93)(63, 89)(64, 94)(97, 122)(98, 124)(99, 126)(100, 114)(101, 119)(102, 120)(103, 128)(104, 115)(105, 117)(106, 123)(107, 127)(108, 125)(109, 116)(110, 118)(111, 113)(112, 121) MAP : A3.789 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 39)(18, 42)(19, 45)(20, 33)(21, 35)(22, 34)(23, 46)(24, 44)(25, 40)(26, 48)(27, 41)(28, 43)(29, 47)(30, 36)(31, 37)(32, 38)(49, 85)(50, 81)(51, 92)(52, 95)(53, 88)(54, 84)(55, 83)(56, 82)(57, 86)(58, 87)(59, 96)(60, 90)(61, 91)(62, 93)(63, 89)(64, 94)(97, 118)(98, 121)(99, 113)(100, 128)(101, 116)(102, 123)(103, 114)(104, 127)(105, 125)(106, 120)(107, 115)(108, 117)(109, 119)(110, 122)(111, 126)(112, 124) MAP : A3.790 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 41)(18, 47)(19, 34)(20, 43)(21, 38)(22, 45)(23, 40)(24, 36)(25, 46)(26, 37)(27, 39)(28, 33)(29, 42)(30, 44)(31, 48)(32, 35)(49, 85)(50, 81)(51, 92)(52, 95)(53, 88)(54, 84)(55, 83)(56, 82)(57, 86)(58, 87)(59, 96)(60, 90)(61, 91)(62, 93)(63, 89)(64, 94)(97, 115)(98, 119)(99, 123)(100, 117)(101, 124)(102, 113)(103, 125)(104, 122)(105, 114)(106, 126)(107, 118)(108, 128)(109, 121)(110, 127)(111, 120)(112, 116) MAP : A3.791 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 44)(18, 35)(19, 48)(20, 40)(21, 42)(22, 37)(23, 43)(24, 39)(25, 33)(26, 45)(27, 36)(28, 46)(29, 38)(30, 41)(31, 34)(32, 47)(49, 85)(50, 81)(51, 92)(52, 95)(53, 88)(54, 84)(55, 83)(56, 82)(57, 86)(58, 87)(59, 96)(60, 90)(61, 91)(62, 93)(63, 89)(64, 94)(97, 127)(98, 116)(99, 120)(100, 125)(101, 121)(102, 126)(103, 117)(104, 118)(105, 128)(106, 113)(107, 122)(108, 114)(109, 124)(110, 115)(111, 123)(112, 119) MAP : A3.792 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 42)(18, 44)(19, 46)(20, 34)(21, 39)(22, 40)(23, 48)(24, 35)(25, 37)(26, 43)(27, 47)(28, 45)(29, 36)(30, 38)(31, 33)(32, 41)(49, 85)(50, 81)(51, 92)(52, 95)(53, 88)(54, 84)(55, 83)(56, 82)(57, 86)(58, 87)(59, 96)(60, 90)(61, 91)(62, 93)(63, 89)(64, 94)(97, 116)(98, 118)(99, 117)(100, 126)(101, 127)(102, 128)(103, 113)(104, 121)(105, 123)(106, 114)(107, 124)(108, 120)(109, 115)(110, 119)(111, 125)(112, 122) MAP : A3.793 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 47)(18, 36)(19, 40)(20, 45)(21, 41)(22, 46)(23, 37)(24, 38)(25, 48)(26, 33)(27, 42)(28, 34)(29, 44)(30, 35)(31, 43)(32, 39)(49, 85)(50, 81)(51, 92)(52, 95)(53, 88)(54, 84)(55, 83)(56, 82)(57, 86)(58, 87)(59, 96)(60, 90)(61, 91)(62, 93)(63, 89)(64, 94)(97, 124)(98, 115)(99, 128)(100, 120)(101, 122)(102, 117)(103, 123)(104, 119)(105, 113)(106, 125)(107, 116)(108, 126)(109, 118)(110, 121)(111, 114)(112, 127) MAP : A3.794 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 34)(18, 40)(19, 39)(20, 38)(21, 33)(22, 41)(23, 42)(24, 37)(25, 47)(26, 44)(27, 45)(28, 35)(29, 46)(30, 48)(31, 36)(32, 43)(49, 83)(50, 87)(51, 91)(52, 85)(53, 92)(54, 81)(55, 93)(56, 90)(57, 82)(58, 94)(59, 86)(60, 96)(61, 89)(62, 95)(63, 88)(64, 84)(97, 116)(98, 118)(99, 117)(100, 126)(101, 127)(102, 128)(103, 113)(104, 121)(105, 123)(106, 114)(107, 124)(108, 120)(109, 115)(110, 119)(111, 125)(112, 122) MAP : A3.795 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 37)(18, 33)(19, 44)(20, 47)(21, 40)(22, 36)(23, 35)(24, 34)(25, 38)(26, 39)(27, 48)(28, 42)(29, 43)(30, 45)(31, 41)(32, 46)(49, 83)(50, 87)(51, 91)(52, 85)(53, 92)(54, 81)(55, 93)(56, 90)(57, 82)(58, 94)(59, 86)(60, 96)(61, 89)(62, 95)(63, 88)(64, 84)(97, 121)(98, 127)(99, 114)(100, 123)(101, 118)(102, 125)(103, 120)(104, 116)(105, 126)(106, 117)(107, 119)(108, 113)(109, 122)(110, 124)(111, 128)(112, 115) MAP : A3.796 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 36)(18, 38)(19, 37)(20, 46)(21, 47)(22, 48)(23, 33)(24, 41)(25, 43)(26, 34)(27, 44)(28, 40)(29, 35)(30, 39)(31, 45)(32, 42)(49, 83)(50, 87)(51, 91)(52, 85)(53, 92)(54, 81)(55, 93)(56, 90)(57, 82)(58, 94)(59, 86)(60, 96)(61, 89)(62, 95)(63, 88)(64, 84)(97, 114)(98, 120)(99, 119)(100, 118)(101, 113)(102, 121)(103, 122)(104, 117)(105, 127)(106, 124)(107, 125)(108, 115)(109, 126)(110, 128)(111, 116)(112, 123) MAP : A3.797 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 39)(18, 42)(19, 45)(20, 33)(21, 35)(22, 34)(23, 46)(24, 44)(25, 40)(26, 48)(27, 41)(28, 43)(29, 47)(30, 36)(31, 37)(32, 38)(49, 83)(50, 87)(51, 91)(52, 85)(53, 92)(54, 81)(55, 93)(56, 90)(57, 82)(58, 94)(59, 86)(60, 96)(61, 89)(62, 95)(63, 88)(64, 84)(97, 128)(98, 123)(99, 116)(100, 122)(101, 126)(102, 124)(103, 118)(104, 125)(105, 115)(106, 121)(107, 117)(108, 127)(109, 113)(110, 114)(111, 119)(112, 120) MAP : A3.798 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 41)(18, 47)(19, 34)(20, 43)(21, 38)(22, 45)(23, 40)(24, 36)(25, 46)(26, 37)(27, 39)(28, 33)(29, 42)(30, 44)(31, 48)(32, 35)(49, 83)(50, 87)(51, 91)(52, 85)(53, 92)(54, 81)(55, 93)(56, 90)(57, 82)(58, 94)(59, 86)(60, 96)(61, 89)(62, 95)(63, 88)(64, 84)(97, 117)(98, 113)(99, 124)(100, 127)(101, 120)(102, 116)(103, 115)(104, 114)(105, 118)(106, 119)(107, 128)(108, 122)(109, 123)(110, 125)(111, 121)(112, 126) MAP : A3.799 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 44)(18, 35)(19, 48)(20, 40)(21, 42)(22, 37)(23, 43)(24, 39)(25, 33)(26, 45)(27, 36)(28, 46)(29, 38)(30, 41)(31, 34)(32, 47)(49, 83)(50, 87)(51, 91)(52, 85)(53, 92)(54, 81)(55, 93)(56, 90)(57, 82)(58, 94)(59, 86)(60, 96)(61, 89)(62, 95)(63, 88)(64, 84)(97, 125)(98, 126)(99, 121)(100, 115)(101, 123)(102, 119)(103, 127)(104, 128)(105, 122)(106, 116)(107, 114)(108, 118)(109, 120)(110, 117)(111, 124)(112, 113) MAP : A3.800 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 45)(18, 46)(19, 41)(20, 35)(21, 43)(22, 39)(23, 47)(24, 48)(25, 42)(26, 36)(27, 34)(28, 38)(29, 40)(30, 37)(31, 44)(32, 33)(49, 83)(50, 87)(51, 91)(52, 85)(53, 92)(54, 81)(55, 93)(56, 90)(57, 82)(58, 94)(59, 86)(60, 96)(61, 89)(62, 95)(63, 88)(64, 84)(97, 124)(98, 115)(99, 128)(100, 120)(101, 122)(102, 117)(103, 123)(104, 119)(105, 113)(106, 125)(107, 116)(108, 126)(109, 118)(110, 121)(111, 114)(112, 127) MAP : A3.801 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 48)(18, 43)(19, 36)(20, 42)(21, 46)(22, 44)(23, 38)(24, 45)(25, 35)(26, 41)(27, 37)(28, 47)(29, 33)(30, 34)(31, 39)(32, 40)(49, 83)(50, 87)(51, 91)(52, 85)(53, 92)(54, 81)(55, 93)(56, 90)(57, 82)(58, 94)(59, 86)(60, 96)(61, 89)(62, 95)(63, 88)(64, 84)(97, 119)(98, 122)(99, 125)(100, 113)(101, 115)(102, 114)(103, 126)(104, 124)(105, 120)(106, 128)(107, 121)(108, 123)(109, 127)(110, 116)(111, 117)(112, 118) MAP : A3.802 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 34)(18, 40)(19, 39)(20, 38)(21, 33)(22, 41)(23, 42)(24, 37)(25, 47)(26, 44)(27, 45)(28, 35)(29, 46)(30, 48)(31, 36)(32, 43)(49, 86)(50, 89)(51, 81)(52, 96)(53, 84)(54, 91)(55, 82)(56, 95)(57, 93)(58, 88)(59, 83)(60, 85)(61, 87)(62, 90)(63, 94)(64, 92)(97, 124)(98, 115)(99, 128)(100, 120)(101, 122)(102, 117)(103, 123)(104, 119)(105, 113)(106, 125)(107, 116)(108, 126)(109, 118)(110, 121)(111, 114)(112, 127) MAP : A3.803 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 37)(18, 33)(19, 44)(20, 47)(21, 40)(22, 36)(23, 35)(24, 34)(25, 38)(26, 39)(27, 48)(28, 42)(29, 43)(30, 45)(31, 41)(32, 46)(49, 86)(50, 89)(51, 81)(52, 96)(53, 84)(54, 91)(55, 82)(56, 95)(57, 93)(58, 88)(59, 83)(60, 85)(61, 87)(62, 90)(63, 94)(64, 92)(97, 119)(98, 122)(99, 125)(100, 113)(101, 115)(102, 114)(103, 126)(104, 124)(105, 120)(106, 128)(107, 121)(108, 123)(109, 127)(110, 116)(111, 117)(112, 118) MAP : A3.804 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 36)(18, 38)(19, 37)(20, 46)(21, 47)(22, 48)(23, 33)(24, 41)(25, 43)(26, 34)(27, 44)(28, 40)(29, 35)(30, 39)(31, 45)(32, 42)(49, 86)(50, 89)(51, 81)(52, 96)(53, 84)(54, 91)(55, 82)(56, 95)(57, 93)(58, 88)(59, 83)(60, 85)(61, 87)(62, 90)(63, 94)(64, 92)(97, 125)(98, 126)(99, 121)(100, 115)(101, 123)(102, 119)(103, 127)(104, 128)(105, 122)(106, 116)(107, 114)(108, 118)(109, 120)(110, 117)(111, 124)(112, 113) MAP : A3.805 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 39)(18, 42)(19, 45)(20, 33)(21, 35)(22, 34)(23, 46)(24, 44)(25, 40)(26, 48)(27, 41)(28, 43)(29, 47)(30, 36)(31, 37)(32, 38)(49, 86)(50, 89)(51, 81)(52, 96)(53, 84)(54, 91)(55, 82)(56, 95)(57, 93)(58, 88)(59, 83)(60, 85)(61, 87)(62, 90)(63, 94)(64, 92)(97, 117)(98, 113)(99, 124)(100, 127)(101, 120)(102, 116)(103, 115)(104, 114)(105, 118)(106, 119)(107, 128)(108, 122)(109, 123)(110, 125)(111, 121)(112, 126) MAP : A3.806 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 38)(18, 41)(19, 33)(20, 48)(21, 36)(22, 43)(23, 34)(24, 47)(25, 45)(26, 40)(27, 35)(28, 37)(29, 39)(30, 42)(31, 46)(32, 44)(49, 93)(50, 94)(51, 89)(52, 83)(53, 91)(54, 87)(55, 95)(56, 96)(57, 90)(58, 84)(59, 82)(60, 86)(61, 88)(62, 85)(63, 92)(64, 81)(97, 116)(98, 118)(99, 117)(100, 126)(101, 127)(102, 128)(103, 113)(104, 121)(105, 123)(106, 114)(107, 124)(108, 120)(109, 115)(110, 119)(111, 125)(112, 122) MAP : A3.807 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 44)(18, 35)(19, 48)(20, 40)(21, 42)(22, 37)(23, 43)(24, 39)(25, 33)(26, 45)(27, 36)(28, 46)(29, 38)(30, 41)(31, 34)(32, 47)(49, 90)(50, 92)(51, 94)(52, 82)(53, 87)(54, 88)(55, 96)(56, 83)(57, 85)(58, 91)(59, 95)(60, 93)(61, 84)(62, 86)(63, 81)(64, 89)(97, 128)(98, 123)(99, 116)(100, 122)(101, 126)(102, 124)(103, 118)(104, 125)(105, 115)(106, 121)(107, 117)(108, 127)(109, 113)(110, 114)(111, 119)(112, 120) MAP : A3.808 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 45)(18, 46)(19, 41)(20, 35)(21, 43)(22, 39)(23, 47)(24, 48)(25, 42)(26, 36)(27, 34)(28, 38)(29, 40)(30, 37)(31, 44)(32, 33)(49, 90)(50, 92)(51, 94)(52, 82)(53, 87)(54, 88)(55, 96)(56, 83)(57, 85)(58, 91)(59, 95)(60, 93)(61, 84)(62, 86)(63, 81)(64, 89)(97, 119)(98, 122)(99, 125)(100, 113)(101, 115)(102, 114)(103, 126)(104, 124)(105, 120)(106, 128)(107, 121)(108, 123)(109, 127)(110, 116)(111, 117)(112, 118) MAP : A3.809 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 48)(18, 43)(19, 36)(20, 42)(21, 46)(22, 44)(23, 38)(24, 45)(25, 35)(26, 41)(27, 37)(28, 47)(29, 33)(30, 34)(31, 39)(32, 40)(49, 90)(50, 92)(51, 94)(52, 82)(53, 87)(54, 88)(55, 96)(56, 83)(57, 85)(58, 91)(59, 95)(60, 93)(61, 84)(62, 86)(63, 81)(64, 89)(97, 124)(98, 115)(99, 128)(100, 120)(101, 122)(102, 117)(103, 123)(104, 119)(105, 113)(106, 125)(107, 116)(108, 126)(109, 118)(110, 121)(111, 114)(112, 127) MAP : A3.810 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 34)(18, 39)(19, 36)(20, 38)(21, 33)(22, 40)(23, 43)(24, 44)(25, 37)(26, 35)(27, 47)(28, 48)(29, 42)(30, 41)(31, 46)(32, 45)(49, 96)(50, 93)(51, 91)(52, 95)(53, 92)(54, 94)(55, 90)(56, 89)(57, 88)(58, 87)(59, 83)(60, 85)(61, 82)(62, 86)(63, 84)(64, 81)(97, 124)(98, 128)(99, 119)(100, 123)(101, 120)(102, 127)(103, 125)(104, 126)(105, 118)(106, 114)(107, 122)(108, 121)(109, 113)(110, 116)(111, 115)(112, 117) MAP : A3.811 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 43)(18, 47)(19, 40)(20, 44)(21, 39)(22, 48)(23, 46)(24, 45)(25, 34)(26, 38)(27, 41)(28, 42)(29, 36)(30, 33)(31, 37)(32, 35)(49, 96)(50, 93)(51, 91)(52, 95)(53, 92)(54, 94)(55, 90)(56, 89)(57, 88)(58, 87)(59, 83)(60, 85)(61, 82)(62, 86)(63, 84)(64, 81)(97, 118)(98, 120)(99, 113)(100, 114)(101, 116)(102, 119)(103, 124)(104, 123)(105, 115)(106, 117)(107, 128)(108, 127)(109, 121)(110, 122)(111, 125)(112, 126) MAP : A3.812 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 36)(18, 38)(19, 37)(20, 46)(21, 47)(22, 48)(23, 33)(24, 41)(25, 43)(26, 34)(27, 44)(28, 40)(29, 35)(30, 39)(31, 45)(32, 42)(49, 95)(50, 84)(51, 88)(52, 93)(53, 89)(54, 94)(55, 85)(56, 86)(57, 96)(58, 81)(59, 90)(60, 82)(61, 92)(62, 83)(63, 91)(64, 87)(97, 128)(98, 123)(99, 116)(100, 122)(101, 126)(102, 124)(103, 118)(104, 125)(105, 115)(106, 121)(107, 117)(108, 127)(109, 113)(110, 114)(111, 119)(112, 120) MAP : A3.813 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 39)(18, 42)(19, 45)(20, 33)(21, 35)(22, 34)(23, 46)(24, 44)(25, 40)(26, 48)(27, 41)(28, 43)(29, 47)(30, 36)(31, 37)(32, 38)(49, 95)(50, 84)(51, 88)(52, 93)(53, 89)(54, 94)(55, 85)(56, 86)(57, 96)(58, 81)(59, 90)(60, 82)(61, 92)(62, 83)(63, 91)(64, 87)(97, 114)(98, 120)(99, 119)(100, 118)(101, 113)(102, 121)(103, 122)(104, 117)(105, 127)(106, 124)(107, 125)(108, 115)(109, 126)(110, 128)(111, 116)(112, 123) MAP : A3.814 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 35)(18, 36)(19, 41)(20, 37)(21, 42)(22, 33)(23, 38)(24, 34)(25, 45)(26, 46)(27, 40)(28, 39)(29, 47)(30, 48)(31, 44)(32, 43)(49, 96)(50, 93)(51, 91)(52, 95)(53, 92)(54, 94)(55, 90)(56, 89)(57, 88)(58, 87)(59, 83)(60, 85)(61, 82)(62, 86)(63, 84)(64, 81)(97, 126)(98, 121)(99, 128)(100, 125)(101, 127)(102, 122)(103, 117)(104, 115)(105, 123)(106, 124)(107, 113)(108, 116)(109, 120)(110, 119)(111, 114)(112, 118) MAP : A3.815 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 45)(18, 42)(19, 47)(20, 46)(21, 48)(22, 41)(23, 35)(24, 37)(25, 44)(26, 43)(27, 36)(28, 33)(29, 39)(30, 40)(31, 38)(32, 34)(49, 96)(50, 93)(51, 91)(52, 95)(53, 92)(54, 94)(55, 90)(56, 89)(57, 88)(58, 87)(59, 83)(60, 85)(61, 82)(62, 86)(63, 84)(64, 81)(97, 117)(98, 113)(99, 122)(100, 115)(101, 121)(102, 116)(103, 114)(104, 118)(105, 126)(106, 125)(107, 119)(108, 120)(109, 128)(110, 127)(111, 123)(112, 124) MAP : A3.816 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 45)(18, 46)(19, 41)(20, 35)(21, 43)(22, 39)(23, 47)(24, 48)(25, 42)(26, 36)(27, 34)(28, 38)(29, 40)(30, 37)(31, 44)(32, 33)(49, 95)(50, 84)(51, 88)(52, 93)(53, 89)(54, 94)(55, 85)(56, 86)(57, 96)(58, 81)(59, 90)(60, 82)(61, 92)(62, 83)(63, 91)(64, 87)(97, 121)(98, 127)(99, 114)(100, 123)(101, 118)(102, 125)(103, 120)(104, 116)(105, 126)(106, 117)(107, 119)(108, 113)(109, 122)(110, 124)(111, 128)(112, 115) MAP : A3.817 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 48)(18, 43)(19, 36)(20, 42)(21, 46)(22, 44)(23, 38)(24, 45)(25, 35)(26, 41)(27, 37)(28, 47)(29, 33)(30, 34)(31, 39)(32, 40)(49, 95)(50, 84)(51, 88)(52, 93)(53, 89)(54, 94)(55, 85)(56, 86)(57, 96)(58, 81)(59, 90)(60, 82)(61, 92)(62, 83)(63, 91)(64, 87)(97, 116)(98, 118)(99, 117)(100, 126)(101, 127)(102, 128)(103, 113)(104, 121)(105, 123)(106, 114)(107, 124)(108, 120)(109, 115)(110, 119)(111, 125)(112, 122) MAP : A3.818 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 35)(18, 39)(19, 43)(20, 37)(21, 44)(22, 33)(23, 45)(24, 42)(25, 34)(26, 46)(27, 38)(28, 48)(29, 41)(30, 47)(31, 40)(32, 36)(49, 93)(50, 94)(51, 89)(52, 83)(53, 91)(54, 87)(55, 95)(56, 96)(57, 90)(58, 84)(59, 82)(60, 86)(61, 88)(62, 85)(63, 92)(64, 81)(97, 124)(98, 115)(99, 128)(100, 120)(101, 122)(102, 117)(103, 123)(104, 119)(105, 113)(106, 125)(107, 116)(108, 126)(109, 118)(110, 121)(111, 114)(112, 127) MAP : A3.819 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 45)(18, 46)(19, 41)(20, 35)(21, 43)(22, 39)(23, 47)(24, 48)(25, 42)(26, 36)(27, 34)(28, 38)(29, 40)(30, 37)(31, 44)(32, 33)(49, 89)(50, 95)(51, 82)(52, 91)(53, 86)(54, 93)(55, 88)(56, 84)(57, 94)(58, 85)(59, 87)(60, 81)(61, 90)(62, 92)(63, 96)(64, 83)(97, 127)(98, 116)(99, 120)(100, 125)(101, 121)(102, 126)(103, 117)(104, 118)(105, 128)(106, 113)(107, 122)(108, 114)(109, 124)(110, 115)(111, 123)(112, 119) MAP : A3.820 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 36)(18, 38)(19, 37)(20, 46)(21, 47)(22, 48)(23, 33)(24, 41)(25, 43)(26, 34)(27, 44)(28, 40)(29, 35)(30, 39)(31, 45)(32, 42)(49, 93)(50, 94)(51, 89)(52, 83)(53, 91)(54, 87)(55, 95)(56, 96)(57, 90)(58, 84)(59, 82)(60, 86)(61, 88)(62, 85)(63, 92)(64, 81)(97, 118)(98, 121)(99, 113)(100, 128)(101, 116)(102, 123)(103, 114)(104, 127)(105, 125)(106, 120)(107, 115)(108, 117)(109, 119)(110, 122)(111, 126)(112, 124) MAP : A3.821 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 39)(18, 42)(19, 45)(20, 33)(21, 35)(22, 34)(23, 46)(24, 44)(25, 40)(26, 48)(27, 41)(28, 43)(29, 47)(30, 36)(31, 37)(32, 38)(49, 93)(50, 94)(51, 89)(52, 83)(53, 91)(54, 87)(55, 95)(56, 96)(57, 90)(58, 84)(59, 82)(60, 86)(61, 88)(62, 85)(63, 92)(64, 81)(97, 122)(98, 124)(99, 126)(100, 114)(101, 119)(102, 120)(103, 128)(104, 115)(105, 117)(106, 123)(107, 127)(108, 125)(109, 116)(110, 118)(111, 113)(112, 121) MAP : A3.822 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 41)(18, 47)(19, 34)(20, 43)(21, 38)(22, 45)(23, 40)(24, 36)(25, 46)(26, 37)(27, 39)(28, 33)(29, 42)(30, 44)(31, 48)(32, 35)(49, 93)(50, 94)(51, 89)(52, 83)(53, 91)(54, 87)(55, 95)(56, 96)(57, 90)(58, 84)(59, 82)(60, 86)(61, 88)(62, 85)(63, 92)(64, 81)(97, 127)(98, 116)(99, 120)(100, 125)(101, 121)(102, 126)(103, 117)(104, 118)(105, 128)(106, 113)(107, 122)(108, 114)(109, 124)(110, 115)(111, 123)(112, 119) MAP : A3.823 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 44)(18, 35)(19, 48)(20, 40)(21, 42)(22, 37)(23, 43)(24, 39)(25, 33)(26, 45)(27, 36)(28, 46)(29, 38)(30, 41)(31, 34)(32, 47)(49, 93)(50, 94)(51, 89)(52, 83)(53, 91)(54, 87)(55, 95)(56, 96)(57, 90)(58, 84)(59, 82)(60, 86)(61, 88)(62, 85)(63, 92)(64, 81)(97, 115)(98, 119)(99, 123)(100, 117)(101, 124)(102, 113)(103, 125)(104, 122)(105, 114)(106, 126)(107, 118)(108, 128)(109, 121)(110, 127)(111, 120)(112, 116) MAP : A3.824 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 45)(18, 46)(19, 41)(20, 35)(21, 43)(22, 39)(23, 47)(24, 48)(25, 42)(26, 36)(27, 34)(28, 38)(29, 40)(30, 37)(31, 44)(32, 33)(49, 87)(50, 90)(51, 93)(52, 81)(53, 83)(54, 82)(55, 94)(56, 92)(57, 88)(58, 96)(59, 89)(60, 91)(61, 95)(62, 84)(63, 85)(64, 86)(97, 122)(98, 124)(99, 126)(100, 114)(101, 119)(102, 120)(103, 128)(104, 115)(105, 117)(106, 123)(107, 127)(108, 125)(109, 116)(110, 118)(111, 113)(112, 121) MAP : A3.825 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 48)(18, 43)(19, 36)(20, 42)(21, 46)(22, 44)(23, 38)(24, 45)(25, 35)(26, 41)(27, 37)(28, 47)(29, 33)(30, 34)(31, 39)(32, 40)(49, 87)(50, 90)(51, 93)(52, 81)(53, 83)(54, 82)(55, 94)(56, 92)(57, 88)(58, 96)(59, 89)(60, 91)(61, 95)(62, 84)(63, 85)(64, 86)(97, 115)(98, 119)(99, 123)(100, 117)(101, 124)(102, 113)(103, 125)(104, 122)(105, 114)(106, 126)(107, 118)(108, 128)(109, 121)(110, 127)(111, 120)(112, 116) MAP : A3.826 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 34)(18, 40)(19, 39)(20, 38)(21, 33)(22, 41)(23, 42)(24, 37)(25, 47)(26, 44)(27, 45)(28, 35)(29, 46)(30, 48)(31, 36)(32, 43)(49, 89)(50, 95)(51, 82)(52, 91)(53, 86)(54, 93)(55, 88)(56, 84)(57, 94)(58, 85)(59, 87)(60, 81)(61, 90)(62, 92)(63, 96)(64, 83)(97, 122)(98, 124)(99, 126)(100, 114)(101, 119)(102, 120)(103, 128)(104, 115)(105, 117)(106, 123)(107, 127)(108, 125)(109, 116)(110, 118)(111, 113)(112, 121) MAP : A3.827 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 37)(18, 33)(19, 44)(20, 47)(21, 40)(22, 36)(23, 35)(24, 34)(25, 38)(26, 39)(27, 48)(28, 42)(29, 43)(30, 45)(31, 41)(32, 46)(49, 89)(50, 95)(51, 82)(52, 91)(53, 86)(54, 93)(55, 88)(56, 84)(57, 94)(58, 85)(59, 87)(60, 81)(61, 90)(62, 92)(63, 96)(64, 83)(97, 115)(98, 119)(99, 123)(100, 117)(101, 124)(102, 113)(103, 125)(104, 122)(105, 114)(106, 126)(107, 118)(108, 128)(109, 121)(110, 127)(111, 120)(112, 116) MAP : A3.828 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 35)(18, 39)(19, 43)(20, 37)(21, 44)(22, 33)(23, 45)(24, 42)(25, 34)(26, 46)(27, 38)(28, 48)(29, 41)(30, 47)(31, 40)(32, 36)(49, 89)(50, 95)(51, 82)(52, 91)(53, 86)(54, 93)(55, 88)(56, 84)(57, 94)(58, 85)(59, 87)(60, 81)(61, 90)(62, 92)(63, 96)(64, 83)(97, 117)(98, 113)(99, 124)(100, 127)(101, 120)(102, 116)(103, 115)(104, 114)(105, 118)(106, 119)(107, 128)(108, 122)(109, 123)(110, 125)(111, 121)(112, 126) MAP : A3.829 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 38)(18, 41)(19, 33)(20, 48)(21, 36)(22, 43)(23, 34)(24, 47)(25, 45)(26, 40)(27, 35)(28, 37)(29, 39)(30, 42)(31, 46)(32, 44)(49, 89)(50, 95)(51, 82)(52, 91)(53, 86)(54, 93)(55, 88)(56, 84)(57, 94)(58, 85)(59, 87)(60, 81)(61, 90)(62, 92)(63, 96)(64, 83)(97, 128)(98, 123)(99, 116)(100, 122)(101, 126)(102, 124)(103, 118)(104, 125)(105, 115)(106, 121)(107, 117)(108, 127)(109, 113)(110, 114)(111, 119)(112, 120) MAP : A3.830 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 42)(18, 44)(19, 46)(20, 34)(21, 39)(22, 40)(23, 48)(24, 35)(25, 37)(26, 43)(27, 47)(28, 45)(29, 36)(30, 38)(31, 33)(32, 41)(49, 89)(50, 95)(51, 82)(52, 91)(53, 86)(54, 93)(55, 88)(56, 84)(57, 94)(58, 85)(59, 87)(60, 81)(61, 90)(62, 92)(63, 96)(64, 83)(97, 114)(98, 120)(99, 119)(100, 118)(101, 113)(102, 121)(103, 122)(104, 117)(105, 127)(106, 124)(107, 125)(108, 115)(109, 126)(110, 128)(111, 116)(112, 123) MAP : A3.831 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 47)(18, 36)(19, 40)(20, 45)(21, 41)(22, 46)(23, 37)(24, 38)(25, 48)(26, 33)(27, 42)(28, 34)(29, 44)(30, 35)(31, 43)(32, 39)(49, 89)(50, 95)(51, 82)(52, 91)(53, 86)(54, 93)(55, 88)(56, 84)(57, 94)(58, 85)(59, 87)(60, 81)(61, 90)(62, 92)(63, 96)(64, 83)(97, 125)(98, 126)(99, 121)(100, 115)(101, 123)(102, 119)(103, 127)(104, 128)(105, 122)(106, 116)(107, 114)(108, 118)(109, 120)(110, 117)(111, 124)(112, 113) MAP : A3.832 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.833 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 48)(18, 43)(19, 36)(20, 42)(21, 46)(22, 44)(23, 38)(24, 45)(25, 35)(26, 41)(27, 37)(28, 47)(29, 33)(30, 34)(31, 39)(32, 40)(49, 89)(50, 95)(51, 82)(52, 91)(53, 86)(54, 93)(55, 88)(56, 84)(57, 94)(58, 85)(59, 87)(60, 81)(61, 90)(62, 92)(63, 96)(64, 83)(97, 118)(98, 121)(99, 113)(100, 128)(101, 116)(102, 123)(103, 114)(104, 127)(105, 125)(106, 120)(107, 115)(108, 117)(109, 119)(110, 122)(111, 126)(112, 124) MAP : A3.834 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 34)(18, 40)(19, 39)(20, 38)(21, 33)(22, 41)(23, 42)(24, 37)(25, 47)(26, 44)(27, 45)(28, 35)(29, 46)(30, 48)(31, 36)(32, 43)(49, 92)(50, 83)(51, 96)(52, 88)(53, 90)(54, 85)(55, 91)(56, 87)(57, 81)(58, 93)(59, 84)(60, 94)(61, 86)(62, 89)(63, 82)(64, 95)(97, 118)(98, 121)(99, 113)(100, 128)(101, 116)(102, 123)(103, 114)(104, 127)(105, 125)(106, 120)(107, 115)(108, 117)(109, 119)(110, 122)(111, 126)(112, 124) MAP : A3.835 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 37)(18, 33)(19, 44)(20, 47)(21, 40)(22, 36)(23, 35)(24, 34)(25, 38)(26, 39)(27, 48)(28, 42)(29, 43)(30, 45)(31, 41)(32, 46)(49, 92)(50, 83)(51, 96)(52, 88)(53, 90)(54, 85)(55, 91)(56, 87)(57, 81)(58, 93)(59, 84)(60, 94)(61, 86)(62, 89)(63, 82)(64, 95)(97, 127)(98, 116)(99, 120)(100, 125)(101, 121)(102, 126)(103, 117)(104, 118)(105, 128)(106, 113)(107, 122)(108, 114)(109, 124)(110, 115)(111, 123)(112, 119) MAP : A3.836 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 35)(18, 39)(19, 43)(20, 37)(21, 44)(22, 33)(23, 45)(24, 42)(25, 34)(26, 46)(27, 38)(28, 48)(29, 41)(30, 47)(31, 40)(32, 36)(49, 92)(50, 83)(51, 96)(52, 88)(53, 90)(54, 85)(55, 91)(56, 87)(57, 81)(58, 93)(59, 84)(60, 94)(61, 86)(62, 89)(63, 82)(64, 95)(97, 125)(98, 126)(99, 121)(100, 115)(101, 123)(102, 119)(103, 127)(104, 128)(105, 122)(106, 116)(107, 114)(108, 118)(109, 120)(110, 117)(111, 124)(112, 113) MAP : A3.837 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 38)(18, 41)(19, 33)(20, 48)(21, 36)(22, 43)(23, 34)(24, 47)(25, 45)(26, 40)(27, 35)(28, 37)(29, 39)(30, 42)(31, 46)(32, 44)(49, 92)(50, 83)(51, 96)(52, 88)(53, 90)(54, 85)(55, 91)(56, 87)(57, 81)(58, 93)(59, 84)(60, 94)(61, 86)(62, 89)(63, 82)(64, 95)(97, 114)(98, 120)(99, 119)(100, 118)(101, 113)(102, 121)(103, 122)(104, 117)(105, 127)(106, 124)(107, 125)(108, 115)(109, 126)(110, 128)(111, 116)(112, 123) MAP : A3.838 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 42)(18, 44)(19, 46)(20, 34)(21, 39)(22, 40)(23, 48)(24, 35)(25, 37)(26, 43)(27, 47)(28, 45)(29, 36)(30, 38)(31, 33)(32, 41)(49, 92)(50, 83)(51, 96)(52, 88)(53, 90)(54, 85)(55, 91)(56, 87)(57, 81)(58, 93)(59, 84)(60, 94)(61, 86)(62, 89)(63, 82)(64, 95)(97, 128)(98, 123)(99, 116)(100, 122)(101, 126)(102, 124)(103, 118)(104, 125)(105, 115)(106, 121)(107, 117)(108, 127)(109, 113)(110, 114)(111, 119)(112, 120) MAP : A3.839 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 47)(18, 36)(19, 40)(20, 45)(21, 41)(22, 46)(23, 37)(24, 38)(25, 48)(26, 33)(27, 42)(28, 34)(29, 44)(30, 35)(31, 43)(32, 39)(49, 92)(50, 83)(51, 96)(52, 88)(53, 90)(54, 85)(55, 91)(56, 87)(57, 81)(58, 93)(59, 84)(60, 94)(61, 86)(62, 89)(63, 82)(64, 95)(97, 117)(98, 113)(99, 124)(100, 127)(101, 120)(102, 116)(103, 115)(104, 114)(105, 118)(106, 119)(107, 128)(108, 122)(109, 123)(110, 125)(111, 121)(112, 126) MAP : A3.840 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 45)(18, 46)(19, 41)(20, 35)(21, 43)(22, 39)(23, 47)(24, 48)(25, 42)(26, 36)(27, 34)(28, 38)(29, 40)(30, 37)(31, 44)(32, 33)(49, 92)(50, 83)(51, 96)(52, 88)(53, 90)(54, 85)(55, 91)(56, 87)(57, 81)(58, 93)(59, 84)(60, 94)(61, 86)(62, 89)(63, 82)(64, 95)(97, 115)(98, 119)(99, 123)(100, 117)(101, 124)(102, 113)(103, 125)(104, 122)(105, 114)(106, 126)(107, 118)(108, 128)(109, 121)(110, 127)(111, 120)(112, 116) MAP : A3.841 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 48)(18, 43)(19, 36)(20, 42)(21, 46)(22, 44)(23, 38)(24, 45)(25, 35)(26, 41)(27, 37)(28, 47)(29, 33)(30, 34)(31, 39)(32, 40)(49, 92)(50, 83)(51, 96)(52, 88)(53, 90)(54, 85)(55, 91)(56, 87)(57, 81)(58, 93)(59, 84)(60, 94)(61, 86)(62, 89)(63, 82)(64, 95)(97, 122)(98, 124)(99, 126)(100, 114)(101, 119)(102, 120)(103, 128)(104, 115)(105, 117)(106, 123)(107, 127)(108, 125)(109, 116)(110, 118)(111, 113)(112, 121) MAP : A3.842 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 34)(18, 40)(19, 39)(20, 38)(21, 33)(22, 41)(23, 42)(24, 37)(25, 47)(26, 44)(27, 45)(28, 35)(29, 46)(30, 48)(31, 36)(32, 43)(49, 90)(50, 92)(51, 94)(52, 82)(53, 87)(54, 88)(55, 96)(56, 83)(57, 85)(58, 91)(59, 95)(60, 93)(61, 84)(62, 86)(63, 81)(64, 89)(97, 121)(98, 127)(99, 114)(100, 123)(101, 118)(102, 125)(103, 120)(104, 116)(105, 126)(106, 117)(107, 119)(108, 113)(109, 122)(110, 124)(111, 128)(112, 115) MAP : A3.843 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 37)(18, 33)(19, 44)(20, 47)(21, 40)(22, 36)(23, 35)(24, 34)(25, 38)(26, 39)(27, 48)(28, 42)(29, 43)(30, 45)(31, 41)(32, 46)(49, 90)(50, 92)(51, 94)(52, 82)(53, 87)(54, 88)(55, 96)(56, 83)(57, 85)(58, 91)(59, 95)(60, 93)(61, 84)(62, 86)(63, 81)(64, 89)(97, 116)(98, 118)(99, 117)(100, 126)(101, 127)(102, 128)(103, 113)(104, 121)(105, 123)(106, 114)(107, 124)(108, 120)(109, 115)(110, 119)(111, 125)(112, 122) MAP : A3.844 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 38)(18, 40)(19, 33)(20, 34)(21, 36)(22, 39)(23, 44)(24, 43)(25, 35)(26, 37)(27, 48)(28, 47)(29, 41)(30, 42)(31, 45)(32, 46)(49, 96)(50, 93)(51, 91)(52, 95)(53, 92)(54, 94)(55, 90)(56, 89)(57, 88)(58, 87)(59, 83)(60, 85)(61, 82)(62, 86)(63, 84)(64, 81)(97, 123)(98, 127)(99, 120)(100, 124)(101, 119)(102, 128)(103, 126)(104, 125)(105, 114)(106, 118)(107, 121)(108, 122)(109, 116)(110, 113)(111, 117)(112, 115) MAP : A3.845 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 112)(34, 100)(35, 108)(36, 107)(37, 99)(38, 103)(39, 97)(40, 105)(41, 111)(42, 101)(43, 109)(44, 106)(45, 98)(46, 104)(47, 110)(48, 102)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.846 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 6> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2 * x.4 * x.3^-1, x.2^2 * x.4^-2, (x.3 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.4^-1, x.4^5 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 43)(18, 48)(19, 45)(20, 37)(21, 46)(22, 40)(23, 38)(24, 35)(25, 44)(26, 41)(27, 47)(28, 39)(29, 42)(30, 33)(31, 34)(32, 36)(49, 88)(50, 86)(51, 84)(52, 83)(53, 87)(54, 82)(55, 85)(56, 81)(57, 96)(58, 94)(59, 92)(60, 91)(61, 95)(62, 90)(63, 93)(64, 89)(97, 118)(98, 119)(99, 128)(100, 120)(101, 124)(102, 127)(103, 116)(104, 126)(105, 114)(106, 117)(107, 121)(108, 113)(109, 123)(110, 125)(111, 115)(112, 122) MAP : A3.847 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 6> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2 * x.4 * x.3^-1, x.2^2 * x.4^-2, (x.3 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.4^-1, x.4^5 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 35)(18, 40)(19, 37)(20, 45)(21, 38)(22, 48)(23, 46)(24, 43)(25, 36)(26, 33)(27, 39)(28, 47)(29, 34)(30, 41)(31, 42)(32, 44)(49, 88)(50, 86)(51, 84)(52, 83)(53, 87)(54, 82)(55, 85)(56, 81)(57, 96)(58, 94)(59, 92)(60, 91)(61, 95)(62, 90)(63, 93)(64, 89)(97, 114)(98, 117)(99, 121)(100, 113)(101, 123)(102, 125)(103, 115)(104, 122)(105, 118)(106, 119)(107, 128)(108, 120)(109, 124)(110, 127)(111, 116)(112, 126) MAP : A3.848 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 6> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.2 * x.4 * x.3^-1, x.2^2 * x.4^-2, (x.3 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.4^-1, x.4^5 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 38)(18, 39)(19, 48)(20, 40)(21, 44)(22, 47)(23, 36)(24, 46)(25, 34)(26, 37)(27, 41)(28, 33)(29, 43)(30, 45)(31, 35)(32, 42)(49, 88)(50, 86)(51, 84)(52, 83)(53, 87)(54, 82)(55, 85)(56, 81)(57, 96)(58, 94)(59, 92)(60, 91)(61, 95)(62, 90)(63, 93)(64, 89)(97, 116)(98, 113)(99, 119)(100, 127)(101, 114)(102, 121)(103, 122)(104, 124)(105, 115)(106, 120)(107, 117)(108, 125)(109, 118)(110, 128)(111, 126)(112, 123) MAP : A3.849 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 37)(18, 33)(19, 42)(20, 35)(21, 41)(22, 36)(23, 34)(24, 38)(25, 46)(26, 45)(27, 39)(28, 40)(29, 48)(30, 47)(31, 43)(32, 44)(49, 96)(50, 93)(51, 91)(52, 95)(53, 92)(54, 94)(55, 90)(56, 89)(57, 88)(58, 87)(59, 83)(60, 85)(61, 82)(62, 86)(63, 84)(64, 81)(97, 125)(98, 122)(99, 127)(100, 126)(101, 128)(102, 121)(103, 115)(104, 117)(105, 124)(106, 123)(107, 116)(108, 113)(109, 119)(110, 120)(111, 118)(112, 114) MAP : A3.850 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 112)(34, 100)(35, 108)(36, 107)(37, 99)(38, 103)(39, 97)(40, 105)(41, 111)(42, 101)(43, 109)(44, 106)(45, 98)(46, 104)(47, 110)(48, 102)(49, 85)(50, 88)(51, 87)(52, 94)(53, 81)(54, 92)(55, 83)(56, 82)(57, 93)(58, 96)(59, 95)(60, 86)(61, 89)(62, 84)(63, 91)(64, 90) MAP : A3.851 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 42)(18, 44)(19, 46)(20, 34)(21, 39)(22, 40)(23, 48)(24, 35)(25, 37)(26, 43)(27, 47)(28, 45)(29, 36)(30, 38)(31, 33)(32, 41)(49, 93)(50, 94)(51, 89)(52, 83)(53, 91)(54, 87)(55, 95)(56, 96)(57, 90)(58, 84)(59, 82)(60, 86)(61, 88)(62, 85)(63, 92)(64, 81)(97, 119)(98, 122)(99, 125)(100, 113)(101, 115)(102, 114)(103, 126)(104, 124)(105, 120)(106, 128)(107, 121)(108, 123)(109, 127)(110, 116)(111, 117)(112, 118) MAP : A3.852 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 46)(18, 41)(19, 48)(20, 45)(21, 47)(22, 42)(23, 37)(24, 35)(25, 43)(26, 44)(27, 33)(28, 36)(29, 40)(30, 39)(31, 34)(32, 38)(49, 96)(50, 93)(51, 91)(52, 95)(53, 92)(54, 94)(55, 90)(56, 89)(57, 88)(58, 87)(59, 83)(60, 85)(61, 82)(62, 86)(63, 84)(64, 81)(97, 115)(98, 116)(99, 121)(100, 117)(101, 122)(102, 113)(103, 118)(104, 114)(105, 125)(106, 126)(107, 120)(108, 119)(109, 127)(110, 128)(111, 124)(112, 123) MAP : A3.853 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.854 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.855 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.856 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {8, 8, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 8, 8, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.3 * u.1^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.4^-1, u.2^8, u.4^8 > CTG (small) : <16, 5> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.3 * x.4, (x.3 * x.1^-1)^2, x.2^8, x.4^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 44)(18, 48)(19, 39)(20, 43)(21, 40)(22, 47)(23, 45)(24, 46)(25, 38)(26, 34)(27, 42)(28, 41)(29, 33)(30, 36)(31, 35)(32, 37)(49, 96)(50, 93)(51, 91)(52, 95)(53, 92)(54, 94)(55, 90)(56, 89)(57, 88)(58, 87)(59, 83)(60, 85)(61, 82)(62, 86)(63, 84)(64, 81)(97, 114)(98, 119)(99, 116)(100, 118)(101, 113)(102, 120)(103, 123)(104, 124)(105, 117)(106, 115)(107, 127)(108, 128)(109, 122)(110, 121)(111, 126)(112, 125) MAP : A3.857 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.858 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 93)(50, 96)(51, 95)(52, 86)(53, 89)(54, 84)(55, 91)(56, 90)(57, 85)(58, 88)(59, 87)(60, 94)(61, 81)(62, 92)(63, 83)(64, 82) MAP : A3.859 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.860 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 101)(34, 104)(35, 103)(36, 110)(37, 97)(38, 108)(39, 99)(40, 98)(41, 109)(42, 112)(43, 111)(44, 102)(45, 105)(46, 100)(47, 107)(48, 106)(49, 94)(50, 83)(51, 82)(52, 85)(53, 84)(54, 89)(55, 88)(56, 87)(57, 86)(58, 91)(59, 90)(60, 93)(61, 92)(62, 81)(63, 96)(64, 95) MAP : A3.861 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.429. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, u.2^4, u.4^4, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^-1 * x.4^-1 * x.2^-1, x.2 * x.3 * x.4, x.2^4, x.4^4, (x.3 * x.1^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 47)(18, 36)(19, 40)(20, 45)(21, 41)(22, 46)(23, 37)(24, 38)(25, 48)(26, 33)(27, 42)(28, 34)(29, 44)(30, 35)(31, 43)(32, 39)(49, 93)(50, 94)(51, 89)(52, 83)(53, 91)(54, 87)(55, 95)(56, 96)(57, 90)(58, 84)(59, 82)(60, 86)(61, 88)(62, 85)(63, 92)(64, 81)(97, 121)(98, 127)(99, 114)(100, 123)(101, 118)(102, 125)(103, 120)(104, 116)(105, 126)(106, 117)(107, 119)(108, 113)(109, 122)(110, 124)(111, 128)(112, 115) MAP : A3.862 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.863 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.864 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 104)(34, 108)(35, 100)(36, 99)(37, 107)(38, 111)(39, 105)(40, 97)(41, 103)(42, 109)(43, 101)(44, 98)(45, 106)(46, 112)(47, 102)(48, 110)(49, 90)(50, 94)(51, 86)(52, 95)(53, 87)(54, 83)(55, 85)(56, 93)(57, 91)(58, 81)(59, 89)(60, 96)(61, 88)(62, 82)(63, 84)(64, 92) MAP : A3.865 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 99)(34, 105)(35, 97)(36, 104)(37, 112)(38, 106)(39, 108)(40, 100)(41, 98)(42, 102)(43, 110)(44, 103)(45, 111)(46, 107)(47, 109)(48, 101)(49, 95)(50, 85)(51, 93)(52, 90)(53, 82)(54, 88)(55, 94)(56, 86)(57, 96)(58, 84)(59, 92)(60, 91)(61, 83)(62, 87)(63, 81)(64, 89) MAP : A3.866 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 84)(50, 87)(51, 88)(52, 81)(53, 94)(54, 93)(55, 82)(56, 83)(57, 92)(58, 95)(59, 96)(60, 89)(61, 86)(62, 85)(63, 90)(64, 91) MAP : A3.867 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 112)(34, 100)(35, 108)(36, 107)(37, 99)(38, 103)(39, 97)(40, 105)(41, 111)(42, 101)(43, 109)(44, 106)(45, 98)(46, 104)(47, 110)(48, 102)(49, 89)(50, 90)(51, 91)(52, 92)(53, 93)(54, 94)(55, 95)(56, 96)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88) MAP : A3.868 NOTES : type I, reflexible, isomorphic to Med2({4,8}), isomorphic to A3.427. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 92)(50, 95)(51, 96)(52, 89)(53, 86)(54, 85)(55, 90)(56, 91)(57, 84)(58, 87)(59, 88)(60, 81)(61, 94)(62, 93)(63, 82)(64, 83) MAP : A3.869 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 119)(18, 125)(19, 117)(20, 114)(21, 122)(22, 128)(23, 118)(24, 126)(25, 120)(26, 124)(27, 116)(28, 115)(29, 123)(30, 127)(31, 121)(32, 113)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 83)(50, 89)(51, 81)(52, 88)(53, 96)(54, 90)(55, 92)(56, 84)(57, 82)(58, 86)(59, 94)(60, 87)(61, 95)(62, 91)(63, 93)(64, 85) MAP : A3.870 NOTES : type II, reflexible, isomorphic to A3.519. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 2, 2, 2 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1, (x.3, x.2^-1), (x.3^-1 * x.2^-1)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.2^2 * x.3^-1, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^4 > SCHREIER VEC. : (x.1, x.2, x.3, x.4) LOCAL TYPE : (4, 4, 4, 8) #DARTS : 128 R = (1, 17, 33, 49)(2, 18, 34, 50)(3, 19, 35, 51)(4, 20, 36, 52)(5, 21, 37, 53)(6, 22, 38, 54)(7, 23, 39, 55)(8, 24, 40, 56)(9, 25, 41, 57)(10, 26, 42, 58)(11, 27, 43, 59)(12, 28, 44, 60)(13, 29, 45, 61)(14, 30, 46, 62)(15, 31, 47, 63)(16, 32, 48, 64)(65, 81, 97, 113)(66, 82, 98, 114)(67, 83, 99, 115)(68, 84, 100, 116)(69, 85, 101, 117)(70, 86, 102, 118)(71, 87, 103, 119)(72, 88, 104, 120)(73, 89, 105, 121)(74, 90, 106, 122)(75, 91, 107, 123)(76, 92, 108, 124)(77, 93, 109, 125)(78, 94, 110, 126)(79, 95, 111, 127)(80, 96, 112, 128) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 114)(18, 118)(19, 126)(20, 119)(21, 127)(22, 123)(23, 125)(24, 117)(25, 115)(26, 121)(27, 113)(28, 120)(29, 128)(30, 122)(31, 124)(32, 116)(33, 112)(34, 100)(35, 108)(36, 107)(37, 99)(38, 103)(39, 97)(40, 105)(41, 111)(42, 101)(43, 109)(44, 106)(45, 98)(46, 104)(47, 110)(48, 102)(49, 88)(50, 92)(51, 84)(52, 83)(53, 91)(54, 95)(55, 89)(56, 81)(57, 87)(58, 93)(59, 85)(60, 82)(61, 90)(62, 96)(63, 86)(64, 94) MAP : A3.871 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3^-1 * u.2)^2, (u.3 * u.1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, (x.3 * x.1)^3, x.3 * x.2 * x.1 * x.3^-2 * x.1 * x.3 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 62)(2, 63)(3, 61)(4, 54)(5, 67)(6, 65)(7, 66)(8, 49)(9, 64)(10, 72)(11, 56)(12, 55)(13, 58)(14, 59)(15, 57)(16, 50)(17, 71)(18, 69)(19, 70)(20, 53)(21, 60)(22, 68)(23, 52)(24, 51)(25, 30)(26, 31)(27, 29)(28, 46)(32, 33)(34, 40)(35, 48)(36, 47)(37, 42)(38, 43)(39, 41)(44, 45)(73, 90)(74, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96) MAP : A3.872 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3^-1 * u.2)^2, (u.3 * u.1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^3, (x.3 * x.2)^2, x.3 * x.1 * x.3^-1 * x.2 * x.1 * x.2, (x.3 * x.1)^3 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 50)(2, 51)(3, 49)(4, 66)(5, 55)(6, 53)(7, 54)(8, 61)(9, 52)(10, 60)(11, 68)(12, 67)(13, 70)(14, 71)(15, 69)(16, 62)(17, 59)(18, 57)(19, 58)(20, 65)(21, 72)(22, 56)(23, 64)(24, 63)(25, 35)(26, 33)(27, 34)(28, 41)(29, 46)(30, 47)(31, 45)(32, 38)(36, 42)(37, 48)(39, 40)(43, 44)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.873 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3^-1 * u.2)^2, (u.3 * u.1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3^-1 * x.2)^2, x.3^4, x.1 * x.2 * x.1 * x.3^-2, (x.3 * x.1)^3 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 62)(2, 63)(3, 61)(4, 54)(5, 67)(6, 65)(7, 66)(8, 49)(9, 64)(10, 72)(11, 56)(12, 55)(13, 58)(14, 59)(15, 57)(16, 50)(17, 71)(18, 69)(19, 70)(20, 53)(21, 60)(22, 68)(23, 52)(24, 51)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(73, 90)(74, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96) MAP : A3.874 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3 * u.1)^2, (u.3^-1 * u.2)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3 * x.1)^2, x.3^4, x.3 * x.2 * x.3^-2 * x.2 * x.1, x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.1, x.3^-1 * x.1 * x.2 * x.3^-2 * x.2, x.2 * x.3^2 * x.2 * x.3^-1 * x.1 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 62)(2, 63)(3, 61)(4, 54)(5, 67)(6, 65)(7, 66)(8, 49)(9, 64)(10, 72)(11, 56)(12, 55)(13, 58)(14, 59)(15, 57)(16, 50)(17, 71)(18, 69)(19, 70)(20, 53)(21, 60)(22, 68)(23, 52)(24, 51)(25, 31)(26, 29)(27, 30)(28, 37)(32, 42)(33, 46)(34, 47)(35, 45)(36, 38)(39, 44)(40, 43)(41, 48)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.875 NOTES : type I, chiral, isomorphic to A3.872. QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3 * u.1)^2, (u.3^-1 * u.2)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^3, (x.3^-1 * x.1)^2, x.2 * x.3^-1 * x.1 * x.2 * x.1 * x.3, (x.3^-1 * x.2)^3 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 50)(2, 51)(3, 49)(4, 66)(5, 55)(6, 53)(7, 54)(8, 61)(9, 52)(10, 60)(11, 68)(12, 67)(13, 70)(14, 71)(15, 69)(16, 62)(17, 59)(18, 57)(19, 58)(20, 65)(21, 72)(22, 56)(23, 64)(24, 63)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(73, 90)(74, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96) MAP : A3.876 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 4)(6, 8) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, u.3 * u.4^-1 * u.3^-1 * u.5^-1, (u.4 * u.1)^3, (u.5 * u.2)^3 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5, x.2 * x.1, x.4^2 * x.5^-1, x.3 * x.4^-1 * x.3^-1 * x.5^-1, x.1 * x.4 * x.1 * x.4 * x.1 * x.5^-1, (x.5 * x.2)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.4^-1) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 39)(14, 37)(15, 38)(16, 45)(17, 44)(18, 40)(19, 48)(20, 47)(21, 42)(22, 43)(23, 41)(24, 46)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(61, 86)(62, 87)(63, 85)(64, 90)(65, 95)(66, 93)(67, 94)(68, 89)(69, 88)(70, 96)(71, 92)(72, 91)(73, 78)(74, 79)(75, 77)(76, 82)(80, 81)(83, 84) MAP : A3.877 NOTES : type I, chiral, isomorphic to A3.874. QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3^-1 * u.2)^2, (u.3 * u.1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3 * x.2)^2, x.3^4, x.1 * x.3^-1 * x.1 * x.3 * x.1 * x.2, (x.3 * x.2 * x.1)^2, x.3^2 * x.1 * x.2 * x.3 * x.1 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 72)(2, 56)(3, 64)(4, 63)(5, 52)(6, 60)(7, 68)(8, 67)(9, 55)(10, 53)(11, 54)(12, 61)(13, 59)(14, 57)(15, 58)(16, 65)(17, 70)(18, 71)(19, 69)(20, 62)(21, 50)(22, 51)(23, 49)(24, 66)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.878 NOTES : type I, reflexible, isomorphic to A3.871. QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3 * u.1)^2, (u.3^-1 * u.2)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3 * x.1)^2, x.3^4, (x.2 * x.1)^2, (x.3^-1 * x.2)^3, x.1 * x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.3 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 62)(2, 63)(3, 61)(4, 54)(5, 67)(6, 65)(7, 66)(8, 49)(9, 64)(10, 72)(11, 56)(12, 55)(13, 58)(14, 59)(15, 57)(16, 50)(17, 71)(18, 69)(19, 70)(20, 53)(21, 60)(22, 68)(23, 52)(24, 51)(25, 42)(26, 43)(27, 41)(28, 34)(29, 39)(30, 37)(31, 38)(32, 45)(33, 44)(35, 36)(40, 46)(47, 48)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.879 NOTES : type I, reflexible, isomorphic to A3.873. QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3 * u.1)^2, (u.3^-1 * u.2)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3 * x.1)^2, x.3^4, x.2 * x.1 * x.2 * x.3^-2, (x.3^-1 * x.2)^3 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 62)(2, 63)(3, 61)(4, 54)(5, 67)(6, 65)(7, 66)(8, 49)(9, 64)(10, 72)(11, 56)(12, 55)(13, 58)(14, 59)(15, 57)(16, 50)(17, 71)(18, 69)(19, 70)(20, 53)(21, 60)(22, 68)(23, 52)(24, 51)(25, 36)(26, 44)(27, 28)(29, 40)(30, 48)(31, 32)(33, 43)(34, 41)(35, 42)(37, 47)(38, 45)(39, 46)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.880 NOTES : type I, reflexible, isomorphic to A3.873. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^3, (u.3 * u.4^-1)^3 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.1 * x.5 * x.4^-1, x.4 * x.2 * x.5^-1, (x.2 * x.1)^2, x.4 * x.1 * x.5^-1 * x.2, (x.5 * x.3^-1)^3, (x.3 * x.4^-1)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 86)(14, 87)(15, 85)(16, 90)(17, 95)(18, 93)(19, 94)(20, 89)(21, 88)(22, 96)(23, 92)(24, 91)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(37, 67)(38, 65)(39, 66)(40, 61)(41, 72)(42, 68)(43, 64)(44, 63)(45, 70)(46, 71)(47, 69)(48, 62)(73, 84)(74, 80)(75, 76)(77, 82)(78, 83)(79, 81) MAP : A3.881 NOTES : type I, chiral, isomorphic to A3.872. QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3 * u.1)^2, (u.3^-1 * u.2)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^3, (x.3^-1 * x.1)^2, x.3^-1 * x.2 * x.3 * x.1 * x.2 * x.1, (x.3^-1 * x.2)^3 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 50)(2, 51)(3, 49)(4, 66)(5, 55)(6, 53)(7, 54)(8, 61)(9, 52)(10, 60)(11, 68)(12, 67)(13, 70)(14, 71)(15, 69)(16, 62)(17, 59)(18, 57)(19, 58)(20, 65)(21, 72)(22, 56)(23, 64)(24, 63)(25, 31)(26, 29)(27, 30)(28, 37)(32, 42)(33, 46)(34, 47)(35, 45)(36, 38)(39, 44)(40, 43)(41, 48)(73, 90)(74, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96) MAP : A3.882 NOTES : type I, reflexible, isomorphic to A3.876. QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3^-1 * u.2)^2, (u.3 * u.1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^3, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, (x.1 * x.3)^3 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 50)(2, 51)(3, 49)(4, 66)(5, 55)(6, 53)(7, 54)(8, 61)(9, 52)(10, 60)(11, 68)(12, 67)(13, 70)(14, 71)(15, 69)(16, 62)(17, 59)(18, 57)(19, 58)(20, 65)(21, 72)(22, 56)(23, 64)(24, 63)(25, 42)(26, 43)(27, 41)(28, 34)(29, 39)(30, 37)(31, 38)(32, 45)(33, 44)(35, 36)(40, 46)(47, 48)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.883 NOTES : type I, chiral, isomorphic to A3.872. QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3^-1 * u.2)^2, (u.3 * u.1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^3, (x.3^-1 * x.2)^2, x.3^-1 * x.1 * x.3 * x.2 * x.1 * x.2, (x.3 * x.1)^3 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 50)(2, 51)(3, 49)(4, 66)(5, 55)(6, 53)(7, 54)(8, 61)(9, 52)(10, 60)(11, 68)(12, 67)(13, 70)(14, 71)(15, 69)(16, 62)(17, 59)(18, 57)(19, 58)(20, 65)(21, 72)(22, 56)(23, 64)(24, 63)(25, 36)(26, 44)(27, 28)(29, 40)(30, 48)(31, 32)(33, 43)(34, 41)(35, 42)(37, 47)(38, 45)(39, 46)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.884 NOTES : type I, reflexible, isomorphic to A3.876. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 4)(6, 8) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, u.3 * u.4^-1 * u.3^-1 * u.5^-1, (u.4 * u.1)^3, (u.5 * u.2)^3 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.5, x.2 * x.1, x.4^2 * x.5^-1, x.3 * x.4^-1 * x.3^-1 * x.5^-1, x.1 * x.4 * x.1 * x.4 * x.1 * x.5^-1, (x.5 * x.2)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.4^-1) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 38)(14, 39)(15, 37)(16, 42)(17, 47)(18, 45)(19, 46)(20, 41)(21, 40)(22, 48)(23, 44)(24, 43)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(61, 87)(62, 85)(63, 86)(64, 93)(65, 92)(66, 88)(67, 96)(68, 95)(69, 90)(70, 91)(71, 89)(72, 94)(73, 78)(74, 79)(75, 77)(76, 82)(80, 81)(83, 84) MAP : A3.885 NOTES : type I, reflexible, isomorphic to A3.871. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^3, (u.3 * u.4^-1)^3 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.1 * x.2, x.5^-1 * x.4^-1 * x.1 * x.4^-1, x.5^-1 * x.2 * x.5^-1 * x.4^-1, (x.5 * x.4^-1)^2, (x.5 * x.3^-1)^3, (x.3 * x.4^-1)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 87)(14, 85)(15, 86)(16, 93)(17, 92)(18, 88)(19, 96)(20, 95)(21, 90)(22, 91)(23, 89)(24, 94)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(37, 70)(38, 71)(39, 69)(40, 62)(41, 67)(42, 65)(43, 66)(44, 61)(45, 72)(46, 68)(47, 64)(48, 63)(73, 78)(74, 79)(75, 77)(76, 82)(80, 81)(83, 84) MAP : A3.886 NOTES : type I, chiral, isomorphic to A3.874. QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3 * u.1)^2, (u.3^-1 * u.2)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3 * x.1)^2, x.3^4, x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.1, (x.2 * x.1)^3, x.3^-1 * x.2 * x.3^2 * x.2 * x.1, x.3^-2 * x.2 * x.1 * x.3^-1 * x.2, x.3 * x.2 * x.3^-1 * x.1 * x.2 * x.1 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 62)(2, 63)(3, 61)(4, 54)(5, 67)(6, 65)(7, 66)(8, 49)(9, 64)(10, 72)(11, 56)(12, 55)(13, 58)(14, 59)(15, 57)(16, 50)(17, 71)(18, 69)(19, 70)(20, 53)(21, 60)(22, 68)(23, 52)(24, 51)(25, 45)(26, 46)(27, 47)(28, 48)(29, 33)(30, 34)(31, 35)(32, 36)(37, 41)(38, 42)(39, 43)(40, 44)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.887 NOTES : type I, reflexible, isomorphic to A3.871. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^3, (u.3 * u.4^-1)^3 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.1 * x.2, x.5^-1 * x.4^-1 * x.1 * x.4^-1, x.5^-1 * x.2 * x.5^-1 * x.4^-1, (x.5 * x.4^-1)^2, (x.5 * x.3^-1)^3, (x.3 * x.4^-1)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 86)(14, 87)(15, 85)(16, 90)(17, 95)(18, 93)(19, 94)(20, 89)(21, 88)(22, 96)(23, 92)(24, 91)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(37, 68)(38, 64)(39, 72)(40, 71)(41, 66)(42, 67)(43, 65)(44, 70)(45, 63)(46, 61)(47, 62)(48, 69)(73, 78)(74, 79)(75, 77)(76, 82)(80, 81)(83, 84) MAP : A3.888 NOTES : type I, reflexible, isomorphic to A3.876. QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 2, 3 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3 * u.1)^2, (u.3^-1 * u.2)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^3, (x.3 * x.1)^2, (x.2 * x.1)^2, (x.2 * x.3)^3 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 50)(2, 51)(3, 49)(4, 66)(5, 55)(6, 53)(7, 54)(8, 61)(9, 52)(10, 60)(11, 68)(12, 67)(13, 70)(14, 71)(15, 69)(16, 62)(17, 59)(18, 57)(19, 58)(20, 65)(21, 72)(22, 56)(23, 64)(24, 63)(25, 30)(26, 31)(27, 29)(28, 46)(32, 33)(34, 40)(35, 48)(36, 47)(37, 42)(38, 43)(39, 41)(44, 45)(73, 90)(74, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96) MAP : A3.889 NOTES : type I, reflexible, isomorphic to A3.873. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.3, u.1^2, u.2^2, u.4 * u.1 * u.5^-1 * u.2, (u.5 * u.3^-1)^3, (u.3 * u.4^-1)^3 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.1 * x.5 * x.4^-1, x.4 * x.2 * x.5^-1, (x.2 * x.1)^2, x.4 * x.1 * x.5^-1 * x.2, (x.5 * x.3^-1)^3, (x.3 * x.4^-1)^3 > SCHREIER VEC. : (x.3, x.4, x.1, x.5) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 13, 25, 37)(2, 14, 26, 38)(3, 15, 27, 39)(4, 16, 28, 40)(5, 17, 29, 41)(6, 18, 30, 42)(7, 19, 31, 43)(8, 20, 32, 44)(9, 21, 33, 45)(10, 22, 34, 46)(11, 23, 35, 47)(12, 24, 36, 48)(49, 61, 73, 85)(50, 62, 74, 86)(51, 63, 75, 87)(52, 64, 76, 88)(53, 65, 77, 89)(54, 66, 78, 90)(55, 67, 79, 91)(56, 68, 80, 92)(57, 69, 81, 93)(58, 70, 82, 94)(59, 71, 83, 95)(60, 72, 84, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 87)(14, 85)(15, 86)(16, 93)(17, 92)(18, 88)(19, 96)(20, 95)(21, 90)(22, 91)(23, 89)(24, 94)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(37, 65)(38, 66)(39, 67)(40, 68)(41, 69)(42, 70)(43, 71)(44, 72)(45, 61)(46, 62)(47, 63)(48, 64)(73, 83)(74, 81)(75, 82)(76, 77)(78, 84)(79, 80) MAP : A3.890 NOTES : type I, chiral, isomorphic to A3.874. QUOTIENT : R = (1, 2, 3, 4) L = (1, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3^-1 * u.2)^2, (u.3 * u.1)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3 * x.2)^2, x.3^4, x.2 * x.3 * x.1 * x.3^-1 * x.2 * x.1, x.3 * x.2 * x.1 * x.3^-2 * x.1, (x.3 * x.1)^3, x.3 * x.1 * x.3^-1 * x.1 * x.2 * x.1 > SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2) LOCAL TYPE : (4, 4, 6, 6) #DARTS : 96 R = (1, 25, 49, 73)(2, 26, 50, 74)(3, 27, 51, 75)(4, 28, 52, 76)(5, 29, 53, 77)(6, 30, 54, 78)(7, 31, 55, 79)(8, 32, 56, 80)(9, 33, 57, 81)(10, 34, 58, 82)(11, 35, 59, 83)(12, 36, 60, 84)(13, 37, 61, 85)(14, 38, 62, 86)(15, 39, 63, 87)(16, 40, 64, 88)(17, 41, 65, 89)(18, 42, 66, 90)(19, 43, 67, 91)(20, 44, 68, 92)(21, 45, 69, 93)(22, 46, 70, 94)(23, 47, 71, 95)(24, 48, 72, 96) L = (1, 72)(2, 56)(3, 64)(4, 63)(5, 52)(6, 60)(7, 68)(8, 67)(9, 55)(10, 53)(11, 54)(12, 61)(13, 59)(14, 57)(15, 58)(16, 65)(17, 70)(18, 71)(19, 69)(20, 62)(21, 50)(22, 51)(23, 49)(24, 66)(25, 31)(26, 29)(27, 30)(28, 37)(32, 42)(33, 46)(34, 47)(35, 45)(36, 38)(39, 44)(40, 43)(41, 48)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.891 NOTES : type I, chiral, isomorphic to Snub({3,7}), representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^3, u.3^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.3^7, x.3 * x.1 * x.2 * x.3 * x.1 * x.2 * x.3 * x.1 * x.3^-1 * x.2^-1 * x.3 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 7) #DARTS : 840 R = (1, 169, 337, 505, 673)(2, 170, 338, 506, 674)(3, 171, 339, 507, 675)(4, 172, 340, 508, 676)(5, 173, 341, 509, 677)(6, 174, 342, 510, 678)(7, 175, 343, 511, 679)(8, 176, 344, 512, 680)(9, 177, 345, 513, 681)(10, 178, 346, 514, 682)(11, 179, 347, 515, 683)(12, 180, 348, 516, 684)(13, 181, 349, 517, 685)(14, 182, 350, 518, 686)(15, 183, 351, 519, 687)(16, 184, 352, 520, 688)(17, 185, 353, 521, 689)(18, 186, 354, 522, 690)(19, 187, 355, 523, 691)(20, 188, 356, 524, 692)(21, 189, 357, 525, 693)(22, 190, 358, 526, 694)(23, 191, 359, 527, 695)(24, 192, 360, 528, 696)(25, 193, 361, 529, 697)(26, 194, 362, 530, 698)(27, 195, 363, 531, 699)(28, 196, 364, 532, 700)(29, 197, 365, 533, 701)(30, 198, 366, 534, 702)(31, 199, 367, 535, 703)(32, 200, 368, 536, 704)(33, 201, 369, 537, 705)(34, 202, 370, 538, 706)(35, 203, 371, 539, 707)(36, 204, 372, 540, 708)(37, 205, 373, 541, 709)(38, 206, 374, 542, 710)(39, 207, 375, 543, 711)(40, 208, 376, 544, 712)(41, 209, 377, 545, 713)(42, 210, 378, 546, 714)(43, 211, 379, 547, 715)(44, 212, 380, 548, 716)(45, 213, 381, 549, 717)(46, 214, 382, 550, 718)(47, 215, 383, 551, 719)(48, 216, 384, 552, 720)(49, 217, 385, 553, 721)(50, 218, 386, 554, 722)(51, 219, 387, 555, 723)(52, 220, 388, 556, 724)(53, 221, 389, 557, 725)(54, 222, 390, 558, 726)(55, 223, 391, 559, 727)(56, 224, 392, 560, 728)(57, 225, 393, 561, 729)(58, 226, 394, 562, 730)(59, 227, 395, 563, 731)(60, 228, 396, 564, 732)(61, 229, 397, 565, 733)(62, 230, 398, 566, 734)(63, 231, 399, 567, 735)(64, 232, 400, 568, 736)(65, 233, 401, 569, 737)(66, 234, 402, 570, 738)(67, 235, 403, 571, 739)(68, 236, 404, 572, 740)(69, 237, 405, 573, 741)(70, 238, 406, 574, 742)(71, 239, 407, 575, 743)(72, 240, 408, 576, 744)(73, 241, 409, 577, 745)(74, 242, 410, 578, 746)(75, 243, 411, 579, 747)(76, 244, 412, 580, 748)(77, 245, 413, 581, 749)(78, 246, 414, 582, 750)(79, 247, 415, 583, 751)(80, 248, 416, 584, 752)(81, 249, 417, 585, 753)(82, 250, 418, 586, 754)(83, 251, 419, 587, 755)(84, 252, 420, 588, 756)(85, 253, 421, 589, 757)(86, 254, 422, 590, 758)(87, 255, 423, 591, 759)(88, 256, 424, 592, 760)(89, 257, 425, 593, 761)(90, 258, 426, 594, 762)(91, 259, 427, 595, 763)(92, 260, 428, 596, 764)(93, 261, 429, 597, 765)(94, 262, 430, 598, 766)(95, 263, 431, 599, 767)(96, 264, 432, 600, 768)(97, 265, 433, 601, 769)(98, 266, 434, 602, 770)(99, 267, 435, 603, 771)(100, 268, 436, 604, 772)(101, 269, 437, 605, 773)(102, 270, 438, 606, 774)(103, 271, 439, 607, 775)(104, 272, 440, 608, 776)(105, 273, 441, 609, 777)(106, 274, 442, 610, 778)(107, 275, 443, 611, 779)(108, 276, 444, 612, 780)(109, 277, 445, 613, 781)(110, 278, 446, 614, 782)(111, 279, 447, 615, 783)(112, 280, 448, 616, 784)(113, 281, 449, 617, 785)(114, 282, 450, 618, 786)(115, 283, 451, 619, 787)(116, 284, 452, 620, 788)(117, 285, 453, 621, 789)(118, 286, 454, 622, 790)(119, 287, 455, 623, 791)(120, 288, 456, 624, 792)(121, 289, 457, 625, 793)(122, 290, 458, 626, 794)(123, 291, 459, 627, 795)(124, 292, 460, 628, 796)(125, 293, 461, 629, 797)(126, 294, 462, 630, 798)(127, 295, 463, 631, 799)(128, 296, 464, 632, 800)(129, 297, 465, 633, 801)(130, 298, 466, 634, 802)(131, 299, 467, 635, 803)(132, 300, 468, 636, 804)(133, 301, 469, 637, 805)(134, 302, 470, 638, 806)(135, 303, 471, 639, 807)(136, 304, 472, 640, 808)(137, 305, 473, 641, 809)(138, 306, 474, 642, 810)(139, 307, 475, 643, 811)(140, 308, 476, 644, 812)(141, 309, 477, 645, 813)(142, 310, 478, 646, 814)(143, 311, 479, 647, 815)(144, 312, 480, 648, 816)(145, 313, 481, 649, 817)(146, 314, 482, 650, 818)(147, 315, 483, 651, 819)(148, 316, 484, 652, 820)(149, 317, 485, 653, 821)(150, 318, 486, 654, 822)(151, 319, 487, 655, 823)(152, 320, 488, 656, 824)(153, 321, 489, 657, 825)(154, 322, 490, 658, 826)(155, 323, 491, 659, 827)(156, 324, 492, 660, 828)(157, 325, 493, 661, 829)(158, 326, 494, 662, 830)(159, 327, 495, 663, 831)(160, 328, 496, 664, 832)(161, 329, 497, 665, 833)(162, 330, 498, 666, 834)(163, 331, 499, 667, 835)(164, 332, 500, 668, 836)(165, 333, 501, 669, 837)(166, 334, 502, 670, 838)(167, 335, 503, 671, 839)(168, 336, 504, 672, 840) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168)(169, 339)(170, 356)(171, 354)(172, 359)(173, 355)(174, 431)(175, 430)(176, 372)(177, 341)(178, 344)(179, 358)(180, 493)(181, 495)(182, 476)(183, 491)(184, 494)(185, 338)(186, 337)(187, 345)(188, 353)(189, 361)(190, 370)(191, 369)(192, 362)(193, 408)(194, 405)(195, 496)(196, 403)(197, 478)(198, 401)(199, 402)(200, 479)(201, 340)(202, 347)(203, 349)(204, 346)(205, 440)(206, 363)(207, 348)(208, 437)(209, 398)(210, 399)(211, 396)(212, 454)(213, 394)(214, 461)(215, 464)(216, 393)(217, 343)(218, 342)(219, 455)(220, 352)(221, 452)(222, 456)(223, 453)(224, 459)(225, 487)(226, 486)(227, 415)(228, 472)(229, 412)(230, 416)(231, 413)(232, 395)(233, 484)(234, 467)(235, 469)(236, 466)(237, 360)(238, 451)(239, 468)(240, 357)(241, 382)(242, 383)(243, 380)(244, 414)(245, 378)(246, 397)(247, 400)(248, 377)(249, 482)(250, 481)(251, 465)(252, 497)(253, 449)(254, 490)(255, 489)(256, 450)(257, 392)(258, 389)(259, 424)(260, 387)(261, 406)(262, 385)(263, 386)(264, 407)(265, 483)(266, 500)(267, 498)(268, 503)(269, 499)(270, 351)(271, 350)(272, 492)(273, 485)(274, 488)(275, 502)(276, 421)(277, 423)(278, 404)(279, 419)(280, 422)(281, 444)(282, 427)(283, 429)(284, 426)(285, 504)(286, 411)(287, 428)(288, 501)(289, 442)(290, 441)(291, 425)(292, 433)(293, 409)(294, 418)(295, 417)(296, 410)(297, 447)(298, 446)(299, 367)(300, 432)(301, 364)(302, 368)(303, 365)(304, 379)(305, 443)(306, 436)(307, 434)(308, 439)(309, 435)(310, 471)(311, 470)(312, 420)(313, 462)(314, 463)(315, 460)(316, 366)(317, 458)(318, 381)(319, 384)(320, 457)(321, 445)(322, 448)(323, 438)(324, 373)(325, 375)(326, 388)(327, 371)(328, 374)(329, 480)(330, 477)(331, 376)(332, 475)(333, 390)(334, 473)(335, 474)(336, 391)(505, 683)(506, 676)(507, 674)(508, 679)(509, 675)(510, 735)(511, 734)(512, 692)(513, 685)(514, 688)(515, 678)(516, 789)(517, 791)(518, 804)(519, 787)(520, 790)(521, 682)(522, 681)(523, 697)(524, 673)(525, 713)(526, 690)(527, 689)(528, 714)(529, 776)(530, 773)(531, 792)(532, 771)(533, 806)(534, 769)(535, 770)(536, 807)(537, 684)(538, 699)(539, 701)(540, 698)(541, 768)(542, 715)(543, 700)(544, 765)(545, 758)(546, 759)(547, 756)(548, 838)(549, 754)(550, 821)(551, 824)(552, 753)(553, 687)(554, 686)(555, 839)(556, 704)(557, 836)(558, 840)(559, 837)(560, 819)(561, 815)(562, 814)(563, 743)(564, 832)(565, 740)(566, 744)(567, 741)(568, 755)(569, 812)(570, 827)(571, 829)(572, 826)(573, 680)(574, 835)(575, 828)(576, 677)(577, 726)(578, 727)(579, 724)(580, 742)(581, 722)(582, 757)(583, 760)(584, 721)(585, 810)(586, 809)(587, 825)(588, 793)(589, 833)(590, 786)(591, 785)(592, 834)(593, 712)(594, 709)(595, 784)(596, 707)(597, 774)(598, 705)(599, 706)(600, 775)(601, 811)(602, 796)(603, 794)(604, 799)(605, 795)(606, 703)(607, 702)(608, 788)(609, 813)(610, 816)(611, 798)(612, 781)(613, 783)(614, 772)(615, 779)(616, 782)(617, 748)(618, 731)(619, 733)(620, 730)(621, 800)(622, 739)(623, 732)(624, 797)(625, 746)(626, 745)(627, 729)(628, 761)(629, 737)(630, 778)(631, 777)(632, 738)(633, 751)(634, 750)(635, 719)(636, 736)(637, 716)(638, 720)(639, 717)(640, 723)(641, 747)(642, 764)(643, 762)(644, 767)(645, 763)(646, 831)(647, 830)(648, 780)(649, 822)(650, 823)(651, 820)(652, 718)(653, 818)(654, 725)(655, 728)(656, 817)(657, 749)(658, 752)(659, 766)(660, 693)(661, 695)(662, 708)(663, 691)(664, 694)(665, 808)(666, 805)(667, 696)(668, 803)(669, 710)(670, 801)(671, 802)(672, 711) MAP : A3.892 NOTES : type I, chiral, isomorphic to Snub({3,7}), isomorphic to A3.891. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^3, u.2^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^3, x.2^7, x.2^2 * x.3 * x.1 * x.2 * x.3 * x.1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 7) #DARTS : 840 R = (1, 169, 337, 505, 673)(2, 170, 338, 506, 674)(3, 171, 339, 507, 675)(4, 172, 340, 508, 676)(5, 173, 341, 509, 677)(6, 174, 342, 510, 678)(7, 175, 343, 511, 679)(8, 176, 344, 512, 680)(9, 177, 345, 513, 681)(10, 178, 346, 514, 682)(11, 179, 347, 515, 683)(12, 180, 348, 516, 684)(13, 181, 349, 517, 685)(14, 182, 350, 518, 686)(15, 183, 351, 519, 687)(16, 184, 352, 520, 688)(17, 185, 353, 521, 689)(18, 186, 354, 522, 690)(19, 187, 355, 523, 691)(20, 188, 356, 524, 692)(21, 189, 357, 525, 693)(22, 190, 358, 526, 694)(23, 191, 359, 527, 695)(24, 192, 360, 528, 696)(25, 193, 361, 529, 697)(26, 194, 362, 530, 698)(27, 195, 363, 531, 699)(28, 196, 364, 532, 700)(29, 197, 365, 533, 701)(30, 198, 366, 534, 702)(31, 199, 367, 535, 703)(32, 200, 368, 536, 704)(33, 201, 369, 537, 705)(34, 202, 370, 538, 706)(35, 203, 371, 539, 707)(36, 204, 372, 540, 708)(37, 205, 373, 541, 709)(38, 206, 374, 542, 710)(39, 207, 375, 543, 711)(40, 208, 376, 544, 712)(41, 209, 377, 545, 713)(42, 210, 378, 546, 714)(43, 211, 379, 547, 715)(44, 212, 380, 548, 716)(45, 213, 381, 549, 717)(46, 214, 382, 550, 718)(47, 215, 383, 551, 719)(48, 216, 384, 552, 720)(49, 217, 385, 553, 721)(50, 218, 386, 554, 722)(51, 219, 387, 555, 723)(52, 220, 388, 556, 724)(53, 221, 389, 557, 725)(54, 222, 390, 558, 726)(55, 223, 391, 559, 727)(56, 224, 392, 560, 728)(57, 225, 393, 561, 729)(58, 226, 394, 562, 730)(59, 227, 395, 563, 731)(60, 228, 396, 564, 732)(61, 229, 397, 565, 733)(62, 230, 398, 566, 734)(63, 231, 399, 567, 735)(64, 232, 400, 568, 736)(65, 233, 401, 569, 737)(66, 234, 402, 570, 738)(67, 235, 403, 571, 739)(68, 236, 404, 572, 740)(69, 237, 405, 573, 741)(70, 238, 406, 574, 742)(71, 239, 407, 575, 743)(72, 240, 408, 576, 744)(73, 241, 409, 577, 745)(74, 242, 410, 578, 746)(75, 243, 411, 579, 747)(76, 244, 412, 580, 748)(77, 245, 413, 581, 749)(78, 246, 414, 582, 750)(79, 247, 415, 583, 751)(80, 248, 416, 584, 752)(81, 249, 417, 585, 753)(82, 250, 418, 586, 754)(83, 251, 419, 587, 755)(84, 252, 420, 588, 756)(85, 253, 421, 589, 757)(86, 254, 422, 590, 758)(87, 255, 423, 591, 759)(88, 256, 424, 592, 760)(89, 257, 425, 593, 761)(90, 258, 426, 594, 762)(91, 259, 427, 595, 763)(92, 260, 428, 596, 764)(93, 261, 429, 597, 765)(94, 262, 430, 598, 766)(95, 263, 431, 599, 767)(96, 264, 432, 600, 768)(97, 265, 433, 601, 769)(98, 266, 434, 602, 770)(99, 267, 435, 603, 771)(100, 268, 436, 604, 772)(101, 269, 437, 605, 773)(102, 270, 438, 606, 774)(103, 271, 439, 607, 775)(104, 272, 440, 608, 776)(105, 273, 441, 609, 777)(106, 274, 442, 610, 778)(107, 275, 443, 611, 779)(108, 276, 444, 612, 780)(109, 277, 445, 613, 781)(110, 278, 446, 614, 782)(111, 279, 447, 615, 783)(112, 280, 448, 616, 784)(113, 281, 449, 617, 785)(114, 282, 450, 618, 786)(115, 283, 451, 619, 787)(116, 284, 452, 620, 788)(117, 285, 453, 621, 789)(118, 286, 454, 622, 790)(119, 287, 455, 623, 791)(120, 288, 456, 624, 792)(121, 289, 457, 625, 793)(122, 290, 458, 626, 794)(123, 291, 459, 627, 795)(124, 292, 460, 628, 796)(125, 293, 461, 629, 797)(126, 294, 462, 630, 798)(127, 295, 463, 631, 799)(128, 296, 464, 632, 800)(129, 297, 465, 633, 801)(130, 298, 466, 634, 802)(131, 299, 467, 635, 803)(132, 300, 468, 636, 804)(133, 301, 469, 637, 805)(134, 302, 470, 638, 806)(135, 303, 471, 639, 807)(136, 304, 472, 640, 808)(137, 305, 473, 641, 809)(138, 306, 474, 642, 810)(139, 307, 475, 643, 811)(140, 308, 476, 644, 812)(141, 309, 477, 645, 813)(142, 310, 478, 646, 814)(143, 311, 479, 647, 815)(144, 312, 480, 648, 816)(145, 313, 481, 649, 817)(146, 314, 482, 650, 818)(147, 315, 483, 651, 819)(148, 316, 484, 652, 820)(149, 317, 485, 653, 821)(150, 318, 486, 654, 822)(151, 319, 487, 655, 823)(152, 320, 488, 656, 824)(153, 321, 489, 657, 825)(154, 322, 490, 658, 826)(155, 323, 491, 659, 827)(156, 324, 492, 660, 828)(157, 325, 493, 661, 829)(158, 326, 494, 662, 830)(159, 327, 495, 663, 831)(160, 328, 496, 664, 832)(161, 329, 497, 665, 833)(162, 330, 498, 666, 834)(163, 331, 499, 667, 835)(164, 332, 500, 668, 836)(165, 333, 501, 669, 837)(166, 334, 502, 670, 838)(167, 335, 503, 671, 839)(168, 336, 504, 672, 840) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168)(169, 472)(170, 469)(171, 360)(172, 467)(173, 374)(174, 465)(175, 466)(176, 375)(177, 486)(178, 487)(179, 484)(180, 382)(181, 482)(182, 389)(183, 392)(184, 481)(185, 413)(186, 416)(187, 430)(188, 357)(189, 359)(190, 372)(191, 355)(192, 358)(193, 415)(194, 414)(195, 383)(196, 400)(197, 380)(198, 384)(199, 381)(200, 387)(201, 411)(202, 428)(203, 426)(204, 431)(205, 427)(206, 495)(207, 494)(208, 444)(209, 412)(210, 395)(211, 397)(212, 394)(213, 464)(214, 403)(215, 396)(216, 461)(217, 410)(218, 409)(219, 393)(220, 425)(221, 401)(222, 442)(223, 441)(224, 402)(225, 349)(226, 352)(227, 342)(228, 453)(229, 455)(230, 468)(231, 451)(232, 454)(233, 440)(234, 437)(235, 456)(236, 435)(237, 470)(238, 433)(239, 434)(240, 471)(241, 347)(242, 340)(243, 338)(244, 343)(245, 339)(246, 399)(247, 398)(248, 356)(249, 422)(250, 423)(251, 420)(252, 502)(253, 418)(254, 485)(255, 488)(256, 417)(257, 346)(258, 345)(259, 361)(260, 337)(261, 377)(262, 354)(263, 353)(264, 378)(265, 351)(266, 350)(267, 503)(268, 368)(269, 500)(270, 504)(271, 501)(272, 483)(273, 348)(274, 363)(275, 365)(276, 362)(277, 432)(278, 379)(279, 364)(280, 429)(281, 474)(282, 473)(283, 489)(284, 457)(285, 497)(286, 450)(287, 449)(288, 498)(289, 475)(290, 460)(291, 458)(292, 463)(293, 459)(294, 367)(295, 366)(296, 452)(297, 476)(298, 491)(299, 493)(300, 490)(301, 344)(302, 499)(303, 492)(304, 341)(305, 477)(306, 480)(307, 462)(308, 445)(309, 447)(310, 436)(311, 443)(312, 446)(313, 479)(314, 478)(315, 407)(316, 496)(317, 404)(318, 408)(319, 405)(320, 419)(321, 376)(322, 373)(323, 448)(324, 371)(325, 438)(326, 369)(327, 370)(328, 439)(329, 390)(330, 391)(331, 388)(332, 406)(333, 386)(334, 421)(335, 424)(336, 385)(505, 839)(506, 838)(507, 759)(508, 824)(509, 756)(510, 760)(511, 757)(512, 771)(513, 836)(514, 819)(515, 821)(516, 818)(517, 728)(518, 803)(519, 820)(520, 725)(521, 686)(522, 687)(523, 684)(524, 758)(525, 682)(526, 773)(527, 776)(528, 681)(529, 834)(530, 833)(531, 817)(532, 825)(533, 801)(534, 810)(535, 809)(536, 802)(537, 704)(538, 701)(539, 768)(540, 699)(541, 782)(542, 697)(543, 698)(544, 783)(545, 835)(546, 828)(547, 826)(548, 831)(549, 827)(550, 695)(551, 694)(552, 812)(553, 837)(554, 840)(555, 830)(556, 765)(557, 767)(558, 780)(559, 763)(560, 766)(561, 732)(562, 739)(563, 741)(564, 738)(565, 832)(566, 755)(567, 740)(568, 829)(569, 730)(570, 729)(571, 737)(572, 745)(573, 753)(574, 762)(575, 761)(576, 754)(577, 735)(578, 734)(579, 679)(580, 744)(581, 676)(582, 680)(583, 677)(584, 683)(585, 731)(586, 748)(587, 746)(588, 751)(589, 747)(590, 823)(591, 822)(592, 764)(593, 790)(594, 791)(595, 788)(596, 678)(597, 786)(598, 685)(599, 688)(600, 785)(601, 733)(602, 736)(603, 750)(604, 717)(605, 719)(606, 700)(607, 715)(608, 718)(609, 800)(610, 797)(611, 720)(612, 795)(613, 702)(614, 793)(615, 794)(616, 703)(617, 707)(618, 724)(619, 722)(620, 727)(621, 723)(622, 743)(623, 742)(624, 716)(625, 709)(626, 712)(627, 726)(628, 813)(629, 815)(630, 796)(631, 811)(632, 814)(633, 706)(634, 705)(635, 689)(636, 721)(637, 673)(638, 714)(639, 713)(640, 674)(641, 784)(642, 781)(643, 816)(644, 779)(645, 798)(646, 777)(647, 778)(648, 799)(649, 708)(650, 691)(651, 693)(652, 690)(653, 752)(654, 675)(655, 692)(656, 749)(657, 774)(658, 775)(659, 772)(660, 806)(661, 770)(662, 789)(663, 792)(664, 769)(665, 711)(666, 710)(667, 807)(668, 696)(669, 804)(670, 808)(671, 805)(672, 787) MAP : A3.893 NOTES : type I, chiral, isomorphic to Snub({3,7}), isomorphic to A3.891. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^3, u.2^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^3, x.2^7, x.2^2 * x.3 * x.1 * x.2 * x.3 * x.1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 7) #DARTS : 840 R = (1, 169, 337, 505, 673)(2, 170, 338, 506, 674)(3, 171, 339, 507, 675)(4, 172, 340, 508, 676)(5, 173, 341, 509, 677)(6, 174, 342, 510, 678)(7, 175, 343, 511, 679)(8, 176, 344, 512, 680)(9, 177, 345, 513, 681)(10, 178, 346, 514, 682)(11, 179, 347, 515, 683)(12, 180, 348, 516, 684)(13, 181, 349, 517, 685)(14, 182, 350, 518, 686)(15, 183, 351, 519, 687)(16, 184, 352, 520, 688)(17, 185, 353, 521, 689)(18, 186, 354, 522, 690)(19, 187, 355, 523, 691)(20, 188, 356, 524, 692)(21, 189, 357, 525, 693)(22, 190, 358, 526, 694)(23, 191, 359, 527, 695)(24, 192, 360, 528, 696)(25, 193, 361, 529, 697)(26, 194, 362, 530, 698)(27, 195, 363, 531, 699)(28, 196, 364, 532, 700)(29, 197, 365, 533, 701)(30, 198, 366, 534, 702)(31, 199, 367, 535, 703)(32, 200, 368, 536, 704)(33, 201, 369, 537, 705)(34, 202, 370, 538, 706)(35, 203, 371, 539, 707)(36, 204, 372, 540, 708)(37, 205, 373, 541, 709)(38, 206, 374, 542, 710)(39, 207, 375, 543, 711)(40, 208, 376, 544, 712)(41, 209, 377, 545, 713)(42, 210, 378, 546, 714)(43, 211, 379, 547, 715)(44, 212, 380, 548, 716)(45, 213, 381, 549, 717)(46, 214, 382, 550, 718)(47, 215, 383, 551, 719)(48, 216, 384, 552, 720)(49, 217, 385, 553, 721)(50, 218, 386, 554, 722)(51, 219, 387, 555, 723)(52, 220, 388, 556, 724)(53, 221, 389, 557, 725)(54, 222, 390, 558, 726)(55, 223, 391, 559, 727)(56, 224, 392, 560, 728)(57, 225, 393, 561, 729)(58, 226, 394, 562, 730)(59, 227, 395, 563, 731)(60, 228, 396, 564, 732)(61, 229, 397, 565, 733)(62, 230, 398, 566, 734)(63, 231, 399, 567, 735)(64, 232, 400, 568, 736)(65, 233, 401, 569, 737)(66, 234, 402, 570, 738)(67, 235, 403, 571, 739)(68, 236, 404, 572, 740)(69, 237, 405, 573, 741)(70, 238, 406, 574, 742)(71, 239, 407, 575, 743)(72, 240, 408, 576, 744)(73, 241, 409, 577, 745)(74, 242, 410, 578, 746)(75, 243, 411, 579, 747)(76, 244, 412, 580, 748)(77, 245, 413, 581, 749)(78, 246, 414, 582, 750)(79, 247, 415, 583, 751)(80, 248, 416, 584, 752)(81, 249, 417, 585, 753)(82, 250, 418, 586, 754)(83, 251, 419, 587, 755)(84, 252, 420, 588, 756)(85, 253, 421, 589, 757)(86, 254, 422, 590, 758)(87, 255, 423, 591, 759)(88, 256, 424, 592, 760)(89, 257, 425, 593, 761)(90, 258, 426, 594, 762)(91, 259, 427, 595, 763)(92, 260, 428, 596, 764)(93, 261, 429, 597, 765)(94, 262, 430, 598, 766)(95, 263, 431, 599, 767)(96, 264, 432, 600, 768)(97, 265, 433, 601, 769)(98, 266, 434, 602, 770)(99, 267, 435, 603, 771)(100, 268, 436, 604, 772)(101, 269, 437, 605, 773)(102, 270, 438, 606, 774)(103, 271, 439, 607, 775)(104, 272, 440, 608, 776)(105, 273, 441, 609, 777)(106, 274, 442, 610, 778)(107, 275, 443, 611, 779)(108, 276, 444, 612, 780)(109, 277, 445, 613, 781)(110, 278, 446, 614, 782)(111, 279, 447, 615, 783)(112, 280, 448, 616, 784)(113, 281, 449, 617, 785)(114, 282, 450, 618, 786)(115, 283, 451, 619, 787)(116, 284, 452, 620, 788)(117, 285, 453, 621, 789)(118, 286, 454, 622, 790)(119, 287, 455, 623, 791)(120, 288, 456, 624, 792)(121, 289, 457, 625, 793)(122, 290, 458, 626, 794)(123, 291, 459, 627, 795)(124, 292, 460, 628, 796)(125, 293, 461, 629, 797)(126, 294, 462, 630, 798)(127, 295, 463, 631, 799)(128, 296, 464, 632, 800)(129, 297, 465, 633, 801)(130, 298, 466, 634, 802)(131, 299, 467, 635, 803)(132, 300, 468, 636, 804)(133, 301, 469, 637, 805)(134, 302, 470, 638, 806)(135, 303, 471, 639, 807)(136, 304, 472, 640, 808)(137, 305, 473, 641, 809)(138, 306, 474, 642, 810)(139, 307, 475, 643, 811)(140, 308, 476, 644, 812)(141, 309, 477, 645, 813)(142, 310, 478, 646, 814)(143, 311, 479, 647, 815)(144, 312, 480, 648, 816)(145, 313, 481, 649, 817)(146, 314, 482, 650, 818)(147, 315, 483, 651, 819)(148, 316, 484, 652, 820)(149, 317, 485, 653, 821)(150, 318, 486, 654, 822)(151, 319, 487, 655, 823)(152, 320, 488, 656, 824)(153, 321, 489, 657, 825)(154, 322, 490, 658, 826)(155, 323, 491, 659, 827)(156, 324, 492, 660, 828)(157, 325, 493, 661, 829)(158, 326, 494, 662, 830)(159, 327, 495, 663, 831)(160, 328, 496, 664, 832)(161, 329, 497, 665, 833)(162, 330, 498, 666, 834)(163, 331, 499, 667, 835)(164, 332, 500, 668, 836)(165, 333, 501, 669, 837)(166, 334, 502, 670, 838)(167, 335, 503, 671, 839)(168, 336, 504, 672, 840) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168)(169, 428)(170, 411)(171, 413)(172, 410)(173, 472)(174, 395)(175, 412)(176, 469)(177, 426)(178, 425)(179, 409)(180, 441)(181, 393)(182, 434)(183, 433)(184, 394)(185, 431)(186, 430)(187, 359)(188, 416)(189, 356)(190, 360)(191, 357)(192, 339)(193, 427)(194, 444)(195, 442)(196, 447)(197, 443)(198, 463)(199, 462)(200, 436)(201, 494)(202, 495)(203, 492)(204, 358)(205, 490)(206, 341)(207, 344)(208, 489)(209, 429)(210, 432)(211, 446)(212, 365)(213, 367)(214, 348)(215, 363)(216, 366)(217, 504)(218, 501)(219, 368)(220, 499)(221, 350)(222, 497)(223, 498)(224, 351)(225, 387)(226, 380)(227, 378)(228, 383)(229, 379)(230, 415)(231, 414)(232, 364)(233, 389)(234, 392)(235, 382)(236, 485)(237, 487)(238, 500)(239, 483)(240, 486)(241, 386)(242, 385)(243, 369)(244, 377)(245, 353)(246, 362)(247, 361)(248, 354)(249, 424)(250, 421)(251, 488)(252, 419)(253, 502)(254, 417)(255, 418)(256, 503)(257, 388)(258, 371)(259, 373)(260, 370)(261, 448)(262, 355)(263, 372)(264, 445)(265, 406)(266, 407)(267, 404)(268, 478)(269, 402)(270, 493)(271, 496)(272, 401)(273, 391)(274, 390)(275, 479)(276, 376)(277, 476)(278, 480)(279, 477)(280, 491)(281, 455)(282, 454)(283, 399)(284, 464)(285, 396)(286, 400)(287, 397)(288, 403)(289, 452)(290, 459)(291, 461)(292, 458)(293, 384)(294, 475)(295, 460)(296, 381)(297, 342)(298, 343)(299, 340)(300, 398)(301, 338)(302, 405)(303, 408)(304, 337)(305, 450)(306, 449)(307, 457)(308, 465)(309, 473)(310, 482)(311, 481)(312, 474)(313, 352)(314, 349)(315, 440)(316, 347)(317, 422)(318, 345)(319, 346)(320, 423)(321, 451)(322, 468)(323, 466)(324, 471)(325, 467)(326, 375)(327, 374)(328, 484)(329, 453)(330, 456)(331, 470)(332, 437)(333, 439)(334, 420)(335, 435)(336, 438)(505, 756)(506, 771)(507, 773)(508, 770)(509, 792)(510, 779)(511, 772)(512, 789)(513, 754)(514, 753)(515, 769)(516, 737)(517, 777)(518, 730)(519, 729)(520, 778)(521, 759)(522, 758)(523, 687)(524, 776)(525, 684)(526, 688)(527, 685)(528, 699)(529, 755)(530, 740)(531, 738)(532, 743)(533, 739)(534, 815)(535, 814)(536, 732)(537, 838)(538, 839)(539, 836)(540, 686)(541, 834)(542, 701)(543, 704)(544, 833)(545, 757)(546, 760)(547, 742)(548, 725)(549, 727)(550, 716)(551, 723)(552, 726)(553, 824)(554, 821)(555, 728)(556, 819)(557, 718)(558, 817)(559, 818)(560, 719)(561, 691)(562, 708)(563, 706)(564, 711)(565, 707)(566, 775)(567, 774)(568, 724)(569, 693)(570, 696)(571, 710)(572, 805)(573, 807)(574, 820)(575, 803)(576, 806)(577, 690)(578, 689)(579, 673)(580, 705)(581, 681)(582, 722)(583, 721)(584, 682)(585, 752)(586, 749)(587, 808)(588, 747)(589, 822)(590, 745)(591, 746)(592, 823)(593, 692)(594, 675)(595, 677)(596, 674)(597, 744)(598, 683)(599, 676)(600, 741)(601, 766)(602, 767)(603, 764)(604, 830)(605, 762)(606, 837)(607, 840)(608, 761)(609, 695)(610, 694)(611, 831)(612, 680)(613, 828)(614, 832)(615, 829)(616, 835)(617, 799)(618, 798)(619, 783)(620, 816)(621, 780)(622, 784)(623, 781)(624, 763)(625, 796)(626, 811)(627, 813)(628, 810)(629, 712)(630, 827)(631, 812)(632, 709)(633, 702)(634, 703)(635, 700)(636, 782)(637, 698)(638, 765)(639, 768)(640, 697)(641, 794)(642, 793)(643, 809)(644, 785)(645, 825)(646, 802)(647, 801)(648, 826)(649, 720)(650, 717)(651, 736)(652, 715)(653, 750)(654, 713)(655, 714)(656, 751)(657, 795)(658, 788)(659, 786)(660, 791)(661, 787)(662, 679)(663, 678)(664, 804)(665, 797)(666, 800)(667, 790)(668, 733)(669, 735)(670, 748)(671, 731)(672, 734) MAP : A3.894 NOTES : type I, chiral, isomorphic to Snub({3,7}), isomorphic to A3.891. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^3, u.3^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.3^7, x.3 * x.1 * x.2 * x.3 * x.1 * x.2 * x.3 * x.1 * x.3^-1 * x.2^-1 * x.3 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 7) #DARTS : 840 R = (1, 169, 337, 505, 673)(2, 170, 338, 506, 674)(3, 171, 339, 507, 675)(4, 172, 340, 508, 676)(5, 173, 341, 509, 677)(6, 174, 342, 510, 678)(7, 175, 343, 511, 679)(8, 176, 344, 512, 680)(9, 177, 345, 513, 681)(10, 178, 346, 514, 682)(11, 179, 347, 515, 683)(12, 180, 348, 516, 684)(13, 181, 349, 517, 685)(14, 182, 350, 518, 686)(15, 183, 351, 519, 687)(16, 184, 352, 520, 688)(17, 185, 353, 521, 689)(18, 186, 354, 522, 690)(19, 187, 355, 523, 691)(20, 188, 356, 524, 692)(21, 189, 357, 525, 693)(22, 190, 358, 526, 694)(23, 191, 359, 527, 695)(24, 192, 360, 528, 696)(25, 193, 361, 529, 697)(26, 194, 362, 530, 698)(27, 195, 363, 531, 699)(28, 196, 364, 532, 700)(29, 197, 365, 533, 701)(30, 198, 366, 534, 702)(31, 199, 367, 535, 703)(32, 200, 368, 536, 704)(33, 201, 369, 537, 705)(34, 202, 370, 538, 706)(35, 203, 371, 539, 707)(36, 204, 372, 540, 708)(37, 205, 373, 541, 709)(38, 206, 374, 542, 710)(39, 207, 375, 543, 711)(40, 208, 376, 544, 712)(41, 209, 377, 545, 713)(42, 210, 378, 546, 714)(43, 211, 379, 547, 715)(44, 212, 380, 548, 716)(45, 213, 381, 549, 717)(46, 214, 382, 550, 718)(47, 215, 383, 551, 719)(48, 216, 384, 552, 720)(49, 217, 385, 553, 721)(50, 218, 386, 554, 722)(51, 219, 387, 555, 723)(52, 220, 388, 556, 724)(53, 221, 389, 557, 725)(54, 222, 390, 558, 726)(55, 223, 391, 559, 727)(56, 224, 392, 560, 728)(57, 225, 393, 561, 729)(58, 226, 394, 562, 730)(59, 227, 395, 563, 731)(60, 228, 396, 564, 732)(61, 229, 397, 565, 733)(62, 230, 398, 566, 734)(63, 231, 399, 567, 735)(64, 232, 400, 568, 736)(65, 233, 401, 569, 737)(66, 234, 402, 570, 738)(67, 235, 403, 571, 739)(68, 236, 404, 572, 740)(69, 237, 405, 573, 741)(70, 238, 406, 574, 742)(71, 239, 407, 575, 743)(72, 240, 408, 576, 744)(73, 241, 409, 577, 745)(74, 242, 410, 578, 746)(75, 243, 411, 579, 747)(76, 244, 412, 580, 748)(77, 245, 413, 581, 749)(78, 246, 414, 582, 750)(79, 247, 415, 583, 751)(80, 248, 416, 584, 752)(81, 249, 417, 585, 753)(82, 250, 418, 586, 754)(83, 251, 419, 587, 755)(84, 252, 420, 588, 756)(85, 253, 421, 589, 757)(86, 254, 422, 590, 758)(87, 255, 423, 591, 759)(88, 256, 424, 592, 760)(89, 257, 425, 593, 761)(90, 258, 426, 594, 762)(91, 259, 427, 595, 763)(92, 260, 428, 596, 764)(93, 261, 429, 597, 765)(94, 262, 430, 598, 766)(95, 263, 431, 599, 767)(96, 264, 432, 600, 768)(97, 265, 433, 601, 769)(98, 266, 434, 602, 770)(99, 267, 435, 603, 771)(100, 268, 436, 604, 772)(101, 269, 437, 605, 773)(102, 270, 438, 606, 774)(103, 271, 439, 607, 775)(104, 272, 440, 608, 776)(105, 273, 441, 609, 777)(106, 274, 442, 610, 778)(107, 275, 443, 611, 779)(108, 276, 444, 612, 780)(109, 277, 445, 613, 781)(110, 278, 446, 614, 782)(111, 279, 447, 615, 783)(112, 280, 448, 616, 784)(113, 281, 449, 617, 785)(114, 282, 450, 618, 786)(115, 283, 451, 619, 787)(116, 284, 452, 620, 788)(117, 285, 453, 621, 789)(118, 286, 454, 622, 790)(119, 287, 455, 623, 791)(120, 288, 456, 624, 792)(121, 289, 457, 625, 793)(122, 290, 458, 626, 794)(123, 291, 459, 627, 795)(124, 292, 460, 628, 796)(125, 293, 461, 629, 797)(126, 294, 462, 630, 798)(127, 295, 463, 631, 799)(128, 296, 464, 632, 800)(129, 297, 465, 633, 801)(130, 298, 466, 634, 802)(131, 299, 467, 635, 803)(132, 300, 468, 636, 804)(133, 301, 469, 637, 805)(134, 302, 470, 638, 806)(135, 303, 471, 639, 807)(136, 304, 472, 640, 808)(137, 305, 473, 641, 809)(138, 306, 474, 642, 810)(139, 307, 475, 643, 811)(140, 308, 476, 644, 812)(141, 309, 477, 645, 813)(142, 310, 478, 646, 814)(143, 311, 479, 647, 815)(144, 312, 480, 648, 816)(145, 313, 481, 649, 817)(146, 314, 482, 650, 818)(147, 315, 483, 651, 819)(148, 316, 484, 652, 820)(149, 317, 485, 653, 821)(150, 318, 486, 654, 822)(151, 319, 487, 655, 823)(152, 320, 488, 656, 824)(153, 321, 489, 657, 825)(154, 322, 490, 658, 826)(155, 323, 491, 659, 827)(156, 324, 492, 660, 828)(157, 325, 493, 661, 829)(158, 326, 494, 662, 830)(159, 327, 495, 663, 831)(160, 328, 496, 664, 832)(161, 329, 497, 665, 833)(162, 330, 498, 666, 834)(163, 331, 499, 667, 835)(164, 332, 500, 668, 836)(165, 333, 501, 669, 837)(166, 334, 502, 670, 838)(167, 335, 503, 671, 839)(168, 336, 504, 672, 840) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168)(169, 420)(170, 435)(171, 437)(172, 434)(173, 456)(174, 443)(175, 436)(176, 453)(177, 418)(178, 417)(179, 433)(180, 401)(181, 441)(182, 394)(183, 393)(184, 442)(185, 423)(186, 422)(187, 351)(188, 440)(189, 348)(190, 352)(191, 349)(192, 363)(193, 419)(194, 404)(195, 402)(196, 407)(197, 403)(198, 479)(199, 478)(200, 396)(201, 502)(202, 503)(203, 500)(204, 350)(205, 498)(206, 365)(207, 368)(208, 497)(209, 421)(210, 424)(211, 406)(212, 389)(213, 391)(214, 380)(215, 387)(216, 390)(217, 488)(218, 485)(219, 392)(220, 483)(221, 382)(222, 481)(223, 482)(224, 383)(225, 355)(226, 372)(227, 370)(228, 375)(229, 371)(230, 439)(231, 438)(232, 388)(233, 357)(234, 360)(235, 374)(236, 469)(237, 471)(238, 484)(239, 467)(240, 470)(241, 354)(242, 353)(243, 337)(244, 369)(245, 345)(246, 386)(247, 385)(248, 346)(249, 416)(250, 413)(251, 472)(252, 411)(253, 486)(254, 409)(255, 410)(256, 487)(257, 356)(258, 339)(259, 341)(260, 338)(261, 408)(262, 347)(263, 340)(264, 405)(265, 430)(266, 431)(267, 428)(268, 494)(269, 426)(270, 501)(271, 504)(272, 425)(273, 359)(274, 358)(275, 495)(276, 344)(277, 492)(278, 496)(279, 493)(280, 499)(281, 463)(282, 462)(283, 447)(284, 480)(285, 444)(286, 448)(287, 445)(288, 427)(289, 460)(290, 475)(291, 477)(292, 474)(293, 376)(294, 491)(295, 476)(296, 373)(297, 366)(298, 367)(299, 364)(300, 446)(301, 362)(302, 429)(303, 432)(304, 361)(305, 458)(306, 457)(307, 473)(308, 449)(309, 489)(310, 466)(311, 465)(312, 490)(313, 384)(314, 381)(315, 400)(316, 379)(317, 414)(318, 377)(319, 378)(320, 415)(321, 459)(322, 452)(323, 450)(324, 455)(325, 451)(326, 343)(327, 342)(328, 468)(329, 461)(330, 464)(331, 454)(332, 397)(333, 399)(334, 412)(335, 395)(336, 398)(505, 838)(506, 839)(507, 836)(508, 686)(509, 834)(510, 701)(511, 704)(512, 833)(513, 759)(514, 758)(515, 687)(516, 776)(517, 684)(518, 688)(519, 685)(520, 699)(521, 824)(522, 821)(523, 728)(524, 819)(525, 718)(526, 817)(527, 818)(528, 719)(529, 756)(530, 771)(531, 773)(532, 770)(533, 792)(534, 779)(535, 772)(536, 789)(537, 757)(538, 760)(539, 742)(540, 725)(541, 727)(542, 716)(543, 723)(544, 726)(545, 754)(546, 753)(547, 769)(548, 737)(549, 777)(550, 730)(551, 729)(552, 778)(553, 755)(554, 740)(555, 738)(556, 743)(557, 739)(558, 815)(559, 814)(560, 732)(561, 766)(562, 767)(563, 764)(564, 830)(565, 762)(566, 837)(567, 840)(568, 761)(569, 695)(570, 694)(571, 831)(572, 680)(573, 828)(574, 832)(575, 829)(576, 835)(577, 752)(578, 749)(579, 808)(580, 747)(581, 822)(582, 745)(583, 746)(584, 823)(585, 692)(586, 675)(587, 677)(588, 674)(589, 744)(590, 683)(591, 676)(592, 741)(593, 693)(594, 696)(595, 710)(596, 805)(597, 807)(598, 820)(599, 803)(600, 806)(601, 690)(602, 689)(603, 673)(604, 705)(605, 681)(606, 722)(607, 721)(608, 682)(609, 691)(610, 708)(611, 706)(612, 711)(613, 707)(614, 775)(615, 774)(616, 724)(617, 702)(618, 703)(619, 700)(620, 782)(621, 698)(622, 765)(623, 768)(624, 697)(625, 799)(626, 798)(627, 783)(628, 816)(629, 780)(630, 784)(631, 781)(632, 763)(633, 720)(634, 717)(635, 736)(636, 715)(637, 750)(638, 713)(639, 714)(640, 751)(641, 796)(642, 811)(643, 813)(644, 810)(645, 712)(646, 827)(647, 812)(648, 709)(649, 797)(650, 800)(651, 790)(652, 733)(653, 735)(654, 748)(655, 731)(656, 734)(657, 794)(658, 793)(659, 809)(660, 785)(661, 825)(662, 802)(663, 801)(664, 826)(665, 795)(666, 788)(667, 786)(668, 791)(669, 787)(670, 679)(671, 678)(672, 804) MAP : A3.895 NOTES : type I, chiral, isomorphic to Snub({3,8}), representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^3, u.2^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^3, x.2^8, x.2^-1 * x.1 * x.2 * x.3 * x.1 * x.3^-1 * x.2^-2 * x.3, x.2^2 * x.3 * x.2^-2 * x.1 * x.2 * x.3^-1 * x.2^-3 * x.1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 8) #DARTS : 480 R = (1, 97, 193, 289, 385)(2, 98, 194, 290, 386)(3, 99, 195, 291, 387)(4, 100, 196, 292, 388)(5, 101, 197, 293, 389)(6, 102, 198, 294, 390)(7, 103, 199, 295, 391)(8, 104, 200, 296, 392)(9, 105, 201, 297, 393)(10, 106, 202, 298, 394)(11, 107, 203, 299, 395)(12, 108, 204, 300, 396)(13, 109, 205, 301, 397)(14, 110, 206, 302, 398)(15, 111, 207, 303, 399)(16, 112, 208, 304, 400)(17, 113, 209, 305, 401)(18, 114, 210, 306, 402)(19, 115, 211, 307, 403)(20, 116, 212, 308, 404)(21, 117, 213, 309, 405)(22, 118, 214, 310, 406)(23, 119, 215, 311, 407)(24, 120, 216, 312, 408)(25, 121, 217, 313, 409)(26, 122, 218, 314, 410)(27, 123, 219, 315, 411)(28, 124, 220, 316, 412)(29, 125, 221, 317, 413)(30, 126, 222, 318, 414)(31, 127, 223, 319, 415)(32, 128, 224, 320, 416)(33, 129, 225, 321, 417)(34, 130, 226, 322, 418)(35, 131, 227, 323, 419)(36, 132, 228, 324, 420)(37, 133, 229, 325, 421)(38, 134, 230, 326, 422)(39, 135, 231, 327, 423)(40, 136, 232, 328, 424)(41, 137, 233, 329, 425)(42, 138, 234, 330, 426)(43, 139, 235, 331, 427)(44, 140, 236, 332, 428)(45, 141, 237, 333, 429)(46, 142, 238, 334, 430)(47, 143, 239, 335, 431)(48, 144, 240, 336, 432)(49, 145, 241, 337, 433)(50, 146, 242, 338, 434)(51, 147, 243, 339, 435)(52, 148, 244, 340, 436)(53, 149, 245, 341, 437)(54, 150, 246, 342, 438)(55, 151, 247, 343, 439)(56, 152, 248, 344, 440)(57, 153, 249, 345, 441)(58, 154, 250, 346, 442)(59, 155, 251, 347, 443)(60, 156, 252, 348, 444)(61, 157, 253, 349, 445)(62, 158, 254, 350, 446)(63, 159, 255, 351, 447)(64, 160, 256, 352, 448)(65, 161, 257, 353, 449)(66, 162, 258, 354, 450)(67, 163, 259, 355, 451)(68, 164, 260, 356, 452)(69, 165, 261, 357, 453)(70, 166, 262, 358, 454)(71, 167, 263, 359, 455)(72, 168, 264, 360, 456)(73, 169, 265, 361, 457)(74, 170, 266, 362, 458)(75, 171, 267, 363, 459)(76, 172, 268, 364, 460)(77, 173, 269, 365, 461)(78, 174, 270, 366, 462)(79, 175, 271, 367, 463)(80, 176, 272, 368, 464)(81, 177, 273, 369, 465)(82, 178, 274, 370, 466)(83, 179, 275, 371, 467)(84, 180, 276, 372, 468)(85, 181, 277, 373, 469)(86, 182, 278, 374, 470)(87, 183, 279, 375, 471)(88, 184, 280, 376, 472)(89, 185, 281, 377, 473)(90, 186, 282, 378, 474)(91, 187, 283, 379, 475)(92, 188, 284, 380, 476)(93, 189, 285, 381, 477)(94, 190, 286, 382, 478)(95, 191, 287, 383, 479)(96, 192, 288, 384, 480) L = (1, 4)(2, 8)(3, 5)(6, 34)(7, 37)(9, 18)(10, 81)(11, 82)(12, 33)(13, 17)(14, 21)(15, 85)(16, 53)(19, 30)(20, 29)(22, 63)(23, 58)(24, 25)(26, 48)(27, 64)(28, 59)(31, 32)(35, 39)(36, 44)(38, 40)(41, 43)(42, 45)(46, 47)(49, 80)(50, 96)(51, 75)(52, 79)(54, 76)(55, 70)(56, 74)(57, 94)(60, 71)(61, 89)(62, 93)(65, 91)(66, 95)(67, 92)(68, 86)(69, 90)(72, 87)(73, 83)(77, 88)(78, 84)(97, 195)(98, 196)(99, 198)(100, 199)(101, 200)(102, 202)(103, 203)(104, 204)(105, 236)(106, 265)(107, 270)(108, 207)(109, 231)(110, 230)(111, 269)(112, 253)(113, 197)(114, 193)(115, 226)(116, 229)(117, 194)(118, 273)(119, 274)(120, 225)(121, 228)(122, 275)(123, 276)(124, 277)(125, 227)(126, 232)(127, 280)(128, 281)(129, 206)(130, 205)(131, 287)(132, 282)(133, 201)(134, 272)(135, 288)(136, 283)(137, 278)(138, 267)(139, 271)(140, 208)(141, 284)(142, 279)(143, 266)(144, 286)(145, 211)(146, 212)(147, 214)(148, 215)(149, 216)(150, 218)(151, 219)(152, 220)(153, 268)(154, 233)(155, 238)(156, 223)(157, 263)(158, 262)(159, 237)(160, 285)(161, 213)(162, 209)(163, 258)(164, 261)(165, 210)(166, 241)(167, 242)(168, 257)(169, 260)(170, 243)(171, 244)(172, 245)(173, 259)(174, 264)(175, 248)(176, 249)(177, 222)(178, 221)(179, 255)(180, 250)(181, 217)(182, 240)(183, 256)(184, 251)(185, 246)(186, 235)(187, 239)(188, 224)(189, 252)(190, 247)(191, 234)(192, 254)(289, 393)(290, 398)(291, 388)(292, 392)(293, 397)(294, 389)(295, 385)(296, 387)(297, 391)(298, 418)(299, 421)(300, 386)(301, 390)(302, 396)(303, 417)(304, 420)(305, 479)(306, 474)(307, 464)(308, 480)(309, 475)(310, 459)(311, 463)(312, 400)(313, 399)(314, 460)(315, 454)(316, 458)(317, 395)(318, 394)(319, 455)(320, 451)(321, 409)(322, 414)(323, 404)(324, 408)(325, 413)(326, 405)(327, 401)(328, 403)(329, 407)(330, 450)(331, 453)(332, 402)(333, 406)(334, 412)(335, 449)(336, 452)(337, 439)(338, 444)(339, 440)(340, 435)(341, 438)(342, 445)(343, 441)(344, 436)(345, 433)(346, 462)(347, 461)(348, 446)(349, 437)(350, 434)(351, 457)(352, 456)(353, 471)(354, 476)(355, 472)(356, 467)(357, 470)(358, 477)(359, 473)(360, 468)(361, 465)(362, 430)(363, 429)(364, 478)(365, 469)(366, 466)(367, 425)(368, 424)(369, 447)(370, 442)(371, 432)(372, 448)(373, 443)(374, 427)(375, 431)(376, 416)(377, 415)(378, 428)(379, 422)(380, 426)(381, 411)(382, 410)(383, 423)(384, 419) MAP : A3.896 NOTES : type I, chiral, isomorphic to Snub({3,8}), isomorphic to A3.895. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^3, u.3^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.3^8, x.2^-1 * x.3 * x.1 * x.2 * x.3 * x.1 * x.3^-1 * x.2^-1 * x.3, x.3 * x.1 * x.3^-2 * x.2 * x.3^2 * x.1 * x.3^-3 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 8) #DARTS : 480 R = (1, 97, 193, 289, 385)(2, 98, 194, 290, 386)(3, 99, 195, 291, 387)(4, 100, 196, 292, 388)(5, 101, 197, 293, 389)(6, 102, 198, 294, 390)(7, 103, 199, 295, 391)(8, 104, 200, 296, 392)(9, 105, 201, 297, 393)(10, 106, 202, 298, 394)(11, 107, 203, 299, 395)(12, 108, 204, 300, 396)(13, 109, 205, 301, 397)(14, 110, 206, 302, 398)(15, 111, 207, 303, 399)(16, 112, 208, 304, 400)(17, 113, 209, 305, 401)(18, 114, 210, 306, 402)(19, 115, 211, 307, 403)(20, 116, 212, 308, 404)(21, 117, 213, 309, 405)(22, 118, 214, 310, 406)(23, 119, 215, 311, 407)(24, 120, 216, 312, 408)(25, 121, 217, 313, 409)(26, 122, 218, 314, 410)(27, 123, 219, 315, 411)(28, 124, 220, 316, 412)(29, 125, 221, 317, 413)(30, 126, 222, 318, 414)(31, 127, 223, 319, 415)(32, 128, 224, 320, 416)(33, 129, 225, 321, 417)(34, 130, 226, 322, 418)(35, 131, 227, 323, 419)(36, 132, 228, 324, 420)(37, 133, 229, 325, 421)(38, 134, 230, 326, 422)(39, 135, 231, 327, 423)(40, 136, 232, 328, 424)(41, 137, 233, 329, 425)(42, 138, 234, 330, 426)(43, 139, 235, 331, 427)(44, 140, 236, 332, 428)(45, 141, 237, 333, 429)(46, 142, 238, 334, 430)(47, 143, 239, 335, 431)(48, 144, 240, 336, 432)(49, 145, 241, 337, 433)(50, 146, 242, 338, 434)(51, 147, 243, 339, 435)(52, 148, 244, 340, 436)(53, 149, 245, 341, 437)(54, 150, 246, 342, 438)(55, 151, 247, 343, 439)(56, 152, 248, 344, 440)(57, 153, 249, 345, 441)(58, 154, 250, 346, 442)(59, 155, 251, 347, 443)(60, 156, 252, 348, 444)(61, 157, 253, 349, 445)(62, 158, 254, 350, 446)(63, 159, 255, 351, 447)(64, 160, 256, 352, 448)(65, 161, 257, 353, 449)(66, 162, 258, 354, 450)(67, 163, 259, 355, 451)(68, 164, 260, 356, 452)(69, 165, 261, 357, 453)(70, 166, 262, 358, 454)(71, 167, 263, 359, 455)(72, 168, 264, 360, 456)(73, 169, 265, 361, 457)(74, 170, 266, 362, 458)(75, 171, 267, 363, 459)(76, 172, 268, 364, 460)(77, 173, 269, 365, 461)(78, 174, 270, 366, 462)(79, 175, 271, 367, 463)(80, 176, 272, 368, 464)(81, 177, 273, 369, 465)(82, 178, 274, 370, 466)(83, 179, 275, 371, 467)(84, 180, 276, 372, 468)(85, 181, 277, 373, 469)(86, 182, 278, 374, 470)(87, 183, 279, 375, 471)(88, 184, 280, 376, 472)(89, 185, 281, 377, 473)(90, 186, 282, 378, 474)(91, 187, 283, 379, 475)(92, 188, 284, 380, 476)(93, 189, 285, 381, 477)(94, 190, 286, 382, 478)(95, 191, 287, 383, 479)(96, 192, 288, 384, 480) L = (1, 4)(2, 8)(3, 5)(6, 34)(7, 37)(9, 18)(10, 81)(11, 82)(12, 33)(13, 17)(14, 21)(15, 85)(16, 53)(19, 30)(20, 29)(22, 63)(23, 58)(24, 25)(26, 48)(27, 64)(28, 59)(31, 32)(35, 39)(36, 44)(38, 40)(41, 43)(42, 45)(46, 47)(49, 80)(50, 96)(51, 75)(52, 79)(54, 76)(55, 70)(56, 74)(57, 94)(60, 71)(61, 89)(62, 93)(65, 91)(66, 95)(67, 92)(68, 86)(69, 90)(72, 87)(73, 83)(77, 88)(78, 84)(97, 194)(98, 197)(99, 209)(100, 210)(101, 193)(102, 211)(103, 212)(104, 213)(105, 261)(106, 214)(107, 215)(108, 216)(109, 258)(110, 257)(111, 220)(112, 268)(113, 226)(114, 229)(115, 273)(116, 274)(117, 225)(118, 275)(119, 276)(120, 277)(121, 245)(122, 278)(123, 279)(124, 280)(125, 242)(126, 241)(127, 284)(128, 252)(129, 200)(130, 195)(131, 205)(132, 201)(133, 196)(134, 222)(135, 221)(136, 206)(137, 282)(138, 255)(139, 250)(140, 217)(141, 287)(142, 283)(143, 251)(144, 246)(145, 230)(146, 231)(147, 234)(148, 235)(149, 236)(150, 249)(151, 254)(152, 239)(153, 240)(154, 244)(155, 248)(156, 253)(157, 224)(158, 256)(159, 243)(160, 247)(161, 232)(162, 227)(163, 237)(164, 233)(165, 228)(166, 286)(167, 285)(168, 238)(169, 218)(170, 271)(171, 266)(172, 281)(173, 223)(174, 219)(175, 267)(176, 262)(177, 198)(178, 199)(179, 202)(180, 203)(181, 204)(182, 265)(183, 270)(184, 207)(185, 208)(186, 260)(187, 264)(188, 269)(189, 288)(190, 272)(191, 259)(192, 263)(289, 387)(290, 388)(291, 390)(292, 391)(293, 392)(294, 394)(295, 395)(296, 396)(297, 428)(298, 457)(299, 462)(300, 399)(301, 423)(302, 422)(303, 461)(304, 445)(305, 389)(306, 385)(307, 418)(308, 421)(309, 386)(310, 465)(311, 466)(312, 417)(313, 420)(314, 467)(315, 468)(316, 469)(317, 419)(318, 424)(319, 472)(320, 473)(321, 398)(322, 397)(323, 479)(324, 474)(325, 393)(326, 464)(327, 480)(328, 475)(329, 470)(330, 459)(331, 463)(332, 400)(333, 476)(334, 471)(335, 458)(336, 478)(337, 403)(338, 404)(339, 406)(340, 407)(341, 408)(342, 410)(343, 411)(344, 412)(345, 460)(346, 425)(347, 430)(348, 415)(349, 455)(350, 454)(351, 429)(352, 477)(353, 405)(354, 401)(355, 450)(356, 453)(357, 402)(358, 433)(359, 434)(360, 449)(361, 452)(362, 435)(363, 436)(364, 437)(365, 451)(366, 456)(367, 440)(368, 441)(369, 414)(370, 413)(371, 447)(372, 442)(373, 409)(374, 432)(375, 448)(376, 443)(377, 438)(378, 427)(379, 431)(380, 416)(381, 444)(382, 439)(383, 426)(384, 446) MAP : A3.897 NOTES : type I, chiral, isomorphic to Snub({3,8}), isomorphic to A3.895. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^3, u.3^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.3^8, x.2^-1 * x.3 * x.1 * x.2 * x.3 * x.1 * x.3^-1 * x.2^-1 * x.3, x.3 * x.1 * x.3^-2 * x.2 * x.3^2 * x.1 * x.3^-3 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 8) #DARTS : 480 R = (1, 97, 193, 289, 385)(2, 98, 194, 290, 386)(3, 99, 195, 291, 387)(4, 100, 196, 292, 388)(5, 101, 197, 293, 389)(6, 102, 198, 294, 390)(7, 103, 199, 295, 391)(8, 104, 200, 296, 392)(9, 105, 201, 297, 393)(10, 106, 202, 298, 394)(11, 107, 203, 299, 395)(12, 108, 204, 300, 396)(13, 109, 205, 301, 397)(14, 110, 206, 302, 398)(15, 111, 207, 303, 399)(16, 112, 208, 304, 400)(17, 113, 209, 305, 401)(18, 114, 210, 306, 402)(19, 115, 211, 307, 403)(20, 116, 212, 308, 404)(21, 117, 213, 309, 405)(22, 118, 214, 310, 406)(23, 119, 215, 311, 407)(24, 120, 216, 312, 408)(25, 121, 217, 313, 409)(26, 122, 218, 314, 410)(27, 123, 219, 315, 411)(28, 124, 220, 316, 412)(29, 125, 221, 317, 413)(30, 126, 222, 318, 414)(31, 127, 223, 319, 415)(32, 128, 224, 320, 416)(33, 129, 225, 321, 417)(34, 130, 226, 322, 418)(35, 131, 227, 323, 419)(36, 132, 228, 324, 420)(37, 133, 229, 325, 421)(38, 134, 230, 326, 422)(39, 135, 231, 327, 423)(40, 136, 232, 328, 424)(41, 137, 233, 329, 425)(42, 138, 234, 330, 426)(43, 139, 235, 331, 427)(44, 140, 236, 332, 428)(45, 141, 237, 333, 429)(46, 142, 238, 334, 430)(47, 143, 239, 335, 431)(48, 144, 240, 336, 432)(49, 145, 241, 337, 433)(50, 146, 242, 338, 434)(51, 147, 243, 339, 435)(52, 148, 244, 340, 436)(53, 149, 245, 341, 437)(54, 150, 246, 342, 438)(55, 151, 247, 343, 439)(56, 152, 248, 344, 440)(57, 153, 249, 345, 441)(58, 154, 250, 346, 442)(59, 155, 251, 347, 443)(60, 156, 252, 348, 444)(61, 157, 253, 349, 445)(62, 158, 254, 350, 446)(63, 159, 255, 351, 447)(64, 160, 256, 352, 448)(65, 161, 257, 353, 449)(66, 162, 258, 354, 450)(67, 163, 259, 355, 451)(68, 164, 260, 356, 452)(69, 165, 261, 357, 453)(70, 166, 262, 358, 454)(71, 167, 263, 359, 455)(72, 168, 264, 360, 456)(73, 169, 265, 361, 457)(74, 170, 266, 362, 458)(75, 171, 267, 363, 459)(76, 172, 268, 364, 460)(77, 173, 269, 365, 461)(78, 174, 270, 366, 462)(79, 175, 271, 367, 463)(80, 176, 272, 368, 464)(81, 177, 273, 369, 465)(82, 178, 274, 370, 466)(83, 179, 275, 371, 467)(84, 180, 276, 372, 468)(85, 181, 277, 373, 469)(86, 182, 278, 374, 470)(87, 183, 279, 375, 471)(88, 184, 280, 376, 472)(89, 185, 281, 377, 473)(90, 186, 282, 378, 474)(91, 187, 283, 379, 475)(92, 188, 284, 380, 476)(93, 189, 285, 381, 477)(94, 190, 286, 382, 478)(95, 191, 287, 383, 479)(96, 192, 288, 384, 480) L = (1, 4)(2, 8)(3, 5)(6, 34)(7, 37)(9, 18)(10, 81)(11, 82)(12, 33)(13, 17)(14, 21)(15, 85)(16, 53)(19, 30)(20, 29)(22, 63)(23, 58)(24, 25)(26, 48)(27, 64)(28, 59)(31, 32)(35, 39)(36, 44)(38, 40)(41, 43)(42, 45)(46, 47)(49, 80)(50, 96)(51, 75)(52, 79)(54, 76)(55, 70)(56, 74)(57, 94)(60, 71)(61, 89)(62, 93)(65, 91)(66, 95)(67, 92)(68, 86)(69, 90)(72, 87)(73, 83)(77, 88)(78, 84)(97, 197)(98, 193)(99, 226)(100, 229)(101, 194)(102, 273)(103, 274)(104, 225)(105, 228)(106, 275)(107, 276)(108, 277)(109, 227)(110, 232)(111, 280)(112, 281)(113, 195)(114, 196)(115, 198)(116, 199)(117, 200)(118, 202)(119, 203)(120, 204)(121, 236)(122, 265)(123, 270)(124, 207)(125, 231)(126, 230)(127, 269)(128, 253)(129, 213)(130, 209)(131, 258)(132, 261)(133, 210)(134, 241)(135, 242)(136, 257)(137, 260)(138, 243)(139, 244)(140, 245)(141, 259)(142, 264)(143, 248)(144, 249)(145, 222)(146, 221)(147, 255)(148, 250)(149, 217)(150, 240)(151, 256)(152, 251)(153, 246)(154, 235)(155, 239)(156, 224)(157, 252)(158, 247)(159, 234)(160, 254)(161, 206)(162, 205)(163, 287)(164, 282)(165, 201)(166, 272)(167, 288)(168, 283)(169, 278)(170, 267)(171, 271)(172, 208)(173, 284)(174, 279)(175, 266)(176, 286)(177, 211)(178, 212)(179, 214)(180, 215)(181, 216)(182, 218)(183, 219)(184, 220)(185, 268)(186, 233)(187, 238)(188, 223)(189, 263)(190, 262)(191, 237)(192, 285)(289, 392)(290, 387)(291, 397)(292, 393)(293, 388)(294, 414)(295, 413)(296, 398)(297, 474)(298, 447)(299, 442)(300, 409)(301, 479)(302, 475)(303, 443)(304, 438)(305, 390)(306, 391)(307, 394)(308, 395)(309, 396)(310, 457)(311, 462)(312, 399)(313, 400)(314, 452)(315, 456)(316, 461)(317, 480)(318, 464)(319, 451)(320, 455)(321, 386)(322, 389)(323, 401)(324, 402)(325, 385)(326, 403)(327, 404)(328, 405)(329, 453)(330, 406)(331, 407)(332, 408)(333, 450)(334, 449)(335, 412)(336, 460)(337, 424)(338, 419)(339, 429)(340, 425)(341, 420)(342, 478)(343, 477)(344, 430)(345, 410)(346, 463)(347, 458)(348, 473)(349, 415)(350, 411)(351, 459)(352, 454)(353, 422)(354, 423)(355, 426)(356, 427)(357, 428)(358, 441)(359, 446)(360, 431)(361, 432)(362, 436)(363, 440)(364, 445)(365, 416)(366, 448)(367, 435)(368, 439)(369, 418)(370, 421)(371, 465)(372, 466)(373, 417)(374, 467)(375, 468)(376, 469)(377, 437)(378, 470)(379, 471)(380, 472)(381, 434)(382, 433)(383, 476)(384, 444) MAP : A3.898 NOTES : type I, chiral, isomorphic to Snub({3,8}), isomorphic to A3.895. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^3, u.2^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^3, x.2^8, x.2^-1 * x.1 * x.2 * x.3 * x.1 * x.3^-1 * x.2^-2 * x.3, x.2^2 * x.3 * x.2^-2 * x.1 * x.2 * x.3^-1 * x.2^-3 * x.1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 8) #DARTS : 480 R = (1, 97, 193, 289, 385)(2, 98, 194, 290, 386)(3, 99, 195, 291, 387)(4, 100, 196, 292, 388)(5, 101, 197, 293, 389)(6, 102, 198, 294, 390)(7, 103, 199, 295, 391)(8, 104, 200, 296, 392)(9, 105, 201, 297, 393)(10, 106, 202, 298, 394)(11, 107, 203, 299, 395)(12, 108, 204, 300, 396)(13, 109, 205, 301, 397)(14, 110, 206, 302, 398)(15, 111, 207, 303, 399)(16, 112, 208, 304, 400)(17, 113, 209, 305, 401)(18, 114, 210, 306, 402)(19, 115, 211, 307, 403)(20, 116, 212, 308, 404)(21, 117, 213, 309, 405)(22, 118, 214, 310, 406)(23, 119, 215, 311, 407)(24, 120, 216, 312, 408)(25, 121, 217, 313, 409)(26, 122, 218, 314, 410)(27, 123, 219, 315, 411)(28, 124, 220, 316, 412)(29, 125, 221, 317, 413)(30, 126, 222, 318, 414)(31, 127, 223, 319, 415)(32, 128, 224, 320, 416)(33, 129, 225, 321, 417)(34, 130, 226, 322, 418)(35, 131, 227, 323, 419)(36, 132, 228, 324, 420)(37, 133, 229, 325, 421)(38, 134, 230, 326, 422)(39, 135, 231, 327, 423)(40, 136, 232, 328, 424)(41, 137, 233, 329, 425)(42, 138, 234, 330, 426)(43, 139, 235, 331, 427)(44, 140, 236, 332, 428)(45, 141, 237, 333, 429)(46, 142, 238, 334, 430)(47, 143, 239, 335, 431)(48, 144, 240, 336, 432)(49, 145, 241, 337, 433)(50, 146, 242, 338, 434)(51, 147, 243, 339, 435)(52, 148, 244, 340, 436)(53, 149, 245, 341, 437)(54, 150, 246, 342, 438)(55, 151, 247, 343, 439)(56, 152, 248, 344, 440)(57, 153, 249, 345, 441)(58, 154, 250, 346, 442)(59, 155, 251, 347, 443)(60, 156, 252, 348, 444)(61, 157, 253, 349, 445)(62, 158, 254, 350, 446)(63, 159, 255, 351, 447)(64, 160, 256, 352, 448)(65, 161, 257, 353, 449)(66, 162, 258, 354, 450)(67, 163, 259, 355, 451)(68, 164, 260, 356, 452)(69, 165, 261, 357, 453)(70, 166, 262, 358, 454)(71, 167, 263, 359, 455)(72, 168, 264, 360, 456)(73, 169, 265, 361, 457)(74, 170, 266, 362, 458)(75, 171, 267, 363, 459)(76, 172, 268, 364, 460)(77, 173, 269, 365, 461)(78, 174, 270, 366, 462)(79, 175, 271, 367, 463)(80, 176, 272, 368, 464)(81, 177, 273, 369, 465)(82, 178, 274, 370, 466)(83, 179, 275, 371, 467)(84, 180, 276, 372, 468)(85, 181, 277, 373, 469)(86, 182, 278, 374, 470)(87, 183, 279, 375, 471)(88, 184, 280, 376, 472)(89, 185, 281, 377, 473)(90, 186, 282, 378, 474)(91, 187, 283, 379, 475)(92, 188, 284, 380, 476)(93, 189, 285, 381, 477)(94, 190, 286, 382, 478)(95, 191, 287, 383, 479)(96, 192, 288, 384, 480) L = (1, 4)(2, 8)(3, 5)(6, 34)(7, 37)(9, 18)(10, 81)(11, 82)(12, 33)(13, 17)(14, 21)(15, 85)(16, 53)(19, 30)(20, 29)(22, 63)(23, 58)(24, 25)(26, 48)(27, 64)(28, 59)(31, 32)(35, 39)(36, 44)(38, 40)(41, 43)(42, 45)(46, 47)(49, 80)(50, 96)(51, 75)(52, 79)(54, 76)(55, 70)(56, 74)(57, 94)(60, 71)(61, 89)(62, 93)(65, 91)(66, 95)(67, 92)(68, 86)(69, 90)(72, 87)(73, 83)(77, 88)(78, 84)(97, 202)(98, 203)(99, 265)(100, 270)(101, 207)(102, 260)(103, 264)(104, 269)(105, 253)(106, 261)(107, 257)(108, 259)(109, 254)(110, 249)(111, 258)(112, 242)(113, 204)(114, 198)(115, 231)(116, 236)(117, 199)(118, 232)(119, 227)(120, 230)(121, 235)(122, 237)(123, 233)(124, 228)(125, 234)(126, 239)(127, 238)(128, 218)(129, 272)(130, 288)(131, 267)(132, 271)(133, 208)(134, 268)(135, 262)(136, 266)(137, 286)(138, 215)(139, 220)(140, 263)(141, 281)(142, 285)(143, 214)(144, 219)(145, 205)(146, 201)(147, 222)(148, 221)(149, 206)(150, 255)(151, 250)(152, 217)(153, 216)(154, 240)(155, 256)(156, 251)(157, 212)(158, 211)(159, 224)(160, 223)(161, 196)(162, 200)(163, 197)(164, 193)(165, 195)(166, 226)(167, 229)(168, 194)(169, 210)(170, 273)(171, 274)(172, 225)(173, 209)(174, 213)(175, 277)(176, 245)(177, 283)(178, 287)(179, 284)(180, 278)(181, 282)(182, 247)(183, 252)(184, 279)(185, 275)(186, 248)(187, 243)(188, 246)(189, 280)(190, 276)(191, 244)(192, 241)(289, 470)(290, 471)(291, 474)(292, 475)(293, 476)(294, 393)(295, 398)(296, 479)(297, 480)(298, 388)(299, 392)(300, 397)(301, 464)(302, 400)(303, 387)(304, 391)(305, 472)(306, 467)(307, 477)(308, 473)(309, 468)(310, 430)(311, 429)(312, 478)(313, 458)(314, 415)(315, 410)(316, 425)(317, 463)(318, 459)(319, 411)(320, 406)(321, 438)(322, 439)(323, 442)(324, 443)(325, 444)(326, 409)(327, 414)(328, 447)(329, 448)(330, 404)(331, 408)(332, 413)(333, 432)(334, 416)(335, 403)(336, 407)(337, 434)(338, 437)(339, 449)(340, 450)(341, 433)(342, 451)(343, 452)(344, 453)(345, 405)(346, 454)(347, 455)(348, 456)(349, 402)(350, 401)(351, 460)(352, 412)(353, 466)(354, 469)(355, 417)(356, 418)(357, 465)(358, 419)(359, 420)(360, 421)(361, 389)(362, 422)(363, 423)(364, 424)(365, 386)(366, 385)(367, 428)(368, 396)(369, 440)(370, 435)(371, 445)(372, 441)(373, 436)(374, 462)(375, 461)(376, 446)(377, 426)(378, 399)(379, 394)(380, 457)(381, 431)(382, 427)(383, 395)(384, 390) MAP : A3.899 NOTES : type I, chiral, isomorphic to Snub({3,12}), representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 12, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^3, u.3^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.1 * x.3^-2 * x.2 * x.3^3, x.3^12 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 12) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 3)(2, 9)(4, 5)(6, 10)(7, 26)(8, 11)(12, 24)(13, 42)(14, 25)(15, 40)(16, 37)(17, 23)(18, 22)(19, 30)(20, 46)(21, 29)(27, 39)(28, 45)(31, 38)(32, 34)(33, 48)(35, 47)(36, 43)(41, 44)(49, 126)(50, 110)(51, 119)(52, 125)(53, 142)(54, 103)(55, 109)(56, 135)(57, 118)(58, 114)(59, 108)(60, 111)(61, 102)(62, 140)(63, 107)(64, 100)(65, 123)(66, 127)(67, 116)(68, 121)(69, 124)(70, 128)(71, 144)(72, 141)(73, 115)(74, 113)(75, 122)(76, 138)(77, 112)(78, 143)(79, 106)(80, 105)(81, 133)(82, 129)(83, 136)(84, 104)(85, 130)(86, 131)(87, 132)(88, 134)(89, 120)(90, 117)(91, 101)(92, 98)(93, 137)(94, 139)(95, 97)(96, 99)(145, 227)(146, 233)(147, 225)(148, 229)(149, 228)(150, 234)(151, 202)(152, 235)(153, 226)(154, 230)(155, 232)(156, 200)(157, 218)(158, 201)(159, 216)(160, 213)(161, 199)(162, 198)(163, 206)(164, 222)(165, 205)(166, 194)(167, 193)(168, 236)(169, 238)(170, 231)(171, 215)(172, 221)(173, 197)(174, 195)(175, 214)(176, 210)(177, 224)(178, 208)(179, 223)(180, 219)(181, 240)(182, 207)(183, 203)(184, 239)(185, 220)(186, 237)(187, 212)(188, 217)(189, 204)(190, 196)(191, 211)(192, 209) MAP : A3.900 NOTES : type I, chiral, isomorphic to Snub({3,12}), isomorphic to A3.899. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 12, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^3, u.2^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^3, x.1 * x.2^3 * x.3 * x.2^-2, x.2^12 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 12) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 3)(2, 9)(4, 5)(6, 10)(7, 26)(8, 11)(12, 24)(13, 42)(14, 25)(15, 40)(16, 37)(17, 23)(18, 22)(19, 30)(20, 46)(21, 29)(27, 39)(28, 45)(31, 38)(32, 34)(33, 48)(35, 47)(36, 43)(41, 44)(49, 115)(50, 121)(51, 113)(52, 117)(53, 116)(54, 122)(55, 138)(56, 123)(57, 114)(58, 118)(59, 120)(60, 136)(61, 106)(62, 137)(63, 104)(64, 101)(65, 135)(66, 134)(67, 142)(68, 110)(69, 141)(70, 130)(71, 129)(72, 124)(73, 126)(74, 119)(75, 103)(76, 109)(77, 133)(78, 131)(79, 102)(80, 98)(81, 112)(82, 144)(83, 111)(84, 107)(85, 128)(86, 143)(87, 139)(88, 127)(89, 108)(90, 125)(91, 100)(92, 105)(93, 140)(94, 132)(95, 99)(96, 97)(145, 225)(146, 226)(147, 227)(148, 228)(149, 229)(150, 230)(151, 231)(152, 232)(153, 233)(154, 234)(155, 235)(156, 236)(157, 237)(158, 238)(159, 239)(160, 240)(161, 193)(162, 194)(163, 195)(164, 196)(165, 197)(166, 198)(167, 199)(168, 200)(169, 201)(170, 202)(171, 203)(172, 204)(173, 205)(174, 206)(175, 207)(176, 208)(177, 209)(178, 210)(179, 211)(180, 212)(181, 213)(182, 214)(183, 215)(184, 216)(185, 217)(186, 218)(187, 219)(188, 220)(189, 221)(190, 222)(191, 223)(192, 224) MAP : A3.901 NOTES : type I, chiral, isomorphic to Snub({3,12}), isomorphic to A3.899. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 12, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^3, u.2^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^3, x.1 * x.2^3 * x.3 * x.2^-2, x.2^12 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 12) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 3)(2, 9)(4, 5)(6, 10)(7, 26)(8, 11)(12, 24)(13, 42)(14, 25)(15, 40)(16, 37)(17, 23)(18, 22)(19, 30)(20, 46)(21, 29)(27, 39)(28, 45)(31, 38)(32, 34)(33, 48)(35, 47)(36, 43)(41, 44)(49, 102)(50, 109)(51, 98)(52, 97)(53, 103)(54, 140)(55, 143)(56, 110)(57, 101)(58, 104)(59, 99)(60, 100)(61, 139)(62, 144)(63, 105)(64, 106)(65, 118)(66, 125)(67, 114)(68, 113)(69, 119)(70, 108)(71, 111)(72, 126)(73, 117)(74, 120)(75, 115)(76, 116)(77, 107)(78, 112)(79, 121)(80, 122)(81, 134)(82, 141)(83, 130)(84, 129)(85, 135)(86, 124)(87, 127)(88, 142)(89, 133)(90, 136)(91, 131)(92, 132)(93, 123)(94, 128)(95, 137)(96, 138)(145, 197)(146, 193)(147, 200)(148, 216)(149, 194)(150, 195)(151, 196)(152, 198)(153, 232)(154, 229)(155, 213)(156, 210)(157, 201)(158, 203)(159, 209)(160, 211)(161, 238)(162, 222)(163, 231)(164, 237)(165, 206)(166, 215)(167, 221)(168, 199)(169, 230)(170, 226)(171, 220)(172, 223)(173, 214)(174, 204)(175, 219)(176, 212)(177, 235)(178, 239)(179, 228)(180, 233)(181, 236)(182, 240)(183, 208)(184, 205)(185, 227)(186, 225)(187, 234)(188, 202)(189, 224)(190, 207)(191, 218)(192, 217) MAP : A3.902 NOTES : type I, chiral, isomorphic to Snub({3,12}), isomorphic to A3.899. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 12, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^3, u.2^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^3, x.1 * x.2^3 * x.3 * x.2^-2, x.2^12 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 12) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 3)(2, 9)(4, 5)(6, 10)(7, 26)(8, 11)(12, 24)(13, 42)(14, 25)(15, 40)(16, 37)(17, 23)(18, 22)(19, 30)(20, 46)(21, 29)(27, 39)(28, 45)(31, 38)(32, 34)(33, 48)(35, 47)(36, 43)(41, 44)(49, 100)(50, 99)(51, 107)(52, 108)(53, 105)(54, 97)(55, 101)(56, 106)(57, 111)(58, 112)(59, 125)(60, 118)(61, 98)(62, 104)(63, 119)(64, 126)(65, 116)(66, 115)(67, 123)(68, 124)(69, 121)(70, 113)(71, 117)(72, 122)(73, 127)(74, 128)(75, 141)(76, 134)(77, 114)(78, 120)(79, 135)(80, 142)(81, 132)(82, 131)(83, 139)(84, 140)(85, 137)(86, 129)(87, 133)(88, 138)(89, 143)(90, 144)(91, 109)(92, 102)(93, 130)(94, 136)(95, 103)(96, 110)(145, 202)(146, 234)(147, 201)(148, 195)(149, 218)(150, 233)(151, 227)(152, 217)(153, 196)(154, 203)(155, 193)(156, 197)(157, 228)(158, 225)(159, 194)(160, 198)(161, 210)(162, 213)(163, 214)(164, 215)(165, 209)(166, 216)(167, 232)(168, 211)(169, 221)(170, 204)(171, 222)(172, 238)(173, 200)(174, 229)(175, 206)(176, 199)(177, 223)(178, 220)(179, 224)(180, 240)(181, 219)(182, 237)(183, 230)(184, 212)(185, 208)(186, 207)(187, 239)(188, 235)(189, 231)(190, 226)(191, 236)(192, 205) MAP : A3.903 NOTES : type I, chiral, isomorphic to Snub({3,12}), isomorphic to A3.899. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 12, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^3, u.3^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.1 * x.3^-2 * x.2 * x.3^3, x.3^12 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 12) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 3)(2, 9)(4, 5)(6, 10)(7, 26)(8, 11)(12, 24)(13, 42)(14, 25)(15, 40)(16, 37)(17, 23)(18, 22)(19, 30)(20, 46)(21, 29)(27, 39)(28, 45)(31, 38)(32, 34)(33, 48)(35, 47)(36, 43)(41, 44)(49, 101)(50, 97)(51, 104)(52, 120)(53, 98)(54, 99)(55, 100)(56, 102)(57, 136)(58, 133)(59, 117)(60, 114)(61, 105)(62, 107)(63, 113)(64, 115)(65, 142)(66, 126)(67, 135)(68, 141)(69, 110)(70, 119)(71, 125)(72, 103)(73, 134)(74, 130)(75, 124)(76, 127)(77, 118)(78, 108)(79, 123)(80, 116)(81, 139)(82, 143)(83, 132)(84, 137)(85, 140)(86, 144)(87, 112)(88, 109)(89, 131)(90, 129)(91, 138)(92, 106)(93, 128)(94, 111)(95, 122)(96, 121)(145, 201)(146, 196)(147, 202)(148, 218)(149, 195)(150, 203)(151, 204)(152, 193)(153, 234)(154, 233)(155, 217)(156, 211)(157, 207)(158, 221)(159, 212)(160, 219)(161, 232)(162, 216)(163, 229)(164, 226)(165, 200)(166, 213)(167, 210)(168, 197)(169, 225)(170, 227)(171, 230)(172, 231)(173, 209)(174, 214)(175, 237)(176, 220)(177, 205)(178, 199)(179, 236)(180, 239)(181, 198)(182, 206)(183, 222)(184, 194)(185, 235)(186, 228)(187, 240)(188, 208)(189, 238)(190, 215)(191, 224)(192, 223) MAP : A3.904 NOTES : type I, chiral, isomorphic to Snub({3,12}), isomorphic to A3.899. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 12, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^3, u.3^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.1 * x.3^-2 * x.2 * x.3^3, x.3^12 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 12) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 3)(2, 9)(4, 5)(6, 10)(7, 26)(8, 11)(12, 24)(13, 42)(14, 25)(15, 40)(16, 37)(17, 23)(18, 22)(19, 30)(20, 46)(21, 29)(27, 39)(28, 45)(31, 38)(32, 34)(33, 48)(35, 47)(36, 43)(41, 44)(49, 98)(50, 101)(51, 102)(52, 103)(53, 97)(54, 104)(55, 120)(56, 99)(57, 109)(58, 140)(59, 110)(60, 126)(61, 136)(62, 117)(63, 142)(64, 135)(65, 111)(66, 108)(67, 112)(68, 128)(69, 107)(70, 125)(71, 118)(72, 100)(73, 144)(74, 143)(75, 127)(76, 123)(77, 119)(78, 114)(79, 124)(80, 141)(81, 138)(82, 122)(83, 137)(84, 131)(85, 106)(86, 121)(87, 115)(88, 105)(89, 132)(90, 139)(91, 129)(92, 133)(93, 116)(94, 113)(95, 130)(96, 134)(145, 196)(146, 195)(147, 203)(148, 204)(149, 201)(150, 193)(151, 197)(152, 202)(153, 207)(154, 208)(155, 221)(156, 214)(157, 194)(158, 200)(159, 215)(160, 222)(161, 212)(162, 211)(163, 219)(164, 220)(165, 217)(166, 209)(167, 213)(168, 218)(169, 223)(170, 224)(171, 237)(172, 230)(173, 210)(174, 216)(175, 231)(176, 238)(177, 228)(178, 227)(179, 235)(180, 236)(181, 233)(182, 225)(183, 229)(184, 234)(185, 239)(186, 240)(187, 205)(188, 198)(189, 226)(190, 232)(191, 199)(192, 206) MAP : A3.905 NOTES : type I, chiral, isomorphic to Snub({3,12}), isomorphic to A3.899. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 12, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^3, u.2^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^3, x.1 * x.2^3 * x.3 * x.2^-2, x.2^12 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 12) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 3)(2, 9)(4, 5)(6, 10)(7, 26)(8, 11)(12, 24)(13, 42)(14, 25)(15, 40)(16, 37)(17, 23)(18, 22)(19, 30)(20, 46)(21, 29)(27, 39)(28, 45)(31, 38)(32, 34)(33, 48)(35, 47)(36, 43)(41, 44)(49, 144)(50, 128)(51, 143)(52, 139)(53, 112)(54, 127)(55, 123)(56, 111)(57, 140)(58, 109)(59, 132)(60, 137)(61, 124)(62, 116)(63, 131)(64, 129)(65, 99)(66, 105)(67, 97)(68, 101)(69, 100)(70, 106)(71, 122)(72, 107)(73, 98)(74, 102)(75, 104)(76, 120)(77, 138)(78, 121)(79, 136)(80, 133)(81, 119)(82, 118)(83, 126)(84, 142)(85, 125)(86, 114)(87, 113)(88, 108)(89, 110)(90, 103)(91, 135)(92, 141)(93, 117)(94, 115)(95, 134)(96, 130)(145, 222)(146, 206)(147, 215)(148, 221)(149, 238)(150, 199)(151, 205)(152, 231)(153, 214)(154, 210)(155, 204)(156, 207)(157, 198)(158, 236)(159, 203)(160, 196)(161, 219)(162, 223)(163, 212)(164, 217)(165, 220)(166, 224)(167, 240)(168, 237)(169, 211)(170, 209)(171, 218)(172, 234)(173, 208)(174, 239)(175, 202)(176, 201)(177, 229)(178, 225)(179, 232)(180, 200)(181, 226)(182, 227)(183, 228)(184, 230)(185, 216)(186, 213)(187, 197)(188, 194)(189, 233)(190, 235)(191, 193)(192, 195) MAP : A3.906 NOTES : type I, chiral, isomorphic to Snub({3,12}), isomorphic to A3.899. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {12, 3, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 12, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^3, u.3^12 > CTG (small) : <48, 33> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.1 * x.3^-2 * x.2 * x.3^3, x.3^12 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 12) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 3)(2, 9)(4, 5)(6, 10)(7, 26)(8, 11)(12, 24)(13, 42)(14, 25)(15, 40)(16, 37)(17, 23)(18, 22)(19, 30)(20, 46)(21, 29)(27, 39)(28, 45)(31, 38)(32, 34)(33, 48)(35, 47)(36, 43)(41, 44)(49, 143)(50, 140)(51, 144)(52, 112)(53, 139)(54, 109)(55, 102)(56, 132)(57, 128)(58, 127)(59, 111)(60, 107)(61, 103)(62, 98)(63, 108)(64, 125)(65, 122)(66, 106)(67, 121)(68, 115)(69, 138)(70, 105)(71, 99)(72, 137)(73, 116)(74, 123)(75, 113)(76, 117)(77, 100)(78, 97)(79, 114)(80, 118)(81, 130)(82, 133)(83, 134)(84, 135)(85, 129)(86, 136)(87, 104)(88, 131)(89, 141)(90, 124)(91, 142)(92, 110)(93, 120)(94, 101)(95, 126)(96, 119)(145, 211)(146, 217)(147, 209)(148, 213)(149, 212)(150, 218)(151, 234)(152, 219)(153, 210)(154, 214)(155, 216)(156, 232)(157, 202)(158, 233)(159, 200)(160, 197)(161, 231)(162, 230)(163, 238)(164, 206)(165, 237)(166, 226)(167, 225)(168, 220)(169, 222)(170, 215)(171, 199)(172, 205)(173, 229)(174, 227)(175, 198)(176, 194)(177, 208)(178, 240)(179, 207)(180, 203)(181, 224)(182, 239)(183, 235)(184, 223)(185, 204)(186, 221)(187, 196)(188, 201)(189, 236)(190, 228)(191, 195)(192, 193) MAP : A3.907 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (3, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, (u.4 * u.3)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^3, x.1 * x.2 * x.4^-1, (x.3 * x.1)^2, (x.4 * x.3)^3 > SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 6, 6) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 6)(2, 7)(3, 5)(4, 22)(8, 9)(10, 16)(11, 24)(12, 23)(13, 18)(14, 19)(15, 17)(20, 21)(25, 31)(26, 29)(27, 30)(28, 37)(32, 42)(33, 46)(34, 47)(35, 45)(36, 38)(39, 44)(40, 43)(41, 48)(49, 98)(50, 99)(51, 97)(52, 114)(53, 103)(54, 101)(55, 102)(56, 109)(57, 100)(58, 108)(59, 116)(60, 115)(61, 118)(62, 119)(63, 117)(64, 110)(65, 107)(66, 105)(67, 106)(68, 113)(69, 120)(70, 104)(71, 112)(72, 111)(73, 90)(74, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96) MAP : A3.908 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (3, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, (u.4 * u.3)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^3, x.1 * x.2 * x.4^-1, x.4 * x.1 * x.4^-1 * x.2, (x.4 * x.3 * x.2)^2, (x.4 * x.3)^3 > SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 6, 6) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 7)(2, 5)(3, 6)(4, 13)(8, 18)(9, 22)(10, 23)(11, 21)(12, 14)(15, 20)(16, 19)(17, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(49, 98)(50, 99)(51, 97)(52, 114)(53, 103)(54, 101)(55, 102)(56, 109)(57, 100)(58, 108)(59, 116)(60, 115)(61, 118)(62, 119)(63, 117)(64, 110)(65, 107)(66, 105)(67, 106)(68, 113)(69, 120)(70, 104)(71, 112)(72, 111)(73, 90)(74, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96) MAP : A3.909 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (3, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, (u.4 * u.3)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, (x.3 * x.1)^2, x.4^4, x.4 * x.3 * x.4^-2 * x.3 * x.2, (x.4 * x.3)^3, (x.3 * x.2)^3 > SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 6, 6) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 18)(2, 19)(3, 17)(4, 10)(5, 15)(6, 13)(7, 14)(8, 21)(9, 20)(11, 12)(16, 22)(23, 24)(25, 31)(26, 29)(27, 30)(28, 37)(32, 42)(33, 46)(34, 47)(35, 45)(36, 38)(39, 44)(40, 43)(41, 48)(49, 110)(50, 111)(51, 109)(52, 102)(53, 115)(54, 113)(55, 114)(56, 97)(57, 112)(58, 120)(59, 104)(60, 103)(61, 106)(62, 107)(63, 105)(64, 98)(65, 119)(66, 117)(67, 118)(68, 101)(69, 108)(70, 116)(71, 100)(72, 99)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.910 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (3, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, (u.4 * u.3)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4^4, x.1 * x.3 * x.4^-2 * x.3, (x.4 * x.3)^3 > SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 6, 6) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 12)(2, 20)(3, 4)(5, 16)(6, 24)(7, 8)(9, 19)(10, 17)(11, 18)(13, 23)(14, 21)(15, 22)(25, 45)(26, 46)(27, 47)(28, 48)(29, 33)(30, 34)(31, 35)(32, 36)(37, 41)(38, 42)(39, 43)(40, 44)(49, 110)(50, 111)(51, 109)(52, 102)(53, 115)(54, 113)(55, 114)(56, 97)(57, 112)(58, 120)(59, 104)(60, 103)(61, 106)(62, 107)(63, 105)(64, 98)(65, 119)(66, 117)(67, 118)(68, 101)(69, 108)(70, 116)(71, 100)(72, 99)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.911 NOTES : type I, reflexible, isomorphic to A3.908. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 5)(3, 8)(4, 9)(7, 10) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.4, u.1^2, u.2^2, u.3 * u.4^-1 * u.5, u.4 * u.5^-1 * u.6, (u.1 * u.3^-1)^3, (u.2 * u.6^-1)^3 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.4, x.4, x.1^2, x.2^2, x.5^-1 * x.3^-1, x.3^3, x.4 * x.5^-1 * x.6, x.3 * x.1 * x.3^-1 * x.2, x.5 * x.2 * x.5^-1 * x.1, (x.2 * x.1)^2, x.1 * x.2 * x.3 * x.2 * x.3^-1, (x.2 * x.6^-1)^3 > SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.3^-1) LOCAL TYPE : (3, 3, 3, 6, 6) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 6)(2, 7)(3, 5)(4, 10)(8, 9)(11, 12)(13, 51)(14, 49)(15, 50)(16, 57)(17, 56)(18, 52)(19, 60)(20, 59)(21, 54)(22, 55)(23, 53)(24, 58)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 98)(38, 99)(39, 97)(40, 102)(41, 107)(42, 105)(43, 106)(44, 101)(45, 100)(46, 108)(47, 104)(48, 103)(61, 72)(62, 68)(63, 64)(65, 70)(66, 71)(67, 69)(73, 110)(74, 111)(75, 109)(76, 114)(77, 119)(78, 117)(79, 118)(80, 113)(81, 112)(82, 120)(83, 116)(84, 115) MAP : A3.912 NOTES : type I, chiral, isomorphic to A3.909. QUOTIENT : R = (1, 2, 3, 4, 5) L = (3, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, (u.4 * u.3)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, (x.3 * x.2)^2, x.4^4, x.4^-1 * x.3 * x.4^2 * x.3 * x.1, (x.4 * x.3)^3, (x.3 * x.1)^3 > SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 6, 6) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 21)(2, 22)(3, 23)(4, 24)(5, 9)(6, 10)(7, 11)(8, 12)(13, 17)(14, 18)(15, 19)(16, 20)(25, 42)(26, 43)(27, 41)(28, 34)(29, 39)(30, 37)(31, 38)(32, 45)(33, 44)(35, 36)(40, 46)(47, 48)(49, 110)(50, 111)(51, 109)(52, 102)(53, 115)(54, 113)(55, 114)(56, 97)(57, 112)(58, 120)(59, 104)(60, 103)(61, 106)(62, 107)(63, 105)(64, 98)(65, 119)(66, 117)(67, 118)(68, 101)(69, 108)(70, 116)(71, 100)(72, 99)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.913 NOTES : type I, chiral, isomorphic to A3.907. QUOTIENT : R = (1, 2, 3, 4, 5) L = (3, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, (u.4 * u.3)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^3, x.1 * x.2 * x.4^-1, (x.3 * x.2)^2, x.4^-1 * x.2 * x.4 * x.1, (x.4 * x.3)^3 > SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 6, 6) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 30)(26, 31)(27, 29)(28, 46)(32, 33)(34, 40)(35, 48)(36, 47)(37, 42)(38, 43)(39, 41)(44, 45)(49, 98)(50, 99)(51, 97)(52, 114)(53, 103)(54, 101)(55, 102)(56, 109)(57, 100)(58, 108)(59, 116)(60, 115)(61, 118)(62, 119)(63, 117)(64, 110)(65, 107)(66, 105)(67, 106)(68, 113)(69, 120)(70, 104)(71, 112)(72, 111)(73, 90)(74, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96) MAP : A3.914 NOTES : type I, chiral, isomorphic to A3.910. QUOTIENT : R = (1, 2, 3, 4, 5) L = (3, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, (u.4 * u.3)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4^4, x.2 * x.3 * x.4^-2 * x.3, (x.4 * x.3)^3 > SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 6, 6) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 7)(2, 5)(3, 6)(4, 13)(8, 18)(9, 22)(10, 23)(11, 21)(12, 14)(15, 20)(16, 19)(17, 24)(25, 36)(26, 44)(27, 28)(29, 40)(30, 48)(31, 32)(33, 43)(34, 41)(35, 42)(37, 47)(38, 45)(39, 46)(49, 110)(50, 111)(51, 109)(52, 102)(53, 115)(54, 113)(55, 114)(56, 97)(57, 112)(58, 120)(59, 104)(60, 103)(61, 106)(62, 107)(63, 105)(64, 98)(65, 119)(66, 117)(67, 118)(68, 101)(69, 108)(70, 116)(71, 100)(72, 99)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.915 NOTES : type I, reflexible, isomorphic to A3.908. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 5)(3, 8)(4, 9)(7, 10) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.4, u.1^2, u.2^2, u.3 * u.4^-1 * u.5, u.4 * u.5^-1 * u.6, (u.1 * u.3^-1)^3, (u.2 * u.6^-1)^3 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.4, x.4, x.1^2, x.2^2, x.5^-1 * x.3^-1, x.3^3, x.4 * x.5^-1 * x.6, x.3 * x.1 * x.3^-1 * x.2, x.5 * x.2 * x.5^-1 * x.1, (x.2 * x.1)^2, x.1 * x.2 * x.3 * x.2 * x.3^-1, (x.2 * x.6^-1)^3 > SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.3^-1) LOCAL TYPE : (3, 3, 3, 6, 6) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 6)(2, 7)(3, 5)(4, 10)(8, 9)(11, 12)(13, 50)(14, 51)(15, 49)(16, 54)(17, 59)(18, 57)(19, 58)(20, 53)(21, 52)(22, 60)(23, 56)(24, 55)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 99)(38, 97)(39, 98)(40, 105)(41, 104)(42, 100)(43, 108)(44, 107)(45, 102)(46, 103)(47, 101)(48, 106)(61, 71)(62, 69)(63, 70)(64, 65)(66, 72)(67, 68)(73, 111)(74, 109)(75, 110)(76, 117)(77, 116)(78, 112)(79, 120)(80, 119)(81, 114)(82, 115)(83, 113)(84, 118) MAP : A3.916 NOTES : type I, chiral, isomorphic to Snub({4,6}), representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 6, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^4, x.3^6, (x.3^-1 * x.2 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 6) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 4)(2, 5)(3, 40)(6, 7)(8, 45)(9, 24)(10, 19)(11, 46)(12, 23)(13, 44)(14, 17)(15, 42)(16, 27)(18, 39)(20, 37)(21, 32)(22, 35)(25, 28)(26, 29)(30, 31)(33, 48)(34, 43)(36, 47)(38, 41)(49, 99)(50, 118)(51, 103)(52, 114)(53, 97)(54, 144)(55, 101)(56, 142)(57, 127)(58, 108)(59, 125)(60, 128)(61, 123)(62, 106)(63, 121)(64, 124)(65, 109)(66, 104)(67, 105)(68, 134)(69, 111)(70, 132)(71, 107)(72, 98)(73, 131)(74, 126)(75, 135)(76, 122)(77, 129)(78, 112)(79, 133)(80, 110)(81, 119)(82, 140)(83, 117)(84, 120)(85, 115)(86, 138)(87, 113)(88, 116)(89, 141)(90, 136)(91, 137)(92, 102)(93, 143)(94, 100)(95, 139)(96, 130)(145, 194)(146, 201)(147, 196)(148, 203)(149, 198)(150, 205)(151, 232)(152, 231)(153, 202)(154, 209)(155, 204)(156, 211)(157, 206)(158, 213)(159, 224)(160, 223)(161, 210)(162, 193)(163, 212)(164, 195)(165, 214)(166, 197)(167, 240)(168, 239)(169, 234)(170, 217)(171, 236)(172, 219)(173, 238)(174, 221)(175, 216)(176, 215)(177, 218)(178, 225)(179, 220)(180, 227)(181, 222)(182, 229)(183, 208)(184, 207)(185, 226)(186, 233)(187, 228)(188, 235)(189, 230)(190, 237)(191, 200)(192, 199) MAP : A3.917 NOTES : type I, chiral, isomorphic to Snub({4,6}), isomorphic to A3.916. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 6, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^4, x.3^6, (x.3^-1 * x.2 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 6) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 13)(2, 8)(3, 9)(4, 38)(5, 15)(6, 36)(7, 11)(10, 22)(12, 18)(14, 48)(16, 46)(17, 31)(19, 29)(20, 32)(21, 27)(23, 25)(24, 28)(26, 44)(30, 42)(33, 45)(34, 40)(35, 41)(37, 47)(39, 43)(49, 102)(50, 143)(51, 98)(52, 141)(53, 136)(54, 139)(55, 100)(56, 97)(57, 116)(58, 117)(59, 144)(60, 113)(61, 114)(62, 119)(63, 118)(64, 125)(65, 112)(66, 107)(67, 126)(68, 111)(69, 124)(70, 105)(71, 122)(72, 131)(73, 128)(74, 123)(75, 110)(76, 127)(77, 108)(78, 121)(79, 106)(80, 115)(81, 142)(82, 103)(83, 138)(84, 101)(85, 120)(86, 99)(87, 140)(88, 137)(89, 132)(90, 133)(91, 104)(92, 129)(93, 130)(94, 135)(95, 134)(96, 109)(145, 194)(146, 201)(147, 196)(148, 203)(149, 198)(150, 205)(151, 232)(152, 231)(153, 202)(154, 209)(155, 204)(156, 211)(157, 206)(158, 213)(159, 224)(160, 223)(161, 210)(162, 193)(163, 212)(164, 195)(165, 214)(166, 197)(167, 240)(168, 239)(169, 234)(170, 217)(171, 236)(172, 219)(173, 238)(174, 221)(175, 216)(176, 215)(177, 218)(178, 225)(179, 220)(180, 227)(181, 222)(182, 229)(183, 208)(184, 207)(185, 226)(186, 233)(187, 228)(188, 235)(189, 230)(190, 237)(191, 200)(192, 199) MAP : A3.918 NOTES : type I, chiral, isomorphic to Snub({4,8}), representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3^-1 * x.2)^2, x.2^4, x.3^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 8) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 8)(2, 3)(4, 25)(5, 7)(6, 9)(10, 21)(11, 19)(12, 26)(13, 24)(14, 17)(15, 20)(16, 27)(18, 32)(22, 31)(23, 28)(29, 30)(33, 82)(34, 86)(35, 84)(36, 87)(37, 81)(38, 92)(39, 93)(40, 91)(41, 69)(42, 94)(43, 95)(44, 77)(45, 96)(46, 80)(47, 76)(48, 70)(49, 83)(50, 89)(51, 73)(52, 85)(53, 88)(54, 74)(55, 72)(56, 67)(57, 90)(58, 65)(59, 68)(60, 78)(61, 75)(62, 66)(63, 71)(64, 79)(97, 140)(98, 157)(99, 141)(100, 144)(101, 134)(102, 155)(103, 150)(104, 156)(105, 139)(106, 159)(107, 158)(108, 148)(109, 154)(110, 151)(111, 146)(112, 145)(113, 135)(114, 136)(115, 142)(116, 130)(117, 143)(118, 131)(119, 153)(120, 138)(121, 160)(122, 132)(123, 129)(124, 137)(125, 133)(126, 149)(127, 147)(128, 152) MAP : A3.919 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3^-1 * x.2)^2, x.2^4, x.3^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 8) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 4)(2, 21)(3, 10)(5, 11)(6, 17)(7, 19)(8, 25)(9, 14)(12, 18)(13, 20)(15, 24)(16, 23)(22, 29)(26, 32)(27, 28)(30, 31)(33, 90)(34, 94)(35, 88)(36, 91)(37, 73)(38, 80)(39, 95)(40, 87)(41, 83)(42, 86)(43, 93)(44, 79)(45, 76)(46, 92)(47, 96)(48, 78)(49, 69)(50, 65)(51, 81)(52, 67)(53, 84)(54, 66)(55, 68)(56, 85)(57, 82)(58, 89)(59, 72)(60, 70)(61, 71)(62, 74)(63, 75)(64, 77)(97, 140)(98, 157)(99, 141)(100, 144)(101, 134)(102, 155)(103, 150)(104, 156)(105, 139)(106, 159)(107, 158)(108, 148)(109, 154)(110, 151)(111, 146)(112, 145)(113, 135)(114, 136)(115, 142)(116, 130)(117, 143)(118, 131)(119, 153)(120, 138)(121, 160)(122, 132)(123, 129)(124, 137)(125, 133)(126, 149)(127, 147)(128, 152) MAP : A3.920 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3^-1 * x.2)^2, x.2^4, x.3^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 8) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 4)(2, 21)(3, 10)(5, 11)(6, 17)(7, 19)(8, 25)(9, 14)(12, 18)(13, 20)(15, 24)(16, 23)(22, 29)(26, 32)(27, 28)(30, 31)(33, 85)(34, 81)(35, 65)(36, 83)(37, 68)(38, 82)(39, 84)(40, 69)(41, 66)(42, 73)(43, 88)(44, 86)(45, 87)(46, 90)(47, 91)(48, 93)(49, 74)(50, 78)(51, 72)(52, 75)(53, 89)(54, 96)(55, 79)(56, 71)(57, 67)(58, 70)(59, 77)(60, 95)(61, 92)(62, 76)(63, 80)(64, 94)(97, 138)(98, 142)(99, 136)(100, 139)(101, 153)(102, 160)(103, 143)(104, 135)(105, 131)(106, 134)(107, 141)(108, 159)(109, 156)(110, 140)(111, 144)(112, 158)(113, 149)(114, 145)(115, 129)(116, 147)(117, 132)(118, 146)(119, 148)(120, 133)(121, 130)(122, 137)(123, 152)(124, 150)(125, 151)(126, 154)(127, 155)(128, 157) MAP : A3.921 NOTES : type I, chiral, isomorphic to Snub({4,8}), representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^4, x.3^2 * x.1 * x.3^-1 * x.2, x.3^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 8) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 2)(3, 6)(4, 5)(7, 19)(8, 26)(9, 28)(10, 12)(11, 20)(13, 17)(14, 27)(15, 22)(16, 18)(21, 30)(23, 31)(24, 25)(29, 32)(33, 94)(34, 78)(35, 77)(36, 73)(37, 89)(38, 93)(39, 96)(40, 71)(41, 70)(42, 67)(43, 88)(44, 83)(45, 91)(46, 90)(47, 81)(48, 85)(49, 75)(50, 69)(51, 80)(52, 72)(53, 76)(54, 65)(55, 66)(56, 79)(57, 95)(58, 87)(59, 74)(60, 86)(61, 68)(62, 92)(63, 82)(64, 84)(97, 143)(98, 159)(99, 140)(100, 160)(101, 144)(102, 156)(103, 154)(104, 139)(105, 133)(106, 142)(107, 141)(108, 158)(109, 134)(110, 129)(111, 153)(112, 135)(113, 150)(114, 151)(115, 138)(116, 157)(117, 146)(118, 137)(119, 136)(120, 148)(121, 132)(122, 155)(123, 145)(124, 149)(125, 131)(126, 130)(127, 152)(128, 147) MAP : A3.922 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3^-1 * x.2)^2, x.2^4, x.3^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 8) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 8)(2, 3)(4, 25)(5, 7)(6, 9)(10, 21)(11, 19)(12, 26)(13, 24)(14, 17)(15, 20)(16, 27)(18, 32)(22, 31)(23, 28)(29, 30)(33, 85)(34, 81)(35, 65)(36, 83)(37, 68)(38, 82)(39, 84)(40, 69)(41, 66)(42, 73)(43, 88)(44, 86)(45, 87)(46, 90)(47, 91)(48, 93)(49, 74)(50, 78)(51, 72)(52, 75)(53, 89)(54, 96)(55, 79)(56, 71)(57, 67)(58, 70)(59, 77)(60, 95)(61, 92)(62, 76)(63, 80)(64, 94)(97, 130)(98, 134)(99, 132)(100, 135)(101, 129)(102, 140)(103, 141)(104, 139)(105, 149)(106, 142)(107, 143)(108, 157)(109, 144)(110, 160)(111, 156)(112, 150)(113, 131)(114, 137)(115, 153)(116, 133)(117, 136)(118, 154)(119, 152)(120, 147)(121, 138)(122, 145)(123, 148)(124, 158)(125, 155)(126, 146)(127, 151)(128, 159) MAP : A3.923 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3^-1 * x.2)^2, x.2^4, x.3^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 8) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 4)(2, 21)(3, 10)(5, 11)(6, 17)(7, 19)(8, 25)(9, 14)(12, 18)(13, 20)(15, 24)(16, 23)(22, 29)(26, 32)(27, 28)(30, 31)(33, 82)(34, 86)(35, 84)(36, 87)(37, 81)(38, 92)(39, 93)(40, 91)(41, 69)(42, 94)(43, 95)(44, 77)(45, 96)(46, 80)(47, 76)(48, 70)(49, 83)(50, 89)(51, 73)(52, 85)(53, 88)(54, 74)(55, 72)(56, 67)(57, 90)(58, 65)(59, 68)(60, 78)(61, 75)(62, 66)(63, 71)(64, 79)(97, 160)(98, 159)(99, 143)(100, 156)(101, 142)(102, 151)(103, 158)(104, 144)(105, 135)(106, 157)(107, 150)(108, 152)(109, 146)(110, 155)(111, 154)(112, 137)(113, 139)(114, 132)(115, 134)(116, 138)(117, 141)(118, 149)(119, 129)(120, 130)(121, 140)(122, 136)(123, 153)(124, 145)(125, 147)(126, 131)(127, 133)(128, 148) MAP : A3.924 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.921. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^4, x.3^2 * x.1 * x.3^-1 * x.2, x.3^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 8) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 2)(3, 6)(4, 5)(7, 19)(8, 26)(9, 28)(10, 12)(11, 20)(13, 17)(14, 27)(15, 22)(16, 18)(21, 30)(23, 31)(24, 25)(29, 32)(33, 86)(34, 87)(35, 74)(36, 93)(37, 82)(38, 73)(39, 72)(40, 84)(41, 68)(42, 91)(43, 81)(44, 85)(45, 67)(46, 66)(47, 88)(48, 83)(49, 79)(50, 95)(51, 76)(52, 96)(53, 80)(54, 92)(55, 90)(56, 75)(57, 69)(58, 78)(59, 77)(60, 94)(61, 70)(62, 65)(63, 89)(64, 71)(97, 149)(98, 155)(99, 145)(100, 156)(101, 152)(102, 160)(103, 157)(104, 147)(105, 131)(106, 134)(107, 153)(108, 135)(109, 142)(110, 136)(111, 141)(112, 158)(113, 148)(114, 132)(115, 146)(116, 154)(117, 138)(118, 130)(119, 129)(120, 150)(121, 151)(122, 159)(123, 140)(124, 143)(125, 133)(126, 137)(127, 144)(128, 139) MAP : A3.925 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3^-1 * x.2)^2, x.2^4, x.3^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 8) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 4)(2, 21)(3, 10)(5, 11)(6, 17)(7, 19)(8, 25)(9, 14)(12, 18)(13, 20)(15, 24)(16, 23)(22, 29)(26, 32)(27, 28)(30, 31)(33, 67)(34, 73)(35, 89)(36, 69)(37, 72)(38, 90)(39, 88)(40, 83)(41, 74)(42, 81)(43, 84)(44, 94)(45, 91)(46, 82)(47, 87)(48, 95)(49, 66)(50, 70)(51, 68)(52, 71)(53, 65)(54, 76)(55, 77)(56, 75)(57, 85)(58, 78)(59, 79)(60, 93)(61, 80)(62, 96)(63, 92)(64, 86)(97, 130)(98, 134)(99, 132)(100, 135)(101, 129)(102, 140)(103, 141)(104, 139)(105, 149)(106, 142)(107, 143)(108, 157)(109, 144)(110, 160)(111, 156)(112, 150)(113, 131)(114, 137)(115, 153)(116, 133)(117, 136)(118, 154)(119, 152)(120, 147)(121, 138)(122, 145)(123, 148)(124, 158)(125, 155)(126, 146)(127, 151)(128, 159) MAP : A3.926 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.921. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^4, x.3^2 * x.1 * x.3^-1 * x.2, x.3^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 8) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 2)(3, 6)(4, 5)(7, 19)(8, 26)(9, 28)(10, 12)(11, 20)(13, 17)(14, 27)(15, 22)(16, 18)(21, 30)(23, 31)(24, 25)(29, 32)(33, 67)(34, 83)(35, 72)(36, 81)(37, 65)(38, 88)(39, 89)(40, 69)(41, 75)(42, 84)(43, 66)(44, 68)(45, 71)(46, 80)(47, 90)(48, 70)(49, 87)(50, 86)(51, 73)(52, 82)(53, 93)(54, 74)(55, 76)(56, 78)(57, 94)(58, 85)(59, 96)(60, 91)(61, 79)(62, 77)(63, 92)(64, 95)(97, 132)(98, 148)(99, 130)(100, 138)(101, 154)(102, 146)(103, 145)(104, 134)(105, 135)(106, 143)(107, 156)(108, 159)(109, 149)(110, 153)(111, 160)(112, 155)(113, 133)(114, 139)(115, 129)(116, 140)(117, 136)(118, 144)(119, 141)(120, 131)(121, 147)(122, 150)(123, 137)(124, 151)(125, 158)(126, 152)(127, 157)(128, 142) MAP : A3.927 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3^-1 * x.2)^2, x.2^4, x.3^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 8) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 8)(2, 3)(4, 25)(5, 7)(6, 9)(10, 21)(11, 19)(12, 26)(13, 24)(14, 17)(15, 20)(16, 27)(18, 32)(22, 31)(23, 28)(29, 30)(33, 67)(34, 73)(35, 89)(36, 69)(37, 72)(38, 90)(39, 88)(40, 83)(41, 74)(42, 81)(43, 84)(44, 94)(45, 91)(46, 82)(47, 87)(48, 95)(49, 66)(50, 70)(51, 68)(52, 71)(53, 65)(54, 76)(55, 77)(56, 75)(57, 85)(58, 78)(59, 79)(60, 93)(61, 80)(62, 96)(63, 92)(64, 86)(97, 138)(98, 142)(99, 136)(100, 139)(101, 153)(102, 160)(103, 143)(104, 135)(105, 131)(106, 134)(107, 141)(108, 159)(109, 156)(110, 140)(111, 144)(112, 158)(113, 149)(114, 145)(115, 129)(116, 147)(117, 132)(118, 146)(119, 148)(120, 133)(121, 130)(122, 137)(123, 152)(124, 150)(125, 151)(126, 154)(127, 155)(128, 157) MAP : A3.928 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3^-1 * x.2)^2, x.2^4, x.3^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 8) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 8)(2, 3)(4, 25)(5, 7)(6, 9)(10, 21)(11, 19)(12, 26)(13, 24)(14, 17)(15, 20)(16, 27)(18, 32)(22, 31)(23, 28)(29, 30)(33, 90)(34, 94)(35, 88)(36, 91)(37, 73)(38, 80)(39, 95)(40, 87)(41, 83)(42, 86)(43, 93)(44, 79)(45, 76)(46, 92)(47, 96)(48, 78)(49, 69)(50, 65)(51, 81)(52, 67)(53, 84)(54, 66)(55, 68)(56, 85)(57, 82)(58, 89)(59, 72)(60, 70)(61, 71)(62, 74)(63, 75)(64, 77)(97, 160)(98, 159)(99, 143)(100, 156)(101, 142)(102, 151)(103, 158)(104, 144)(105, 135)(106, 157)(107, 150)(108, 152)(109, 146)(110, 155)(111, 154)(112, 137)(113, 139)(114, 132)(115, 134)(116, 138)(117, 141)(118, 149)(119, 129)(120, 130)(121, 140)(122, 136)(123, 153)(124, 145)(125, 147)(126, 131)(127, 133)(128, 148) MAP : A3.929 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.921. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 8, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^4, x.3^2 * x.1 * x.3^-1 * x.2, x.3^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 4, 3, 8) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 2)(3, 6)(4, 5)(7, 19)(8, 26)(9, 28)(10, 12)(11, 20)(13, 17)(14, 27)(15, 22)(16, 18)(21, 30)(23, 31)(24, 25)(29, 32)(33, 69)(34, 75)(35, 65)(36, 76)(37, 72)(38, 80)(39, 77)(40, 67)(41, 83)(42, 86)(43, 73)(44, 87)(45, 94)(46, 88)(47, 93)(48, 78)(49, 68)(50, 84)(51, 66)(52, 74)(53, 90)(54, 82)(55, 81)(56, 70)(57, 71)(58, 79)(59, 92)(60, 95)(61, 85)(62, 89)(63, 96)(64, 91)(97, 134)(98, 135)(99, 154)(100, 141)(101, 130)(102, 153)(103, 152)(104, 132)(105, 148)(106, 139)(107, 129)(108, 133)(109, 147)(110, 146)(111, 136)(112, 131)(113, 159)(114, 143)(115, 156)(116, 144)(117, 160)(118, 140)(119, 138)(120, 155)(121, 149)(122, 158)(123, 157)(124, 142)(125, 150)(126, 145)(127, 137)(128, 151) MAP : A3.930 NOTES : type I, chiral, isomorphic to Snub({4,6}), isomorphic to A3.916. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^4, x.2^6, (x.2^-1 * x.3 * x.2^-1)^2, x.2^-1 * x.1 * x.2 * x.3 * x.2^-1 * x.1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 6, 3, 4) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 4)(2, 5)(3, 40)(6, 7)(8, 45)(9, 24)(10, 19)(11, 46)(12, 23)(13, 44)(14, 17)(15, 42)(16, 27)(18, 39)(20, 37)(21, 32)(22, 35)(25, 28)(26, 29)(30, 31)(33, 48)(34, 43)(36, 47)(38, 41)(49, 98)(50, 105)(51, 100)(52, 107)(53, 102)(54, 109)(55, 136)(56, 135)(57, 106)(58, 113)(59, 108)(60, 115)(61, 110)(62, 117)(63, 128)(64, 127)(65, 114)(66, 97)(67, 116)(68, 99)(69, 118)(70, 101)(71, 144)(72, 143)(73, 138)(74, 121)(75, 140)(76, 123)(77, 142)(78, 125)(79, 120)(80, 119)(81, 122)(82, 129)(83, 124)(84, 131)(85, 126)(86, 133)(87, 112)(88, 111)(89, 130)(90, 137)(91, 132)(92, 139)(93, 134)(94, 141)(95, 104)(96, 103)(145, 231)(146, 196)(147, 229)(148, 232)(149, 227)(150, 194)(151, 225)(152, 228)(153, 197)(154, 216)(155, 193)(156, 238)(157, 199)(158, 236)(159, 195)(160, 210)(161, 211)(162, 206)(163, 215)(164, 202)(165, 209)(166, 224)(167, 213)(168, 222)(169, 221)(170, 240)(171, 217)(172, 214)(173, 223)(174, 212)(175, 219)(176, 234)(177, 235)(178, 230)(179, 239)(180, 226)(181, 233)(182, 200)(183, 237)(184, 198)(185, 207)(186, 220)(187, 205)(188, 208)(189, 203)(190, 218)(191, 201)(192, 204) MAP : A3.931 NOTES : type I, chiral, isomorphic to Snub({4,6}), isomorphic to A3.916. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {6, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^6 > CTG (small) : <48, 48> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^4, x.2^6, (x.2^-1 * x.3 * x.2^-1)^2, x.2^-1 * x.1 * x.2 * x.3 * x.2^-1 * x.1 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 6, 3, 4) #DARTS : 240 R = (1, 49, 97, 145, 193)(2, 50, 98, 146, 194)(3, 51, 99, 147, 195)(4, 52, 100, 148, 196)(5, 53, 101, 149, 197)(6, 54, 102, 150, 198)(7, 55, 103, 151, 199)(8, 56, 104, 152, 200)(9, 57, 105, 153, 201)(10, 58, 106, 154, 202)(11, 59, 107, 155, 203)(12, 60, 108, 156, 204)(13, 61, 109, 157, 205)(14, 62, 110, 158, 206)(15, 63, 111, 159, 207)(16, 64, 112, 160, 208)(17, 65, 113, 161, 209)(18, 66, 114, 162, 210)(19, 67, 115, 163, 211)(20, 68, 116, 164, 212)(21, 69, 117, 165, 213)(22, 70, 118, 166, 214)(23, 71, 119, 167, 215)(24, 72, 120, 168, 216)(25, 73, 121, 169, 217)(26, 74, 122, 170, 218)(27, 75, 123, 171, 219)(28, 76, 124, 172, 220)(29, 77, 125, 173, 221)(30, 78, 126, 174, 222)(31, 79, 127, 175, 223)(32, 80, 128, 176, 224)(33, 81, 129, 177, 225)(34, 82, 130, 178, 226)(35, 83, 131, 179, 227)(36, 84, 132, 180, 228)(37, 85, 133, 181, 229)(38, 86, 134, 182, 230)(39, 87, 135, 183, 231)(40, 88, 136, 184, 232)(41, 89, 137, 185, 233)(42, 90, 138, 186, 234)(43, 91, 139, 187, 235)(44, 92, 140, 188, 236)(45, 93, 141, 189, 237)(46, 94, 142, 190, 238)(47, 95, 143, 191, 239)(48, 96, 144, 192, 240) L = (1, 13)(2, 8)(3, 9)(4, 38)(5, 15)(6, 36)(7, 11)(10, 22)(12, 18)(14, 48)(16, 46)(17, 31)(19, 29)(20, 32)(21, 27)(23, 25)(24, 28)(26, 44)(30, 42)(33, 45)(34, 40)(35, 41)(37, 47)(39, 43)(49, 98)(50, 105)(51, 100)(52, 107)(53, 102)(54, 109)(55, 136)(56, 135)(57, 106)(58, 113)(59, 108)(60, 115)(61, 110)(62, 117)(63, 128)(64, 127)(65, 114)(66, 97)(67, 116)(68, 99)(69, 118)(70, 101)(71, 144)(72, 143)(73, 138)(74, 121)(75, 140)(76, 123)(77, 142)(78, 125)(79, 120)(80, 119)(81, 122)(82, 129)(83, 124)(84, 131)(85, 126)(86, 133)(87, 112)(88, 111)(89, 130)(90, 137)(91, 132)(92, 139)(93, 134)(94, 141)(95, 104)(96, 103)(145, 204)(146, 205)(147, 224)(148, 201)(149, 202)(150, 207)(151, 206)(152, 229)(153, 200)(154, 195)(155, 230)(156, 199)(157, 228)(158, 193)(159, 226)(160, 235)(161, 214)(162, 223)(163, 210)(164, 221)(165, 240)(166, 219)(167, 212)(168, 209)(169, 236)(170, 237)(171, 216)(172, 233)(173, 234)(174, 239)(175, 238)(176, 197)(177, 232)(178, 227)(179, 198)(180, 231)(181, 196)(182, 225)(183, 194)(184, 203)(185, 222)(186, 215)(187, 218)(188, 213)(189, 208)(190, 211)(191, 220)(192, 217) MAP : A3.932 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3 * x.2^-1)^2, x.3^4, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 8, 3, 4) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 4)(2, 21)(3, 10)(5, 11)(6, 17)(7, 19)(8, 25)(9, 14)(12, 18)(13, 20)(15, 24)(16, 23)(22, 29)(26, 32)(27, 28)(30, 31)(33, 76)(34, 93)(35, 77)(36, 80)(37, 70)(38, 91)(39, 86)(40, 92)(41, 75)(42, 95)(43, 94)(44, 84)(45, 90)(46, 87)(47, 82)(48, 81)(49, 71)(50, 72)(51, 78)(52, 66)(53, 79)(54, 67)(55, 89)(56, 74)(57, 96)(58, 68)(59, 65)(60, 73)(61, 69)(62, 85)(63, 83)(64, 88)(97, 156)(98, 141)(99, 157)(100, 160)(101, 150)(102, 139)(103, 134)(104, 140)(105, 155)(106, 143)(107, 142)(108, 132)(109, 138)(110, 135)(111, 130)(112, 129)(113, 151)(114, 152)(115, 158)(116, 146)(117, 159)(118, 147)(119, 137)(120, 154)(121, 144)(122, 148)(123, 145)(124, 153)(125, 149)(126, 133)(127, 131)(128, 136) MAP : A3.933 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3 * x.2^-1)^2, x.3^4, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 8, 3, 4) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 8)(2, 3)(4, 25)(5, 7)(6, 9)(10, 21)(11, 19)(12, 26)(13, 24)(14, 17)(15, 20)(16, 27)(18, 32)(22, 31)(23, 28)(29, 30)(33, 76)(34, 93)(35, 77)(36, 80)(37, 70)(38, 91)(39, 86)(40, 92)(41, 75)(42, 95)(43, 94)(44, 84)(45, 90)(46, 87)(47, 82)(48, 81)(49, 71)(50, 72)(51, 78)(52, 66)(53, 79)(54, 67)(55, 89)(56, 74)(57, 96)(58, 68)(59, 65)(60, 73)(61, 69)(62, 85)(63, 83)(64, 88)(97, 144)(98, 143)(99, 159)(100, 140)(101, 158)(102, 135)(103, 142)(104, 160)(105, 151)(106, 141)(107, 134)(108, 136)(109, 130)(110, 139)(111, 138)(112, 153)(113, 155)(114, 148)(115, 150)(116, 154)(117, 157)(118, 133)(119, 145)(120, 146)(121, 156)(122, 152)(123, 137)(124, 129)(125, 131)(126, 147)(127, 149)(128, 132) MAP : A3.934 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3 * x.2^-1)^2, x.3^4, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 8, 3, 4) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 8)(2, 3)(4, 25)(5, 7)(6, 9)(10, 21)(11, 19)(12, 26)(13, 24)(14, 17)(15, 20)(16, 27)(18, 32)(22, 31)(23, 28)(29, 30)(33, 91)(34, 84)(35, 86)(36, 90)(37, 93)(38, 69)(39, 81)(40, 82)(41, 92)(42, 88)(43, 73)(44, 65)(45, 67)(46, 83)(47, 85)(48, 68)(49, 80)(50, 79)(51, 95)(52, 76)(53, 94)(54, 71)(55, 78)(56, 96)(57, 87)(58, 77)(59, 70)(60, 72)(61, 66)(62, 75)(63, 74)(64, 89)(97, 154)(98, 158)(99, 152)(100, 155)(101, 137)(102, 144)(103, 159)(104, 151)(105, 147)(106, 150)(107, 157)(108, 143)(109, 140)(110, 156)(111, 160)(112, 142)(113, 133)(114, 129)(115, 145)(116, 131)(117, 148)(118, 130)(119, 132)(120, 149)(121, 146)(122, 153)(123, 136)(124, 134)(125, 135)(126, 138)(127, 139)(128, 141) MAP : A3.935 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3 * x.2^-1)^2, x.3^4, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 8, 3, 4) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 4)(2, 21)(3, 10)(5, 11)(6, 17)(7, 19)(8, 25)(9, 14)(12, 18)(13, 20)(15, 24)(16, 23)(22, 29)(26, 32)(27, 28)(30, 31)(33, 91)(34, 84)(35, 86)(36, 90)(37, 93)(38, 69)(39, 81)(40, 82)(41, 92)(42, 88)(43, 73)(44, 65)(45, 67)(46, 83)(47, 85)(48, 68)(49, 80)(50, 79)(51, 95)(52, 76)(53, 94)(54, 71)(55, 78)(56, 96)(57, 87)(58, 77)(59, 70)(60, 72)(61, 66)(62, 75)(63, 74)(64, 89)(97, 146)(98, 150)(99, 148)(100, 151)(101, 145)(102, 156)(103, 157)(104, 155)(105, 133)(106, 158)(107, 159)(108, 141)(109, 160)(110, 144)(111, 140)(112, 134)(113, 147)(114, 153)(115, 137)(116, 149)(117, 152)(118, 138)(119, 136)(120, 131)(121, 154)(122, 129)(123, 132)(124, 142)(125, 139)(126, 130)(127, 135)(128, 143) MAP : A3.936 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3 * x.2^-1)^2, x.3^4, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 8, 3, 4) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 4)(2, 21)(3, 10)(5, 11)(6, 17)(7, 19)(8, 25)(9, 14)(12, 18)(13, 20)(15, 24)(16, 23)(22, 29)(26, 32)(27, 28)(30, 31)(33, 66)(34, 70)(35, 68)(36, 71)(37, 65)(38, 76)(39, 77)(40, 75)(41, 85)(42, 78)(43, 79)(44, 93)(45, 80)(46, 96)(47, 92)(48, 86)(49, 67)(50, 73)(51, 89)(52, 69)(53, 72)(54, 90)(55, 88)(56, 83)(57, 74)(58, 81)(59, 84)(60, 94)(61, 91)(62, 82)(63, 87)(64, 95)(97, 139)(98, 132)(99, 134)(100, 138)(101, 141)(102, 149)(103, 129)(104, 130)(105, 140)(106, 136)(107, 153)(108, 145)(109, 147)(110, 131)(111, 133)(112, 148)(113, 160)(114, 159)(115, 143)(116, 156)(117, 142)(118, 151)(119, 158)(120, 144)(121, 135)(122, 157)(123, 150)(124, 152)(125, 146)(126, 155)(127, 154)(128, 137) MAP : A3.937 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3 * x.2^-1)^2, x.3^4, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 8, 3, 4) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 4)(2, 21)(3, 10)(5, 11)(6, 17)(7, 19)(8, 25)(9, 14)(12, 18)(13, 20)(15, 24)(16, 23)(22, 29)(26, 32)(27, 28)(30, 31)(33, 69)(34, 65)(35, 81)(36, 67)(37, 84)(38, 66)(39, 68)(40, 85)(41, 82)(42, 89)(43, 72)(44, 70)(45, 71)(46, 74)(47, 75)(48, 77)(49, 90)(50, 94)(51, 88)(52, 91)(53, 73)(54, 80)(55, 95)(56, 87)(57, 83)(58, 86)(59, 93)(60, 79)(61, 76)(62, 92)(63, 96)(64, 78)(97, 149)(98, 145)(99, 129)(100, 147)(101, 132)(102, 146)(103, 148)(104, 133)(105, 130)(106, 137)(107, 152)(108, 150)(109, 151)(110, 154)(111, 155)(112, 157)(113, 138)(114, 142)(115, 136)(116, 139)(117, 153)(118, 160)(119, 143)(120, 135)(121, 131)(122, 134)(123, 141)(124, 159)(125, 156)(126, 140)(127, 144)(128, 158) MAP : A3.938 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.921. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^-1 * x.1 * x.2^-1, x.3^4, x.2 * x.3 * x.2^-1 * x.1 * x.2, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 8, 3, 4) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 2)(3, 6)(4, 5)(7, 19)(8, 26)(9, 28)(10, 12)(11, 20)(13, 17)(14, 27)(15, 22)(16, 18)(21, 30)(23, 31)(24, 25)(29, 32)(33, 78)(34, 94)(35, 93)(36, 89)(37, 73)(38, 77)(39, 80)(40, 87)(41, 86)(42, 83)(43, 72)(44, 67)(45, 75)(46, 74)(47, 65)(48, 69)(49, 91)(50, 85)(51, 96)(52, 88)(53, 92)(54, 81)(55, 82)(56, 95)(57, 79)(58, 71)(59, 90)(60, 70)(61, 84)(62, 76)(63, 66)(64, 68)(97, 150)(98, 151)(99, 138)(100, 157)(101, 146)(102, 137)(103, 136)(104, 148)(105, 132)(106, 155)(107, 145)(108, 149)(109, 131)(110, 130)(111, 152)(112, 147)(113, 143)(114, 159)(115, 140)(116, 160)(117, 144)(118, 156)(119, 154)(120, 139)(121, 133)(122, 142)(123, 141)(124, 158)(125, 134)(126, 129)(127, 153)(128, 135) MAP : A3.939 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.921. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^-1 * x.1 * x.2^-1, x.3^4, x.2 * x.3 * x.2^-1 * x.1 * x.2, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 8, 3, 4) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 2)(3, 6)(4, 5)(7, 19)(8, 26)(9, 28)(10, 12)(11, 20)(13, 17)(14, 27)(15, 22)(16, 18)(21, 30)(23, 31)(24, 25)(29, 32)(33, 79)(34, 95)(35, 76)(36, 96)(37, 80)(38, 92)(39, 90)(40, 75)(41, 69)(42, 78)(43, 77)(44, 94)(45, 70)(46, 65)(47, 89)(48, 71)(49, 86)(50, 87)(51, 74)(52, 93)(53, 82)(54, 73)(55, 72)(56, 84)(57, 68)(58, 91)(59, 81)(60, 85)(61, 67)(62, 66)(63, 88)(64, 83)(97, 155)(98, 149)(99, 160)(100, 152)(101, 156)(102, 145)(103, 146)(104, 159)(105, 143)(106, 135)(107, 154)(108, 134)(109, 148)(110, 140)(111, 130)(112, 132)(113, 142)(114, 158)(115, 157)(116, 153)(117, 137)(118, 141)(119, 144)(120, 151)(121, 150)(122, 147)(123, 136)(124, 131)(125, 139)(126, 138)(127, 129)(128, 133) MAP : A3.940 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3 * x.2^-1)^2, x.3^4, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 8, 3, 4) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 8)(2, 3)(4, 25)(5, 7)(6, 9)(10, 21)(11, 19)(12, 26)(13, 24)(14, 17)(15, 20)(16, 27)(18, 32)(22, 31)(23, 28)(29, 30)(33, 66)(34, 70)(35, 68)(36, 71)(37, 65)(38, 76)(39, 77)(40, 75)(41, 85)(42, 78)(43, 79)(44, 93)(45, 80)(46, 96)(47, 92)(48, 86)(49, 67)(50, 73)(51, 89)(52, 69)(53, 72)(54, 90)(55, 88)(56, 83)(57, 74)(58, 81)(59, 84)(60, 94)(61, 91)(62, 82)(63, 87)(64, 95)(97, 135)(98, 136)(99, 142)(100, 130)(101, 143)(102, 131)(103, 153)(104, 138)(105, 160)(106, 132)(107, 129)(108, 137)(109, 133)(110, 149)(111, 147)(112, 152)(113, 140)(114, 157)(115, 141)(116, 144)(117, 134)(118, 155)(119, 150)(120, 156)(121, 139)(122, 159)(123, 158)(124, 148)(125, 154)(126, 151)(127, 146)(128, 145) MAP : A3.941 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.921. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^-1 * x.1 * x.2^-1, x.3^4, x.2 * x.3 * x.2^-1 * x.1 * x.2, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 8, 3, 4) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 2)(3, 6)(4, 5)(7, 19)(8, 26)(9, 28)(10, 12)(11, 20)(13, 17)(14, 27)(15, 22)(16, 18)(21, 30)(23, 31)(24, 25)(29, 32)(33, 68)(34, 84)(35, 66)(36, 74)(37, 90)(38, 82)(39, 81)(40, 70)(41, 71)(42, 79)(43, 92)(44, 95)(45, 85)(46, 89)(47, 96)(48, 91)(49, 69)(50, 75)(51, 65)(52, 76)(53, 72)(54, 80)(55, 77)(56, 67)(57, 83)(58, 86)(59, 73)(60, 87)(61, 94)(62, 88)(63, 93)(64, 78)(97, 135)(98, 134)(99, 153)(100, 130)(101, 141)(102, 154)(103, 156)(104, 158)(105, 142)(106, 133)(107, 144)(108, 139)(109, 159)(110, 157)(111, 140)(112, 143)(113, 147)(114, 131)(115, 152)(116, 129)(117, 145)(118, 136)(119, 137)(120, 149)(121, 155)(122, 132)(123, 146)(124, 148)(125, 151)(126, 160)(127, 138)(128, 150) MAP : A3.942 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.921. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^8 > CTG (small) : <32, 11> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^-1 * x.1 * x.2^-1, x.3^4, x.2 * x.3 * x.2^-1 * x.1 * x.2, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 8, 3, 4) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 2)(3, 6)(4, 5)(7, 19)(8, 26)(9, 28)(10, 12)(11, 20)(13, 17)(14, 27)(15, 22)(16, 18)(21, 30)(23, 31)(24, 25)(29, 32)(33, 83)(34, 67)(35, 88)(36, 65)(37, 81)(38, 72)(39, 73)(40, 85)(41, 91)(42, 68)(43, 82)(44, 84)(45, 87)(46, 96)(47, 74)(48, 86)(49, 71)(50, 70)(51, 89)(52, 66)(53, 77)(54, 90)(55, 92)(56, 94)(57, 78)(58, 69)(59, 80)(60, 75)(61, 95)(62, 93)(63, 76)(64, 79)(97, 133)(98, 139)(99, 129)(100, 140)(101, 136)(102, 144)(103, 141)(104, 131)(105, 147)(106, 150)(107, 137)(108, 151)(109, 158)(110, 152)(111, 157)(112, 142)(113, 132)(114, 148)(115, 130)(116, 138)(117, 154)(118, 146)(119, 145)(120, 134)(121, 135)(122, 143)(123, 156)(124, 159)(125, 149)(126, 153)(127, 160)(128, 155) MAP : A3.943 NOTES : type I, chiral, isomorphic to Snub({4,8}), isomorphic to A3.918. QUOTIENT : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5) ORBIFOLD : O(0, {8, 4, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 8, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^8 > CTG (small) : <32, 9> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.3 * x.2^-1)^2, x.3^4, x.2^8 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 8, 3, 4) #DARTS : 160 R = (1, 33, 65, 97, 129)(2, 34, 66, 98, 130)(3, 35, 67, 99, 131)(4, 36, 68, 100, 132)(5, 37, 69, 101, 133)(6, 38, 70, 102, 134)(7, 39, 71, 103, 135)(8, 40, 72, 104, 136)(9, 41, 73, 105, 137)(10, 42, 74, 106, 138)(11, 43, 75, 107, 139)(12, 44, 76, 108, 140)(13, 45, 77, 109, 141)(14, 46, 78, 110, 142)(15, 47, 79, 111, 143)(16, 48, 80, 112, 144)(17, 49, 81, 113, 145)(18, 50, 82, 114, 146)(19, 51, 83, 115, 147)(20, 52, 84, 116, 148)(21, 53, 85, 117, 149)(22, 54, 86, 118, 150)(23, 55, 87, 119, 151)(24, 56, 88, 120, 152)(25, 57, 89, 121, 153)(26, 58, 90, 122, 154)(27, 59, 91, 123, 155)(28, 60, 92, 124, 156)(29, 61, 93, 125, 157)(30, 62, 94, 126, 158)(31, 63, 95, 127, 159)(32, 64, 96, 128, 160) L = (1, 8)(2, 3)(4, 25)(5, 7)(6, 9)(10, 21)(11, 19)(12, 26)(13, 24)(14, 17)(15, 20)(16, 27)(18, 32)(22, 31)(23, 28)(29, 30)(33, 69)(34, 65)(35, 81)(36, 67)(37, 84)(38, 66)(39, 68)(40, 85)(41, 82)(42, 89)(43, 72)(44, 70)(45, 71)(46, 74)(47, 75)(48, 77)(49, 90)(50, 94)(51, 88)(52, 91)(53, 73)(54, 80)(55, 95)(56, 87)(57, 83)(58, 86)(59, 93)(60, 79)(61, 76)(62, 92)(63, 96)(64, 78)(97, 131)(98, 137)(99, 153)(100, 133)(101, 136)(102, 154)(103, 152)(104, 147)(105, 138)(106, 145)(107, 148)(108, 158)(109, 155)(110, 146)(111, 151)(112, 159)(113, 130)(114, 134)(115, 132)(116, 135)(117, 129)(118, 140)(119, 141)(120, 139)(121, 149)(122, 142)(123, 143)(124, 157)(125, 144)(126, 160)(127, 156)(128, 150) MAP : A3.944 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.3^3, (u.2 * u.3^-1)^2, (u.2^-1 * u.1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^3, (x.2 * x.3^-1)^2, x.3^-1 * x.1 * x.3^-1 * x.2^-1, (x.2^-1 * x.1)^2, x.2^4 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 96)(2, 80)(3, 88)(4, 87)(5, 76)(6, 84)(7, 92)(8, 91)(9, 79)(10, 77)(11, 78)(12, 85)(13, 83)(14, 81)(15, 82)(16, 89)(17, 94)(18, 95)(19, 93)(20, 86)(21, 74)(22, 75)(23, 73)(24, 90)(25, 65)(26, 66)(27, 67)(28, 68)(29, 61)(30, 62)(31, 63)(32, 64)(33, 49)(34, 50)(35, 51)(36, 52)(37, 69)(38, 70)(39, 71)(40, 72)(41, 57)(42, 58)(43, 59)(44, 60)(45, 53)(46, 54)(47, 55)(48, 56)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.945 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(5, 7)(9, 10) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1, u.2^3, u.5^3, (u.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.5^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^2, x.2^3, x.5^3, x.4 * x.5 * x.4^-1 * x.2, x.5 * x.4 * x.5 * x.2^-1, x.1 * x.2^-1 * x.3 * x.5^-1, x.5 * x.2 * x.3 * x.4, (x.4 * x.1^-1)^2, x.3 * x.5 * x.2 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 26)(14, 27)(15, 25)(16, 30)(17, 35)(18, 33)(19, 34)(20, 29)(21, 28)(22, 36)(23, 32)(24, 31)(37, 90)(38, 91)(39, 89)(40, 94)(41, 87)(42, 85)(43, 86)(44, 93)(45, 92)(46, 88)(47, 96)(48, 95)(49, 83)(50, 81)(51, 82)(52, 77)(53, 76)(54, 84)(55, 80)(56, 79)(57, 74)(58, 75)(59, 73)(60, 78)(97, 112)(98, 120)(99, 116)(100, 115)(101, 110)(102, 111)(103, 109)(104, 114)(105, 119)(106, 117)(107, 118)(108, 113) MAP : A3.946 NOTES : type I, reflexible, isomorphic to A3.944. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(5, 7)(9, 10) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1, u.2^3, u.5^3, (u.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.5^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^2, x.4^2, x.2^3, x.2 * x.4 * x.5, x.5^3, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3 * x.5^-1, (x.3 * x.4)^2, x.5 * x.4 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 27)(14, 25)(15, 26)(16, 33)(17, 32)(18, 28)(19, 36)(20, 35)(21, 30)(22, 31)(23, 29)(24, 34)(37, 90)(38, 91)(39, 89)(40, 94)(41, 87)(42, 85)(43, 86)(44, 93)(45, 92)(46, 88)(47, 96)(48, 95)(49, 83)(50, 81)(51, 82)(52, 77)(53, 76)(54, 84)(55, 80)(56, 79)(57, 74)(58, 75)(59, 73)(60, 78)(97, 117)(98, 118)(99, 119)(100, 120)(101, 109)(102, 110)(103, 111)(104, 112)(105, 113)(106, 114)(107, 115)(108, 116) MAP : A3.947 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.3^3, (u.2 * u.3^-1)^2, (u.2^-1 * u.1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^3, x.2^3, (x.1 * x.2)^2, (x.2 * x.3^-1)^2, x.1 * x.3^-1 * x.1 * x.2 * x.3 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 74)(2, 75)(3, 73)(4, 90)(5, 79)(6, 77)(7, 78)(8, 85)(9, 76)(10, 84)(11, 92)(12, 91)(13, 94)(14, 95)(15, 93)(16, 86)(17, 83)(18, 81)(19, 82)(20, 89)(21, 96)(22, 80)(23, 88)(24, 87)(25, 57)(26, 58)(27, 59)(28, 60)(29, 69)(30, 70)(31, 71)(32, 72)(33, 65)(34, 66)(35, 67)(36, 68)(37, 53)(38, 54)(39, 55)(40, 56)(41, 49)(42, 50)(43, 51)(44, 52)(45, 61)(46, 62)(47, 63)(48, 64)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.948 NOTES : type I, reflexible, isomorphic to A3.944. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(5, 7)(9, 10) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1, u.2^3, u.5^3, (u.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.5^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^2, x.4^2, x.2^3, x.2 * x.4 * x.5, x.5^3, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3 * x.5^-1, (x.3 * x.4)^2, x.5 * x.4 * x.2 * x.3 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 26)(14, 27)(15, 25)(16, 30)(17, 35)(18, 33)(19, 34)(20, 29)(21, 28)(22, 36)(23, 32)(24, 31)(37, 90)(38, 91)(39, 89)(40, 94)(41, 87)(42, 85)(43, 86)(44, 93)(45, 92)(46, 88)(47, 96)(48, 95)(49, 84)(50, 80)(51, 76)(52, 75)(53, 82)(54, 83)(55, 81)(56, 74)(57, 79)(58, 77)(59, 78)(60, 73)(97, 112)(98, 120)(99, 116)(100, 115)(101, 110)(102, 111)(103, 109)(104, 114)(105, 119)(106, 117)(107, 118)(108, 113) MAP : A3.949 NOTES : type I, chiral, isomorphic to A3.947. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.3^3, (u.2 * u.3^-1)^2, (u.2^-1 * u.1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^3, x.2^3, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.2 * x.1 * x.3^-1 * x.1 * x.3 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 74)(2, 75)(3, 73)(4, 90)(5, 79)(6, 77)(7, 78)(8, 85)(9, 76)(10, 84)(11, 92)(12, 91)(13, 94)(14, 95)(15, 93)(16, 86)(17, 83)(18, 81)(19, 82)(20, 89)(21, 96)(22, 80)(23, 88)(24, 87)(25, 67)(26, 65)(27, 66)(28, 49)(29, 62)(30, 63)(31, 61)(32, 54)(33, 58)(34, 59)(35, 57)(36, 50)(37, 64)(38, 72)(39, 56)(40, 55)(41, 60)(42, 68)(43, 52)(44, 51)(45, 71)(46, 69)(47, 70)(48, 53)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.950 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.3^3, (u.2 * u.3^-1)^2, (u.2^-1 * u.1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^3, x.2^3, (x.2^-1 * x.3)^2, (x.2^-1 * x.1)^2, (x.3^-1 * x.1)^2 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 74)(2, 75)(3, 73)(4, 90)(5, 79)(6, 77)(7, 78)(8, 85)(9, 76)(10, 84)(11, 92)(12, 91)(13, 94)(14, 95)(15, 93)(16, 86)(17, 83)(18, 81)(19, 82)(20, 89)(21, 96)(22, 80)(23, 88)(24, 87)(25, 68)(26, 52)(27, 60)(28, 59)(29, 56)(30, 64)(31, 72)(32, 71)(33, 51)(34, 49)(35, 50)(36, 57)(37, 63)(38, 61)(39, 62)(40, 69)(41, 66)(42, 67)(43, 65)(44, 58)(45, 54)(46, 55)(47, 53)(48, 70)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.951 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.3^3, (u.2 * u.3^-1)^2, (u.2^-1 * u.1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^3, (x.2 * x.3^-1)^2, (x.2^-1 * x.1)^2, x.2^4, x.1 * x.2^-1 * x.3 * x.2 * x.3 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 86)(2, 87)(3, 85)(4, 78)(5, 91)(6, 89)(7, 90)(8, 73)(9, 88)(10, 96)(11, 80)(12, 79)(13, 82)(14, 83)(15, 81)(16, 74)(17, 95)(18, 93)(19, 94)(20, 77)(21, 84)(22, 92)(23, 76)(24, 75)(25, 50)(26, 51)(27, 49)(28, 66)(29, 55)(30, 53)(31, 54)(32, 61)(33, 52)(34, 60)(35, 68)(36, 67)(37, 70)(38, 71)(39, 69)(40, 62)(41, 59)(42, 57)(43, 58)(44, 65)(45, 72)(46, 56)(47, 64)(48, 63)(97, 114)(98, 115)(99, 113)(100, 106)(101, 111)(102, 109)(103, 110)(104, 117)(105, 116)(107, 108)(112, 118)(119, 120) MAP : A3.952 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4^3, u.4 * u.1 * u.2 * u.3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^3, x.4 * x.1 * x.2 * x.3, (x.4 * x.2)^2, x.4^-1 * x.3 * x.4^-1 * x.1 * x.3 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 105)(2, 106)(3, 107)(4, 108)(5, 117)(6, 118)(7, 119)(8, 120)(9, 113)(10, 114)(11, 115)(12, 116)(13, 101)(14, 102)(15, 103)(16, 104)(17, 97)(18, 98)(19, 99)(20, 100)(21, 109)(22, 110)(23, 111)(24, 112)(25, 42)(26, 43)(27, 41)(28, 34)(29, 39)(30, 37)(31, 38)(32, 45)(33, 44)(35, 36)(40, 46)(47, 48)(49, 53)(50, 54)(51, 55)(52, 56)(57, 61)(58, 62)(59, 63)(60, 64)(65, 69)(66, 70)(67, 71)(68, 72)(73, 79)(74, 77)(75, 78)(76, 85)(80, 90)(81, 94)(82, 95)(83, 93)(84, 86)(87, 92)(88, 91)(89, 96) MAP : A3.953 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4^3, u.4 * u.1 * u.2 * u.3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^3, x.4 * x.1 * x.2 * x.3, x.4^-1 * x.1 * x.4 * x.3, x.2 * x.3 * x.1 * x.2 * x.4^-1, x.1 * x.2 * x.4^-1 * x.2 * x.3, (x.3 * x.1)^3 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 109)(6, 110)(7, 111)(8, 112)(9, 97)(10, 98)(11, 99)(12, 100)(13, 117)(14, 118)(15, 119)(16, 120)(17, 105)(18, 106)(19, 107)(20, 108)(21, 101)(22, 102)(23, 103)(24, 104)(25, 30)(26, 31)(27, 29)(28, 46)(32, 33)(34, 40)(35, 48)(36, 47)(37, 42)(38, 43)(39, 41)(44, 45)(49, 60)(50, 68)(51, 52)(53, 64)(54, 72)(55, 56)(57, 67)(58, 65)(59, 66)(61, 71)(62, 69)(63, 70)(73, 79)(74, 77)(75, 78)(76, 85)(80, 90)(81, 94)(82, 95)(83, 93)(84, 86)(87, 92)(88, 91)(89, 96) MAP : A3.954 NOTES : type I, reflexible, isomorphic to A3.945. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.3^3, (u.2 * u.3^-1)^2, (u.2^-1 * u.1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^3, (x.2 * x.3^-1)^2, (x.2^-1 * x.1)^2, (x.3^-1 * x.1)^2, x.2^4, x.2^2 * x.3 * x.2 * x.3 * x.1 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 96)(2, 80)(3, 88)(4, 87)(5, 76)(6, 84)(7, 92)(8, 91)(9, 79)(10, 77)(11, 78)(12, 85)(13, 83)(14, 81)(15, 82)(16, 89)(17, 94)(18, 95)(19, 93)(20, 86)(21, 74)(22, 75)(23, 73)(24, 90)(25, 50)(26, 51)(27, 49)(28, 66)(29, 55)(30, 53)(31, 54)(32, 61)(33, 52)(34, 60)(35, 68)(36, 67)(37, 70)(38, 71)(39, 69)(40, 62)(41, 59)(42, 57)(43, 58)(44, 65)(45, 72)(46, 56)(47, 64)(48, 63)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.955 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4^3, u.4 * u.1 * u.2 * u.3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^3, x.1 * x.4^-1 * x.3 * x.2, x.3 * x.4^-1 * x.2 * x.4, (x.3 * x.1)^2 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 100)(2, 108)(3, 116)(4, 115)(5, 120)(6, 104)(7, 112)(8, 111)(9, 107)(10, 105)(11, 106)(12, 113)(13, 103)(14, 101)(15, 102)(16, 109)(17, 98)(18, 99)(19, 97)(20, 114)(21, 118)(22, 119)(23, 117)(24, 110)(25, 42)(26, 43)(27, 41)(28, 34)(29, 39)(30, 37)(31, 38)(32, 45)(33, 44)(35, 36)(40, 46)(47, 48)(49, 53)(50, 54)(51, 55)(52, 56)(57, 61)(58, 62)(59, 63)(60, 64)(65, 69)(66, 70)(67, 71)(68, 72)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93) MAP : A3.956 NOTES : type I, chiral, isomorphic to A3.952. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4^3, u.4 * u.1 * u.2 * u.3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^3, x.4 * x.1 * x.2 * x.3, (x.4 * x.2)^2, x.1 * x.4 * x.1 * x.4 * x.3 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 105)(2, 106)(3, 107)(4, 108)(5, 117)(6, 118)(7, 119)(8, 120)(9, 113)(10, 114)(11, 115)(12, 116)(13, 101)(14, 102)(15, 103)(16, 104)(17, 97)(18, 98)(19, 99)(20, 100)(21, 109)(22, 110)(23, 111)(24, 112)(25, 30)(26, 31)(27, 29)(28, 46)(32, 33)(34, 40)(35, 48)(36, 47)(37, 42)(38, 43)(39, 41)(44, 45)(49, 53)(50, 54)(51, 55)(52, 56)(57, 61)(58, 62)(59, 63)(60, 64)(65, 69)(66, 70)(67, 71)(68, 72)(73, 83)(74, 81)(75, 82)(76, 89)(77, 94)(78, 95)(79, 93)(80, 86)(84, 90)(85, 96)(87, 88)(91, 92) MAP : A3.957 NOTES : type I, reflexible, isomorphic to A3.950. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 5)(3, 4)(7, 10)(8, 9) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1, u.3^3, u.5^3, u.1 * u.2^-1 * u.1^-1 * u.4^-1, (u.2 * u.3^-1)^2, (u.4 * u.5^-1)^2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1, x.2 * x.4, x.5^-1 * x.3^-1, x.3^3, x.5^3, x.2^2 * x.4^-1, x.1 * x.2^-1 * x.1^-1 * x.4^-1, x.4 * x.3 * x.2^-1 * x.5^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.2^-1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 51)(14, 49)(15, 50)(16, 57)(17, 56)(18, 52)(19, 60)(20, 59)(21, 54)(22, 55)(23, 53)(24, 58)(25, 46)(26, 47)(27, 45)(28, 38)(29, 43)(30, 41)(31, 42)(32, 37)(33, 48)(34, 44)(35, 40)(36, 39)(73, 110)(74, 111)(75, 109)(76, 114)(77, 119)(78, 117)(79, 118)(80, 113)(81, 112)(82, 120)(83, 116)(84, 115)(85, 104)(86, 100)(87, 108)(88, 107)(89, 102)(90, 103)(91, 101)(92, 106)(93, 99)(94, 97)(95, 98)(96, 105) MAP : A3.958 NOTES : type I, reflexible, isomorphic to A3.945. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(5, 7)(9, 10) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1, u.2^3, u.5^3, (u.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.5^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^2, x.2^3, x.5^3, x.4 * x.5 * x.4^-1 * x.2, x.5 * x.4 * x.5 * x.2^-1, x.1 * x.2^-1 * x.3 * x.5^-1, x.5 * x.2 * x.3 * x.4, (x.4 * x.1^-1)^2, x.3 * x.5 * x.2 * x.4^-1 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 27)(14, 25)(15, 26)(16, 33)(17, 32)(18, 28)(19, 36)(20, 35)(21, 30)(22, 31)(23, 29)(24, 34)(37, 90)(38, 91)(39, 89)(40, 94)(41, 87)(42, 85)(43, 86)(44, 93)(45, 92)(46, 88)(47, 96)(48, 95)(49, 84)(50, 80)(51, 76)(52, 75)(53, 82)(54, 83)(55, 81)(56, 74)(57, 79)(58, 77)(59, 78)(60, 73)(97, 117)(98, 118)(99, 119)(100, 120)(101, 109)(102, 110)(103, 111)(104, 112)(105, 113)(106, 114)(107, 115)(108, 116) MAP : A3.959 NOTES : type I, chiral, isomorphic to A3.951. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.1^2, u.3^3, (u.2 * u.3^-1)^2, (u.2^-1 * u.1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^2, x.3^3, (x.3 * x.2^-1)^2, (x.2 * x.1)^2, x.2^4, x.2^2 * x.3^-1 * x.1 * x.3, (x.3 * x.1)^3 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 86)(2, 87)(3, 85)(4, 78)(5, 91)(6, 89)(7, 90)(8, 73)(9, 88)(10, 96)(11, 80)(12, 79)(13, 82)(14, 83)(15, 81)(16, 74)(17, 95)(18, 93)(19, 94)(20, 77)(21, 84)(22, 92)(23, 76)(24, 75)(25, 58)(26, 59)(27, 57)(28, 50)(29, 71)(30, 69)(31, 70)(32, 53)(33, 60)(34, 68)(35, 52)(36, 51)(37, 62)(38, 63)(39, 61)(40, 54)(41, 67)(42, 65)(43, 66)(44, 49)(45, 64)(46, 72)(47, 56)(48, 55)(97, 114)(98, 115)(99, 113)(100, 106)(101, 111)(102, 109)(103, 110)(104, 117)(105, 116)(107, 108)(112, 118)(119, 120) MAP : A3.960 NOTES : type I, chiral, isomorphic to A3.955. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4^3, u.4 * u.1 * u.2 * u.3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^3, x.2 * x.1 * x.4^-1 * x.3, x.4^-1 * x.1 * x.4 * x.2, (x.3 * x.1)^2, (x.3 * x.4)^3 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 25, 49, 73, 97)(2, 26, 50, 74, 98)(3, 27, 51, 75, 99)(4, 28, 52, 76, 100)(5, 29, 53, 77, 101)(6, 30, 54, 78, 102)(7, 31, 55, 79, 103)(8, 32, 56, 80, 104)(9, 33, 57, 81, 105)(10, 34, 58, 82, 106)(11, 35, 59, 83, 107)(12, 36, 60, 84, 108)(13, 37, 61, 85, 109)(14, 38, 62, 86, 110)(15, 39, 63, 87, 111)(16, 40, 64, 88, 112)(17, 41, 65, 89, 113)(18, 42, 66, 90, 114)(19, 43, 67, 91, 115)(20, 44, 68, 92, 116)(21, 45, 69, 93, 117)(22, 46, 70, 94, 118)(23, 47, 71, 95, 119)(24, 48, 72, 96, 120) L = (1, 115)(2, 113)(3, 114)(4, 97)(5, 110)(6, 111)(7, 109)(8, 102)(9, 106)(10, 107)(11, 105)(12, 98)(13, 112)(14, 120)(15, 104)(16, 103)(17, 108)(18, 116)(19, 100)(20, 99)(21, 119)(22, 117)(23, 118)(24, 101)(25, 30)(26, 31)(27, 29)(28, 46)(32, 33)(34, 40)(35, 48)(36, 47)(37, 42)(38, 43)(39, 41)(44, 45)(49, 53)(50, 54)(51, 55)(52, 56)(57, 61)(58, 62)(59, 63)(60, 64)(65, 69)(66, 70)(67, 71)(68, 72)(73, 90)(74, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96) MAP : A3.961 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.5^3, u.6^3, u.4 * u.5^-1 * u.1 * u.3^-1, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.5^3, x.6^3, x.4 * x.2 * x.5^-1, x.1 * x.5^-1 * x.6^-1, x.2 * x.6 * x.1 * x.6^-1, x.4 * x.5^-1 * x.1 * x.3^-1, (x.2 * x.1)^2, x.3 * x.4^-1 * x.2 * x.6^-1, x.4 * x.1 * x.2 * x.6 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 63)(14, 61)(15, 62)(16, 69)(17, 68)(18, 64)(19, 72)(20, 71)(21, 66)(22, 67)(23, 65)(24, 70)(25, 40)(26, 48)(27, 44)(28, 43)(29, 38)(30, 39)(31, 37)(32, 42)(33, 47)(34, 45)(35, 46)(36, 41)(49, 60)(50, 56)(51, 52)(53, 58)(54, 59)(55, 57)(73, 78)(74, 79)(75, 77)(76, 82)(80, 81)(83, 84)(85, 105)(86, 106)(87, 107)(88, 108)(89, 97)(90, 98)(91, 99)(92, 100)(93, 101)(94, 102)(95, 103)(96, 104) MAP : A3.962 NOTES : type I, reflexible, isomorphic to A3.953. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4^3, u.6^3, u.1 * u.3^-1 * u.6^-1 * u.5, u.3 * u.4^-1 * u.5^-1 * u.2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.4^3, x.6^3, x.1 * x.6 * x.4, x.2 * x.6^-1 * x.4^-1, x.1 * x.3^-1 * x.6^-1 * x.5, (x.2 * x.1)^2, x.3 * x.4^-1 * x.5^-1 * x.2 > SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 12)(2, 8)(3, 4)(5, 10)(6, 11)(7, 9)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 38)(26, 39)(27, 37)(28, 42)(29, 47)(30, 45)(31, 46)(32, 41)(33, 40)(34, 48)(35, 44)(36, 43)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 109)(58, 110)(59, 111)(60, 112)(61, 66)(62, 67)(63, 65)(64, 70)(68, 69)(71, 72)(85, 100)(86, 108)(87, 104)(88, 103)(89, 98)(90, 99)(91, 97)(92, 102)(93, 107)(94, 105)(95, 106)(96, 101) MAP : A3.963 NOTES : type II, reflexible, isomorphic to A3.961. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.5^3, u.6^3, u.4 * u.5^-1 * u.1 * u.3^-1, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.5^3, x.6^3, x.4 * x.2 * x.5^-1, x.1 * x.5^-1 * x.6^-1, x.2 * x.6 * x.1 * x.6^-1, x.4 * x.5^-1 * x.1 * x.3^-1, (x.2 * x.1)^2, x.3 * x.4^-1 * x.2 * x.6^-1, x.4 * x.1 * x.2 * x.6 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 62)(14, 63)(15, 61)(16, 66)(17, 71)(18, 69)(19, 70)(20, 65)(21, 64)(22, 72)(23, 68)(24, 67)(25, 45)(26, 46)(27, 47)(28, 48)(29, 37)(30, 38)(31, 39)(32, 40)(33, 41)(34, 42)(35, 43)(36, 44)(49, 59)(50, 57)(51, 58)(52, 53)(54, 60)(55, 56)(73, 78)(74, 79)(75, 77)(76, 82)(80, 81)(83, 84)(85, 100)(86, 108)(87, 104)(88, 103)(89, 98)(90, 99)(91, 97)(92, 102)(93, 107)(94, 105)(95, 106)(96, 101) MAP : A3.964 NOTES : type I, reflexible, isomorphic to A3.953. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4^3, u.6^3, u.1 * u.3^-1 * u.6^-1 * u.5, u.3 * u.4^-1 * u.5^-1 * u.2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.4^3, x.6^3, x.1 * x.6 * x.4, x.2 * x.6^-1 * x.4^-1, x.1 * x.3^-1 * x.6^-1 * x.5, (x.2 * x.1)^2, x.3 * x.4^-1 * x.5^-1 * x.2 > SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 11)(2, 9)(3, 10)(4, 5)(6, 12)(7, 8)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 39)(26, 37)(27, 38)(28, 45)(29, 44)(30, 40)(31, 48)(32, 47)(33, 42)(34, 43)(35, 41)(36, 46)(49, 115)(50, 113)(51, 114)(52, 109)(53, 120)(54, 116)(55, 112)(56, 111)(57, 118)(58, 119)(59, 117)(60, 110)(61, 66)(62, 67)(63, 65)(64, 70)(68, 69)(71, 72)(85, 105)(86, 106)(87, 107)(88, 108)(89, 97)(90, 98)(91, 99)(92, 100)(93, 101)(94, 102)(95, 103)(96, 104) MAP : A3.965 NOTES : type I, reflexible, isomorphic to A3.950. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 5)(3, 4)(7, 10)(8, 9) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1, u.3^3, u.5^3, u.1 * u.2^-1 * u.1^-1 * u.4^-1, (u.2 * u.3^-1)^2, (u.4 * u.5^-1)^2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1, x.2 * x.4, x.5^-1 * x.3^-1, x.3^3, x.5^3, x.2^2 * x.4^-1, x.1 * x.2^-1 * x.1^-1 * x.4^-1, x.4 * x.3 * x.2^-1 * x.5^-1 > SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.2^-1) LOCAL TYPE : (3, 4, 4, 4, 4) #DARTS : 120 R = (1, 13, 25, 37, 49)(2, 14, 26, 38, 50)(3, 15, 27, 39, 51)(4, 16, 28, 40, 52)(5, 17, 29, 41, 53)(6, 18, 30, 42, 54)(7, 19, 31, 43, 55)(8, 20, 32, 44, 56)(9, 21, 33, 45, 57)(10, 22, 34, 46, 58)(11, 23, 35, 47, 59)(12, 24, 36, 48, 60)(61, 73, 85, 97, 109)(62, 74, 86, 98, 110)(63, 75, 87, 99, 111)(64, 76, 88, 100, 112)(65, 77, 89, 101, 113)(66, 78, 90, 102, 114)(67, 79, 91, 103, 115)(68, 80, 92, 104, 116)(69, 81, 93, 105, 117)(70, 82, 94, 106, 118)(71, 83, 95, 107, 119)(72, 84, 96, 108, 120) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 50)(14, 51)(15, 49)(16, 54)(17, 59)(18, 57)(19, 58)(20, 53)(21, 52)(22, 60)(23, 56)(24, 55)(25, 44)(26, 40)(27, 48)(28, 47)(29, 42)(30, 43)(31, 41)(32, 46)(33, 39)(34, 37)(35, 38)(36, 45)(73, 111)(74, 109)(75, 110)(76, 117)(77, 116)(78, 112)(79, 120)(80, 119)(81, 114)(82, 115)(83, 113)(84, 118)(85, 106)(86, 107)(87, 105)(88, 98)(89, 103)(90, 101)(91, 102)(92, 97)(93, 108)(94, 104)(95, 100)(96, 99) MAP : A3.966 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.2 * x.1, x.5^-1 * x.6^-1, x.4 * x.1 * x.5^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6 * x.4^-1 * x.5^-1 * x.4^-1, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 45)(10, 48)(11, 47)(12, 41)(13, 46)(14, 44)(15, 42)(16, 43)(17, 32)(18, 29)(19, 28)(20, 26)(21, 27)(22, 31)(23, 25)(24, 30)(33, 34)(35, 38)(36, 39)(37, 40)(49, 50)(51, 54)(52, 55)(53, 56)(57, 71)(58, 68)(59, 69)(60, 67)(61, 66)(62, 72)(63, 70)(64, 65) MAP : A3.967 NOTES : type II, reflexible, isomorphic to A3.966. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.2 * x.1, x.5^-1 * x.6^-1, x.4 * x.1 * x.5^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6 * x.4^-1 * x.5^-1 * x.4^-1, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 47)(10, 44)(11, 45)(12, 43)(13, 42)(14, 48)(15, 46)(16, 41)(17, 29)(18, 32)(19, 31)(20, 25)(21, 30)(22, 28)(23, 26)(24, 27)(33, 35)(34, 38)(36, 40)(37, 39)(49, 51)(50, 54)(52, 56)(53, 55)(57, 68)(58, 71)(59, 72)(60, 70)(61, 65)(62, 69)(63, 67)(64, 66) MAP : A3.968 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.6^-1 * x.5, x.1 * x.4^-1 * x.5, x.1 * x.6^-1 * x.4, x.1 * x.6 * x.4^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 44)(10, 47)(11, 48)(12, 46)(13, 41)(14, 45)(15, 43)(16, 42)(17, 32)(18, 29)(19, 28)(20, 26)(21, 27)(22, 31)(23, 25)(24, 30)(33, 35)(34, 38)(36, 40)(37, 39)(49, 50)(51, 54)(52, 55)(53, 56)(57, 72)(58, 69)(59, 68)(60, 66)(61, 67)(62, 71)(63, 65)(64, 70) MAP : A3.969 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4 * u.1 * u.2 * u.3, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.1 * x.3 * x.2, x.4 * x.1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4, x.4^-1 * x.1 * x.4 * x.1, x.4^4 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 17, 33, 49, 65)(2, 18, 34, 50, 66)(3, 19, 35, 51, 67)(4, 20, 36, 52, 68)(5, 21, 37, 53, 69)(6, 22, 38, 54, 70)(7, 23, 39, 55, 71)(8, 24, 40, 56, 72)(9, 25, 41, 57, 73)(10, 26, 42, 58, 74)(11, 27, 43, 59, 75)(12, 28, 44, 60, 76)(13, 29, 45, 61, 77)(14, 30, 46, 62, 78)(15, 31, 47, 63, 79)(16, 32, 48, 64, 80) L = (1, 66)(2, 70)(3, 71)(4, 75)(5, 65)(6, 69)(7, 80)(8, 68)(9, 74)(10, 78)(11, 79)(12, 67)(13, 73)(14, 77)(15, 72)(16, 76)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 35)(34, 39)(36, 42)(37, 44)(38, 48)(40, 41)(43, 46)(45, 47)(49, 63)(50, 56)(51, 58)(52, 54)(53, 59)(55, 62)(57, 60)(61, 64) MAP : A3.970 NOTES : type II, reflexible, isomorphic to A3.966. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.2 * x.1, x.5^-1 * x.6^-1, x.4 * x.1 * x.5^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6 * x.4^-1 * x.5^-1 * x.4^-1, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 44)(10, 47)(11, 48)(12, 46)(13, 41)(14, 45)(15, 43)(16, 42)(17, 31)(18, 28)(19, 29)(20, 27)(21, 26)(22, 32)(23, 30)(24, 25)(33, 34)(35, 38)(36, 39)(37, 40)(49, 50)(51, 54)(52, 55)(53, 56)(57, 72)(58, 69)(59, 68)(60, 66)(61, 67)(62, 71)(63, 65)(64, 70) MAP : A3.971 NOTES : type II, reflexible, isomorphic to A3.968. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.6^-1 * x.5, x.1 * x.4^-1 * x.5, x.1 * x.6^-1 * x.4, x.1 * x.6 * x.4^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 45)(10, 48)(11, 47)(12, 41)(13, 46)(14, 44)(15, 42)(16, 43)(17, 32)(18, 29)(19, 28)(20, 26)(21, 27)(22, 31)(23, 25)(24, 30)(33, 34)(35, 38)(36, 39)(37, 40)(49, 51)(50, 54)(52, 56)(53, 55)(57, 72)(58, 69)(59, 68)(60, 66)(61, 67)(62, 71)(63, 65)(64, 70) MAP : A3.972 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4 * u.1 * u.2 * u.3, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.1 * x.3 * x.2, x.4 * x.1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4, x.4^-1 * x.1 * x.4 * x.1, x.4^4 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 17, 33, 49, 65)(2, 18, 34, 50, 66)(3, 19, 35, 51, 67)(4, 20, 36, 52, 68)(5, 21, 37, 53, 69)(6, 22, 38, 54, 70)(7, 23, 39, 55, 71)(8, 24, 40, 56, 72)(9, 25, 41, 57, 73)(10, 26, 42, 58, 74)(11, 27, 43, 59, 75)(12, 28, 44, 60, 76)(13, 29, 45, 61, 77)(14, 30, 46, 62, 78)(15, 31, 47, 63, 79)(16, 32, 48, 64, 80) L = (1, 69)(2, 65)(3, 76)(4, 72)(5, 70)(6, 66)(7, 67)(8, 79)(9, 77)(10, 73)(11, 68)(12, 80)(13, 78)(14, 74)(15, 75)(16, 71)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 35)(34, 39)(36, 42)(37, 44)(38, 48)(40, 41)(43, 46)(45, 47)(49, 52)(50, 59)(51, 61)(53, 56)(54, 63)(55, 57)(58, 64)(60, 62) MAP : A3.973 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4 * u.1 * u.2 * u.3, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.1 * x.3 * x.2, x.4 * x.1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4, x.4^-1 * x.1 * x.4 * x.1, x.4^4 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 17, 33, 49, 65)(2, 18, 34, 50, 66)(3, 19, 35, 51, 67)(4, 20, 36, 52, 68)(5, 21, 37, 53, 69)(6, 22, 38, 54, 70)(7, 23, 39, 55, 71)(8, 24, 40, 56, 72)(9, 25, 41, 57, 73)(10, 26, 42, 58, 74)(11, 27, 43, 59, 75)(12, 28, 44, 60, 76)(13, 29, 45, 61, 77)(14, 30, 46, 62, 78)(15, 31, 47, 63, 79)(16, 32, 48, 64, 80) L = (1, 66)(2, 70)(3, 71)(4, 75)(5, 65)(6, 69)(7, 80)(8, 68)(9, 74)(10, 78)(11, 79)(12, 67)(13, 73)(14, 77)(15, 72)(16, 76)(17, 19)(18, 23)(20, 26)(21, 28)(22, 32)(24, 25)(27, 30)(29, 31)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 52)(50, 59)(51, 61)(53, 56)(54, 63)(55, 57)(58, 64)(60, 62) MAP : A3.974 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4 * u.1 * u.2 * u.3, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.1 * x.3 * x.2, x.4 * x.1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4, x.4^-1 * x.1 * x.4 * x.1, x.4^4 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 17, 33, 49, 65)(2, 18, 34, 50, 66)(3, 19, 35, 51, 67)(4, 20, 36, 52, 68)(5, 21, 37, 53, 69)(6, 22, 38, 54, 70)(7, 23, 39, 55, 71)(8, 24, 40, 56, 72)(9, 25, 41, 57, 73)(10, 26, 42, 58, 74)(11, 27, 43, 59, 75)(12, 28, 44, 60, 76)(13, 29, 45, 61, 77)(14, 30, 46, 62, 78)(15, 31, 47, 63, 79)(16, 32, 48, 64, 80) L = (1, 66)(2, 70)(3, 71)(4, 75)(5, 65)(6, 69)(7, 80)(8, 68)(9, 74)(10, 78)(11, 79)(12, 67)(13, 73)(14, 77)(15, 72)(16, 76)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 36)(34, 43)(35, 45)(37, 40)(38, 47)(39, 41)(42, 48)(44, 46)(49, 51)(50, 55)(52, 58)(53, 60)(54, 64)(56, 57)(59, 62)(61, 63) MAP : A3.975 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4 * u.1 * u.2 * u.3, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.1 * x.3 * x.2, x.4 * x.1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4, x.4^-1 * x.1 * x.4 * x.1, x.4^4 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 17, 33, 49, 65)(2, 18, 34, 50, 66)(3, 19, 35, 51, 67)(4, 20, 36, 52, 68)(5, 21, 37, 53, 69)(6, 22, 38, 54, 70)(7, 23, 39, 55, 71)(8, 24, 40, 56, 72)(9, 25, 41, 57, 73)(10, 26, 42, 58, 74)(11, 27, 43, 59, 75)(12, 28, 44, 60, 76)(13, 29, 45, 61, 77)(14, 30, 46, 62, 78)(15, 31, 47, 63, 79)(16, 32, 48, 64, 80) L = (1, 69)(2, 65)(3, 76)(4, 72)(5, 70)(6, 66)(7, 67)(8, 79)(9, 77)(10, 73)(11, 68)(12, 80)(13, 78)(14, 74)(15, 75)(16, 71)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 36)(34, 43)(35, 45)(37, 40)(38, 47)(39, 41)(42, 48)(44, 46)(49, 64)(50, 60)(51, 54)(52, 61)(53, 55)(56, 62)(57, 59)(58, 63) MAP : A3.976 NOTES : type II, reflexible, isomorphic to A3.966. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.2 * x.1, x.5^-1 * x.6^-1, x.4 * x.1 * x.5^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6 * x.4^-1 * x.5^-1 * x.4^-1, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 47)(10, 44)(11, 45)(12, 43)(13, 42)(14, 48)(15, 46)(16, 41)(17, 28)(18, 31)(19, 32)(20, 30)(21, 25)(22, 29)(23, 27)(24, 26)(33, 34)(35, 38)(36, 39)(37, 40)(49, 50)(51, 54)(52, 55)(53, 56)(57, 69)(58, 72)(59, 71)(60, 65)(61, 70)(62, 68)(63, 66)(64, 67) MAP : A3.977 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4 * u.1 * u.2 * u.3, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.1 * x.3 * x.2, x.4 * x.1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4, x.4^-1 * x.1 * x.4 * x.1, x.4^4 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 17, 33, 49, 65)(2, 18, 34, 50, 66)(3, 19, 35, 51, 67)(4, 20, 36, 52, 68)(5, 21, 37, 53, 69)(6, 22, 38, 54, 70)(7, 23, 39, 55, 71)(8, 24, 40, 56, 72)(9, 25, 41, 57, 73)(10, 26, 42, 58, 74)(11, 27, 43, 59, 75)(12, 28, 44, 60, 76)(13, 29, 45, 61, 77)(14, 30, 46, 62, 78)(15, 31, 47, 63, 79)(16, 32, 48, 64, 80) L = (1, 69)(2, 65)(3, 76)(4, 72)(5, 70)(6, 66)(7, 67)(8, 79)(9, 77)(10, 73)(11, 68)(12, 80)(13, 78)(14, 74)(15, 75)(16, 71)(17, 20)(18, 27)(19, 29)(21, 24)(22, 31)(23, 25)(26, 32)(28, 30)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 51)(50, 55)(52, 58)(53, 60)(54, 64)(56, 57)(59, 62)(61, 63) MAP : A3.978 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.1 * u.3^-1 * u.6^-1 * u.5, u.4^4, u.6^4, u.3 * u.4^-1 * u.5^-1 * u.2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.1^2, x.2^2, x.6 * x.4^-1, x.1 * x.4 * x.5^-1, x.1 * x.4^-1 * x.5, x.6^4, x.4^4, x.3 * x.4^-1 * x.5^-1 * x.2, (x.2 * x.1)^2 > SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 3)(2, 6)(4, 8)(5, 7)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 32)(18, 29)(19, 28)(20, 26)(21, 27)(22, 31)(23, 25)(24, 30)(33, 76)(34, 79)(35, 80)(36, 78)(37, 73)(38, 77)(39, 75)(40, 74)(41, 42)(43, 46)(44, 47)(45, 48)(57, 72)(58, 69)(59, 68)(60, 66)(61, 67)(62, 71)(63, 65)(64, 70) MAP : A3.979 NOTES : type II, reflexible, isomorphic to A3.966. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.2 * x.1, x.5^-1 * x.6^-1, x.4 * x.1 * x.5^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6 * x.4^-1 * x.5^-1 * x.4^-1, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 44)(10, 47)(11, 48)(12, 46)(13, 41)(14, 45)(15, 43)(16, 42)(17, 32)(18, 29)(19, 28)(20, 26)(21, 27)(22, 31)(23, 25)(24, 30)(33, 35)(34, 38)(36, 40)(37, 39)(49, 51)(50, 54)(52, 56)(53, 55)(57, 71)(58, 68)(59, 69)(60, 67)(61, 66)(62, 72)(63, 70)(64, 65) MAP : A3.980 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.1 * u.3^-1 * u.6^-1 * u.5, u.4^4, u.6^4, u.3 * u.4^-1 * u.5^-1 * u.2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.1^2, x.2^2, x.6 * x.4^-1, x.1 * x.4 * x.5^-1, x.1 * x.4^-1 * x.5, x.6^4, x.4^4, x.3 * x.4^-1 * x.5^-1 * x.2, (x.2 * x.1)^2 > SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 3)(2, 6)(4, 8)(5, 7)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 29)(18, 32)(19, 31)(20, 25)(21, 30)(22, 28)(23, 26)(24, 27)(33, 79)(34, 76)(35, 77)(36, 75)(37, 74)(38, 80)(39, 78)(40, 73)(41, 42)(43, 46)(44, 47)(45, 48)(57, 69)(58, 72)(59, 71)(60, 65)(61, 70)(62, 68)(63, 66)(64, 67) MAP : A3.981 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.1 * u.3^-1 * u.6^-1 * u.5, u.4^4, u.6^4, u.3 * u.4^-1 * u.5^-1 * u.2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.1^2, x.2^2, x.6 * x.4^-1, x.1 * x.4 * x.5^-1, x.1 * x.4^-1 * x.5, x.6^4, x.4^4, x.3 * x.4^-1 * x.5^-1 * x.2, (x.2 * x.1)^2 > SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 3)(2, 6)(4, 8)(5, 7)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 31)(18, 28)(19, 29)(20, 27)(21, 26)(22, 32)(23, 30)(24, 25)(33, 77)(34, 80)(35, 79)(36, 73)(37, 78)(38, 76)(39, 74)(40, 75)(41, 42)(43, 46)(44, 47)(45, 48)(57, 71)(58, 68)(59, 69)(60, 67)(61, 66)(62, 72)(63, 70)(64, 65) MAP : A3.982 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4 * u.1 * u.2 * u.3, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.1 * x.3 * x.2, x.4 * x.1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4, x.4^-1 * x.1 * x.4 * x.1, x.4^4 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 17, 33, 49, 65)(2, 18, 34, 50, 66)(3, 19, 35, 51, 67)(4, 20, 36, 52, 68)(5, 21, 37, 53, 69)(6, 22, 38, 54, 70)(7, 23, 39, 55, 71)(8, 24, 40, 56, 72)(9, 25, 41, 57, 73)(10, 26, 42, 58, 74)(11, 27, 43, 59, 75)(12, 28, 44, 60, 76)(13, 29, 45, 61, 77)(14, 30, 46, 62, 78)(15, 31, 47, 63, 79)(16, 32, 48, 64, 80) L = (1, 69)(2, 65)(3, 76)(4, 72)(5, 70)(6, 66)(7, 67)(8, 79)(9, 77)(10, 73)(11, 68)(12, 80)(13, 78)(14, 74)(15, 75)(16, 71)(17, 19)(18, 23)(20, 26)(21, 28)(22, 32)(24, 25)(27, 30)(29, 31)(33, 36)(34, 43)(35, 45)(37, 40)(38, 47)(39, 41)(42, 48)(44, 46)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64) MAP : A3.983 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.1 * u.3^-1 * u.6^-1 * u.5, u.4^4, u.6^4, u.3 * u.4^-1 * u.5^-1 * u.2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.1^2, x.2^2, x.6 * x.4^-1, x.1 * x.4 * x.5^-1, x.1 * x.4^-1 * x.5, x.6^4, x.4^4, x.3 * x.4^-1 * x.5^-1 * x.2, (x.2 * x.1)^2 > SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 2)(3, 6)(4, 7)(5, 8)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 28)(18, 31)(19, 32)(20, 30)(21, 25)(22, 29)(23, 27)(24, 26)(33, 79)(34, 76)(35, 77)(36, 75)(37, 74)(38, 80)(39, 78)(40, 73)(41, 43)(42, 46)(44, 48)(45, 47)(57, 68)(58, 71)(59, 72)(60, 70)(61, 65)(62, 69)(63, 67)(64, 66) MAP : A3.984 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.1 * u.3^-1 * u.6^-1 * u.5, u.4^4, u.6^4, u.3 * u.4^-1 * u.5^-1 * u.2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.1^2, x.2^2, x.6 * x.4^-1, x.1 * x.4 * x.5^-1, x.1 * x.4^-1 * x.5, x.6^4, x.4^4, x.3 * x.4^-1 * x.5^-1 * x.2, (x.2 * x.1)^2 > SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 2)(3, 6)(4, 7)(5, 8)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 29)(18, 32)(19, 31)(20, 25)(21, 30)(22, 28)(23, 26)(24, 27)(33, 80)(34, 77)(35, 76)(36, 74)(37, 75)(38, 79)(39, 73)(40, 78)(41, 43)(42, 46)(44, 48)(45, 47)(57, 69)(58, 72)(59, 71)(60, 65)(61, 70)(62, 68)(63, 66)(64, 67) MAP : A3.985 NOTES : type II, reflexible, isomorphic to A3.968. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.6^-1 * x.5, x.1 * x.4^-1 * x.5, x.1 * x.6^-1 * x.4, x.1 * x.6 * x.4^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 45)(10, 48)(11, 47)(12, 41)(13, 46)(14, 44)(15, 42)(16, 43)(17, 31)(18, 28)(19, 29)(20, 27)(21, 26)(22, 32)(23, 30)(24, 25)(33, 35)(34, 38)(36, 40)(37, 39)(49, 50)(51, 54)(52, 55)(53, 56)(57, 71)(58, 68)(59, 69)(60, 67)(61, 66)(62, 72)(63, 70)(64, 65) MAP : A3.986 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 10)(4, 8) ORBIFOLD : O(0, {2, 2, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^2, u.4^2, u.7 * u.2 * u.5^-1 * u.3, (u.5 * u.6^-1)^2, u.6 * u.1 * u.7^-1 * u.4 > CTG (small) : <8, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.5, x.3^2, x.4^2, x.2^2, x.1^2, x.3 * x.1, x.4 * x.2, x.2 * x.1 * x.7, x.1 * x.4 * x.7^-1, x.6^-1 * x.7 * x.6^-1 * x.7^-1, x.6 * x.2 * x.6 * x.4, x.6^-1 * x.4 * x.7 * x.1, (x.5 * x.6^-1)^2 > SCHREIER VEC. : (x.5, x.6, x.1, x.7, x.2) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 74)(10, 73)(11, 76)(12, 75)(13, 78)(14, 77)(15, 80)(16, 79)(17, 21)(18, 22)(19, 23)(20, 24)(25, 63)(26, 64)(27, 61)(28, 62)(29, 60)(30, 59)(31, 58)(32, 57)(33, 35)(34, 36)(37, 40)(38, 39)(49, 53)(50, 54)(51, 55)(52, 56)(65, 67)(66, 68)(69, 72)(70, 71) MAP : A3.987 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4 * u.1 * u.2 * u.3, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.1 * x.3 * x.2, x.4 * x.1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4, x.4^-1 * x.1 * x.4 * x.1, x.4^4 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 17, 33, 49, 65)(2, 18, 34, 50, 66)(3, 19, 35, 51, 67)(4, 20, 36, 52, 68)(5, 21, 37, 53, 69)(6, 22, 38, 54, 70)(7, 23, 39, 55, 71)(8, 24, 40, 56, 72)(9, 25, 41, 57, 73)(10, 26, 42, 58, 74)(11, 27, 43, 59, 75)(12, 28, 44, 60, 76)(13, 29, 45, 61, 77)(14, 30, 46, 62, 78)(15, 31, 47, 63, 79)(16, 32, 48, 64, 80) L = (1, 66)(2, 70)(3, 71)(4, 75)(5, 65)(6, 69)(7, 80)(8, 68)(9, 74)(10, 78)(11, 79)(12, 67)(13, 73)(14, 77)(15, 72)(16, 76)(17, 20)(18, 27)(19, 29)(21, 24)(22, 31)(23, 25)(26, 32)(28, 30)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 64)(50, 60)(51, 54)(52, 61)(53, 55)(56, 62)(57, 59)(58, 63) MAP : A3.988 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.1 * u.3^-1 * u.6^-1 * u.5, u.4^4, u.6^4, u.3 * u.4^-1 * u.5^-1 * u.2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.1^2, x.2^2, x.6 * x.4^-1, x.1 * x.4 * x.5^-1, x.1 * x.4^-1 * x.5, x.6^4, x.4^4, x.3 * x.4^-1 * x.5^-1 * x.2, (x.2 * x.1)^2 > SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 3)(2, 6)(4, 8)(5, 7)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 28)(18, 31)(19, 32)(20, 30)(21, 25)(22, 29)(23, 27)(24, 26)(33, 80)(34, 77)(35, 76)(36, 74)(37, 75)(38, 79)(39, 73)(40, 78)(41, 42)(43, 46)(44, 47)(45, 48)(57, 68)(58, 71)(59, 72)(60, 70)(61, 65)(62, 69)(63, 67)(64, 66) MAP : A3.989 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 10)(4, 8) ORBIFOLD : O(0, {2, 2, 2, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^2, u.4^2, u.7 * u.2 * u.5^-1 * u.3, (u.5 * u.6^-1)^2, u.6 * u.1 * u.7^-1 * u.4 > CTG (small) : <8, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.5, x.3^2, x.4^2, x.2^2, x.1^2, x.3 * x.1, x.4 * x.2, x.2 * x.1 * x.7, x.1 * x.4 * x.7^-1, x.6^-1 * x.7 * x.6^-1 * x.7^-1, x.6 * x.2 * x.6 * x.4, x.6^-1 * x.4 * x.7 * x.1, (x.5 * x.6^-1)^2 > SCHREIER VEC. : (x.5, x.6, x.1, x.7, x.2) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 74)(10, 73)(11, 76)(12, 75)(13, 78)(14, 77)(15, 80)(16, 79)(17, 19)(18, 20)(21, 24)(22, 23)(25, 64)(26, 63)(27, 62)(28, 61)(29, 59)(30, 60)(31, 57)(32, 58)(33, 37)(34, 38)(35, 39)(36, 40)(49, 51)(50, 52)(53, 56)(54, 55)(65, 69)(66, 70)(67, 71)(68, 72) MAP : A3.990 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.1 * u.3^-1 * u.6^-1 * u.5, u.4^4, u.6^4, u.3 * u.4^-1 * u.5^-1 * u.2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.1^2, x.2^2, x.6 * x.4^-1, x.1 * x.4 * x.5^-1, x.1 * x.4^-1 * x.5, x.6^4, x.4^4, x.3 * x.4^-1 * x.5^-1 * x.2, (x.2 * x.1)^2 > SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 2)(3, 6)(4, 7)(5, 8)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 31)(18, 28)(19, 29)(20, 27)(21, 26)(22, 32)(23, 30)(24, 25)(33, 76)(34, 79)(35, 80)(36, 78)(37, 73)(38, 77)(39, 75)(40, 74)(41, 43)(42, 46)(44, 48)(45, 47)(57, 71)(58, 68)(59, 69)(60, 67)(61, 66)(62, 72)(63, 70)(64, 65) MAP : A3.991 NOTES : type II, reflexible, isomorphic to A3.966. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.2 * x.1, x.5^-1 * x.6^-1, x.4 * x.1 * x.5^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6 * x.4^-1 * x.5^-1 * x.4^-1, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 45)(10, 48)(11, 47)(12, 41)(13, 46)(14, 44)(15, 42)(16, 43)(17, 31)(18, 28)(19, 29)(20, 27)(21, 26)(22, 32)(23, 30)(24, 25)(33, 35)(34, 38)(36, 40)(37, 39)(49, 51)(50, 54)(52, 56)(53, 55)(57, 72)(58, 69)(59, 68)(60, 66)(61, 67)(62, 71)(63, 65)(64, 70) MAP : A3.992 NOTES : type II, reflexible, isomorphic to A3.968. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.6^-1 * x.5, x.1 * x.4^-1 * x.5, x.1 * x.6^-1 * x.4, x.1 * x.6 * x.4^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 47)(10, 44)(11, 45)(12, 43)(13, 42)(14, 48)(15, 46)(16, 41)(17, 28)(18, 31)(19, 32)(20, 30)(21, 25)(22, 29)(23, 27)(24, 26)(33, 34)(35, 38)(36, 39)(37, 40)(49, 51)(50, 54)(52, 56)(53, 55)(57, 68)(58, 71)(59, 72)(60, 70)(61, 65)(62, 69)(63, 67)(64, 66) MAP : A3.993 NOTES : type II, reflexible, isomorphic to A3.968. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.6^-1 * x.5, x.1 * x.4^-1 * x.5, x.1 * x.6^-1 * x.4, x.1 * x.6 * x.4^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 44)(10, 47)(11, 48)(12, 46)(13, 41)(14, 45)(15, 43)(16, 42)(17, 31)(18, 28)(19, 29)(20, 27)(21, 26)(22, 32)(23, 30)(24, 25)(33, 34)(35, 38)(36, 39)(37, 40)(49, 51)(50, 54)(52, 56)(53, 55)(57, 71)(58, 68)(59, 69)(60, 67)(61, 66)(62, 72)(63, 70)(64, 65) MAP : A3.994 NOTES : type II, reflexible, isomorphic to A3.966. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.2 * x.1, x.5^-1 * x.6^-1, x.4 * x.1 * x.5^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6 * x.4^-1 * x.5^-1 * x.4^-1, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 48)(10, 45)(11, 44)(12, 42)(13, 43)(14, 47)(15, 41)(16, 46)(17, 29)(18, 32)(19, 31)(20, 25)(21, 30)(22, 28)(23, 26)(24, 27)(33, 34)(35, 38)(36, 39)(37, 40)(49, 50)(51, 54)(52, 55)(53, 56)(57, 68)(58, 71)(59, 72)(60, 70)(61, 65)(62, 69)(63, 67)(64, 66) MAP : A3.995 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.1 * u.3^-1 * u.6^-1 * u.5, u.4^4, u.6^4, u.3 * u.4^-1 * u.5^-1 * u.2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.1^2, x.2^2, x.6 * x.4^-1, x.1 * x.4 * x.5^-1, x.1 * x.4^-1 * x.5, x.6^4, x.4^4, x.3 * x.4^-1 * x.5^-1 * x.2, (x.2 * x.1)^2 > SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 2)(3, 6)(4, 7)(5, 8)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 32)(18, 29)(19, 28)(20, 26)(21, 27)(22, 31)(23, 25)(24, 30)(33, 77)(34, 80)(35, 79)(36, 73)(37, 78)(38, 76)(39, 74)(40, 75)(41, 43)(42, 46)(44, 48)(45, 47)(57, 72)(58, 69)(59, 68)(60, 66)(61, 67)(62, 71)(63, 65)(64, 70) MAP : A3.996 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4 * u.1 * u.2 * u.3, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.1 * x.3 * x.2, x.4 * x.1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4, x.4^-1 * x.1 * x.4 * x.1, x.4^4 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 17, 33, 49, 65)(2, 18, 34, 50, 66)(3, 19, 35, 51, 67)(4, 20, 36, 52, 68)(5, 21, 37, 53, 69)(6, 22, 38, 54, 70)(7, 23, 39, 55, 71)(8, 24, 40, 56, 72)(9, 25, 41, 57, 73)(10, 26, 42, 58, 74)(11, 27, 43, 59, 75)(12, 28, 44, 60, 76)(13, 29, 45, 61, 77)(14, 30, 46, 62, 78)(15, 31, 47, 63, 79)(16, 32, 48, 64, 80) L = (1, 69)(2, 65)(3, 76)(4, 72)(5, 70)(6, 66)(7, 67)(8, 79)(9, 77)(10, 73)(11, 68)(12, 80)(13, 78)(14, 74)(15, 75)(16, 71)(17, 19)(18, 23)(20, 26)(21, 28)(22, 32)(24, 25)(27, 30)(29, 31)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)(49, 63)(50, 56)(51, 58)(52, 54)(53, 59)(55, 62)(57, 60)(61, 64) MAP : A3.997 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4 * u.1 * u.2 * u.3, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.1 * x.3 * x.2, x.4 * x.1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4, x.4^-1 * x.1 * x.4 * x.1, x.4^4 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 17, 33, 49, 65)(2, 18, 34, 50, 66)(3, 19, 35, 51, 67)(4, 20, 36, 52, 68)(5, 21, 37, 53, 69)(6, 22, 38, 54, 70)(7, 23, 39, 55, 71)(8, 24, 40, 56, 72)(9, 25, 41, 57, 73)(10, 26, 42, 58, 74)(11, 27, 43, 59, 75)(12, 28, 44, 60, 76)(13, 29, 45, 61, 77)(14, 30, 46, 62, 78)(15, 31, 47, 63, 79)(16, 32, 48, 64, 80) L = (1, 66)(2, 70)(3, 71)(4, 75)(5, 65)(6, 69)(7, 80)(8, 68)(9, 74)(10, 78)(11, 79)(12, 67)(13, 73)(14, 77)(15, 72)(16, 76)(17, 19)(18, 23)(20, 26)(21, 28)(22, 32)(24, 25)(27, 30)(29, 31)(33, 36)(34, 43)(35, 45)(37, 40)(38, 47)(39, 41)(42, 48)(44, 46)(49, 62)(50, 61)(51, 56)(52, 55)(53, 58)(54, 57)(59, 64)(60, 63) MAP : A3.998 NOTES : type II, reflexible, isomorphic to A3.968. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.6^-1 * x.5, x.1 * x.4^-1 * x.5, x.1 * x.6^-1 * x.4, x.1 * x.6 * x.4^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 47)(10, 44)(11, 45)(12, 43)(13, 42)(14, 48)(15, 46)(16, 41)(17, 29)(18, 32)(19, 31)(20, 25)(21, 30)(22, 28)(23, 26)(24, 27)(33, 35)(34, 38)(36, 40)(37, 39)(49, 50)(51, 54)(52, 55)(53, 56)(57, 69)(58, 72)(59, 71)(60, 65)(61, 70)(62, 68)(63, 66)(64, 67) MAP : A3.999 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4 * u.1 * u.2 * u.3, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.1 * x.3 * x.2, x.4 * x.1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4, x.4^-1 * x.1 * x.4 * x.1, x.4^4 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 17, 33, 49, 65)(2, 18, 34, 50, 66)(3, 19, 35, 51, 67)(4, 20, 36, 52, 68)(5, 21, 37, 53, 69)(6, 22, 38, 54, 70)(7, 23, 39, 55, 71)(8, 24, 40, 56, 72)(9, 25, 41, 57, 73)(10, 26, 42, 58, 74)(11, 27, 43, 59, 75)(12, 28, 44, 60, 76)(13, 29, 45, 61, 77)(14, 30, 46, 62, 78)(15, 31, 47, 63, 79)(16, 32, 48, 64, 80) L = (1, 66)(2, 70)(3, 71)(4, 75)(5, 65)(6, 69)(7, 80)(8, 68)(9, 74)(10, 78)(11, 79)(12, 67)(13, 73)(14, 77)(15, 72)(16, 76)(17, 20)(18, 27)(19, 29)(21, 24)(22, 31)(23, 25)(26, 32)(28, 30)(33, 35)(34, 39)(36, 42)(37, 44)(38, 48)(40, 41)(43, 46)(45, 47)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64) MAP : A3.1000 NOTES : type I, reflexible, isomorphic to A3.969. QUOTIENT : R = (1, 2, 3, 4, 5) L = (1, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^2, u.4 * u.1 * u.2 * u.3, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.1 * x.3 * x.2, x.4 * x.1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4, x.4^-1 * x.1 * x.4 * x.1, x.4^4 > SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 17, 33, 49, 65)(2, 18, 34, 50, 66)(3, 19, 35, 51, 67)(4, 20, 36, 52, 68)(5, 21, 37, 53, 69)(6, 22, 38, 54, 70)(7, 23, 39, 55, 71)(8, 24, 40, 56, 72)(9, 25, 41, 57, 73)(10, 26, 42, 58, 74)(11, 27, 43, 59, 75)(12, 28, 44, 60, 76)(13, 29, 45, 61, 77)(14, 30, 46, 62, 78)(15, 31, 47, 63, 79)(16, 32, 48, 64, 80) L = (1, 69)(2, 65)(3, 76)(4, 72)(5, 70)(6, 66)(7, 67)(8, 79)(9, 77)(10, 73)(11, 68)(12, 80)(13, 78)(14, 74)(15, 75)(16, 71)(17, 20)(18, 27)(19, 29)(21, 24)(22, 31)(23, 25)(26, 32)(28, 30)(33, 35)(34, 39)(36, 42)(37, 44)(38, 48)(40, 41)(43, 46)(45, 47)(49, 62)(50, 61)(51, 56)(52, 55)(53, 58)(54, 57)(59, 64)(60, 63) MAP : A3.1001 NOTES : type II, reflexible, isomorphic to A3.968. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.6^-1 * x.5, x.1 * x.4^-1 * x.5, x.1 * x.6^-1 * x.4, x.1 * x.6 * x.4^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 48)(10, 45)(11, 44)(12, 42)(13, 43)(14, 47)(15, 41)(16, 46)(17, 28)(18, 31)(19, 32)(20, 30)(21, 25)(22, 29)(23, 27)(24, 26)(33, 35)(34, 38)(36, 40)(37, 39)(49, 50)(51, 54)(52, 55)(53, 56)(57, 68)(58, 71)(59, 72)(60, 70)(61, 65)(62, 69)(63, 67)(64, 66) MAP : A3.1002 NOTES : type II, reflexible, isomorphic to A3.968. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.6^-1 * x.5, x.1 * x.4^-1 * x.5, x.1 * x.6^-1 * x.4, x.1 * x.6 * x.4^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 48)(10, 45)(11, 44)(12, 42)(13, 43)(14, 47)(15, 41)(16, 46)(17, 29)(18, 32)(19, 31)(20, 25)(21, 30)(22, 28)(23, 26)(24, 27)(33, 34)(35, 38)(36, 39)(37, 40)(49, 51)(50, 54)(52, 56)(53, 55)(57, 69)(58, 72)(59, 71)(60, 65)(61, 70)(62, 68)(63, 66)(64, 67) MAP : A3.1003 NOTES : type II, reflexible, isomorphic to A3.966. QUOTIENT : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.1^2, u.2^2, u.4 * u.5^-1 * u.1 * u.3^-1, u.5^4, u.6^4, u.3 * u.4^-1 * u.2 * u.6^-1 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.2 * x.1, x.5^-1 * x.6^-1, x.4 * x.1 * x.5^-1, x.4 * x.5^-1 * x.1 * x.3^-1, x.5^4, x.6 * x.4^-1 * x.5^-1 * x.4^-1, x.6^4, x.3 * x.4^-1 * x.2 * x.6^-1 > SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1) LOCAL TYPE : (4, 4, 4, 4, 4) #DARTS : 80 R = (1, 9, 17, 25, 33)(2, 10, 18, 26, 34)(3, 11, 19, 27, 35)(4, 12, 20, 28, 36)(5, 13, 21, 29, 37)(6, 14, 22, 30, 38)(7, 15, 23, 31, 39)(8, 16, 24, 32, 40)(41, 49, 57, 65, 73)(42, 50, 58, 66, 74)(43, 51, 59, 67, 75)(44, 52, 60, 68, 76)(45, 53, 61, 69, 77)(46, 54, 62, 70, 78)(47, 55, 63, 71, 79)(48, 56, 64, 72, 80) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 48)(10, 45)(11, 44)(12, 42)(13, 43)(14, 47)(15, 41)(16, 46)(17, 28)(18, 31)(19, 32)(20, 30)(21, 25)(22, 29)(23, 27)(24, 26)(33, 35)(34, 38)(36, 40)(37, 39)(49, 51)(50, 54)(52, 56)(53, 55)(57, 69)(58, 72)(59, 71)(60, 65)(61, 70)(62, 68)(63, 66)(64, 67) MAP : A3.1004 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^4, x.2 * x.3 * x.1 * x.2^-1 * x.1^-1 * x.3^-1, x.1 * x.2^-1 * x.3^-1 * x.2^-1 * x.1^-1 * x.2^-1 * x.3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 149)(98, 145)(99, 172)(100, 161)(101, 163)(102, 148)(103, 147)(104, 150)(105, 181)(106, 155)(107, 162)(108, 165)(109, 156)(110, 157)(111, 192)(112, 173)(113, 152)(114, 183)(115, 146)(116, 170)(117, 158)(118, 151)(119, 184)(120, 178)(121, 167)(122, 153)(123, 175)(124, 166)(125, 168)(126, 177)(127, 174)(128, 187)(129, 171)(130, 160)(131, 185)(132, 188)(133, 164)(134, 189)(135, 154)(136, 190)(137, 159)(138, 182)(139, 180)(140, 176)(141, 191)(142, 169)(143, 186)(144, 179)(193, 277)(194, 273)(195, 252)(196, 241)(197, 243)(198, 276)(199, 275)(200, 278)(201, 261)(202, 283)(203, 242)(204, 245)(205, 284)(206, 285)(207, 272)(208, 253)(209, 280)(210, 263)(211, 274)(212, 250)(213, 286)(214, 279)(215, 264)(216, 258)(217, 247)(218, 281)(219, 255)(220, 246)(221, 248)(222, 257)(223, 254)(224, 267)(225, 251)(226, 288)(227, 265)(228, 268)(229, 244)(230, 269)(231, 282)(232, 270)(233, 287)(234, 262)(235, 260)(236, 256)(237, 271)(238, 249)(239, 266)(240, 259) MAP : A3.1005 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^4, x.2 * x.3 * x.1 * x.2^-1 * x.1^-1 * x.3^-1, x.1 * x.2^-1 * x.3^-1 * x.2^-1 * x.1^-1 * x.2^-1 * x.3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 146)(98, 163)(99, 151)(100, 150)(101, 145)(102, 152)(103, 166)(104, 161)(105, 170)(106, 183)(107, 154)(108, 157)(109, 158)(110, 165)(111, 185)(112, 178)(113, 148)(114, 155)(115, 149)(116, 181)(117, 156)(118, 172)(119, 169)(120, 173)(121, 190)(122, 164)(123, 177)(124, 147)(125, 160)(126, 175)(127, 171)(128, 188)(129, 174)(130, 168)(131, 192)(132, 187)(133, 153)(134, 186)(135, 162)(136, 167)(137, 179)(138, 191)(139, 176)(140, 180)(141, 182)(142, 184)(143, 189)(144, 159)(193, 274)(194, 243)(195, 279)(196, 278)(197, 273)(198, 280)(199, 246)(200, 241)(201, 250)(202, 263)(203, 282)(204, 285)(205, 286)(206, 245)(207, 265)(208, 258)(209, 276)(210, 283)(211, 277)(212, 261)(213, 284)(214, 252)(215, 249)(216, 253)(217, 270)(218, 244)(219, 257)(220, 275)(221, 288)(222, 255)(223, 251)(224, 268)(225, 254)(226, 248)(227, 272)(228, 267)(229, 281)(230, 266)(231, 242)(232, 247)(233, 259)(234, 271)(235, 256)(236, 260)(237, 262)(238, 264)(239, 269)(240, 287) MAP : A3.1006 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^4, x.2 * x.3 * x.1 * x.2^-1 * x.1^-1 * x.3^-1, x.1 * x.2^-1 * x.3^-1 * x.2^-1 * x.1^-1 * x.2^-1 * x.3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 188)(98, 180)(99, 164)(100, 158)(101, 176)(102, 165)(103, 181)(104, 156)(105, 177)(106, 161)(107, 152)(108, 185)(109, 179)(110, 192)(111, 162)(112, 166)(113, 157)(114, 150)(115, 187)(116, 175)(117, 159)(118, 153)(119, 145)(120, 147)(121, 146)(122, 174)(123, 173)(124, 170)(125, 151)(126, 178)(127, 168)(128, 186)(129, 160)(130, 172)(131, 154)(132, 189)(133, 171)(134, 190)(135, 148)(136, 149)(137, 155)(138, 184)(139, 182)(140, 191)(141, 169)(142, 163)(143, 167)(144, 183)(193, 251)(194, 288)(195, 265)(196, 268)(197, 244)(198, 269)(199, 282)(200, 270)(201, 287)(202, 262)(203, 260)(204, 256)(205, 271)(206, 249)(207, 266)(208, 259)(209, 277)(210, 273)(211, 252)(212, 241)(213, 243)(214, 276)(215, 275)(216, 278)(217, 261)(218, 283)(219, 242)(220, 245)(221, 284)(222, 285)(223, 272)(224, 253)(225, 280)(226, 263)(227, 274)(228, 250)(229, 286)(230, 279)(231, 264)(232, 258)(233, 247)(234, 281)(235, 255)(236, 246)(237, 248)(238, 257)(239, 254)(240, 267) MAP : A3.1007 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^4, x.2 * x.3^-1 * x.2 * x.3 * x.1^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 92)(2, 84)(3, 68)(4, 62)(5, 80)(6, 69)(7, 85)(8, 60)(9, 81)(10, 65)(11, 56)(12, 89)(13, 83)(14, 96)(15, 66)(16, 70)(17, 61)(18, 54)(19, 91)(20, 79)(21, 63)(22, 57)(23, 49)(24, 51)(25, 50)(26, 78)(27, 77)(28, 74)(29, 55)(30, 82)(31, 72)(32, 90)(33, 64)(34, 76)(35, 58)(36, 93)(37, 75)(38, 94)(39, 52)(40, 53)(41, 59)(42, 88)(43, 86)(44, 95)(45, 73)(46, 67)(47, 71)(48, 87)(97, 150)(98, 154)(99, 145)(100, 153)(101, 157)(102, 147)(103, 190)(104, 160)(105, 184)(106, 181)(107, 174)(108, 151)(109, 178)(110, 171)(111, 177)(112, 180)(113, 175)(114, 173)(115, 159)(116, 176)(117, 170)(118, 191)(119, 155)(120, 169)(121, 192)(122, 189)(123, 188)(124, 187)(125, 186)(126, 167)(127, 182)(128, 185)(129, 163)(130, 149)(131, 166)(132, 152)(133, 146)(134, 161)(135, 172)(136, 148)(137, 164)(138, 162)(139, 183)(140, 158)(141, 165)(142, 156)(143, 179)(144, 168)(193, 264)(194, 247)(195, 258)(196, 282)(197, 270)(198, 263)(199, 248)(200, 242)(201, 279)(202, 265)(203, 287)(204, 278)(205, 280)(206, 241)(207, 286)(208, 251)(209, 283)(210, 272)(211, 249)(212, 252)(213, 276)(214, 253)(215, 266)(216, 254)(217, 271)(218, 246)(219, 244)(220, 288)(221, 255)(222, 281)(223, 250)(224, 243)(225, 261)(226, 257)(227, 284)(228, 273)(229, 275)(230, 260)(231, 259)(232, 262)(233, 245)(234, 267)(235, 274)(236, 277)(237, 268)(238, 269)(239, 256)(240, 285) MAP : A3.1008 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^4, x.2 * x.3 * x.1 * x.2^-1 * x.1^-1 * x.3^-1, x.1 * x.2^-1 * x.3^-1 * x.2^-1 * x.1^-1 * x.2^-1 * x.3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 188)(98, 180)(99, 164)(100, 158)(101, 176)(102, 165)(103, 181)(104, 156)(105, 177)(106, 161)(107, 152)(108, 185)(109, 179)(110, 192)(111, 162)(112, 166)(113, 157)(114, 150)(115, 187)(116, 175)(117, 159)(118, 153)(119, 145)(120, 147)(121, 146)(122, 174)(123, 173)(124, 170)(125, 151)(126, 178)(127, 168)(128, 186)(129, 160)(130, 172)(131, 154)(132, 189)(133, 171)(134, 190)(135, 148)(136, 149)(137, 155)(138, 184)(139, 182)(140, 191)(141, 169)(142, 163)(143, 167)(144, 183)(193, 270)(194, 264)(195, 288)(196, 283)(197, 249)(198, 282)(199, 258)(200, 263)(201, 275)(202, 287)(203, 272)(204, 276)(205, 278)(206, 280)(207, 285)(208, 255)(209, 242)(210, 259)(211, 247)(212, 246)(213, 241)(214, 248)(215, 262)(216, 257)(217, 266)(218, 279)(219, 250)(220, 253)(221, 254)(222, 261)(223, 281)(224, 274)(225, 244)(226, 251)(227, 245)(228, 277)(229, 252)(230, 268)(231, 265)(232, 269)(233, 286)(234, 260)(235, 273)(236, 243)(237, 256)(238, 271)(239, 267)(240, 284) MAP : A3.1009 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.3^4, x.3 * x.1 * x.2 * x.3^-1 * x.2^-1 * x.1^-1, x.1 * x.2 * x.3^-1 * x.1^-1 * x.3^-1 * x.2^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 165)(98, 161)(99, 188)(100, 177)(101, 179)(102, 164)(103, 163)(104, 166)(105, 149)(106, 171)(107, 178)(108, 181)(109, 172)(110, 173)(111, 160)(112, 189)(113, 168)(114, 151)(115, 162)(116, 186)(117, 174)(118, 167)(119, 152)(120, 146)(121, 183)(122, 169)(123, 191)(124, 182)(125, 184)(126, 145)(127, 190)(128, 155)(129, 187)(130, 176)(131, 153)(132, 156)(133, 180)(134, 157)(135, 170)(136, 158)(137, 175)(138, 150)(139, 148)(140, 192)(141, 159)(142, 185)(143, 154)(144, 147)(193, 263)(194, 265)(195, 264)(196, 279)(197, 280)(198, 258)(199, 269)(200, 251)(201, 262)(202, 275)(203, 281)(204, 248)(205, 257)(206, 244)(207, 261)(208, 273)(209, 250)(210, 255)(211, 286)(212, 243)(213, 246)(214, 256)(215, 287)(216, 271)(217, 285)(218, 268)(219, 277)(220, 274)(221, 267)(222, 266)(223, 260)(224, 245)(225, 249)(226, 270)(227, 253)(228, 242)(229, 247)(230, 283)(231, 288)(232, 282)(233, 252)(234, 272)(235, 259)(236, 241)(237, 276)(238, 278)(239, 284)(240, 254) MAP : A3.1010 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^4, x.2 * x.3^-1 * x.2 * x.3 * x.1^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 50)(2, 67)(3, 55)(4, 54)(5, 49)(6, 56)(7, 70)(8, 65)(9, 74)(10, 87)(11, 58)(12, 61)(13, 62)(14, 69)(15, 89)(16, 82)(17, 52)(18, 59)(19, 53)(20, 85)(21, 60)(22, 76)(23, 73)(24, 77)(25, 94)(26, 68)(27, 81)(28, 51)(29, 64)(30, 79)(31, 75)(32, 92)(33, 78)(34, 72)(35, 96)(36, 91)(37, 57)(38, 90)(39, 66)(40, 71)(41, 83)(42, 95)(43, 80)(44, 84)(45, 86)(46, 88)(47, 93)(48, 63)(97, 150)(98, 154)(99, 145)(100, 153)(101, 157)(102, 147)(103, 190)(104, 160)(105, 184)(106, 181)(107, 174)(108, 151)(109, 178)(110, 171)(111, 177)(112, 180)(113, 175)(114, 173)(115, 159)(116, 176)(117, 170)(118, 191)(119, 155)(120, 169)(121, 192)(122, 189)(123, 188)(124, 187)(125, 186)(126, 167)(127, 182)(128, 185)(129, 163)(130, 149)(131, 166)(132, 152)(133, 146)(134, 161)(135, 172)(136, 148)(137, 164)(138, 162)(139, 183)(140, 158)(141, 165)(142, 156)(143, 179)(144, 168)(193, 268)(194, 260)(195, 244)(196, 286)(197, 256)(198, 245)(199, 261)(200, 284)(201, 257)(202, 241)(203, 280)(204, 265)(205, 259)(206, 272)(207, 242)(208, 246)(209, 285)(210, 278)(211, 267)(212, 255)(213, 287)(214, 281)(215, 273)(216, 275)(217, 274)(218, 254)(219, 253)(220, 250)(221, 279)(222, 258)(223, 248)(224, 266)(225, 288)(226, 252)(227, 282)(228, 269)(229, 251)(230, 270)(231, 276)(232, 277)(233, 283)(234, 264)(235, 262)(236, 271)(237, 249)(238, 243)(239, 247)(240, 263) MAP : A3.1011 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.3^4, x.3 * x.1 * x.2 * x.3^-1 * x.2^-1 * x.1^-1, x.1 * x.2 * x.3^-1 * x.1^-1 * x.3^-1 * x.2^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 151)(98, 153)(99, 152)(100, 167)(101, 168)(102, 146)(103, 157)(104, 187)(105, 150)(106, 163)(107, 169)(108, 184)(109, 145)(110, 180)(111, 149)(112, 161)(113, 186)(114, 191)(115, 174)(116, 179)(117, 182)(118, 192)(119, 175)(120, 159)(121, 173)(122, 156)(123, 165)(124, 162)(125, 155)(126, 154)(127, 148)(128, 181)(129, 185)(130, 158)(131, 189)(132, 178)(133, 183)(134, 171)(135, 176)(136, 170)(137, 188)(138, 160)(139, 147)(140, 177)(141, 164)(142, 166)(143, 172)(144, 190)(193, 245)(194, 241)(195, 268)(196, 257)(197, 259)(198, 244)(199, 243)(200, 246)(201, 277)(202, 251)(203, 258)(204, 261)(205, 252)(206, 253)(207, 288)(208, 269)(209, 248)(210, 279)(211, 242)(212, 266)(213, 254)(214, 247)(215, 280)(216, 274)(217, 263)(218, 249)(219, 271)(220, 262)(221, 264)(222, 273)(223, 270)(224, 283)(225, 267)(226, 256)(227, 281)(228, 284)(229, 260)(230, 285)(231, 250)(232, 286)(233, 255)(234, 278)(235, 276)(236, 272)(237, 287)(238, 265)(239, 282)(240, 275) MAP : A3.1012 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^4, x.2 * x.3 * x.1 * x.2^-1 * x.1^-1 * x.3^-1, x.1 * x.2^-1 * x.3^-1 * x.2^-1 * x.1^-1 * x.2^-1 * x.3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 146)(98, 163)(99, 151)(100, 150)(101, 145)(102, 152)(103, 166)(104, 161)(105, 170)(106, 183)(107, 154)(108, 157)(109, 158)(110, 165)(111, 185)(112, 178)(113, 148)(114, 155)(115, 149)(116, 181)(117, 156)(118, 172)(119, 169)(120, 173)(121, 190)(122, 164)(123, 177)(124, 147)(125, 160)(126, 175)(127, 171)(128, 188)(129, 174)(130, 168)(131, 192)(132, 187)(133, 153)(134, 186)(135, 162)(136, 167)(137, 179)(138, 191)(139, 176)(140, 180)(141, 182)(142, 184)(143, 189)(144, 159)(193, 253)(194, 246)(195, 283)(196, 271)(197, 255)(198, 249)(199, 241)(200, 243)(201, 242)(202, 270)(203, 269)(204, 266)(205, 247)(206, 274)(207, 264)(208, 282)(209, 256)(210, 268)(211, 250)(212, 285)(213, 267)(214, 286)(215, 244)(216, 245)(217, 251)(218, 280)(219, 278)(220, 287)(221, 265)(222, 259)(223, 263)(224, 279)(225, 284)(226, 276)(227, 260)(228, 254)(229, 272)(230, 261)(231, 277)(232, 252)(233, 273)(234, 257)(235, 248)(236, 281)(237, 275)(238, 288)(239, 258)(240, 262) MAP : A3.1013 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.3^4, x.3 * x.1 * x.2 * x.3^-1 * x.2^-1 * x.1^-1, x.1 * x.2 * x.3^-1 * x.1^-1 * x.3^-1 * x.2^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 155)(98, 192)(99, 169)(100, 172)(101, 148)(102, 173)(103, 186)(104, 174)(105, 191)(106, 166)(107, 164)(108, 160)(109, 175)(110, 153)(111, 170)(112, 163)(113, 181)(114, 177)(115, 156)(116, 145)(117, 147)(118, 180)(119, 179)(120, 182)(121, 165)(122, 187)(123, 146)(124, 149)(125, 188)(126, 189)(127, 176)(128, 157)(129, 184)(130, 167)(131, 178)(132, 154)(133, 190)(134, 183)(135, 168)(136, 162)(137, 151)(138, 185)(139, 159)(140, 150)(141, 152)(142, 161)(143, 158)(144, 171)(193, 272)(194, 284)(195, 266)(196, 253)(197, 283)(198, 254)(199, 260)(200, 261)(201, 267)(202, 248)(203, 246)(204, 255)(205, 281)(206, 275)(207, 279)(208, 247)(209, 252)(210, 244)(211, 276)(212, 270)(213, 288)(214, 277)(215, 245)(216, 268)(217, 241)(218, 273)(219, 264)(220, 249)(221, 243)(222, 256)(223, 274)(224, 278)(225, 269)(226, 262)(227, 251)(228, 287)(229, 271)(230, 265)(231, 257)(232, 259)(233, 258)(234, 286)(235, 285)(236, 282)(237, 263)(238, 242)(239, 280)(240, 250) MAP : A3.1014 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^4, x.2 * x.3 * x.1 * x.2^-1 * x.1^-1 * x.3^-1, x.1 * x.2^-1 * x.3^-1 * x.2^-1 * x.1^-1 * x.2^-1 * x.3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 167)(98, 169)(99, 168)(100, 183)(101, 184)(102, 162)(103, 173)(104, 155)(105, 166)(106, 179)(107, 185)(108, 152)(109, 161)(110, 148)(111, 165)(112, 177)(113, 154)(114, 159)(115, 190)(116, 147)(117, 150)(118, 160)(119, 191)(120, 175)(121, 189)(122, 172)(123, 181)(124, 178)(125, 171)(126, 170)(127, 164)(128, 149)(129, 153)(130, 174)(131, 157)(132, 146)(133, 151)(134, 187)(135, 192)(136, 186)(137, 156)(138, 176)(139, 163)(140, 145)(141, 180)(142, 182)(143, 188)(144, 158)(193, 254)(194, 248)(195, 272)(196, 267)(197, 281)(198, 266)(199, 242)(200, 247)(201, 259)(202, 271)(203, 256)(204, 260)(205, 262)(206, 264)(207, 269)(208, 287)(209, 274)(210, 243)(211, 279)(212, 278)(213, 273)(214, 280)(215, 246)(216, 241)(217, 250)(218, 263)(219, 282)(220, 285)(221, 286)(222, 245)(223, 265)(224, 258)(225, 276)(226, 283)(227, 277)(228, 261)(229, 284)(230, 252)(231, 249)(232, 253)(233, 270)(234, 244)(235, 257)(236, 275)(237, 288)(238, 255)(239, 251)(240, 268) MAP : A3.1015 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.3^4, x.3 * x.1 * x.2 * x.3^-1 * x.2^-1 * x.1^-1, x.1 * x.2 * x.3^-1 * x.1^-1 * x.3^-1 * x.2^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 157)(98, 150)(99, 187)(100, 175)(101, 159)(102, 153)(103, 145)(104, 147)(105, 146)(106, 174)(107, 173)(108, 170)(109, 151)(110, 178)(111, 168)(112, 186)(113, 160)(114, 172)(115, 154)(116, 189)(117, 171)(118, 190)(119, 148)(120, 149)(121, 155)(122, 184)(123, 182)(124, 191)(125, 169)(126, 163)(127, 167)(128, 183)(129, 188)(130, 180)(131, 164)(132, 158)(133, 176)(134, 165)(135, 181)(136, 156)(137, 177)(138, 161)(139, 152)(140, 185)(141, 179)(142, 192)(143, 162)(144, 166)(193, 286)(194, 280)(195, 256)(196, 251)(197, 265)(198, 250)(199, 274)(200, 279)(201, 243)(202, 255)(203, 288)(204, 244)(205, 246)(206, 248)(207, 253)(208, 271)(209, 258)(210, 275)(211, 263)(212, 262)(213, 257)(214, 264)(215, 278)(216, 273)(217, 282)(218, 247)(219, 266)(220, 269)(221, 270)(222, 277)(223, 249)(224, 242)(225, 260)(226, 267)(227, 261)(228, 245)(229, 268)(230, 284)(231, 281)(232, 285)(233, 254)(234, 276)(235, 241)(236, 259)(237, 272)(238, 287)(239, 283)(240, 252) MAP : A3.1016 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^4, x.2 * x.3^-1 * x.2 * x.3 * x.1^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 53)(2, 49)(3, 76)(4, 65)(5, 67)(6, 52)(7, 51)(8, 54)(9, 85)(10, 59)(11, 66)(12, 69)(13, 60)(14, 61)(15, 96)(16, 77)(17, 56)(18, 87)(19, 50)(20, 74)(21, 62)(22, 55)(23, 88)(24, 82)(25, 71)(26, 57)(27, 79)(28, 70)(29, 72)(30, 81)(31, 78)(32, 91)(33, 75)(34, 64)(35, 89)(36, 92)(37, 68)(38, 93)(39, 58)(40, 94)(41, 63)(42, 86)(43, 84)(44, 80)(45, 95)(46, 73)(47, 90)(48, 83)(97, 147)(98, 181)(99, 150)(100, 184)(101, 178)(102, 145)(103, 156)(104, 180)(105, 148)(106, 146)(107, 167)(108, 190)(109, 149)(110, 188)(111, 163)(112, 152)(113, 182)(114, 186)(115, 177)(116, 185)(117, 189)(118, 179)(119, 174)(120, 192)(121, 168)(122, 165)(123, 158)(124, 183)(125, 162)(126, 155)(127, 161)(128, 164)(129, 159)(130, 157)(131, 191)(132, 160)(133, 154)(134, 175)(135, 187)(136, 153)(137, 176)(138, 173)(139, 172)(140, 171)(141, 170)(142, 151)(143, 166)(144, 169)(193, 248)(194, 279)(195, 242)(196, 266)(197, 254)(198, 247)(199, 280)(200, 274)(201, 263)(202, 249)(203, 271)(204, 262)(205, 264)(206, 273)(207, 270)(208, 283)(209, 267)(210, 256)(211, 281)(212, 284)(213, 260)(214, 285)(215, 250)(216, 286)(217, 255)(218, 278)(219, 276)(220, 272)(221, 287)(222, 265)(223, 282)(224, 275)(225, 245)(226, 241)(227, 268)(228, 257)(229, 259)(230, 244)(231, 243)(232, 246)(233, 277)(234, 251)(235, 258)(236, 261)(237, 252)(238, 253)(239, 288)(240, 269) MAP : A3.1017 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^4, x.2 * x.3^-1 * x.2 * x.3 * x.1^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 53)(2, 49)(3, 76)(4, 65)(5, 67)(6, 52)(7, 51)(8, 54)(9, 85)(10, 59)(11, 66)(12, 69)(13, 60)(14, 61)(15, 96)(16, 77)(17, 56)(18, 87)(19, 50)(20, 74)(21, 62)(22, 55)(23, 88)(24, 82)(25, 71)(26, 57)(27, 79)(28, 70)(29, 72)(30, 81)(31, 78)(32, 91)(33, 75)(34, 64)(35, 89)(36, 92)(37, 68)(38, 93)(39, 58)(40, 94)(41, 63)(42, 86)(43, 84)(44, 80)(45, 95)(46, 73)(47, 90)(48, 83)(97, 150)(98, 154)(99, 145)(100, 153)(101, 157)(102, 147)(103, 190)(104, 160)(105, 184)(106, 181)(107, 174)(108, 151)(109, 178)(110, 171)(111, 177)(112, 180)(113, 175)(114, 173)(115, 159)(116, 176)(117, 170)(118, 191)(119, 155)(120, 169)(121, 192)(122, 189)(123, 188)(124, 187)(125, 186)(126, 167)(127, 182)(128, 185)(129, 163)(130, 149)(131, 166)(132, 152)(133, 146)(134, 161)(135, 172)(136, 148)(137, 164)(138, 162)(139, 183)(140, 158)(141, 165)(142, 156)(143, 179)(144, 168)(193, 247)(194, 249)(195, 248)(196, 263)(197, 264)(198, 242)(199, 253)(200, 283)(201, 246)(202, 259)(203, 265)(204, 280)(205, 241)(206, 276)(207, 245)(208, 257)(209, 282)(210, 287)(211, 270)(212, 275)(213, 278)(214, 288)(215, 271)(216, 255)(217, 269)(218, 252)(219, 261)(220, 258)(221, 251)(222, 250)(223, 244)(224, 277)(225, 281)(226, 254)(227, 285)(228, 274)(229, 279)(230, 267)(231, 272)(232, 266)(233, 284)(234, 256)(235, 243)(236, 273)(237, 260)(238, 262)(239, 268)(240, 286) MAP : A3.1018 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^4, x.2 * x.3 * x.1 * x.2^-1 * x.1^-1 * x.3^-1, x.1 * x.2^-1 * x.3^-1 * x.2^-1 * x.1^-1 * x.2^-1 * x.3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 167)(98, 169)(99, 168)(100, 183)(101, 184)(102, 162)(103, 173)(104, 155)(105, 166)(106, 179)(107, 185)(108, 152)(109, 161)(110, 148)(111, 165)(112, 177)(113, 154)(114, 159)(115, 190)(116, 147)(117, 150)(118, 160)(119, 191)(120, 175)(121, 189)(122, 172)(123, 181)(124, 178)(125, 171)(126, 170)(127, 164)(128, 149)(129, 153)(130, 174)(131, 157)(132, 146)(133, 151)(134, 187)(135, 192)(136, 186)(137, 156)(138, 176)(139, 163)(140, 145)(141, 180)(142, 182)(143, 188)(144, 158)(193, 267)(194, 256)(195, 281)(196, 284)(197, 260)(198, 285)(199, 250)(200, 286)(201, 255)(202, 278)(203, 276)(204, 272)(205, 287)(206, 265)(207, 282)(208, 275)(209, 245)(210, 241)(211, 268)(212, 257)(213, 259)(214, 244)(215, 243)(216, 246)(217, 277)(218, 251)(219, 258)(220, 261)(221, 252)(222, 253)(223, 288)(224, 269)(225, 248)(226, 279)(227, 242)(228, 266)(229, 254)(230, 247)(231, 280)(232, 274)(233, 263)(234, 249)(235, 271)(236, 262)(237, 264)(238, 273)(239, 270)(240, 283) MAP : A3.1019 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^4, x.2 * x.3^-1 * x.2 * x.3 * x.1^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 50)(2, 67)(3, 55)(4, 54)(5, 49)(6, 56)(7, 70)(8, 65)(9, 74)(10, 87)(11, 58)(12, 61)(13, 62)(14, 69)(15, 89)(16, 82)(17, 52)(18, 59)(19, 53)(20, 85)(21, 60)(22, 76)(23, 73)(24, 77)(25, 94)(26, 68)(27, 81)(28, 51)(29, 64)(30, 79)(31, 75)(32, 92)(33, 78)(34, 72)(35, 96)(36, 91)(37, 57)(38, 90)(39, 66)(40, 71)(41, 83)(42, 95)(43, 80)(44, 84)(45, 86)(46, 88)(47, 93)(48, 63)(97, 147)(98, 181)(99, 150)(100, 184)(101, 178)(102, 145)(103, 156)(104, 180)(105, 148)(106, 146)(107, 167)(108, 190)(109, 149)(110, 188)(111, 163)(112, 152)(113, 182)(114, 186)(115, 177)(116, 185)(117, 189)(118, 179)(119, 174)(120, 192)(121, 168)(122, 165)(123, 158)(124, 183)(125, 162)(126, 155)(127, 161)(128, 164)(129, 159)(130, 157)(131, 191)(132, 160)(133, 154)(134, 175)(135, 187)(136, 153)(137, 176)(138, 173)(139, 172)(140, 171)(141, 170)(142, 151)(143, 166)(144, 169)(193, 244)(194, 251)(195, 245)(196, 277)(197, 252)(198, 268)(199, 265)(200, 269)(201, 286)(202, 260)(203, 273)(204, 243)(205, 256)(206, 271)(207, 267)(208, 284)(209, 270)(210, 264)(211, 288)(212, 283)(213, 249)(214, 282)(215, 258)(216, 263)(217, 275)(218, 287)(219, 272)(220, 276)(221, 278)(222, 280)(223, 285)(224, 255)(225, 242)(226, 259)(227, 247)(228, 246)(229, 241)(230, 248)(231, 262)(232, 257)(233, 266)(234, 279)(235, 250)(236, 253)(237, 254)(238, 261)(239, 281)(240, 274) MAP : A3.1020 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.3^4, x.3 * x.1 * x.2 * x.3^-1 * x.2^-1 * x.1^-1, x.1 * x.2 * x.3^-1 * x.1^-1 * x.3^-1 * x.2^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 174)(98, 168)(99, 192)(100, 187)(101, 153)(102, 186)(103, 162)(104, 167)(105, 179)(106, 191)(107, 176)(108, 180)(109, 182)(110, 184)(111, 189)(112, 159)(113, 146)(114, 163)(115, 151)(116, 150)(117, 145)(118, 152)(119, 166)(120, 161)(121, 170)(122, 183)(123, 154)(124, 157)(125, 158)(126, 165)(127, 185)(128, 178)(129, 148)(130, 155)(131, 149)(132, 181)(133, 156)(134, 172)(135, 169)(136, 173)(137, 190)(138, 164)(139, 177)(140, 147)(141, 160)(142, 175)(143, 171)(144, 188)(193, 285)(194, 278)(195, 267)(196, 255)(197, 287)(198, 281)(199, 273)(200, 275)(201, 274)(202, 254)(203, 253)(204, 250)(205, 279)(206, 258)(207, 248)(208, 266)(209, 288)(210, 252)(211, 282)(212, 269)(213, 251)(214, 270)(215, 276)(216, 277)(217, 283)(218, 264)(219, 262)(220, 271)(221, 249)(222, 243)(223, 247)(224, 263)(225, 268)(226, 260)(227, 244)(228, 286)(229, 256)(230, 245)(231, 261)(232, 284)(233, 257)(234, 241)(235, 280)(236, 265)(237, 259)(238, 272)(239, 242)(240, 246) MAP : A3.1021 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.3^4, x.3 * x.1 * x.2 * x.3^-1 * x.2^-1 * x.1^-1, x.1 * x.2 * x.3^-1 * x.1^-1 * x.3^-1 * x.2^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 178)(98, 147)(99, 183)(100, 182)(101, 177)(102, 184)(103, 150)(104, 145)(105, 154)(106, 167)(107, 186)(108, 189)(109, 190)(110, 149)(111, 169)(112, 162)(113, 180)(114, 187)(115, 181)(116, 165)(117, 188)(118, 156)(119, 153)(120, 157)(121, 174)(122, 148)(123, 161)(124, 179)(125, 192)(126, 159)(127, 155)(128, 172)(129, 158)(130, 152)(131, 176)(132, 171)(133, 185)(134, 170)(135, 146)(136, 151)(137, 163)(138, 175)(139, 160)(140, 164)(141, 166)(142, 168)(143, 173)(144, 191)(193, 276)(194, 283)(195, 277)(196, 261)(197, 284)(198, 252)(199, 249)(200, 253)(201, 270)(202, 244)(203, 257)(204, 275)(205, 288)(206, 255)(207, 251)(208, 268)(209, 254)(210, 248)(211, 272)(212, 267)(213, 281)(214, 266)(215, 242)(216, 247)(217, 259)(218, 271)(219, 256)(220, 260)(221, 262)(222, 264)(223, 269)(224, 287)(225, 274)(226, 243)(227, 279)(228, 278)(229, 273)(230, 280)(231, 246)(232, 241)(233, 250)(234, 263)(235, 282)(236, 285)(237, 286)(238, 245)(239, 265)(240, 258) MAP : A3.1022 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.3^4, x.3 * x.1 * x.2 * x.3^-1 * x.2^-1 * x.1^-1, x.1 * x.2 * x.3^-1 * x.1^-1 * x.3^-1 * x.2^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 152)(98, 183)(99, 146)(100, 170)(101, 158)(102, 151)(103, 184)(104, 178)(105, 167)(106, 153)(107, 175)(108, 166)(109, 168)(110, 177)(111, 174)(112, 187)(113, 171)(114, 160)(115, 185)(116, 188)(117, 164)(118, 189)(119, 154)(120, 190)(121, 159)(122, 182)(123, 180)(124, 176)(125, 191)(126, 169)(127, 186)(128, 179)(129, 149)(130, 145)(131, 172)(132, 161)(133, 163)(134, 148)(135, 147)(136, 150)(137, 181)(138, 155)(139, 162)(140, 165)(141, 156)(142, 157)(143, 192)(144, 173)(193, 245)(194, 241)(195, 268)(196, 257)(197, 259)(198, 244)(199, 243)(200, 246)(201, 277)(202, 251)(203, 258)(204, 261)(205, 252)(206, 253)(207, 288)(208, 269)(209, 248)(210, 279)(211, 242)(212, 266)(213, 254)(214, 247)(215, 280)(216, 274)(217, 263)(218, 249)(219, 271)(220, 262)(221, 264)(222, 273)(223, 270)(224, 283)(225, 267)(226, 256)(227, 281)(228, 284)(229, 260)(230, 285)(231, 250)(232, 286)(233, 255)(234, 278)(235, 276)(236, 272)(237, 287)(238, 265)(239, 282)(240, 275) MAP : A3.1023 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^4, x.2 * x.3^-1 * x.2 * x.3 * x.1^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 71)(2, 73)(3, 72)(4, 87)(5, 88)(6, 66)(7, 77)(8, 59)(9, 70)(10, 83)(11, 89)(12, 56)(13, 65)(14, 52)(15, 69)(16, 81)(17, 58)(18, 63)(19, 94)(20, 51)(21, 54)(22, 64)(23, 95)(24, 79)(25, 93)(26, 76)(27, 85)(28, 82)(29, 75)(30, 74)(31, 68)(32, 53)(33, 57)(34, 78)(35, 61)(36, 50)(37, 55)(38, 91)(39, 96)(40, 90)(41, 60)(42, 80)(43, 67)(44, 49)(45, 84)(46, 86)(47, 92)(48, 62)(97, 147)(98, 181)(99, 150)(100, 184)(101, 178)(102, 145)(103, 156)(104, 180)(105, 148)(106, 146)(107, 167)(108, 190)(109, 149)(110, 188)(111, 163)(112, 152)(113, 182)(114, 186)(115, 177)(116, 185)(117, 189)(118, 179)(119, 174)(120, 192)(121, 168)(122, 165)(123, 158)(124, 183)(125, 162)(126, 155)(127, 161)(128, 164)(129, 159)(130, 157)(131, 191)(132, 160)(133, 154)(134, 175)(135, 187)(136, 153)(137, 176)(138, 173)(139, 172)(140, 171)(141, 170)(142, 151)(143, 166)(144, 169)(193, 261)(194, 257)(195, 284)(196, 273)(197, 275)(198, 260)(199, 259)(200, 262)(201, 245)(202, 267)(203, 274)(204, 277)(205, 268)(206, 269)(207, 256)(208, 285)(209, 264)(210, 247)(211, 258)(212, 282)(213, 270)(214, 263)(215, 248)(216, 242)(217, 279)(218, 265)(219, 287)(220, 278)(221, 280)(222, 241)(223, 286)(224, 251)(225, 283)(226, 272)(227, 249)(228, 252)(229, 276)(230, 253)(231, 266)(232, 254)(233, 271)(234, 246)(235, 244)(236, 288)(237, 255)(238, 281)(239, 250)(240, 243) MAP : A3.1024 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^4, x.2 * x.3^-1 * x.2 * x.3 * x.1^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 71)(2, 73)(3, 72)(4, 87)(5, 88)(6, 66)(7, 77)(8, 59)(9, 70)(10, 83)(11, 89)(12, 56)(13, 65)(14, 52)(15, 69)(16, 81)(17, 58)(18, 63)(19, 94)(20, 51)(21, 54)(22, 64)(23, 95)(24, 79)(25, 93)(26, 76)(27, 85)(28, 82)(29, 75)(30, 74)(31, 68)(32, 53)(33, 57)(34, 78)(35, 61)(36, 50)(37, 55)(38, 91)(39, 96)(40, 90)(41, 60)(42, 80)(43, 67)(44, 49)(45, 84)(46, 86)(47, 92)(48, 62)(97, 150)(98, 154)(99, 145)(100, 153)(101, 157)(102, 147)(103, 190)(104, 160)(105, 184)(106, 181)(107, 174)(108, 151)(109, 178)(110, 171)(111, 177)(112, 180)(113, 175)(114, 173)(115, 159)(116, 176)(117, 170)(118, 191)(119, 155)(120, 169)(121, 192)(122, 189)(123, 188)(124, 187)(125, 186)(126, 167)(127, 182)(128, 185)(129, 163)(130, 149)(131, 166)(132, 152)(133, 146)(134, 161)(135, 172)(136, 148)(137, 164)(138, 162)(139, 183)(140, 158)(141, 165)(142, 156)(143, 179)(144, 168)(193, 260)(194, 267)(195, 261)(196, 245)(197, 268)(198, 284)(199, 281)(200, 285)(201, 254)(202, 276)(203, 241)(204, 259)(205, 272)(206, 287)(207, 283)(208, 252)(209, 286)(210, 280)(211, 256)(212, 251)(213, 265)(214, 250)(215, 274)(216, 279)(217, 243)(218, 255)(219, 288)(220, 244)(221, 246)(222, 248)(223, 253)(224, 271)(225, 258)(226, 275)(227, 263)(228, 262)(229, 257)(230, 264)(231, 278)(232, 273)(233, 282)(234, 247)(235, 266)(236, 269)(237, 270)(238, 277)(239, 249)(240, 242) MAP : A3.1025 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^4, x.2 * x.3^-1 * x.2 * x.3 * x.1^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 92)(2, 84)(3, 68)(4, 62)(5, 80)(6, 69)(7, 85)(8, 60)(9, 81)(10, 65)(11, 56)(12, 89)(13, 83)(14, 96)(15, 66)(16, 70)(17, 61)(18, 54)(19, 91)(20, 79)(21, 63)(22, 57)(23, 49)(24, 51)(25, 50)(26, 78)(27, 77)(28, 74)(29, 55)(30, 82)(31, 72)(32, 90)(33, 64)(34, 76)(35, 58)(36, 93)(37, 75)(38, 94)(39, 52)(40, 53)(41, 59)(42, 88)(43, 86)(44, 95)(45, 73)(46, 67)(47, 71)(48, 87)(97, 147)(98, 181)(99, 150)(100, 184)(101, 178)(102, 145)(103, 156)(104, 180)(105, 148)(106, 146)(107, 167)(108, 190)(109, 149)(110, 188)(111, 163)(112, 152)(113, 182)(114, 186)(115, 177)(116, 185)(117, 189)(118, 179)(119, 174)(120, 192)(121, 168)(122, 165)(123, 158)(124, 183)(125, 162)(126, 155)(127, 161)(128, 164)(129, 159)(130, 157)(131, 191)(132, 160)(133, 154)(134, 175)(135, 187)(136, 153)(137, 176)(138, 173)(139, 172)(140, 171)(141, 170)(142, 151)(143, 166)(144, 169)(193, 258)(194, 275)(195, 263)(196, 262)(197, 257)(198, 264)(199, 278)(200, 273)(201, 282)(202, 247)(203, 266)(204, 269)(205, 270)(206, 277)(207, 249)(208, 242)(209, 260)(210, 267)(211, 261)(212, 245)(213, 268)(214, 284)(215, 281)(216, 285)(217, 254)(218, 276)(219, 241)(220, 259)(221, 272)(222, 287)(223, 283)(224, 252)(225, 286)(226, 280)(227, 256)(228, 251)(229, 265)(230, 250)(231, 274)(232, 279)(233, 243)(234, 255)(235, 288)(236, 244)(237, 246)(238, 248)(239, 253)(240, 271) MAP : A3.1026 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^4, x.2 * x.3 * x.1 * x.2^-1 * x.1^-1 * x.3^-1, x.1 * x.2^-1 * x.3^-1 * x.2^-1 * x.1^-1 * x.2^-1 * x.3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73)(97, 149)(98, 145)(99, 172)(100, 161)(101, 163)(102, 148)(103, 147)(104, 150)(105, 181)(106, 155)(107, 162)(108, 165)(109, 156)(110, 157)(111, 192)(112, 173)(113, 152)(114, 183)(115, 146)(116, 170)(117, 158)(118, 151)(119, 184)(120, 178)(121, 167)(122, 153)(123, 175)(124, 166)(125, 168)(126, 177)(127, 174)(128, 187)(129, 171)(130, 160)(131, 185)(132, 188)(133, 164)(134, 189)(135, 154)(136, 190)(137, 159)(138, 182)(139, 180)(140, 176)(141, 191)(142, 169)(143, 186)(144, 179)(193, 250)(194, 255)(195, 286)(196, 243)(197, 246)(198, 256)(199, 287)(200, 271)(201, 285)(202, 268)(203, 277)(204, 274)(205, 267)(206, 266)(207, 260)(208, 245)(209, 249)(210, 270)(211, 253)(212, 242)(213, 247)(214, 283)(215, 288)(216, 282)(217, 252)(218, 272)(219, 259)(220, 241)(221, 276)(222, 278)(223, 284)(224, 254)(225, 263)(226, 265)(227, 264)(228, 279)(229, 280)(230, 258)(231, 269)(232, 251)(233, 262)(234, 275)(235, 281)(236, 248)(237, 257)(238, 244)(239, 261)(240, 273) MAP : A3.1027 NOTES : type I, reflexible, isomorphic to A3.1004. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.3^4, x.3 * x.1 * x.2 * x.3^-1 * x.2^-1 * x.1^-1, x.1 * x.2 * x.3^-1 * x.1^-1 * x.3^-1 * x.2^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 4) #DARTS : 288 R = (1, 49, 97, 145, 193, 241)(2, 50, 98, 146, 194, 242)(3, 51, 99, 147, 195, 243)(4, 52, 100, 148, 196, 244)(5, 53, 101, 149, 197, 245)(6, 54, 102, 150, 198, 246)(7, 55, 103, 151, 199, 247)(8, 56, 104, 152, 200, 248)(9, 57, 105, 153, 201, 249)(10, 58, 106, 154, 202, 250)(11, 59, 107, 155, 203, 251)(12, 60, 108, 156, 204, 252)(13, 61, 109, 157, 205, 253)(14, 62, 110, 158, 206, 254)(15, 63, 111, 159, 207, 255)(16, 64, 112, 160, 208, 256)(17, 65, 113, 161, 209, 257)(18, 66, 114, 162, 210, 258)(19, 67, 115, 163, 211, 259)(20, 68, 116, 164, 212, 260)(21, 69, 117, 165, 213, 261)(22, 70, 118, 166, 214, 262)(23, 71, 119, 167, 215, 263)(24, 72, 120, 168, 216, 264)(25, 73, 121, 169, 217, 265)(26, 74, 122, 170, 218, 266)(27, 75, 123, 171, 219, 267)(28, 76, 124, 172, 220, 268)(29, 77, 125, 173, 221, 269)(30, 78, 126, 174, 222, 270)(31, 79, 127, 175, 223, 271)(32, 80, 128, 176, 224, 272)(33, 81, 129, 177, 225, 273)(34, 82, 130, 178, 226, 274)(35, 83, 131, 179, 227, 275)(36, 84, 132, 180, 228, 276)(37, 85, 133, 181, 229, 277)(38, 86, 134, 182, 230, 278)(39, 87, 135, 183, 231, 279)(40, 88, 136, 184, 232, 280)(41, 89, 137, 185, 233, 281)(42, 90, 138, 186, 234, 282)(43, 91, 139, 187, 235, 283)(44, 92, 140, 188, 236, 284)(45, 93, 141, 189, 237, 285)(46, 94, 142, 190, 238, 286)(47, 95, 143, 191, 239, 287)(48, 96, 144, 192, 240, 288) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72)(97, 164)(98, 171)(99, 165)(100, 149)(101, 172)(102, 188)(103, 185)(104, 189)(105, 158)(106, 180)(107, 145)(108, 163)(109, 176)(110, 191)(111, 187)(112, 156)(113, 190)(114, 184)(115, 160)(116, 155)(117, 169)(118, 154)(119, 178)(120, 183)(121, 147)(122, 159)(123, 192)(124, 148)(125, 150)(126, 152)(127, 157)(128, 175)(129, 162)(130, 179)(131, 167)(132, 166)(133, 161)(134, 168)(135, 182)(136, 177)(137, 186)(138, 151)(139, 170)(140, 173)(141, 174)(142, 181)(143, 153)(144, 146)(193, 263)(194, 265)(195, 264)(196, 279)(197, 280)(198, 258)(199, 269)(200, 251)(201, 262)(202, 275)(203, 281)(204, 248)(205, 257)(206, 244)(207, 261)(208, 273)(209, 250)(210, 255)(211, 286)(212, 243)(213, 246)(214, 256)(215, 287)(216, 271)(217, 285)(218, 268)(219, 277)(220, 274)(221, 267)(222, 266)(223, 260)(224, 245)(225, 249)(226, 270)(227, 253)(228, 242)(229, 247)(230, 283)(231, 288)(232, 282)(233, 252)(234, 272)(235, 259)(236, 241)(237, 276)(238, 278)(239, 284)(240, 254) MAP : A3.1028 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 6, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^-1 * x.3 * x.1 * x.3^-1, x.3^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 6) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 26)(2, 29)(3, 31)(4, 35)(5, 25)(6, 39)(7, 42)(8, 47)(9, 36)(10, 44)(11, 37)(12, 38)(13, 28)(14, 33)(15, 45)(16, 34)(17, 32)(18, 27)(19, 46)(20, 40)(21, 30)(22, 48)(23, 41)(24, 43)(49, 76)(50, 84)(51, 77)(52, 78)(53, 92)(54, 73)(55, 85)(56, 74)(57, 96)(58, 91)(59, 86)(60, 80)(61, 94)(62, 88)(63, 81)(64, 83)(65, 90)(66, 93)(67, 95)(68, 75)(69, 89)(70, 79)(71, 82)(72, 87)(97, 141)(98, 137)(99, 130)(100, 125)(101, 138)(102, 133)(103, 139)(104, 129)(105, 126)(106, 128)(107, 140)(108, 121)(109, 123)(110, 124)(111, 142)(112, 132)(113, 135)(114, 143)(115, 136)(116, 122)(117, 127)(118, 131)(119, 144)(120, 134) MAP : A3.1029 NOTES : type I, reflexible, isomorphic to A3.1028. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 6, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^-1 * x.1 * x.2 * x.3^-1, x.2^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 6) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 29)(2, 25)(3, 42)(4, 37)(5, 26)(6, 45)(7, 27)(8, 41)(9, 38)(10, 40)(11, 28)(12, 33)(13, 35)(14, 36)(15, 30)(16, 44)(17, 47)(18, 31)(19, 48)(20, 34)(21, 39)(22, 43)(23, 32)(24, 46)(49, 83)(50, 86)(51, 73)(52, 87)(53, 88)(54, 74)(55, 76)(56, 77)(57, 91)(58, 94)(59, 81)(60, 95)(61, 96)(62, 82)(63, 84)(64, 85)(65, 75)(66, 78)(67, 89)(68, 79)(69, 80)(70, 90)(71, 92)(72, 93)(97, 127)(98, 135)(99, 128)(100, 138)(101, 143)(102, 123)(103, 136)(104, 126)(105, 133)(106, 129)(107, 122)(108, 141)(109, 130)(110, 125)(111, 131)(112, 121)(113, 142)(114, 144)(115, 132)(116, 137)(117, 139)(118, 140)(119, 134)(120, 124) MAP : A3.1030 NOTES : type I, reflexible, isomorphic to A3.1028. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 6, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^-1 * x.3 * x.1 * x.3^-1, x.3^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 6) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 29)(2, 25)(3, 42)(4, 37)(5, 26)(6, 45)(7, 27)(8, 41)(9, 38)(10, 40)(11, 28)(12, 33)(13, 35)(14, 36)(15, 30)(16, 44)(17, 47)(18, 31)(19, 48)(20, 34)(21, 39)(22, 43)(23, 32)(24, 46)(49, 78)(50, 80)(51, 92)(52, 73)(53, 75)(54, 76)(55, 94)(56, 84)(57, 87)(58, 95)(59, 88)(60, 74)(61, 79)(62, 83)(63, 96)(64, 86)(65, 93)(66, 89)(67, 82)(68, 77)(69, 90)(70, 85)(71, 91)(72, 81)(97, 131)(98, 134)(99, 121)(100, 135)(101, 136)(102, 122)(103, 124)(104, 125)(105, 139)(106, 142)(107, 129)(108, 143)(109, 144)(110, 130)(111, 132)(112, 133)(113, 123)(114, 126)(115, 137)(116, 127)(117, 128)(118, 138)(119, 140)(120, 141) MAP : A3.1031 NOTES : type I, reflexible, isomorphic to A3.1028. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 6, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^-1 * x.1 * x.2 * x.3^-1, x.2^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 6) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 26)(2, 29)(3, 31)(4, 35)(5, 25)(6, 39)(7, 42)(8, 47)(9, 36)(10, 44)(11, 37)(12, 38)(13, 28)(14, 33)(15, 45)(16, 34)(17, 32)(18, 27)(19, 46)(20, 40)(21, 30)(22, 48)(23, 41)(24, 43)(49, 75)(50, 78)(51, 89)(52, 79)(53, 80)(54, 90)(55, 92)(56, 93)(57, 83)(58, 86)(59, 73)(60, 87)(61, 88)(62, 74)(63, 76)(64, 77)(65, 91)(66, 94)(67, 81)(68, 95)(69, 96)(70, 82)(71, 84)(72, 85)(97, 124)(98, 132)(99, 125)(100, 126)(101, 140)(102, 121)(103, 133)(104, 122)(105, 144)(106, 139)(107, 134)(108, 128)(109, 142)(110, 136)(111, 129)(112, 131)(113, 138)(114, 141)(115, 143)(116, 123)(117, 137)(118, 127)(119, 130)(120, 135) MAP : A3.1032 NOTES : type I, reflexible, isomorphic to A3.1028. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.3^-1 * x.1 * x.2 * x.1^-1, x.1^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 6) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 35)(2, 38)(3, 25)(4, 39)(5, 40)(6, 26)(7, 28)(8, 29)(9, 43)(10, 46)(11, 33)(12, 47)(13, 48)(14, 34)(15, 36)(16, 37)(17, 27)(18, 30)(19, 41)(20, 31)(21, 32)(22, 42)(23, 44)(24, 45)(49, 77)(50, 73)(51, 90)(52, 85)(53, 74)(54, 93)(55, 75)(56, 89)(57, 86)(58, 88)(59, 76)(60, 81)(61, 83)(62, 84)(63, 78)(64, 92)(65, 95)(66, 79)(67, 96)(68, 82)(69, 87)(70, 91)(71, 80)(72, 94)(97, 126)(98, 128)(99, 140)(100, 121)(101, 123)(102, 124)(103, 142)(104, 132)(105, 135)(106, 143)(107, 136)(108, 122)(109, 127)(110, 131)(111, 144)(112, 134)(113, 141)(114, 137)(115, 130)(116, 125)(117, 138)(118, 133)(119, 139)(120, 129) MAP : A3.1033 NOTES : type I, reflexible, isomorphic to A3.1028. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {6, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 6, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^6 > CTG (small) : <24, 3> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.3^-1 * x.1 * x.2 * x.1^-1, x.1^6 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 6) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 27)(2, 30)(3, 41)(4, 31)(5, 32)(6, 42)(7, 44)(8, 45)(9, 35)(10, 38)(11, 25)(12, 39)(13, 40)(14, 26)(15, 28)(16, 29)(17, 43)(18, 46)(19, 33)(20, 47)(21, 48)(22, 34)(23, 36)(24, 37)(49, 74)(50, 77)(51, 79)(52, 83)(53, 73)(54, 87)(55, 90)(56, 95)(57, 84)(58, 92)(59, 85)(60, 86)(61, 76)(62, 81)(63, 93)(64, 82)(65, 80)(66, 75)(67, 94)(68, 88)(69, 78)(70, 96)(71, 89)(72, 91)(97, 136)(98, 131)(99, 126)(100, 144)(101, 134)(102, 128)(103, 121)(104, 123)(105, 130)(106, 133)(107, 135)(108, 139)(109, 129)(110, 143)(111, 122)(112, 127)(113, 140)(114, 124)(115, 141)(116, 142)(117, 132)(118, 137)(119, 125)(120, 138) MAP : A3.1034 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^-1 * x.3^-1 * x.2^-2, x.2^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 7) #DARTS : 126 R = (1, 22, 43, 64, 85, 106)(2, 23, 44, 65, 86, 107)(3, 24, 45, 66, 87, 108)(4, 25, 46, 67, 88, 109)(5, 26, 47, 68, 89, 110)(6, 27, 48, 69, 90, 111)(7, 28, 49, 70, 91, 112)(8, 29, 50, 71, 92, 113)(9, 30, 51, 72, 93, 114)(10, 31, 52, 73, 94, 115)(11, 32, 53, 74, 95, 116)(12, 33, 54, 75, 96, 117)(13, 34, 55, 76, 97, 118)(14, 35, 56, 77, 98, 119)(15, 36, 57, 78, 99, 120)(16, 37, 58, 79, 100, 121)(17, 38, 59, 80, 101, 122)(18, 39, 60, 81, 102, 123)(19, 40, 61, 82, 103, 124)(20, 41, 62, 83, 104, 125)(21, 42, 63, 84, 105, 126) L = (1, 23)(2, 26)(3, 33)(4, 28)(5, 22)(6, 39)(7, 36)(8, 34)(9, 42)(10, 29)(11, 24)(12, 32)(13, 31)(14, 41)(15, 25)(16, 27)(17, 30)(18, 37)(19, 35)(20, 40)(21, 38)(43, 67)(44, 69)(45, 72)(46, 79)(47, 77)(48, 82)(49, 80)(50, 65)(51, 68)(52, 75)(53, 70)(54, 64)(55, 81)(56, 78)(57, 76)(58, 84)(59, 71)(60, 66)(61, 74)(62, 73)(63, 83)(85, 108)(86, 115)(87, 111)(88, 110)(89, 122)(90, 106)(91, 117)(92, 126)(93, 116)(94, 119)(95, 125)(96, 118)(97, 112)(98, 107)(99, 124)(100, 120)(101, 109)(102, 113)(103, 121)(104, 114)(105, 123) MAP : A3.1035 NOTES : type I, reflexible, isomorphic to A3.1034. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 7, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.3^-2 * x.2^-1 * x.1^-1, x.3^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 7) #DARTS : 126 R = (1, 22, 43, 64, 85, 106)(2, 23, 44, 65, 86, 107)(3, 24, 45, 66, 87, 108)(4, 25, 46, 67, 88, 109)(5, 26, 47, 68, 89, 110)(6, 27, 48, 69, 90, 111)(7, 28, 49, 70, 91, 112)(8, 29, 50, 71, 92, 113)(9, 30, 51, 72, 93, 114)(10, 31, 52, 73, 94, 115)(11, 32, 53, 74, 95, 116)(12, 33, 54, 75, 96, 117)(13, 34, 55, 76, 97, 118)(14, 35, 56, 77, 98, 119)(15, 36, 57, 78, 99, 120)(16, 37, 58, 79, 100, 121)(17, 38, 59, 80, 101, 122)(18, 39, 60, 81, 102, 123)(19, 40, 61, 82, 103, 124)(20, 41, 62, 83, 104, 125)(21, 42, 63, 84, 105, 126) L = (1, 26)(2, 22)(3, 32)(4, 36)(5, 23)(6, 37)(7, 25)(8, 31)(9, 38)(10, 34)(11, 33)(12, 24)(13, 29)(14, 40)(15, 28)(16, 39)(17, 42)(18, 27)(19, 41)(20, 35)(21, 30)(43, 70)(44, 81)(45, 84)(46, 69)(47, 83)(48, 77)(49, 72)(50, 68)(51, 64)(52, 74)(53, 78)(54, 65)(55, 79)(56, 67)(57, 73)(58, 80)(59, 76)(60, 75)(61, 66)(62, 71)(63, 82)(85, 126)(86, 116)(87, 119)(88, 125)(89, 118)(90, 112)(91, 107)(92, 124)(93, 120)(94, 109)(95, 113)(96, 121)(97, 114)(98, 123)(99, 108)(100, 115)(101, 111)(102, 110)(103, 122)(104, 106)(105, 117) MAP : A3.1036 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^-1 * x.1^-1 * x.2 * x.3^-1, x.2^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 7) #DARTS : 126 R = (1, 22, 43, 64, 85, 106)(2, 23, 44, 65, 86, 107)(3, 24, 45, 66, 87, 108)(4, 25, 46, 67, 88, 109)(5, 26, 47, 68, 89, 110)(6, 27, 48, 69, 90, 111)(7, 28, 49, 70, 91, 112)(8, 29, 50, 71, 92, 113)(9, 30, 51, 72, 93, 114)(10, 31, 52, 73, 94, 115)(11, 32, 53, 74, 95, 116)(12, 33, 54, 75, 96, 117)(13, 34, 55, 76, 97, 118)(14, 35, 56, 77, 98, 119)(15, 36, 57, 78, 99, 120)(16, 37, 58, 79, 100, 121)(17, 38, 59, 80, 101, 122)(18, 39, 60, 81, 102, 123)(19, 40, 61, 82, 103, 124)(20, 41, 62, 83, 104, 125)(21, 42, 63, 84, 105, 126) L = (1, 26)(2, 22)(3, 32)(4, 36)(5, 23)(6, 37)(7, 25)(8, 31)(9, 38)(10, 34)(11, 33)(12, 24)(13, 29)(14, 40)(15, 28)(16, 39)(17, 42)(18, 27)(19, 41)(20, 35)(21, 30)(43, 67)(44, 69)(45, 72)(46, 79)(47, 77)(48, 82)(49, 80)(50, 65)(51, 68)(52, 75)(53, 70)(54, 64)(55, 81)(56, 78)(57, 76)(58, 84)(59, 71)(60, 66)(61, 74)(62, 73)(63, 83)(85, 116)(86, 118)(87, 121)(88, 107)(89, 126)(90, 110)(91, 108)(92, 114)(93, 117)(94, 124)(95, 119)(96, 113)(97, 109)(98, 106)(99, 125)(100, 112)(101, 120)(102, 115)(103, 123)(104, 122)(105, 111) MAP : A3.1037 NOTES : type I, reflexible, isomorphic to A3.1034. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^-1 * x.3^-1 * x.2^-2, x.2^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 7) #DARTS : 126 R = (1, 22, 43, 64, 85, 106)(2, 23, 44, 65, 86, 107)(3, 24, 45, 66, 87, 108)(4, 25, 46, 67, 88, 109)(5, 26, 47, 68, 89, 110)(6, 27, 48, 69, 90, 111)(7, 28, 49, 70, 91, 112)(8, 29, 50, 71, 92, 113)(9, 30, 51, 72, 93, 114)(10, 31, 52, 73, 94, 115)(11, 32, 53, 74, 95, 116)(12, 33, 54, 75, 96, 117)(13, 34, 55, 76, 97, 118)(14, 35, 56, 77, 98, 119)(15, 36, 57, 78, 99, 120)(16, 37, 58, 79, 100, 121)(17, 38, 59, 80, 101, 122)(18, 39, 60, 81, 102, 123)(19, 40, 61, 82, 103, 124)(20, 41, 62, 83, 104, 125)(21, 42, 63, 84, 105, 126) L = (1, 23)(2, 26)(3, 33)(4, 28)(5, 22)(6, 39)(7, 36)(8, 34)(9, 42)(10, 29)(11, 24)(12, 32)(13, 31)(14, 41)(15, 25)(16, 27)(17, 30)(18, 37)(19, 35)(20, 40)(21, 38)(43, 84)(44, 74)(45, 77)(46, 83)(47, 76)(48, 70)(49, 65)(50, 82)(51, 78)(52, 67)(53, 71)(54, 79)(55, 72)(56, 81)(57, 66)(58, 73)(59, 69)(60, 68)(61, 80)(62, 64)(63, 75)(85, 119)(86, 109)(87, 112)(88, 118)(89, 111)(90, 126)(91, 121)(92, 117)(93, 113)(94, 123)(95, 106)(96, 114)(97, 107)(98, 116)(99, 122)(100, 108)(101, 125)(102, 124)(103, 115)(104, 120)(105, 110) MAP : A3.1038 NOTES : type I, reflexible, isomorphic to A3.1036. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3 | x.3 * x.2 * x.1, x.2^3, x.3^3, x.3 * x.1 * x.2 * x.1^-1, x.1^3 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 7) #DARTS : 126 R = (1, 22, 43, 64, 85, 106)(2, 23, 44, 65, 86, 107)(3, 24, 45, 66, 87, 108)(4, 25, 46, 67, 88, 109)(5, 26, 47, 68, 89, 110)(6, 27, 48, 69, 90, 111)(7, 28, 49, 70, 91, 112)(8, 29, 50, 71, 92, 113)(9, 30, 51, 72, 93, 114)(10, 31, 52, 73, 94, 115)(11, 32, 53, 74, 95, 116)(12, 33, 54, 75, 96, 117)(13, 34, 55, 76, 97, 118)(14, 35, 56, 77, 98, 119)(15, 36, 57, 78, 99, 120)(16, 37, 58, 79, 100, 121)(17, 38, 59, 80, 101, 122)(18, 39, 60, 81, 102, 123)(19, 40, 61, 82, 103, 124)(20, 41, 62, 83, 104, 125)(21, 42, 63, 84, 105, 126) L = (1, 25)(2, 27)(3, 30)(4, 37)(5, 35)(6, 40)(7, 38)(8, 23)(9, 26)(10, 33)(11, 28)(12, 22)(13, 39)(14, 36)(15, 34)(16, 42)(17, 29)(18, 24)(19, 32)(20, 31)(21, 41)(43, 65)(44, 68)(45, 75)(46, 70)(47, 64)(48, 81)(49, 78)(50, 76)(51, 84)(52, 71)(53, 66)(54, 74)(55, 73)(56, 83)(57, 67)(58, 69)(59, 72)(60, 79)(61, 77)(62, 82)(63, 80)(85, 114)(86, 117)(87, 124)(88, 119)(89, 113)(90, 109)(91, 106)(92, 125)(93, 112)(94, 120)(95, 115)(96, 123)(97, 122)(98, 111)(99, 116)(100, 118)(101, 121)(102, 107)(103, 126)(104, 110)(105, 108) MAP : A3.1039 NOTES : type I, reflexible, isomorphic to A3.1036. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 7, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2 * x.1 * x.3, x.2^3, x.2 * x.3 * x.1 * x.3^-1, x.1 * x.2 * x.3^-3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 7) #DARTS : 126 R = (1, 22, 43, 64, 85, 106)(2, 23, 44, 65, 86, 107)(3, 24, 45, 66, 87, 108)(4, 25, 46, 67, 88, 109)(5, 26, 47, 68, 89, 110)(6, 27, 48, 69, 90, 111)(7, 28, 49, 70, 91, 112)(8, 29, 50, 71, 92, 113)(9, 30, 51, 72, 93, 114)(10, 31, 52, 73, 94, 115)(11, 32, 53, 74, 95, 116)(12, 33, 54, 75, 96, 117)(13, 34, 55, 76, 97, 118)(14, 35, 56, 77, 98, 119)(15, 36, 57, 78, 99, 120)(16, 37, 58, 79, 100, 121)(17, 38, 59, 80, 101, 122)(18, 39, 60, 81, 102, 123)(19, 40, 61, 82, 103, 124)(20, 41, 62, 83, 104, 125)(21, 42, 63, 84, 105, 126) L = (1, 23)(2, 26)(3, 33)(4, 28)(5, 22)(6, 39)(7, 36)(8, 34)(9, 42)(10, 29)(11, 24)(12, 32)(13, 31)(14, 41)(15, 25)(16, 27)(17, 30)(18, 37)(19, 35)(20, 40)(21, 38)(43, 77)(44, 67)(45, 70)(46, 76)(47, 69)(48, 84)(49, 79)(50, 75)(51, 71)(52, 81)(53, 64)(54, 72)(55, 65)(56, 74)(57, 80)(58, 66)(59, 83)(60, 82)(61, 73)(62, 78)(63, 68)(85, 117)(86, 113)(87, 123)(88, 106)(89, 114)(90, 107)(91, 116)(92, 122)(93, 108)(94, 125)(95, 124)(96, 115)(97, 120)(98, 110)(99, 119)(100, 109)(101, 112)(102, 118)(103, 111)(104, 126)(105, 121) MAP : A3.1040 NOTES : type I, reflexible, isomorphic to A3.1036. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 7, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2 * x.1 * x.3, x.2^3, x.2 * x.3 * x.1 * x.3^-1, x.1 * x.2 * x.3^-3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 7) #DARTS : 126 R = (1, 22, 43, 64, 85, 106)(2, 23, 44, 65, 86, 107)(3, 24, 45, 66, 87, 108)(4, 25, 46, 67, 88, 109)(5, 26, 47, 68, 89, 110)(6, 27, 48, 69, 90, 111)(7, 28, 49, 70, 91, 112)(8, 29, 50, 71, 92, 113)(9, 30, 51, 72, 93, 114)(10, 31, 52, 73, 94, 115)(11, 32, 53, 74, 95, 116)(12, 33, 54, 75, 96, 117)(13, 34, 55, 76, 97, 118)(14, 35, 56, 77, 98, 119)(15, 36, 57, 78, 99, 120)(16, 37, 58, 79, 100, 121)(17, 38, 59, 80, 101, 122)(18, 39, 60, 81, 102, 123)(19, 40, 61, 82, 103, 124)(20, 41, 62, 83, 104, 125)(21, 42, 63, 84, 105, 126) L = (1, 23)(2, 26)(3, 33)(4, 28)(5, 22)(6, 39)(7, 36)(8, 34)(9, 42)(10, 29)(11, 24)(12, 32)(13, 31)(14, 41)(15, 25)(16, 27)(17, 30)(18, 37)(19, 35)(20, 40)(21, 38)(43, 72)(44, 75)(45, 82)(46, 77)(47, 71)(48, 67)(49, 64)(50, 83)(51, 70)(52, 78)(53, 73)(54, 81)(55, 80)(56, 69)(57, 74)(58, 76)(59, 79)(60, 65)(61, 84)(62, 68)(63, 66)(85, 109)(86, 111)(87, 114)(88, 121)(89, 119)(90, 124)(91, 122)(92, 107)(93, 110)(94, 117)(95, 112)(96, 106)(97, 123)(98, 120)(99, 118)(100, 126)(101, 113)(102, 108)(103, 116)(104, 115)(105, 125) MAP : A3.1041 NOTES : type I, reflexible, isomorphic to A3.1034. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^-1 * x.3^-1 * x.2^-1 * x.1^-1, x.1^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 7) #DARTS : 126 R = (1, 22, 43, 64, 85, 106)(2, 23, 44, 65, 86, 107)(3, 24, 45, 66, 87, 108)(4, 25, 46, 67, 88, 109)(5, 26, 47, 68, 89, 110)(6, 27, 48, 69, 90, 111)(7, 28, 49, 70, 91, 112)(8, 29, 50, 71, 92, 113)(9, 30, 51, 72, 93, 114)(10, 31, 52, 73, 94, 115)(11, 32, 53, 74, 95, 116)(12, 33, 54, 75, 96, 117)(13, 34, 55, 76, 97, 118)(14, 35, 56, 77, 98, 119)(15, 36, 57, 78, 99, 120)(16, 37, 58, 79, 100, 121)(17, 38, 59, 80, 101, 122)(18, 39, 60, 81, 102, 123)(19, 40, 61, 82, 103, 124)(20, 41, 62, 83, 104, 125)(21, 42, 63, 84, 105, 126) L = (1, 42)(2, 32)(3, 35)(4, 41)(5, 34)(6, 28)(7, 23)(8, 40)(9, 36)(10, 25)(11, 29)(12, 37)(13, 30)(14, 39)(15, 24)(16, 31)(17, 27)(18, 26)(19, 38)(20, 22)(21, 33)(43, 68)(44, 64)(45, 74)(46, 78)(47, 65)(48, 79)(49, 67)(50, 73)(51, 80)(52, 76)(53, 75)(54, 66)(55, 71)(56, 82)(57, 70)(58, 81)(59, 84)(60, 69)(61, 83)(62, 77)(63, 72)(85, 112)(86, 123)(87, 126)(88, 111)(89, 125)(90, 119)(91, 114)(92, 110)(93, 106)(94, 116)(95, 120)(96, 107)(97, 121)(98, 109)(99, 115)(100, 122)(101, 118)(102, 117)(103, 108)(104, 113)(105, 124) MAP : A3.1042 NOTES : type I, reflexible, isomorphic to A3.1036. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 7, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2^-1 * x.1^-1 * x.2 * x.3^-1, x.2^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 7) #DARTS : 126 R = (1, 22, 43, 64, 85, 106)(2, 23, 44, 65, 86, 107)(3, 24, 45, 66, 87, 108)(4, 25, 46, 67, 88, 109)(5, 26, 47, 68, 89, 110)(6, 27, 48, 69, 90, 111)(7, 28, 49, 70, 91, 112)(8, 29, 50, 71, 92, 113)(9, 30, 51, 72, 93, 114)(10, 31, 52, 73, 94, 115)(11, 32, 53, 74, 95, 116)(12, 33, 54, 75, 96, 117)(13, 34, 55, 76, 97, 118)(14, 35, 56, 77, 98, 119)(15, 36, 57, 78, 99, 120)(16, 37, 58, 79, 100, 121)(17, 38, 59, 80, 101, 122)(18, 39, 60, 81, 102, 123)(19, 40, 61, 82, 103, 124)(20, 41, 62, 83, 104, 125)(21, 42, 63, 84, 105, 126) L = (1, 26)(2, 22)(3, 32)(4, 36)(5, 23)(6, 37)(7, 25)(8, 31)(9, 38)(10, 34)(11, 33)(12, 24)(13, 29)(14, 40)(15, 28)(16, 39)(17, 42)(18, 27)(19, 41)(20, 35)(21, 30)(43, 84)(44, 74)(45, 77)(46, 83)(47, 76)(48, 70)(49, 65)(50, 82)(51, 78)(52, 67)(53, 71)(54, 79)(55, 72)(56, 81)(57, 66)(58, 73)(59, 69)(60, 68)(61, 80)(62, 64)(63, 75)(85, 124)(86, 120)(87, 109)(88, 113)(89, 121)(90, 114)(91, 123)(92, 108)(93, 115)(94, 111)(95, 110)(96, 122)(97, 106)(98, 117)(99, 126)(100, 116)(101, 119)(102, 125)(103, 118)(104, 112)(105, 107) MAP : A3.1043 NOTES : type I, reflexible, isomorphic to A3.1034. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.1^-1 * x.3^-1 * x.2^-1 * x.1^-1, x.1^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 7) #DARTS : 126 R = (1, 22, 43, 64, 85, 106)(2, 23, 44, 65, 86, 107)(3, 24, 45, 66, 87, 108)(4, 25, 46, 67, 88, 109)(5, 26, 47, 68, 89, 110)(6, 27, 48, 69, 90, 111)(7, 28, 49, 70, 91, 112)(8, 29, 50, 71, 92, 113)(9, 30, 51, 72, 93, 114)(10, 31, 52, 73, 94, 115)(11, 32, 53, 74, 95, 116)(12, 33, 54, 75, 96, 117)(13, 34, 55, 76, 97, 118)(14, 35, 56, 77, 98, 119)(15, 36, 57, 78, 99, 120)(16, 37, 58, 79, 100, 121)(17, 38, 59, 80, 101, 122)(18, 39, 60, 81, 102, 123)(19, 40, 61, 82, 103, 124)(20, 41, 62, 83, 104, 125)(21, 42, 63, 84, 105, 126) L = (1, 25)(2, 27)(3, 30)(4, 37)(5, 35)(6, 40)(7, 38)(8, 23)(9, 26)(10, 33)(11, 28)(12, 22)(13, 39)(14, 36)(15, 34)(16, 42)(17, 29)(18, 24)(19, 32)(20, 31)(21, 41)(43, 68)(44, 64)(45, 74)(46, 78)(47, 65)(48, 79)(49, 67)(50, 73)(51, 80)(52, 76)(53, 75)(54, 66)(55, 71)(56, 82)(57, 70)(58, 81)(59, 84)(60, 69)(61, 83)(62, 77)(63, 72)(85, 113)(86, 114)(87, 115)(88, 116)(89, 117)(90, 118)(91, 119)(92, 120)(93, 121)(94, 122)(95, 123)(96, 124)(97, 125)(98, 126)(99, 106)(100, 107)(101, 108)(102, 109)(103, 110)(104, 111)(105, 112) MAP : A3.1044 NOTES : type I, reflexible, isomorphic to A3.1034. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 7, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.3^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.2^3, x.1^-1 * x.2^-1 * x.3^-1, x.3^-2 * x.2^-1 * x.1^-1, x.3^7 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 7) #DARTS : 126 R = (1, 22, 43, 64, 85, 106)(2, 23, 44, 65, 86, 107)(3, 24, 45, 66, 87, 108)(4, 25, 46, 67, 88, 109)(5, 26, 47, 68, 89, 110)(6, 27, 48, 69, 90, 111)(7, 28, 49, 70, 91, 112)(8, 29, 50, 71, 92, 113)(9, 30, 51, 72, 93, 114)(10, 31, 52, 73, 94, 115)(11, 32, 53, 74, 95, 116)(12, 33, 54, 75, 96, 117)(13, 34, 55, 76, 97, 118)(14, 35, 56, 77, 98, 119)(15, 36, 57, 78, 99, 120)(16, 37, 58, 79, 100, 121)(17, 38, 59, 80, 101, 122)(18, 39, 60, 81, 102, 123)(19, 40, 61, 82, 103, 124)(20, 41, 62, 83, 104, 125)(21, 42, 63, 84, 105, 126) L = (1, 26)(2, 22)(3, 32)(4, 36)(5, 23)(6, 37)(7, 25)(8, 31)(9, 38)(10, 34)(11, 33)(12, 24)(13, 29)(14, 40)(15, 28)(16, 39)(17, 42)(18, 27)(19, 41)(20, 35)(21, 30)(43, 74)(44, 76)(45, 79)(46, 65)(47, 84)(48, 68)(49, 66)(50, 72)(51, 75)(52, 82)(53, 77)(54, 71)(55, 67)(56, 64)(57, 83)(58, 70)(59, 78)(60, 73)(61, 81)(62, 80)(63, 69)(85, 125)(86, 112)(87, 120)(88, 115)(89, 123)(90, 122)(91, 111)(92, 116)(93, 118)(94, 121)(95, 107)(96, 126)(97, 110)(98, 108)(99, 114)(100, 117)(101, 124)(102, 119)(103, 113)(104, 109)(105, 106) MAP : A3.1045 NOTES : type I, reflexible, isomorphic to A3.1036. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {7, 3, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 7, 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^7 > CTG (small) : <21, 1> CTG (fp) : < x.1, x.2, x.3 | x.3 * x.2 * x.1, x.2^3, x.3^3, x.3 * x.1 * x.2 * x.1^-1, x.1^3 * x.3^-1 * x.2^-1 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 7) #DARTS : 126 R = (1, 22, 43, 64, 85, 106)(2, 23, 44, 65, 86, 107)(3, 24, 45, 66, 87, 108)(4, 25, 46, 67, 88, 109)(5, 26, 47, 68, 89, 110)(6, 27, 48, 69, 90, 111)(7, 28, 49, 70, 91, 112)(8, 29, 50, 71, 92, 113)(9, 30, 51, 72, 93, 114)(10, 31, 52, 73, 94, 115)(11, 32, 53, 74, 95, 116)(12, 33, 54, 75, 96, 117)(13, 34, 55, 76, 97, 118)(14, 35, 56, 77, 98, 119)(15, 36, 57, 78, 99, 120)(16, 37, 58, 79, 100, 121)(17, 38, 59, 80, 101, 122)(18, 39, 60, 81, 102, 123)(19, 40, 61, 82, 103, 124)(20, 41, 62, 83, 104, 125)(21, 42, 63, 84, 105, 126) L = (1, 42)(2, 32)(3, 35)(4, 41)(5, 34)(6, 28)(7, 23)(8, 40)(9, 36)(10, 25)(11, 29)(12, 37)(13, 30)(14, 39)(15, 24)(16, 31)(17, 27)(18, 26)(19, 38)(20, 22)(21, 33)(43, 65)(44, 68)(45, 75)(46, 70)(47, 64)(48, 81)(49, 78)(50, 76)(51, 84)(52, 71)(53, 66)(54, 74)(55, 73)(56, 83)(57, 67)(58, 69)(59, 72)(60, 79)(61, 77)(62, 82)(63, 80)(85, 123)(86, 125)(87, 107)(88, 114)(89, 112)(90, 117)(91, 115)(92, 121)(93, 124)(94, 110)(95, 126)(96, 120)(97, 116)(98, 113)(99, 111)(100, 119)(101, 106)(102, 122)(103, 109)(104, 108)(105, 118) MAP : A3.1046 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, (u.3^-1 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.4^3, x.3 * x.4 * x.2 * x.4, (x.3^-1 * x.2)^2, x.4 * x.1 * x.3 * x.4, x.3^4, (x.2 * x.1)^3 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 120)(2, 104)(3, 112)(4, 111)(5, 100)(6, 108)(7, 116)(8, 115)(9, 103)(10, 101)(11, 102)(12, 109)(13, 107)(14, 105)(15, 106)(16, 113)(17, 118)(18, 119)(19, 117)(20, 110)(21, 98)(22, 99)(23, 97)(24, 114)(25, 65)(26, 66)(27, 67)(28, 68)(29, 61)(30, 62)(31, 63)(32, 64)(33, 49)(34, 50)(35, 51)(36, 52)(37, 69)(38, 70)(39, 71)(40, 72)(41, 57)(42, 58)(43, 59)(44, 60)(45, 53)(46, 54)(47, 55)(48, 56)(73, 79)(74, 77)(75, 78)(76, 85)(80, 90)(81, 94)(82, 95)(83, 93)(84, 86)(87, 92)(88, 91)(89, 96)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1047 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^3, (u.4 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.3^3, (x.2 * x.4^-1)^2, (x.2 * x.1)^2, x.4^4, x.1 * x.3 * x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.4^2 * x.3^-1 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 6)(2, 7)(3, 5)(4, 22)(8, 9)(10, 16)(11, 24)(12, 23)(13, 18)(14, 19)(15, 17)(20, 21)(25, 52)(26, 60)(27, 68)(28, 67)(29, 72)(30, 56)(31, 64)(32, 63)(33, 59)(34, 57)(35, 58)(36, 65)(37, 55)(38, 53)(39, 54)(40, 61)(41, 50)(42, 51)(43, 49)(44, 66)(45, 70)(46, 71)(47, 69)(48, 62)(73, 134)(74, 135)(75, 133)(76, 126)(77, 139)(78, 137)(79, 138)(80, 121)(81, 136)(82, 144)(83, 128)(84, 127)(85, 130)(86, 131)(87, 129)(88, 122)(89, 143)(90, 141)(91, 142)(92, 125)(93, 132)(94, 140)(95, 124)(96, 123)(97, 114)(98, 115)(99, 113)(100, 106)(101, 111)(102, 109)(103, 110)(104, 117)(105, 116)(107, 108)(112, 118)(119, 120) MAP : A3.1048 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^3, u.6^3, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.6 * x.3^-1, x.2 * x.1, x.3^3, x.4^2 * x.7^-1, x.6^3, x.6 * x.2 * x.7^-1, x.3^-1 * x.4^-1 * x.1, x.4 * x.5^-1 * x.7 * x.5, x.3 * x.4 * x.1 * x.4^-1 * x.3^-1 * x.1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 13, 25, 37, 49, 61)(2, 14, 26, 38, 50, 62)(3, 15, 27, 39, 51, 63)(4, 16, 28, 40, 52, 64)(5, 17, 29, 41, 53, 65)(6, 18, 30, 42, 54, 66)(7, 19, 31, 43, 55, 67)(8, 20, 32, 44, 56, 68)(9, 21, 33, 45, 57, 69)(10, 22, 34, 46, 58, 70)(11, 23, 35, 47, 59, 71)(12, 24, 36, 48, 60, 72)(73, 85, 97, 109, 121, 133)(74, 86, 98, 110, 122, 134)(75, 87, 99, 111, 123, 135)(76, 88, 100, 112, 124, 136)(77, 89, 101, 113, 125, 137)(78, 90, 102, 114, 126, 138)(79, 91, 103, 115, 127, 139)(80, 92, 104, 116, 128, 140)(81, 93, 105, 117, 129, 141)(82, 94, 106, 118, 130, 142)(83, 95, 107, 119, 131, 143)(84, 96, 108, 120, 132, 144) L = (1, 15)(2, 13)(3, 14)(4, 21)(5, 20)(6, 16)(7, 24)(8, 23)(9, 18)(10, 19)(11, 17)(12, 22)(25, 55)(26, 53)(27, 54)(28, 49)(29, 60)(30, 56)(31, 52)(32, 51)(33, 58)(34, 59)(35, 57)(36, 50)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(61, 66)(62, 67)(63, 65)(64, 70)(68, 69)(71, 72)(73, 135)(74, 133)(75, 134)(76, 141)(77, 140)(78, 136)(79, 144)(80, 143)(81, 138)(82, 139)(83, 137)(84, 142)(85, 90)(86, 91)(87, 89)(88, 94)(92, 93)(95, 96)(97, 124)(98, 132)(99, 128)(100, 127)(101, 122)(102, 123)(103, 121)(104, 126)(105, 131)(106, 129)(107, 130)(108, 125) MAP : A3.1049 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^3, (u.4 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.3^3, x.4^3, (x.4 * x.2)^2, x.2 * x.3 * x.4^-1 * x.2 * x.3^-1 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 11)(2, 9)(3, 10)(4, 17)(5, 22)(6, 23)(7, 21)(8, 14)(12, 18)(13, 24)(15, 16)(19, 20)(25, 65)(26, 66)(27, 67)(28, 68)(29, 61)(30, 62)(31, 63)(32, 64)(33, 49)(34, 50)(35, 51)(36, 52)(37, 69)(38, 70)(39, 71)(40, 72)(41, 57)(42, 58)(43, 59)(44, 60)(45, 53)(46, 54)(47, 55)(48, 56)(73, 122)(74, 123)(75, 121)(76, 138)(77, 127)(78, 125)(79, 126)(80, 133)(81, 124)(82, 132)(83, 140)(84, 139)(85, 142)(86, 143)(87, 141)(88, 134)(89, 131)(90, 129)(91, 130)(92, 137)(93, 144)(94, 128)(95, 136)(96, 135)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.1050 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^3, (u.4 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.3^3, x.4^3, (x.3 * x.2)^2, (x.4 * x.2)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 12)(2, 20)(3, 4)(5, 16)(6, 24)(7, 8)(9, 19)(10, 17)(11, 18)(13, 23)(14, 21)(15, 22)(25, 58)(26, 59)(27, 57)(28, 50)(29, 71)(30, 69)(31, 70)(32, 53)(33, 60)(34, 68)(35, 52)(36, 51)(37, 62)(38, 63)(39, 61)(40, 54)(41, 67)(42, 65)(43, 66)(44, 49)(45, 64)(46, 72)(47, 56)(48, 55)(73, 122)(74, 123)(75, 121)(76, 138)(77, 127)(78, 125)(79, 126)(80, 133)(81, 124)(82, 132)(83, 140)(84, 139)(85, 142)(86, 143)(87, 141)(88, 134)(89, 131)(90, 129)(91, 130)(92, 137)(93, 144)(94, 128)(95, 136)(96, 135)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.1051 NOTES : type I, chiral, isomorphic to A3.1050. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, (u.3^-1 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.4^3, x.3^3, (x.4^-1 * x.2)^2, (x.3^-1 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 98)(2, 99)(3, 97)(4, 114)(5, 103)(6, 101)(7, 102)(8, 109)(9, 100)(10, 108)(11, 116)(12, 115)(13, 118)(14, 119)(15, 117)(16, 110)(17, 107)(18, 105)(19, 106)(20, 113)(21, 120)(22, 104)(23, 112)(24, 111)(25, 68)(26, 52)(27, 60)(28, 59)(29, 56)(30, 64)(31, 72)(32, 71)(33, 51)(34, 49)(35, 50)(36, 57)(37, 63)(38, 61)(39, 62)(40, 69)(41, 66)(42, 67)(43, 65)(44, 58)(45, 54)(46, 55)(47, 53)(48, 70)(73, 84)(74, 92)(75, 76)(77, 88)(78, 96)(79, 80)(81, 91)(82, 89)(83, 90)(85, 95)(86, 93)(87, 94)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1052 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, (u.3^-1 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.4^3, x.3^-1 * x.4^-1 * x.2 * x.1, (x.3^-1 * x.2)^2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 110)(2, 111)(3, 109)(4, 102)(5, 115)(6, 113)(7, 114)(8, 97)(9, 112)(10, 120)(11, 104)(12, 103)(13, 106)(14, 107)(15, 105)(16, 98)(17, 119)(18, 117)(19, 118)(20, 101)(21, 108)(22, 116)(23, 100)(24, 99)(25, 58)(26, 59)(27, 57)(28, 50)(29, 71)(30, 69)(31, 70)(32, 53)(33, 60)(34, 68)(35, 52)(36, 51)(37, 62)(38, 63)(39, 61)(40, 54)(41, 67)(42, 65)(43, 66)(44, 49)(45, 64)(46, 72)(47, 56)(48, 55)(73, 77)(74, 78)(75, 79)(76, 80)(81, 85)(82, 86)(83, 87)(84, 88)(89, 93)(90, 94)(91, 95)(92, 96)(121, 138)(122, 139)(123, 137)(124, 130)(125, 135)(126, 133)(127, 134)(128, 141)(129, 140)(131, 132)(136, 142)(143, 144) MAP : A3.1053 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^3, (u.4 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.3^3, x.4^3, (x.2 * x.4^-1)^2, (x.2 * x.1)^2, x.3 * x.4 * x.1 * x.4^-1 * x.3^-1 * x.1 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 18)(2, 19)(3, 17)(4, 10)(5, 15)(6, 13)(7, 14)(8, 21)(9, 20)(11, 12)(16, 22)(23, 24)(25, 52)(26, 60)(27, 68)(28, 67)(29, 72)(30, 56)(31, 64)(32, 63)(33, 59)(34, 57)(35, 58)(36, 65)(37, 55)(38, 53)(39, 54)(40, 61)(41, 50)(42, 51)(43, 49)(44, 66)(45, 70)(46, 71)(47, 69)(48, 62)(73, 122)(74, 123)(75, 121)(76, 138)(77, 127)(78, 125)(79, 126)(80, 133)(81, 124)(82, 132)(83, 140)(84, 139)(85, 142)(86, 143)(87, 141)(88, 134)(89, 131)(90, 129)(91, 130)(92, 137)(93, 144)(94, 128)(95, 136)(96, 135)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.1054 NOTES : type I, chiral, isomorphic to A3.1046. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^3, (u.4 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.3^3, (x.2 * x.4)^2, x.3 * x.4^-1 * x.3 * x.2, x.4^4, (x.2 * x.1)^3 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 7)(2, 5)(3, 6)(4, 13)(8, 18)(9, 22)(10, 23)(11, 21)(12, 14)(15, 20)(16, 19)(17, 24)(25, 57)(26, 58)(27, 59)(28, 60)(29, 69)(30, 70)(31, 71)(32, 72)(33, 65)(34, 66)(35, 67)(36, 68)(37, 53)(38, 54)(39, 55)(40, 56)(41, 49)(42, 50)(43, 51)(44, 52)(45, 61)(46, 62)(47, 63)(48, 64)(73, 144)(74, 128)(75, 136)(76, 135)(77, 124)(78, 132)(79, 140)(80, 139)(81, 127)(82, 125)(83, 126)(84, 133)(85, 131)(86, 129)(87, 130)(88, 137)(89, 142)(90, 143)(91, 141)(92, 134)(93, 122)(94, 123)(95, 121)(96, 138)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.1055 NOTES : type II, reflexible, isomorphic to A3.1048. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^3, u.6^3, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.6 * x.3^-1, x.2 * x.1, x.3^3, x.4^2 * x.7^-1, x.6^3, x.6 * x.2 * x.7^-1, x.3^-1 * x.4^-1 * x.1, x.4 * x.5^-1 * x.7 * x.5, x.3 * x.4 * x.1 * x.4^-1 * x.3^-1 * x.1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 13, 25, 37, 49, 61)(2, 14, 26, 38, 50, 62)(3, 15, 27, 39, 51, 63)(4, 16, 28, 40, 52, 64)(5, 17, 29, 41, 53, 65)(6, 18, 30, 42, 54, 66)(7, 19, 31, 43, 55, 67)(8, 20, 32, 44, 56, 68)(9, 21, 33, 45, 57, 69)(10, 22, 34, 46, 58, 70)(11, 23, 35, 47, 59, 71)(12, 24, 36, 48, 60, 72)(73, 85, 97, 109, 121, 133)(74, 86, 98, 110, 122, 134)(75, 87, 99, 111, 123, 135)(76, 88, 100, 112, 124, 136)(77, 89, 101, 113, 125, 137)(78, 90, 102, 114, 126, 138)(79, 91, 103, 115, 127, 139)(80, 92, 104, 116, 128, 140)(81, 93, 105, 117, 129, 141)(82, 94, 106, 118, 130, 142)(83, 95, 107, 119, 131, 143)(84, 96, 108, 120, 132, 144) L = (1, 14)(2, 15)(3, 13)(4, 18)(5, 23)(6, 21)(7, 22)(8, 17)(9, 16)(10, 24)(11, 20)(12, 19)(25, 53)(26, 54)(27, 55)(28, 56)(29, 57)(30, 58)(31, 59)(32, 60)(33, 49)(34, 50)(35, 51)(36, 52)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(61, 66)(62, 67)(63, 65)(64, 70)(68, 69)(71, 72)(73, 134)(74, 135)(75, 133)(76, 138)(77, 143)(78, 141)(79, 142)(80, 137)(81, 136)(82, 144)(83, 140)(84, 139)(85, 90)(86, 91)(87, 89)(88, 94)(92, 93)(95, 96)(97, 129)(98, 130)(99, 131)(100, 132)(101, 121)(102, 122)(103, 123)(104, 124)(105, 125)(106, 126)(107, 127)(108, 128) MAP : A3.1056 NOTES : type I, chiral, isomorphic to A3.1049. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, (u.3^-1 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.4^3, x.3^3, (x.3^-1 * x.2)^2, x.2 * x.4 * x.1 * x.2 * x.4, x.1 * x.4^-1 * x.2 * x.4^-1 * x.2, x.2 * x.1 * x.3^-1 * x.4 * x.2 * x.1 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 98)(2, 99)(3, 97)(4, 114)(5, 103)(6, 101)(7, 102)(8, 109)(9, 100)(10, 108)(11, 116)(12, 115)(13, 118)(14, 119)(15, 117)(16, 110)(17, 107)(18, 105)(19, 106)(20, 113)(21, 120)(22, 104)(23, 112)(24, 111)(25, 57)(26, 58)(27, 59)(28, 60)(29, 69)(30, 70)(31, 71)(32, 72)(33, 65)(34, 66)(35, 67)(36, 68)(37, 53)(38, 54)(39, 55)(40, 56)(41, 49)(42, 50)(43, 51)(44, 52)(45, 61)(46, 62)(47, 63)(48, 64)(73, 83)(74, 81)(75, 82)(76, 89)(77, 94)(78, 95)(79, 93)(80, 86)(84, 90)(85, 96)(87, 88)(91, 92)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1057 NOTES : type I, chiral, isomorphic to A3.1047. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, (u.3^-1 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.4^3, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, x.3^4, x.2 * x.4 * x.1 * x.4^-1 * x.3 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 110)(2, 111)(3, 109)(4, 102)(5, 115)(6, 113)(7, 114)(8, 97)(9, 112)(10, 120)(11, 104)(12, 103)(13, 106)(14, 107)(15, 105)(16, 98)(17, 119)(18, 117)(19, 118)(20, 101)(21, 108)(22, 116)(23, 100)(24, 99)(25, 67)(26, 65)(27, 66)(28, 49)(29, 62)(30, 63)(31, 61)(32, 54)(33, 58)(34, 59)(35, 57)(36, 50)(37, 64)(38, 72)(39, 56)(40, 55)(41, 60)(42, 68)(43, 52)(44, 51)(45, 71)(46, 69)(47, 70)(48, 53)(73, 78)(74, 79)(75, 77)(76, 94)(80, 81)(82, 88)(83, 96)(84, 95)(85, 90)(86, 91)(87, 89)(92, 93)(121, 138)(122, 139)(123, 137)(124, 130)(125, 135)(126, 133)(127, 134)(128, 141)(129, 140)(131, 132)(136, 142)(143, 144) MAP : A3.1058 NOTES : type I, chiral, isomorphic to A3.1053. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, (u.3^-1 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.4^3, x.3^3, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, x.1 * x.3^-1 * x.4^-1 * x.3 * x.4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 98)(2, 99)(3, 97)(4, 114)(5, 103)(6, 101)(7, 102)(8, 109)(9, 100)(10, 108)(11, 116)(12, 115)(13, 118)(14, 119)(15, 117)(16, 110)(17, 107)(18, 105)(19, 106)(20, 113)(21, 120)(22, 104)(23, 112)(24, 111)(25, 67)(26, 65)(27, 66)(28, 49)(29, 62)(30, 63)(31, 61)(32, 54)(33, 58)(34, 59)(35, 57)(36, 50)(37, 64)(38, 72)(39, 56)(40, 55)(41, 60)(42, 68)(43, 52)(44, 51)(45, 71)(46, 69)(47, 70)(48, 53)(73, 90)(74, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1059 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, (u.3^-1 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.4^3, (x.3^-1 * x.2)^2, x.3^4, (x.4 * x.2)^2, x.1 * x.3^-1 * x.4 * x.1 * x.2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 120)(2, 104)(3, 112)(4, 111)(5, 100)(6, 108)(7, 116)(8, 115)(9, 103)(10, 101)(11, 102)(12, 109)(13, 107)(14, 105)(15, 106)(16, 113)(17, 118)(18, 119)(19, 117)(20, 110)(21, 98)(22, 99)(23, 97)(24, 114)(25, 68)(26, 52)(27, 60)(28, 59)(29, 56)(30, 64)(31, 72)(32, 71)(33, 51)(34, 49)(35, 50)(36, 57)(37, 63)(38, 61)(39, 62)(40, 69)(41, 66)(42, 67)(43, 65)(44, 58)(45, 54)(46, 55)(47, 53)(48, 70)(73, 77)(74, 78)(75, 79)(76, 80)(81, 85)(82, 86)(83, 87)(84, 88)(89, 93)(90, 94)(91, 95)(92, 96)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1060 NOTES : type I, chiral, isomorphic to A3.1052. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^3, (u.4 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.3^3, x.4^-1 * x.3 * x.2 * x.1, (x.4 * x.2)^2, x.4^4 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 68)(26, 52)(27, 60)(28, 59)(29, 56)(30, 64)(31, 72)(32, 71)(33, 51)(34, 49)(35, 50)(36, 57)(37, 63)(38, 61)(39, 62)(40, 69)(41, 66)(42, 67)(43, 65)(44, 58)(45, 54)(46, 55)(47, 53)(48, 70)(73, 134)(74, 135)(75, 133)(76, 126)(77, 139)(78, 137)(79, 138)(80, 121)(81, 136)(82, 144)(83, 128)(84, 127)(85, 130)(86, 131)(87, 129)(88, 122)(89, 143)(90, 141)(91, 142)(92, 125)(93, 132)(94, 140)(95, 124)(96, 123)(97, 114)(98, 115)(99, 113)(100, 106)(101, 111)(102, 109)(103, 110)(104, 117)(105, 116)(107, 108)(112, 118)(119, 120) MAP : A3.1061 NOTES : type I, chiral, isomorphic to A3.1059. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^3, (u.4 * u.2)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.3^3, (x.3 * x.2)^2, (x.4 * x.2)^2, x.4^4, x.1 * x.2 * x.1 * x.4^-1 * x.3^-1 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 58)(26, 59)(27, 57)(28, 50)(29, 71)(30, 69)(31, 70)(32, 53)(33, 60)(34, 68)(35, 52)(36, 51)(37, 62)(38, 63)(39, 61)(40, 54)(41, 67)(42, 65)(43, 66)(44, 49)(45, 64)(46, 72)(47, 56)(48, 55)(73, 144)(74, 128)(75, 136)(76, 135)(77, 124)(78, 132)(79, 140)(80, 139)(81, 127)(82, 125)(83, 126)(84, 133)(85, 131)(86, 129)(87, 130)(88, 137)(89, 142)(90, 143)(91, 141)(92, 134)(93, 122)(94, 123)(95, 121)(96, 138)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117) MAP : A3.1062 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.4^3, u.3^-1 * u.1 * u.2, (u.3 * u.4^-1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.4^3, x.3^-1 * x.1 * x.2, (x.4^-1 * x.2)^2, (x.3 * x.4^-1)^2, x.3^4, x.1 * x.4 * x.3 * x.4 * x.3 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 86)(2, 87)(3, 85)(4, 78)(5, 91)(6, 89)(7, 90)(8, 73)(9, 88)(10, 96)(11, 80)(12, 79)(13, 82)(14, 83)(15, 81)(16, 74)(17, 95)(18, 93)(19, 94)(20, 77)(21, 84)(22, 92)(23, 76)(24, 75)(25, 50)(26, 51)(27, 49)(28, 66)(29, 55)(30, 53)(31, 54)(32, 61)(33, 52)(34, 60)(35, 68)(36, 67)(37, 70)(38, 71)(39, 69)(40, 62)(41, 59)(42, 57)(43, 58)(44, 65)(45, 72)(46, 56)(47, 64)(48, 63)(97, 114)(98, 115)(99, 113)(100, 106)(101, 111)(102, 109)(103, 110)(104, 117)(105, 116)(107, 108)(112, 118)(119, 120)(121, 127)(122, 125)(123, 126)(124, 133)(128, 138)(129, 142)(130, 143)(131, 141)(132, 134)(135, 140)(136, 139)(137, 144) MAP : A3.1063 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.4^3, u.3^-1 * u.1 * u.2, (u.3 * u.4^-1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.4^3, x.3^-1 * x.1 * x.2, x.4 * x.3 * x.4 * x.2, (x.3 * x.4^-1)^2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 86)(2, 87)(3, 85)(4, 78)(5, 91)(6, 89)(7, 90)(8, 73)(9, 88)(10, 96)(11, 80)(12, 79)(13, 82)(14, 83)(15, 81)(16, 74)(17, 95)(18, 93)(19, 94)(20, 77)(21, 84)(22, 92)(23, 76)(24, 75)(25, 50)(26, 51)(27, 49)(28, 66)(29, 55)(30, 53)(31, 54)(32, 61)(33, 52)(34, 60)(35, 68)(36, 67)(37, 70)(38, 71)(39, 69)(40, 62)(41, 59)(42, 57)(43, 58)(44, 65)(45, 72)(46, 56)(47, 64)(48, 63)(97, 108)(98, 116)(99, 100)(101, 112)(102, 120)(103, 104)(105, 115)(106, 113)(107, 114)(109, 119)(110, 117)(111, 118)(121, 141)(122, 142)(123, 143)(124, 144)(125, 129)(126, 130)(127, 131)(128, 132)(133, 137)(134, 138)(135, 139)(136, 140) MAP : A3.1064 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 3, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.2^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.3^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.2^3, x.1^-1 * x.2^-1 * x.3^-1, (x.1^-1 * x.2)^2, (x.3 * x.2^-1)^2, x.1^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 26)(2, 39)(3, 32)(4, 25)(5, 31)(6, 36)(7, 42)(8, 34)(9, 44)(10, 41)(11, 33)(12, 47)(13, 30)(14, 35)(15, 28)(16, 29)(17, 27)(18, 40)(19, 46)(20, 38)(21, 48)(22, 45)(23, 37)(24, 43)(49, 86)(50, 75)(51, 92)(52, 85)(53, 91)(54, 96)(55, 78)(56, 94)(57, 80)(58, 77)(59, 93)(60, 83)(61, 90)(62, 95)(63, 88)(64, 89)(65, 87)(66, 76)(67, 82)(68, 74)(69, 84)(70, 81)(71, 73)(72, 79)(97, 132)(98, 129)(99, 121)(100, 127)(101, 128)(102, 125)(103, 141)(104, 131)(105, 139)(106, 144)(107, 126)(108, 142)(109, 135)(110, 124)(111, 130)(112, 122)(113, 138)(114, 143)(115, 136)(116, 137)(117, 134)(118, 123)(119, 140)(120, 133) MAP : A3.1065 NOTES : type I, reflexible, isomorphic to A3.1064. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^3, u.1^-1 * u.2^-1 * u.3^-1, u.2^4, u.3^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.1^3, x.1^-1 * x.2^-1 * x.3^-1, (x.2 * x.1^-1)^2, (x.3 * x.1^-1)^2, x.2^4, x.3^4, x.1 * x.2 * x.3^-1 * x.2^-1 * x.3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 38)(2, 27)(3, 44)(4, 37)(5, 43)(6, 48)(7, 30)(8, 46)(9, 32)(10, 29)(11, 45)(12, 35)(13, 42)(14, 47)(15, 40)(16, 41)(17, 39)(18, 28)(19, 34)(20, 26)(21, 36)(22, 33)(23, 25)(24, 31)(49, 74)(50, 87)(51, 80)(52, 73)(53, 79)(54, 84)(55, 90)(56, 82)(57, 92)(58, 89)(59, 81)(60, 95)(61, 78)(62, 83)(63, 76)(64, 77)(65, 75)(66, 88)(67, 94)(68, 86)(69, 96)(70, 93)(71, 85)(72, 91)(97, 138)(98, 143)(99, 136)(100, 137)(101, 135)(102, 124)(103, 130)(104, 122)(105, 132)(106, 129)(107, 121)(108, 127)(109, 134)(110, 123)(111, 140)(112, 133)(113, 139)(114, 144)(115, 126)(116, 142)(117, 128)(118, 125)(119, 141)(120, 131) MAP : A3.1066 NOTES : type I, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.4^3, u.3^-1 * u.1 * u.2, (u.3 * u.4^-1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.2 * x.1 * x.3, x.4^3, x.4 * x.1 * x.4^-1 * x.2, (x.3 * x.4^-1)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 74)(2, 75)(3, 73)(4, 90)(5, 79)(6, 77)(7, 78)(8, 85)(9, 76)(10, 84)(11, 92)(12, 91)(13, 94)(14, 95)(15, 93)(16, 86)(17, 83)(18, 81)(19, 82)(20, 89)(21, 96)(22, 80)(23, 88)(24, 87)(25, 68)(26, 52)(27, 60)(28, 59)(29, 56)(30, 64)(31, 72)(32, 71)(33, 51)(34, 49)(35, 50)(36, 57)(37, 63)(38, 61)(39, 62)(40, 69)(41, 66)(42, 67)(43, 65)(44, 58)(45, 54)(46, 55)(47, 53)(48, 70)(97, 103)(98, 101)(99, 102)(100, 109)(104, 114)(105, 118)(106, 119)(107, 117)(108, 110)(111, 116)(112, 115)(113, 120)(121, 125)(122, 126)(123, 127)(124, 128)(129, 133)(130, 134)(131, 135)(132, 136)(137, 141)(138, 142)(139, 143)(140, 144) MAP : A3.1067 NOTES : type I, reflexible, isomorphic to A3.1064. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 9)(2, 3)(4, 8)(5, 7)(6, 10)(11, 12) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1, u.2^3, u.6^3, u.1 * u.2^-1 * u.3^-1, u.4 * u.5^-1 * u.6^-1, (u.5 * u.1^-1)^2, (u.3 * u.4^-1)^2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.3 * x.2, x.3 * x.6 * x.4, x.4^3, x.2^3, x.2 * x.5 * x.6, x.6^3, x.4 * x.5^-1 * x.6^-1, (x.5 * x.1^-1)^2, x.4 * x.6^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 144 R = (1, 13, 25, 37, 49, 61)(2, 14, 26, 38, 50, 62)(3, 15, 27, 39, 51, 63)(4, 16, 28, 40, 52, 64)(5, 17, 29, 41, 53, 65)(6, 18, 30, 42, 54, 66)(7, 19, 31, 43, 55, 67)(8, 20, 32, 44, 56, 68)(9, 21, 33, 45, 57, 69)(10, 22, 34, 46, 58, 70)(11, 23, 35, 47, 59, 71)(12, 24, 36, 48, 60, 72)(73, 85, 97, 109, 121, 133)(74, 86, 98, 110, 122, 134)(75, 87, 99, 111, 123, 135)(76, 88, 100, 112, 124, 136)(77, 89, 101, 113, 125, 137)(78, 90, 102, 114, 126, 138)(79, 91, 103, 115, 127, 139)(80, 92, 104, 116, 128, 140)(81, 93, 105, 117, 129, 141)(82, 94, 106, 118, 130, 142)(83, 95, 107, 119, 131, 143)(84, 96, 108, 120, 132, 144) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 26)(14, 27)(15, 25)(16, 30)(17, 35)(18, 33)(19, 34)(20, 29)(21, 28)(22, 36)(23, 32)(24, 31)(37, 87)(38, 85)(39, 86)(40, 93)(41, 92)(42, 88)(43, 96)(44, 95)(45, 90)(46, 91)(47, 89)(48, 94)(49, 82)(50, 83)(51, 81)(52, 74)(53, 79)(54, 77)(55, 78)(56, 73)(57, 84)(58, 80)(59, 76)(60, 75)(61, 114)(62, 115)(63, 113)(64, 118)(65, 111)(66, 109)(67, 110)(68, 117)(69, 116)(70, 112)(71, 120)(72, 119)(121, 137)(122, 138)(123, 139)(124, 140)(125, 141)(126, 142)(127, 143)(128, 144)(129, 133)(130, 134)(131, 135)(132, 136) MAP : A3.1068 NOTES : type I, chiral, isomorphic to A3.1063. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.4^3, u.3^-1 * u.1 * u.2, (u.3 * u.4^-1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3 * x.2, x.4^3, x.1 * x.4 * x.3 * x.4, (x.3 * x.4^-1)^2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 86)(2, 87)(3, 85)(4, 78)(5, 91)(6, 89)(7, 90)(8, 73)(9, 88)(10, 96)(11, 80)(12, 79)(13, 82)(14, 83)(15, 81)(16, 74)(17, 95)(18, 93)(19, 94)(20, 77)(21, 84)(22, 92)(23, 76)(24, 75)(25, 50)(26, 51)(27, 49)(28, 66)(29, 55)(30, 53)(31, 54)(32, 61)(33, 52)(34, 60)(35, 68)(36, 67)(37, 70)(38, 71)(39, 69)(40, 62)(41, 59)(42, 57)(43, 58)(44, 65)(45, 72)(46, 56)(47, 64)(48, 63)(97, 117)(98, 118)(99, 119)(100, 120)(101, 105)(102, 106)(103, 107)(104, 108)(109, 113)(110, 114)(111, 115)(112, 116)(121, 138)(122, 139)(123, 137)(124, 130)(125, 135)(126, 133)(127, 134)(128, 141)(129, 140)(131, 132)(136, 142)(143, 144) MAP : A3.1069 NOTES : type I, reflexible, isomorphic to A3.1066. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 6)(4, 9)(5, 10)(7, 12)(8, 11) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.3 * u.4^-1 * u.6, (u.1^-1 * u.2^-1)^2, (u.5 * u.6^-1)^2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.4 * x.2, x.1^3, x.4 * x.1 * x.5, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.6, x.5^3, (x.1^-1 * x.2^-1)^2, (x.5 * x.1^-1)^2, (x.5 * x.6^-1)^2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 144 R = (1, 13, 25, 37, 49, 61)(2, 14, 26, 38, 50, 62)(3, 15, 27, 39, 51, 63)(4, 16, 28, 40, 52, 64)(5, 17, 29, 41, 53, 65)(6, 18, 30, 42, 54, 66)(7, 19, 31, 43, 55, 67)(8, 20, 32, 44, 56, 68)(9, 21, 33, 45, 57, 69)(10, 22, 34, 46, 58, 70)(11, 23, 35, 47, 59, 71)(12, 24, 36, 48, 60, 72)(73, 85, 97, 109, 121, 133)(74, 86, 98, 110, 122, 134)(75, 87, 99, 111, 123, 135)(76, 88, 100, 112, 124, 136)(77, 89, 101, 113, 125, 137)(78, 90, 102, 114, 126, 138)(79, 91, 103, 115, 127, 139)(80, 92, 104, 116, 128, 140)(81, 93, 105, 117, 129, 141)(82, 94, 106, 118, 130, 142)(83, 95, 107, 119, 131, 143)(84, 96, 108, 120, 132, 144) L = (1, 14)(2, 15)(3, 13)(4, 18)(5, 23)(6, 21)(7, 22)(8, 17)(9, 16)(10, 24)(11, 20)(12, 19)(25, 70)(26, 71)(27, 69)(28, 62)(29, 67)(30, 65)(31, 66)(32, 61)(33, 72)(34, 68)(35, 64)(36, 63)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 116)(50, 112)(51, 120)(52, 119)(53, 114)(54, 115)(55, 113)(56, 118)(57, 111)(58, 109)(59, 110)(60, 117)(73, 139)(74, 137)(75, 138)(76, 133)(77, 144)(78, 140)(79, 136)(80, 135)(81, 142)(82, 143)(83, 141)(84, 134)(85, 128)(86, 124)(87, 132)(88, 131)(89, 126)(90, 127)(91, 125)(92, 130)(93, 123)(94, 121)(95, 122)(96, 129) MAP : A3.1070 NOTES : type I, chiral, isomorphic to A3.1062. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.4^3, u.3^-1 * u.1 * u.2, (u.3 * u.4^-1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.2 * x.1 * x.3, x.4^3, (x.3 * x.4^-1)^2, x.3^4, (x.4 * x.1)^2, x.2 * x.3 * x.4 * x.3 * x.4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 86)(2, 87)(3, 85)(4, 78)(5, 91)(6, 89)(7, 90)(8, 73)(9, 88)(10, 96)(11, 80)(12, 79)(13, 82)(14, 83)(15, 81)(16, 74)(17, 95)(18, 93)(19, 94)(20, 77)(21, 84)(22, 92)(23, 76)(24, 75)(25, 50)(26, 51)(27, 49)(28, 66)(29, 55)(30, 53)(31, 54)(32, 61)(33, 52)(34, 60)(35, 68)(36, 67)(37, 70)(38, 71)(39, 69)(40, 62)(41, 59)(42, 57)(43, 58)(44, 65)(45, 72)(46, 56)(47, 64)(48, 63)(97, 103)(98, 101)(99, 102)(100, 109)(104, 114)(105, 118)(106, 119)(107, 117)(108, 110)(111, 116)(112, 115)(113, 120)(121, 132)(122, 140)(123, 124)(125, 136)(126, 144)(127, 128)(129, 139)(130, 137)(131, 138)(133, 143)(134, 141)(135, 142) MAP : A3.1071 NOTES : type I, reflexible, isomorphic to A3.1064. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 3}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 3, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.3^3, u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1^-1 * x.3^-1, x.1^4, x.2^4, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 26)(2, 39)(3, 32)(4, 25)(5, 31)(6, 36)(7, 42)(8, 34)(9, 44)(10, 41)(11, 33)(12, 47)(13, 30)(14, 35)(15, 28)(16, 29)(17, 27)(18, 40)(19, 46)(20, 38)(21, 48)(22, 45)(23, 37)(24, 43)(49, 83)(50, 80)(51, 86)(52, 78)(53, 94)(54, 91)(55, 84)(56, 93)(57, 82)(58, 79)(59, 96)(60, 81)(61, 88)(62, 85)(63, 77)(64, 75)(65, 76)(66, 73)(67, 89)(68, 87)(69, 95)(70, 92)(71, 74)(72, 90)(97, 127)(98, 132)(99, 138)(100, 130)(101, 122)(102, 135)(103, 128)(104, 121)(105, 126)(106, 131)(107, 124)(108, 125)(109, 140)(110, 137)(111, 129)(112, 143)(113, 144)(114, 141)(115, 133)(116, 139)(117, 123)(118, 136)(119, 142)(120, 134) MAP : A3.1072 NOTES : type I, reflexible, isomorphic to A3.1066. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 6)(4, 9)(5, 10)(7, 12)(8, 11) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.3, u.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.3 * u.4^-1 * u.6, (u.1^-1 * u.2^-1)^2, (u.5 * u.6^-1)^2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.4 * x.2, x.1^3, x.4 * x.1 * x.5, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.6, x.5^3, (x.1^-1 * x.2^-1)^2, (x.5 * x.1^-1)^2, (x.5 * x.6^-1)^2 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 144 R = (1, 13, 25, 37, 49, 61)(2, 14, 26, 38, 50, 62)(3, 15, 27, 39, 51, 63)(4, 16, 28, 40, 52, 64)(5, 17, 29, 41, 53, 65)(6, 18, 30, 42, 54, 66)(7, 19, 31, 43, 55, 67)(8, 20, 32, 44, 56, 68)(9, 21, 33, 45, 57, 69)(10, 22, 34, 46, 58, 70)(11, 23, 35, 47, 59, 71)(12, 24, 36, 48, 60, 72)(73, 85, 97, 109, 121, 133)(74, 86, 98, 110, 122, 134)(75, 87, 99, 111, 123, 135)(76, 88, 100, 112, 124, 136)(77, 89, 101, 113, 125, 137)(78, 90, 102, 114, 126, 138)(79, 91, 103, 115, 127, 139)(80, 92, 104, 116, 128, 140)(81, 93, 105, 117, 129, 141)(82, 94, 106, 118, 130, 142)(83, 95, 107, 119, 131, 143)(84, 96, 108, 120, 132, 144) L = (1, 15)(2, 13)(3, 14)(4, 21)(5, 20)(6, 16)(7, 24)(8, 23)(9, 18)(10, 19)(11, 17)(12, 22)(25, 68)(26, 64)(27, 72)(28, 71)(29, 66)(30, 67)(31, 65)(32, 70)(33, 63)(34, 61)(35, 62)(36, 69)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 118)(50, 119)(51, 117)(52, 110)(53, 115)(54, 113)(55, 114)(56, 109)(57, 120)(58, 116)(59, 112)(60, 111)(73, 137)(74, 138)(75, 139)(76, 140)(77, 141)(78, 142)(79, 143)(80, 144)(81, 133)(82, 134)(83, 135)(84, 136)(85, 130)(86, 131)(87, 129)(88, 122)(89, 127)(90, 125)(91, 126)(92, 121)(93, 132)(94, 128)(95, 124)(96, 123) MAP : A3.1073 NOTES : type I, reflexible, isomorphic to A3.1064. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 9)(2, 3)(4, 8)(5, 7)(6, 10)(11, 12) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1, u.2^3, u.6^3, u.1 * u.2^-1 * u.3^-1, u.4 * u.5^-1 * u.6^-1, (u.5 * u.1^-1)^2, (u.3 * u.4^-1)^2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.3 * x.2, x.3 * x.6 * x.4, x.4^3, x.2^3, x.2 * x.5 * x.6, x.6^3, x.4 * x.5^-1 * x.6^-1, (x.5 * x.1^-1)^2, x.4 * x.6^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^2 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 144 R = (1, 13, 25, 37, 49, 61)(2, 14, 26, 38, 50, 62)(3, 15, 27, 39, 51, 63)(4, 16, 28, 40, 52, 64)(5, 17, 29, 41, 53, 65)(6, 18, 30, 42, 54, 66)(7, 19, 31, 43, 55, 67)(8, 20, 32, 44, 56, 68)(9, 21, 33, 45, 57, 69)(10, 22, 34, 46, 58, 70)(11, 23, 35, 47, 59, 71)(12, 24, 36, 48, 60, 72)(73, 85, 97, 109, 121, 133)(74, 86, 98, 110, 122, 134)(75, 87, 99, 111, 123, 135)(76, 88, 100, 112, 124, 136)(77, 89, 101, 113, 125, 137)(78, 90, 102, 114, 126, 138)(79, 91, 103, 115, 127, 139)(80, 92, 104, 116, 128, 140)(81, 93, 105, 117, 129, 141)(82, 94, 106, 118, 130, 142)(83, 95, 107, 119, 131, 143)(84, 96, 108, 120, 132, 144) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 27)(14, 25)(15, 26)(16, 33)(17, 32)(18, 28)(19, 36)(20, 35)(21, 30)(22, 31)(23, 29)(24, 34)(37, 86)(38, 87)(39, 85)(40, 90)(41, 95)(42, 93)(43, 94)(44, 89)(45, 88)(46, 96)(47, 92)(48, 91)(49, 80)(50, 76)(51, 84)(52, 83)(53, 78)(54, 79)(55, 77)(56, 82)(57, 75)(58, 73)(59, 74)(60, 81)(61, 114)(62, 115)(63, 113)(64, 118)(65, 111)(66, 109)(67, 110)(68, 117)(69, 116)(70, 112)(71, 120)(72, 119)(121, 139)(122, 137)(123, 138)(124, 133)(125, 144)(126, 140)(127, 136)(128, 135)(129, 142)(130, 143)(131, 141)(132, 134) MAP : A3.1074 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.4^3, u.3^-1 * u.1 * u.2, (u.3 * u.4^-1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.2 * x.1 * x.3, x.4^3, (x.3 * x.4^-1)^2, (x.4 * x.1)^2, x.2 * x.4^-1 * x.2 * x.3 * x.4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 74)(2, 75)(3, 73)(4, 90)(5, 79)(6, 77)(7, 78)(8, 85)(9, 76)(10, 84)(11, 92)(12, 91)(13, 94)(14, 95)(15, 93)(16, 86)(17, 83)(18, 81)(19, 82)(20, 89)(21, 96)(22, 80)(23, 88)(24, 87)(25, 68)(26, 52)(27, 60)(28, 59)(29, 56)(30, 64)(31, 72)(32, 71)(33, 51)(34, 49)(35, 50)(36, 57)(37, 63)(38, 61)(39, 62)(40, 69)(41, 66)(42, 67)(43, 65)(44, 58)(45, 54)(46, 55)(47, 53)(48, 70)(97, 102)(98, 103)(99, 101)(100, 118)(104, 105)(106, 112)(107, 120)(108, 119)(109, 114)(110, 115)(111, 113)(116, 117)(121, 127)(122, 125)(123, 126)(124, 133)(128, 138)(129, 142)(130, 143)(131, 141)(132, 134)(135, 140)(136, 139)(137, 144) MAP : A3.1075 NOTES : type I, chiral, isomorphic to A3.1074. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 4)(2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.4^3, u.3^-1 * u.1 * u.2, (u.3 * u.4^-1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.4^3, x.3^-1 * x.1 * x.2, (x.3 * x.4^-1)^2, (x.4 * x.2)^2, x.4 * x.1 * x.3^-1 * x.4^-1 * x.1 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.3^-1, x.1, x.2) LOCAL TYPE : (3, 3, 3, 4, 3, 4) #DARTS : 144 R = (1, 25, 49, 73, 97, 121)(2, 26, 50, 74, 98, 122)(3, 27, 51, 75, 99, 123)(4, 28, 52, 76, 100, 124)(5, 29, 53, 77, 101, 125)(6, 30, 54, 78, 102, 126)(7, 31, 55, 79, 103, 127)(8, 32, 56, 80, 104, 128)(9, 33, 57, 81, 105, 129)(10, 34, 58, 82, 106, 130)(11, 35, 59, 83, 107, 131)(12, 36, 60, 84, 108, 132)(13, 37, 61, 85, 109, 133)(14, 38, 62, 86, 110, 134)(15, 39, 63, 87, 111, 135)(16, 40, 64, 88, 112, 136)(17, 41, 65, 89, 113, 137)(18, 42, 66, 90, 114, 138)(19, 43, 67, 91, 115, 139)(20, 44, 68, 92, 116, 140)(21, 45, 69, 93, 117, 141)(22, 46, 70, 94, 118, 142)(23, 47, 71, 95, 119, 143)(24, 48, 72, 96, 120, 144) L = (1, 74)(2, 75)(3, 73)(4, 90)(5, 79)(6, 77)(7, 78)(8, 85)(9, 76)(10, 84)(11, 92)(12, 91)(13, 94)(14, 95)(15, 93)(16, 86)(17, 83)(18, 81)(19, 82)(20, 89)(21, 96)(22, 80)(23, 88)(24, 87)(25, 68)(26, 52)(27, 60)(28, 59)(29, 56)(30, 64)(31, 72)(32, 71)(33, 51)(34, 49)(35, 50)(36, 57)(37, 63)(38, 61)(39, 62)(40, 69)(41, 66)(42, 67)(43, 65)(44, 58)(45, 54)(46, 55)(47, 53)(48, 70)(97, 101)(98, 102)(99, 103)(100, 104)(105, 109)(106, 110)(107, 111)(108, 112)(113, 117)(114, 118)(115, 119)(116, 120)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1076 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 4)(2, 7)(3, 8)(5, 14)(6, 13)(9, 12)(10, 15)(11, 16)(17, 48)(18, 36)(19, 44)(20, 43)(21, 35)(22, 39)(23, 33)(24, 41)(25, 47)(26, 37)(27, 45)(28, 42)(29, 34)(30, 40)(31, 46)(32, 38)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84)(65, 72)(66, 76)(67, 68)(69, 75)(70, 79)(71, 73)(74, 77)(78, 80) MAP : A3.1077 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, (x.2 * x.4^-1)^2, x.3^4, (x.4 * x.3^-1)^2, x.3 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 37)(18, 33)(19, 44)(20, 40)(21, 38)(22, 34)(23, 35)(24, 47)(25, 45)(26, 41)(27, 36)(28, 48)(29, 46)(30, 42)(31, 43)(32, 39)(49, 90)(50, 94)(51, 95)(52, 83)(53, 89)(54, 93)(55, 88)(56, 92)(57, 82)(58, 86)(59, 87)(60, 91)(61, 81)(62, 85)(63, 96)(64, 84)(65, 67)(66, 71)(68, 74)(69, 76)(70, 80)(72, 73)(75, 78)(77, 79) MAP : A3.1078 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 13)(2, 16)(3, 15)(4, 6)(5, 9)(7, 11)(8, 10)(12, 14)(17, 34)(18, 38)(19, 46)(20, 39)(21, 47)(22, 43)(23, 45)(24, 37)(25, 35)(26, 41)(27, 33)(28, 40)(29, 48)(30, 42)(31, 44)(32, 36)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81)(65, 69)(66, 72)(67, 71)(68, 78)(70, 76)(73, 77)(74, 80)(75, 79) MAP : A3.1079 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, (x.2 * x.4^-1)^2, x.3^4, (x.4 * x.3^-1)^2, x.3 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 37)(18, 33)(19, 44)(20, 40)(21, 38)(22, 34)(23, 35)(24, 47)(25, 45)(26, 41)(27, 36)(28, 48)(29, 46)(30, 42)(31, 43)(32, 39)(49, 90)(50, 94)(51, 95)(52, 83)(53, 89)(54, 93)(55, 88)(56, 92)(57, 82)(58, 86)(59, 87)(60, 91)(61, 81)(62, 85)(63, 96)(64, 84)(65, 68)(66, 75)(67, 77)(69, 72)(70, 79)(71, 73)(74, 80)(76, 78) MAP : A3.1080 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 4)(2, 7)(3, 8)(5, 14)(6, 13)(9, 12)(10, 15)(11, 16)(17, 43)(18, 33)(19, 41)(20, 48)(21, 40)(22, 34)(23, 36)(24, 44)(25, 42)(26, 46)(27, 38)(28, 47)(29, 39)(30, 35)(31, 37)(32, 45)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81)(65, 69)(66, 72)(67, 71)(68, 78)(70, 76)(73, 77)(74, 80)(75, 79) MAP : A3.1081 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 13)(2, 16)(3, 15)(4, 6)(5, 9)(7, 11)(8, 10)(12, 14)(17, 39)(18, 45)(19, 37)(20, 34)(21, 42)(22, 48)(23, 38)(24, 46)(25, 40)(26, 44)(27, 36)(28, 35)(29, 43)(30, 47)(31, 41)(32, 33)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84)(65, 72)(66, 76)(67, 68)(69, 75)(70, 79)(71, 73)(74, 77)(78, 80) MAP : A3.1082 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, (x.2 * x.4^-1)^2, x.3^4, (x.4 * x.3^-1)^2, x.3 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 15)(2, 8)(3, 10)(4, 6)(5, 11)(7, 14)(9, 12)(13, 16)(17, 37)(18, 33)(19, 44)(20, 40)(21, 38)(22, 34)(23, 35)(24, 47)(25, 45)(26, 41)(27, 36)(28, 48)(29, 46)(30, 42)(31, 43)(32, 39)(49, 88)(50, 84)(51, 94)(52, 85)(53, 95)(54, 91)(55, 93)(56, 86)(57, 83)(58, 87)(59, 81)(60, 90)(61, 92)(62, 96)(63, 82)(64, 89)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80) MAP : A3.1083 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, (x.2 * x.4^-1)^2, x.3^4, (x.4 * x.3^-1)^2, x.3 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 14)(2, 13)(3, 8)(4, 7)(5, 10)(6, 9)(11, 16)(12, 15)(17, 34)(18, 38)(19, 39)(20, 43)(21, 33)(22, 37)(23, 48)(24, 36)(25, 42)(26, 46)(27, 47)(28, 35)(29, 41)(30, 45)(31, 40)(32, 44)(49, 90)(50, 94)(51, 95)(52, 83)(53, 89)(54, 93)(55, 88)(56, 92)(57, 82)(58, 86)(59, 87)(60, 91)(61, 81)(62, 85)(63, 96)(64, 84)(65, 68)(66, 75)(67, 77)(69, 72)(70, 79)(71, 73)(74, 80)(76, 78) MAP : A3.1084 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 13)(2, 16)(3, 15)(4, 6)(5, 9)(7, 11)(8, 10)(12, 14)(17, 39)(18, 45)(19, 37)(20, 34)(21, 42)(22, 48)(23, 38)(24, 46)(25, 40)(26, 44)(27, 36)(28, 35)(29, 43)(30, 47)(31, 41)(32, 33)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84)(65, 67)(66, 73)(68, 72)(69, 80)(70, 74)(71, 76)(75, 78)(77, 79) MAP : A3.1085 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, (x.2 * x.4^-1)^2, x.3^4, (x.4 * x.3^-1)^2, x.3 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 16)(2, 12)(3, 6)(4, 13)(5, 7)(8, 14)(9, 11)(10, 15)(17, 34)(18, 38)(19, 39)(20, 43)(21, 33)(22, 37)(23, 48)(24, 36)(25, 42)(26, 46)(27, 47)(28, 35)(29, 41)(30, 45)(31, 40)(32, 44)(49, 87)(50, 96)(51, 82)(52, 94)(53, 83)(54, 92)(55, 86)(56, 90)(57, 84)(58, 91)(59, 93)(60, 81)(61, 88)(62, 95)(63, 89)(64, 85)(65, 68)(66, 75)(67, 77)(69, 72)(70, 79)(71, 73)(74, 80)(76, 78) MAP : A3.1086 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, (x.2 * x.4^-1)^2, x.3^4, (x.4 * x.3^-1)^2, x.3 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 15)(2, 8)(3, 10)(4, 6)(5, 11)(7, 14)(9, 12)(13, 16)(17, 37)(18, 33)(19, 44)(20, 40)(21, 38)(22, 34)(23, 35)(24, 47)(25, 45)(26, 41)(27, 36)(28, 48)(29, 46)(30, 42)(31, 43)(32, 39)(49, 88)(50, 84)(51, 94)(52, 85)(53, 95)(54, 91)(55, 93)(56, 86)(57, 83)(58, 87)(59, 81)(60, 90)(61, 92)(62, 96)(63, 82)(64, 89)(65, 67)(66, 71)(68, 74)(69, 76)(70, 80)(72, 73)(75, 78)(77, 79) MAP : A3.1087 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 4)(2, 7)(3, 8)(5, 14)(6, 13)(9, 12)(10, 15)(11, 16)(17, 48)(18, 36)(19, 44)(20, 43)(21, 35)(22, 39)(23, 33)(24, 41)(25, 47)(26, 37)(27, 45)(28, 42)(29, 34)(30, 40)(31, 46)(32, 38)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84)(65, 69)(66, 72)(67, 71)(68, 78)(70, 76)(73, 77)(74, 80)(75, 79) MAP : A3.1088 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 13)(2, 16)(3, 15)(4, 6)(5, 9)(7, 11)(8, 10)(12, 14)(17, 34)(18, 38)(19, 46)(20, 39)(21, 47)(22, 43)(23, 45)(24, 37)(25, 35)(26, 41)(27, 33)(28, 40)(29, 48)(30, 42)(31, 44)(32, 36)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81)(65, 67)(66, 73)(68, 72)(69, 80)(70, 74)(71, 76)(75, 78)(77, 79) MAP : A3.1089 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, (x.2 * x.4^-1)^2, x.3^4, (x.4 * x.3^-1)^2, x.3 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 4)(2, 11)(3, 13)(5, 8)(6, 15)(7, 9)(10, 16)(12, 14)(17, 34)(18, 38)(19, 39)(20, 43)(21, 33)(22, 37)(23, 48)(24, 36)(25, 42)(26, 46)(27, 47)(28, 35)(29, 41)(30, 45)(31, 40)(32, 44)(49, 88)(50, 84)(51, 94)(52, 85)(53, 95)(54, 91)(55, 93)(56, 86)(57, 83)(58, 87)(59, 81)(60, 90)(61, 92)(62, 96)(63, 82)(64, 89)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80) MAP : A3.1090 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 4)(2, 7)(3, 8)(5, 14)(6, 13)(9, 12)(10, 15)(11, 16)(17, 48)(18, 36)(19, 44)(20, 43)(21, 35)(22, 39)(23, 33)(24, 41)(25, 47)(26, 37)(27, 45)(28, 42)(29, 34)(30, 40)(31, 46)(32, 38)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80) MAP : A3.1091 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, (x.2 * x.4^-1)^2, x.3^4, (x.4 * x.3^-1)^2, x.3 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 16)(2, 12)(3, 6)(4, 13)(5, 7)(8, 14)(9, 11)(10, 15)(17, 34)(18, 38)(19, 39)(20, 43)(21, 33)(22, 37)(23, 48)(24, 36)(25, 42)(26, 46)(27, 47)(28, 35)(29, 41)(30, 45)(31, 40)(32, 44)(49, 87)(50, 96)(51, 82)(52, 94)(53, 83)(54, 92)(55, 86)(56, 90)(57, 84)(58, 91)(59, 93)(60, 81)(61, 88)(62, 95)(63, 89)(64, 85)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80) MAP : A3.1092 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 4)(2, 7)(3, 8)(5, 14)(6, 13)(9, 12)(10, 15)(11, 16)(17, 48)(18, 36)(19, 44)(20, 43)(21, 35)(22, 39)(23, 33)(24, 41)(25, 47)(26, 37)(27, 45)(28, 42)(29, 34)(30, 40)(31, 46)(32, 38)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84)(65, 67)(66, 73)(68, 72)(69, 80)(70, 74)(71, 76)(75, 78)(77, 79) MAP : A3.1093 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, (x.2 * x.4^-1)^2, x.3^4, (x.4 * x.3^-1)^2, x.3 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 4)(2, 11)(3, 13)(5, 8)(6, 15)(7, 9)(10, 16)(12, 14)(17, 34)(18, 38)(19, 39)(20, 43)(21, 33)(22, 37)(23, 48)(24, 36)(25, 42)(26, 46)(27, 47)(28, 35)(29, 41)(30, 45)(31, 40)(32, 44)(49, 88)(50, 84)(51, 94)(52, 85)(53, 95)(54, 91)(55, 93)(56, 86)(57, 83)(58, 87)(59, 81)(60, 90)(61, 92)(62, 96)(63, 82)(64, 89)(65, 67)(66, 71)(68, 74)(69, 76)(70, 80)(72, 73)(75, 78)(77, 79) MAP : A3.1094 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, (x.2 * x.4^-1)^2, x.3^4, (x.4 * x.3^-1)^2, x.3 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 3)(2, 7)(4, 10)(5, 12)(6, 16)(8, 9)(11, 14)(13, 15)(17, 37)(18, 33)(19, 44)(20, 40)(21, 38)(22, 34)(23, 35)(24, 47)(25, 45)(26, 41)(27, 36)(28, 48)(29, 46)(30, 42)(31, 43)(32, 39)(49, 87)(50, 96)(51, 82)(52, 94)(53, 83)(54, 92)(55, 86)(56, 90)(57, 84)(58, 91)(59, 93)(60, 81)(61, 88)(62, 95)(63, 89)(64, 85)(65, 68)(66, 75)(67, 77)(69, 72)(70, 79)(71, 73)(74, 80)(76, 78) MAP : A3.1095 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, (x.2 * x.4^-1)^2, x.3^4, (x.4 * x.3^-1)^2, x.3 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 3)(2, 7)(4, 10)(5, 12)(6, 16)(8, 9)(11, 14)(13, 15)(17, 37)(18, 33)(19, 44)(20, 40)(21, 38)(22, 34)(23, 35)(24, 47)(25, 45)(26, 41)(27, 36)(28, 48)(29, 46)(30, 42)(31, 43)(32, 39)(49, 87)(50, 96)(51, 82)(52, 94)(53, 83)(54, 92)(55, 86)(56, 90)(57, 84)(58, 91)(59, 93)(60, 81)(61, 88)(62, 95)(63, 89)(64, 85)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80) MAP : A3.1096 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 13)(2, 16)(3, 15)(4, 6)(5, 9)(7, 11)(8, 10)(12, 14)(17, 39)(18, 45)(19, 37)(20, 34)(21, 42)(22, 48)(23, 38)(24, 46)(25, 40)(26, 44)(27, 36)(28, 35)(29, 43)(30, 47)(31, 41)(32, 33)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84)(65, 69)(66, 72)(67, 71)(68, 78)(70, 76)(73, 77)(74, 80)(75, 79) MAP : A3.1097 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, (x.2 * x.4^-1)^2, x.3^4, (x.4 * x.3^-1)^2, x.3 * x.2 * x.3^-1 * x.2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 14)(2, 13)(3, 8)(4, 7)(5, 10)(6, 9)(11, 16)(12, 15)(17, 34)(18, 38)(19, 39)(20, 43)(21, 33)(22, 37)(23, 48)(24, 36)(25, 42)(26, 46)(27, 47)(28, 35)(29, 41)(30, 45)(31, 40)(32, 44)(49, 90)(50, 94)(51, 95)(52, 83)(53, 89)(54, 93)(55, 88)(56, 92)(57, 82)(58, 86)(59, 87)(60, 91)(61, 81)(62, 85)(63, 96)(64, 84)(65, 67)(66, 71)(68, 74)(69, 76)(70, 80)(72, 73)(75, 78)(77, 79) MAP : A3.1098 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 13)(2, 16)(3, 15)(4, 6)(5, 9)(7, 11)(8, 10)(12, 14)(17, 34)(18, 38)(19, 46)(20, 39)(21, 47)(22, 43)(23, 45)(24, 37)(25, 35)(26, 41)(27, 33)(28, 40)(29, 48)(30, 42)(31, 44)(32, 36)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81)(65, 72)(66, 76)(67, 68)(69, 75)(70, 79)(71, 73)(74, 77)(78, 80) MAP : A3.1099 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 4)(2, 7)(3, 8)(5, 14)(6, 13)(9, 12)(10, 15)(11, 16)(17, 43)(18, 33)(19, 41)(20, 48)(21, 40)(22, 34)(23, 36)(24, 44)(25, 42)(26, 46)(27, 38)(28, 47)(29, 39)(30, 35)(31, 37)(32, 45)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80) MAP : A3.1100 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 4)(2, 7)(3, 8)(5, 14)(6, 13)(9, 12)(10, 15)(11, 16)(17, 43)(18, 33)(19, 41)(20, 48)(21, 40)(22, 34)(23, 36)(24, 44)(25, 42)(26, 46)(27, 38)(28, 47)(29, 39)(30, 35)(31, 37)(32, 45)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81)(65, 72)(66, 76)(67, 68)(69, 75)(70, 79)(71, 73)(74, 77)(78, 80) MAP : A3.1101 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 13)(2, 16)(3, 15)(4, 6)(5, 9)(7, 11)(8, 10)(12, 14)(17, 34)(18, 38)(19, 46)(20, 39)(21, 47)(22, 43)(23, 45)(24, 37)(25, 35)(26, 41)(27, 33)(28, 40)(29, 48)(30, 42)(31, 44)(32, 36)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80) MAP : A3.1102 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 4)(2, 7)(3, 8)(5, 14)(6, 13)(9, 12)(10, 15)(11, 16)(17, 43)(18, 33)(19, 41)(20, 48)(21, 40)(22, 34)(23, 36)(24, 44)(25, 42)(26, 46)(27, 38)(28, 47)(29, 39)(30, 35)(31, 37)(32, 45)(49, 87)(50, 93)(51, 85)(52, 82)(53, 90)(54, 96)(55, 86)(56, 94)(57, 88)(58, 92)(59, 84)(60, 83)(61, 91)(62, 95)(63, 89)(64, 81)(65, 67)(66, 73)(68, 72)(69, 80)(70, 74)(71, 76)(75, 78)(77, 79) MAP : A3.1103 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.1 * u.3^-1 * u.4^-1, u.3^4, (u.4 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.3^-1 * x.4^-1, x.1 * x.3 * x.4, x.3^4, (x.4 * x.2)^2, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, (x.4 * x.3^-1)^2 > SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 13)(2, 16)(3, 15)(4, 6)(5, 9)(7, 11)(8, 10)(12, 14)(17, 39)(18, 45)(19, 37)(20, 34)(21, 42)(22, 48)(23, 38)(24, 46)(25, 40)(26, 44)(27, 36)(28, 35)(29, 43)(30, 47)(31, 41)(32, 33)(49, 82)(50, 86)(51, 94)(52, 87)(53, 95)(54, 91)(55, 93)(56, 85)(57, 83)(58, 89)(59, 81)(60, 88)(61, 96)(62, 90)(63, 92)(64, 84)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80) MAP : A3.1104 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.4 * x.7, x.6 * x.3^-1, x.2 * x.1, x.6 * x.2 * x.7^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.4 * x.3^-1 * x.7^-1 * x.3^-1, x.6^4, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 13)(2, 16)(3, 15)(4, 9)(5, 14)(6, 12)(7, 10)(8, 11)(17, 40)(18, 37)(19, 36)(20, 34)(21, 35)(22, 39)(23, 33)(24, 38)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 43)(42, 46)(44, 48)(45, 47)(49, 93)(50, 96)(51, 95)(52, 89)(53, 94)(54, 92)(55, 90)(56, 91)(57, 59)(58, 62)(60, 64)(61, 63)(65, 87)(66, 84)(67, 85)(68, 83)(69, 82)(70, 88)(71, 86)(72, 81) MAP : A3.1105 NOTES : type II, reflexible, isomorphic to A3.1104. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.4 * x.7, x.6 * x.3^-1, x.2 * x.1, x.6 * x.2 * x.7^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.4 * x.3^-1 * x.7^-1 * x.3^-1, x.6^4, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 16)(2, 13)(3, 12)(4, 10)(5, 11)(6, 15)(7, 9)(8, 14)(17, 36)(18, 39)(19, 40)(20, 38)(21, 33)(22, 37)(23, 35)(24, 34)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 42)(43, 46)(44, 47)(45, 48)(49, 96)(50, 93)(51, 92)(52, 90)(53, 91)(54, 95)(55, 89)(56, 94)(57, 58)(59, 62)(60, 63)(61, 64)(65, 85)(66, 88)(67, 87)(68, 81)(69, 86)(70, 84)(71, 82)(72, 83) MAP : A3.1106 NOTES : type II, reflexible, isomorphic to A3.1104. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.4 * x.7, x.6 * x.3^-1, x.2 * x.1, x.6 * x.2 * x.7^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.4 * x.3^-1 * x.7^-1 * x.3^-1, x.6^4, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 16)(2, 13)(3, 12)(4, 10)(5, 11)(6, 15)(7, 9)(8, 14)(17, 37)(18, 40)(19, 39)(20, 33)(21, 38)(22, 36)(23, 34)(24, 35)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 43)(42, 46)(44, 48)(45, 47)(49, 96)(50, 93)(51, 92)(52, 90)(53, 91)(54, 95)(55, 89)(56, 94)(57, 59)(58, 62)(60, 64)(61, 63)(65, 84)(66, 87)(67, 88)(68, 86)(69, 81)(70, 85)(71, 83)(72, 82) MAP : A3.1107 NOTES : type II, reflexible, isomorphic to A3.1104. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.4 * x.7, x.6 * x.3^-1, x.2 * x.1, x.6 * x.2 * x.7^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.4 * x.3^-1 * x.7^-1 * x.3^-1, x.6^4, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 15)(2, 12)(3, 13)(4, 11)(5, 10)(6, 16)(7, 14)(8, 9)(17, 36)(18, 39)(19, 40)(20, 38)(21, 33)(22, 37)(23, 35)(24, 34)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 43)(42, 46)(44, 48)(45, 47)(49, 95)(50, 92)(51, 93)(52, 91)(53, 90)(54, 96)(55, 94)(56, 89)(57, 59)(58, 62)(60, 64)(61, 63)(65, 85)(66, 88)(67, 87)(68, 81)(69, 86)(70, 84)(71, 82)(72, 83) MAP : A3.1108 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.6^-1 * x.3^-1, x.1 * x.6^-1 * x.7^-1, x.1 * x.6 * x.4^-1, x.6 * x.2 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.6^4, (x.2 * x.1)^2, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 16)(2, 13)(3, 12)(4, 10)(5, 11)(6, 15)(7, 9)(8, 14)(17, 37)(18, 40)(19, 39)(20, 33)(21, 38)(22, 36)(23, 34)(24, 35)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 43)(42, 46)(44, 48)(45, 47)(49, 95)(50, 92)(51, 93)(52, 91)(53, 90)(54, 96)(55, 94)(56, 89)(57, 58)(59, 62)(60, 63)(61, 64)(65, 84)(66, 87)(67, 88)(68, 86)(69, 81)(70, 85)(71, 83)(72, 82) MAP : A3.1109 NOTES : type II, reflexible, isomorphic to A3.1104. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.4 * x.7, x.6 * x.3^-1, x.2 * x.1, x.6 * x.2 * x.7^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.4 * x.3^-1 * x.7^-1 * x.3^-1, x.6^4, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 15)(2, 12)(3, 13)(4, 11)(5, 10)(6, 16)(7, 14)(8, 9)(17, 37)(18, 40)(19, 39)(20, 33)(21, 38)(22, 36)(23, 34)(24, 35)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 42)(43, 46)(44, 47)(45, 48)(49, 95)(50, 92)(51, 93)(52, 91)(53, 90)(54, 96)(55, 94)(56, 89)(57, 58)(59, 62)(60, 63)(61, 64)(65, 84)(66, 87)(67, 88)(68, 86)(69, 81)(70, 85)(71, 83)(72, 82) MAP : A3.1110 NOTES : type II, reflexible, isomorphic to A3.1108. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.6^-1 * x.3^-1, x.1 * x.6^-1 * x.7^-1, x.1 * x.6 * x.4^-1, x.6 * x.2 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.6^4, (x.2 * x.1)^2, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 15)(2, 12)(3, 13)(4, 11)(5, 10)(6, 16)(7, 14)(8, 9)(17, 36)(18, 39)(19, 40)(20, 38)(21, 33)(22, 37)(23, 35)(24, 34)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 43)(42, 46)(44, 48)(45, 47)(49, 96)(50, 93)(51, 92)(52, 90)(53, 91)(54, 95)(55, 89)(56, 94)(57, 58)(59, 62)(60, 63)(61, 64)(65, 85)(66, 88)(67, 87)(68, 81)(69, 86)(70, 84)(71, 82)(72, 83) MAP : A3.1111 NOTES : type II, reflexible, isomorphic to A3.1108. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.6^-1 * x.3^-1, x.1 * x.6^-1 * x.7^-1, x.1 * x.6 * x.4^-1, x.6 * x.2 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.6^4, (x.2 * x.1)^2, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 15)(2, 12)(3, 13)(4, 11)(5, 10)(6, 16)(7, 14)(8, 9)(17, 37)(18, 40)(19, 39)(20, 33)(21, 38)(22, 36)(23, 34)(24, 35)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 42)(43, 46)(44, 47)(45, 48)(49, 96)(50, 93)(51, 92)(52, 90)(53, 91)(54, 95)(55, 89)(56, 94)(57, 59)(58, 62)(60, 64)(61, 63)(65, 84)(66, 87)(67, 88)(68, 86)(69, 81)(70, 85)(71, 83)(72, 82) MAP : A3.1112 NOTES : type II, reflexible, isomorphic to A3.1108. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.6^-1 * x.3^-1, x.1 * x.6^-1 * x.7^-1, x.1 * x.6 * x.4^-1, x.6 * x.2 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.6^4, (x.2 * x.1)^2, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 12)(2, 15)(3, 16)(4, 14)(5, 9)(6, 13)(7, 11)(8, 10)(17, 39)(18, 36)(19, 37)(20, 35)(21, 34)(22, 40)(23, 38)(24, 33)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 43)(42, 46)(44, 48)(45, 47)(49, 93)(50, 96)(51, 95)(52, 89)(53, 94)(54, 92)(55, 90)(56, 91)(57, 58)(59, 62)(60, 63)(61, 64)(65, 88)(66, 85)(67, 84)(68, 82)(69, 83)(70, 87)(71, 81)(72, 86) MAP : A3.1113 NOTES : type II, reflexible, isomorphic to A3.1108. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.6^-1 * x.3^-1, x.1 * x.6^-1 * x.7^-1, x.1 * x.6 * x.4^-1, x.6 * x.2 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.6^4, (x.2 * x.1)^2, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 12)(2, 15)(3, 16)(4, 14)(5, 9)(6, 13)(7, 11)(8, 10)(17, 40)(18, 37)(19, 36)(20, 34)(21, 35)(22, 39)(23, 33)(24, 38)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 42)(43, 46)(44, 47)(45, 48)(49, 93)(50, 96)(51, 95)(52, 89)(53, 94)(54, 92)(55, 90)(56, 91)(57, 59)(58, 62)(60, 64)(61, 63)(65, 87)(66, 84)(67, 85)(68, 83)(69, 82)(70, 88)(71, 86)(72, 81) MAP : A3.1114 NOTES : type II, reflexible, isomorphic to A3.1108. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.6^-1 * x.3^-1, x.1 * x.6^-1 * x.7^-1, x.1 * x.6 * x.4^-1, x.6 * x.2 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.6^4, (x.2 * x.1)^2, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 16)(2, 13)(3, 12)(4, 10)(5, 11)(6, 15)(7, 9)(8, 14)(17, 36)(18, 39)(19, 40)(20, 38)(21, 33)(22, 37)(23, 35)(24, 34)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 42)(43, 46)(44, 47)(45, 48)(49, 95)(50, 92)(51, 93)(52, 91)(53, 90)(54, 96)(55, 94)(56, 89)(57, 59)(58, 62)(60, 64)(61, 63)(65, 85)(66, 88)(67, 87)(68, 81)(69, 86)(70, 84)(71, 82)(72, 83) MAP : A3.1115 NOTES : type II, reflexible, isomorphic to A3.1108. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.6^-1 * x.3^-1, x.1 * x.6^-1 * x.7^-1, x.1 * x.6 * x.4^-1, x.6 * x.2 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.6^4, (x.2 * x.1)^2, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 13)(2, 16)(3, 15)(4, 9)(5, 14)(6, 12)(7, 10)(8, 11)(17, 40)(18, 37)(19, 36)(20, 34)(21, 35)(22, 39)(23, 33)(24, 38)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 43)(42, 46)(44, 48)(45, 47)(49, 92)(50, 95)(51, 96)(52, 94)(53, 89)(54, 93)(55, 91)(56, 90)(57, 58)(59, 62)(60, 63)(61, 64)(65, 87)(66, 84)(67, 85)(68, 83)(69, 82)(70, 88)(71, 86)(72, 81) MAP : A3.1116 NOTES : type II, reflexible, isomorphic to A3.1108. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.6^-1 * x.3^-1, x.1 * x.6^-1 * x.7^-1, x.1 * x.6 * x.4^-1, x.6 * x.2 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.6^4, (x.2 * x.1)^2, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 13)(2, 16)(3, 15)(4, 9)(5, 14)(6, 12)(7, 10)(8, 11)(17, 39)(18, 36)(19, 37)(20, 35)(21, 34)(22, 40)(23, 38)(24, 33)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 42)(43, 46)(44, 47)(45, 48)(49, 92)(50, 95)(51, 96)(52, 94)(53, 89)(54, 93)(55, 91)(56, 90)(57, 59)(58, 62)(60, 64)(61, 63)(65, 88)(66, 85)(67, 84)(68, 82)(69, 83)(70, 87)(71, 81)(72, 86) MAP : A3.1117 NOTES : type II, reflexible, isomorphic to A3.1104. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.4 * x.7, x.6 * x.3^-1, x.2 * x.1, x.6 * x.2 * x.7^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.4 * x.3^-1 * x.7^-1 * x.3^-1, x.6^4, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 12)(2, 15)(3, 16)(4, 14)(5, 9)(6, 13)(7, 11)(8, 10)(17, 40)(18, 37)(19, 36)(20, 34)(21, 35)(22, 39)(23, 33)(24, 38)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 42)(43, 46)(44, 47)(45, 48)(49, 92)(50, 95)(51, 96)(52, 94)(53, 89)(54, 93)(55, 91)(56, 90)(57, 58)(59, 62)(60, 63)(61, 64)(65, 87)(66, 84)(67, 85)(68, 83)(69, 82)(70, 88)(71, 86)(72, 81) MAP : A3.1118 NOTES : type II, reflexible, isomorphic to A3.1104. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.4 * x.7, x.6 * x.3^-1, x.2 * x.1, x.6 * x.2 * x.7^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.4 * x.3^-1 * x.7^-1 * x.3^-1, x.6^4, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 12)(2, 15)(3, 16)(4, 14)(5, 9)(6, 13)(7, 11)(8, 10)(17, 39)(18, 36)(19, 37)(20, 35)(21, 34)(22, 40)(23, 38)(24, 33)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 43)(42, 46)(44, 48)(45, 47)(49, 92)(50, 95)(51, 96)(52, 94)(53, 89)(54, 93)(55, 91)(56, 90)(57, 59)(58, 62)(60, 64)(61, 63)(65, 88)(66, 85)(67, 84)(68, 82)(69, 83)(70, 87)(71, 81)(72, 86) MAP : A3.1119 NOTES : type II, reflexible, isomorphic to A3.1104. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 5)(4, 10)(7, 12)(9, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.3^-1 * u.4^-1 * u.1, u.6 * u.2 * u.7^-1, u.4 * u.5^-1 * u.7 * u.5, u.3^4, u.6^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.4 * x.7, x.6 * x.3^-1, x.2 * x.1, x.6 * x.2 * x.7^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.7^-1, x.4 * x.5^-1 * x.7 * x.5, x.4 * x.3^-1 * x.7^-1 * x.3^-1, x.6^4, x.3^4 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1) LOCAL TYPE : (3, 3, 4, 3, 4, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 13)(2, 16)(3, 15)(4, 9)(5, 14)(6, 12)(7, 10)(8, 11)(17, 39)(18, 36)(19, 37)(20, 35)(21, 34)(22, 40)(23, 38)(24, 33)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(41, 42)(43, 46)(44, 47)(45, 48)(49, 93)(50, 96)(51, 95)(52, 89)(53, 94)(54, 92)(55, 90)(56, 91)(57, 58)(59, 62)(60, 63)(61, 64)(65, 88)(66, 85)(67, 84)(68, 82)(69, 83)(70, 87)(71, 81)(72, 86) MAP : A3.1120 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, (x.2 * x.3)^2, x.4^4, x.4 * x.2 * x.4^-1 * x.2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 71)(2, 80)(3, 66)(4, 78)(5, 67)(6, 76)(7, 70)(8, 74)(9, 68)(10, 75)(11, 77)(12, 65)(13, 72)(14, 79)(15, 73)(16, 69)(17, 37)(18, 33)(19, 44)(20, 40)(21, 38)(22, 34)(23, 35)(24, 47)(25, 45)(26, 41)(27, 36)(28, 48)(29, 46)(30, 42)(31, 43)(32, 39)(49, 64)(50, 60)(51, 54)(52, 61)(53, 55)(56, 62)(57, 59)(58, 63)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.1121 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, (x.2 * x.3)^2, x.4^4, x.4 * x.2 * x.4^-1 * x.2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 72)(2, 68)(3, 78)(4, 69)(5, 79)(6, 75)(7, 77)(8, 70)(9, 67)(10, 71)(11, 65)(12, 74)(13, 76)(14, 80)(15, 66)(16, 73)(17, 34)(18, 38)(19, 39)(20, 43)(21, 33)(22, 37)(23, 48)(24, 36)(25, 42)(26, 46)(27, 47)(28, 35)(29, 41)(30, 45)(31, 40)(32, 44)(49, 63)(50, 56)(51, 58)(52, 54)(53, 59)(55, 62)(57, 60)(61, 64)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.1122 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 71)(2, 77)(3, 69)(4, 66)(5, 74)(6, 80)(7, 70)(8, 78)(9, 72)(10, 76)(11, 68)(12, 67)(13, 75)(14, 79)(15, 73)(16, 65)(17, 43)(18, 33)(19, 41)(20, 48)(21, 40)(22, 34)(23, 36)(24, 44)(25, 42)(26, 46)(27, 38)(28, 47)(29, 39)(30, 35)(31, 37)(32, 45)(49, 61)(50, 64)(51, 63)(52, 54)(53, 57)(55, 59)(56, 58)(60, 62)(81, 88)(82, 92)(83, 84)(85, 91)(86, 95)(87, 89)(90, 93)(94, 96) MAP : A3.1123 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, (x.2 * x.3)^2, x.4^4, x.4 * x.2 * x.4^-1 * x.2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 74)(2, 78)(3, 79)(4, 67)(5, 73)(6, 77)(7, 72)(8, 76)(9, 66)(10, 70)(11, 71)(12, 75)(13, 65)(14, 69)(15, 80)(16, 68)(17, 34)(18, 38)(19, 39)(20, 43)(21, 33)(22, 37)(23, 48)(24, 36)(25, 42)(26, 46)(27, 47)(28, 35)(29, 41)(30, 45)(31, 40)(32, 44)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(81, 83)(82, 87)(84, 90)(85, 92)(86, 96)(88, 89)(91, 94)(93, 95) MAP : A3.1124 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, (x.2 * x.3)^2, x.4^4, x.4 * x.2 * x.4^-1 * x.2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 72)(2, 68)(3, 78)(4, 69)(5, 79)(6, 75)(7, 77)(8, 70)(9, 67)(10, 71)(11, 65)(12, 74)(13, 76)(14, 80)(15, 66)(16, 73)(17, 37)(18, 33)(19, 44)(20, 40)(21, 38)(22, 34)(23, 35)(24, 47)(25, 45)(26, 41)(27, 36)(28, 48)(29, 46)(30, 42)(31, 43)(32, 39)(49, 52)(50, 59)(51, 61)(53, 56)(54, 63)(55, 57)(58, 64)(60, 62)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.1125 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, (x.2 * x.3)^2, x.4^4, x.4 * x.2 * x.4^-1 * x.2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 72)(2, 68)(3, 78)(4, 69)(5, 79)(6, 75)(7, 77)(8, 70)(9, 67)(10, 71)(11, 65)(12, 74)(13, 76)(14, 80)(15, 66)(16, 73)(17, 37)(18, 33)(19, 44)(20, 40)(21, 38)(22, 34)(23, 35)(24, 47)(25, 45)(26, 41)(27, 36)(28, 48)(29, 46)(30, 42)(31, 43)(32, 39)(49, 52)(50, 59)(51, 61)(53, 56)(54, 63)(55, 57)(58, 64)(60, 62)(81, 83)(82, 87)(84, 90)(85, 92)(86, 96)(88, 89)(91, 94)(93, 95) MAP : A3.1126 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 66)(2, 70)(3, 78)(4, 71)(5, 79)(6, 75)(7, 77)(8, 69)(9, 67)(10, 73)(11, 65)(12, 72)(13, 80)(14, 74)(15, 76)(16, 68)(17, 48)(18, 36)(19, 44)(20, 43)(21, 35)(22, 39)(23, 33)(24, 41)(25, 47)(26, 37)(27, 45)(28, 42)(29, 34)(30, 40)(31, 46)(32, 38)(49, 61)(50, 64)(51, 63)(52, 54)(53, 57)(55, 59)(56, 58)(60, 62)(81, 83)(82, 89)(84, 88)(85, 96)(86, 90)(87, 92)(91, 94)(93, 95) MAP : A3.1127 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, (x.2 * x.3)^2, x.4^4, x.4 * x.2 * x.4^-1 * x.2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 71)(2, 80)(3, 66)(4, 78)(5, 67)(6, 76)(7, 70)(8, 74)(9, 68)(10, 75)(11, 77)(12, 65)(13, 72)(14, 79)(15, 73)(16, 69)(17, 34)(18, 38)(19, 39)(20, 43)(21, 33)(22, 37)(23, 48)(24, 36)(25, 42)(26, 46)(27, 47)(28, 35)(29, 41)(30, 45)(31, 40)(32, 44)(49, 51)(50, 55)(52, 58)(53, 60)(54, 64)(56, 57)(59, 62)(61, 63)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.1128 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 71)(2, 77)(3, 69)(4, 66)(5, 74)(6, 80)(7, 70)(8, 78)(9, 72)(10, 76)(11, 68)(12, 67)(13, 75)(14, 79)(15, 73)(16, 65)(17, 43)(18, 33)(19, 41)(20, 48)(21, 40)(22, 34)(23, 36)(24, 44)(25, 42)(26, 46)(27, 38)(28, 47)(29, 39)(30, 35)(31, 37)(32, 45)(49, 61)(50, 64)(51, 63)(52, 54)(53, 57)(55, 59)(56, 58)(60, 62)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.1129 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 71)(2, 77)(3, 69)(4, 66)(5, 74)(6, 80)(7, 70)(8, 78)(9, 72)(10, 76)(11, 68)(12, 67)(13, 75)(14, 79)(15, 73)(16, 65)(17, 34)(18, 38)(19, 46)(20, 39)(21, 47)(22, 43)(23, 45)(24, 37)(25, 35)(26, 41)(27, 33)(28, 40)(29, 48)(30, 42)(31, 44)(32, 36)(49, 52)(50, 55)(51, 56)(53, 62)(54, 61)(57, 60)(58, 63)(59, 64)(81, 88)(82, 92)(83, 84)(85, 91)(86, 95)(87, 89)(90, 93)(94, 96) MAP : A3.1130 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, (x.2 * x.3)^2, x.4^4, x.4 * x.2 * x.4^-1 * x.2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 71)(2, 80)(3, 66)(4, 78)(5, 67)(6, 76)(7, 70)(8, 74)(9, 68)(10, 75)(11, 77)(12, 65)(13, 72)(14, 79)(15, 73)(16, 69)(17, 34)(18, 38)(19, 39)(20, 43)(21, 33)(22, 37)(23, 48)(24, 36)(25, 42)(26, 46)(27, 47)(28, 35)(29, 41)(30, 45)(31, 40)(32, 44)(49, 51)(50, 55)(52, 58)(53, 60)(54, 64)(56, 57)(59, 62)(61, 63)(81, 84)(82, 91)(83, 93)(85, 88)(86, 95)(87, 89)(90, 96)(92, 94) MAP : A3.1131 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 66)(2, 70)(3, 78)(4, 71)(5, 79)(6, 75)(7, 77)(8, 69)(9, 67)(10, 73)(11, 65)(12, 72)(13, 80)(14, 74)(15, 76)(16, 68)(17, 39)(18, 45)(19, 37)(20, 34)(21, 42)(22, 48)(23, 38)(24, 46)(25, 40)(26, 44)(27, 36)(28, 35)(29, 43)(30, 47)(31, 41)(32, 33)(49, 52)(50, 55)(51, 56)(53, 62)(54, 61)(57, 60)(58, 63)(59, 64)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.1132 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, (x.2 * x.3)^2, x.4^4, x.4 * x.2 * x.4^-1 * x.2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 74)(2, 78)(3, 79)(4, 67)(5, 73)(6, 77)(7, 72)(8, 76)(9, 66)(10, 70)(11, 71)(12, 75)(13, 65)(14, 69)(15, 80)(16, 68)(17, 37)(18, 33)(19, 44)(20, 40)(21, 38)(22, 34)(23, 35)(24, 47)(25, 45)(26, 41)(27, 36)(28, 48)(29, 46)(30, 42)(31, 43)(32, 39)(49, 62)(50, 61)(51, 56)(52, 55)(53, 58)(54, 57)(59, 64)(60, 63)(81, 84)(82, 91)(83, 93)(85, 88)(86, 95)(87, 89)(90, 96)(92, 94) MAP : A3.1133 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 66)(2, 70)(3, 78)(4, 71)(5, 79)(6, 75)(7, 77)(8, 69)(9, 67)(10, 73)(11, 65)(12, 72)(13, 80)(14, 74)(15, 76)(16, 68)(17, 39)(18, 45)(19, 37)(20, 34)(21, 42)(22, 48)(23, 38)(24, 46)(25, 40)(26, 44)(27, 36)(28, 35)(29, 43)(30, 47)(31, 41)(32, 33)(49, 52)(50, 55)(51, 56)(53, 62)(54, 61)(57, 60)(58, 63)(59, 64)(81, 83)(82, 89)(84, 88)(85, 96)(86, 90)(87, 92)(91, 94)(93, 95) MAP : A3.1134 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 71)(2, 77)(3, 69)(4, 66)(5, 74)(6, 80)(7, 70)(8, 78)(9, 72)(10, 76)(11, 68)(12, 67)(13, 75)(14, 79)(15, 73)(16, 65)(17, 34)(18, 38)(19, 46)(20, 39)(21, 47)(22, 43)(23, 45)(24, 37)(25, 35)(26, 41)(27, 33)(28, 40)(29, 48)(30, 42)(31, 44)(32, 36)(49, 52)(50, 55)(51, 56)(53, 62)(54, 61)(57, 60)(58, 63)(59, 64)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.1135 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, (x.2 * x.3)^2, x.4^4, x.4 * x.2 * x.4^-1 * x.2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 72)(2, 68)(3, 78)(4, 69)(5, 79)(6, 75)(7, 77)(8, 70)(9, 67)(10, 71)(11, 65)(12, 74)(13, 76)(14, 80)(15, 66)(16, 73)(17, 34)(18, 38)(19, 39)(20, 43)(21, 33)(22, 37)(23, 48)(24, 36)(25, 42)(26, 46)(27, 47)(28, 35)(29, 41)(30, 45)(31, 40)(32, 44)(49, 63)(50, 56)(51, 58)(52, 54)(53, 59)(55, 62)(57, 60)(61, 64)(81, 83)(82, 87)(84, 90)(85, 92)(86, 96)(88, 89)(91, 94)(93, 95) MAP : A3.1136 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, (x.2 * x.3)^2, x.4^4, x.4 * x.2 * x.4^-1 * x.2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 74)(2, 78)(3, 79)(4, 67)(5, 73)(6, 77)(7, 72)(8, 76)(9, 66)(10, 70)(11, 71)(12, 75)(13, 65)(14, 69)(15, 80)(16, 68)(17, 37)(18, 33)(19, 44)(20, 40)(21, 38)(22, 34)(23, 35)(24, 47)(25, 45)(26, 41)(27, 36)(28, 48)(29, 46)(30, 42)(31, 43)(32, 39)(49, 62)(50, 61)(51, 56)(52, 55)(53, 58)(54, 57)(59, 64)(60, 63)(81, 83)(82, 87)(84, 90)(85, 92)(86, 96)(88, 89)(91, 94)(93, 95) MAP : A3.1137 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 66)(2, 70)(3, 78)(4, 71)(5, 79)(6, 75)(7, 77)(8, 69)(9, 67)(10, 73)(11, 65)(12, 72)(13, 80)(14, 74)(15, 76)(16, 68)(17, 48)(18, 36)(19, 44)(20, 43)(21, 35)(22, 39)(23, 33)(24, 41)(25, 47)(26, 37)(27, 45)(28, 42)(29, 34)(30, 40)(31, 46)(32, 38)(49, 61)(50, 64)(51, 63)(52, 54)(53, 57)(55, 59)(56, 58)(60, 62)(81, 88)(82, 92)(83, 84)(85, 91)(86, 95)(87, 89)(90, 93)(94, 96) MAP : A3.1138 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 71)(2, 77)(3, 69)(4, 66)(5, 74)(6, 80)(7, 70)(8, 78)(9, 72)(10, 76)(11, 68)(12, 67)(13, 75)(14, 79)(15, 73)(16, 65)(17, 43)(18, 33)(19, 41)(20, 48)(21, 40)(22, 34)(23, 36)(24, 44)(25, 42)(26, 46)(27, 38)(28, 47)(29, 39)(30, 35)(31, 37)(32, 45)(49, 61)(50, 64)(51, 63)(52, 54)(53, 57)(55, 59)(56, 58)(60, 62)(81, 83)(82, 89)(84, 88)(85, 96)(86, 90)(87, 92)(91, 94)(93, 95) MAP : A3.1139 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 71)(2, 77)(3, 69)(4, 66)(5, 74)(6, 80)(7, 70)(8, 78)(9, 72)(10, 76)(11, 68)(12, 67)(13, 75)(14, 79)(15, 73)(16, 65)(17, 34)(18, 38)(19, 46)(20, 39)(21, 47)(22, 43)(23, 45)(24, 37)(25, 35)(26, 41)(27, 33)(28, 40)(29, 48)(30, 42)(31, 44)(32, 36)(49, 52)(50, 55)(51, 56)(53, 62)(54, 61)(57, 60)(58, 63)(59, 64)(81, 85)(82, 88)(83, 87)(84, 94)(86, 92)(89, 93)(90, 96)(91, 95) MAP : A3.1140 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 71)(2, 77)(3, 69)(4, 66)(5, 74)(6, 80)(7, 70)(8, 78)(9, 72)(10, 76)(11, 68)(12, 67)(13, 75)(14, 79)(15, 73)(16, 65)(17, 34)(18, 38)(19, 46)(20, 39)(21, 47)(22, 43)(23, 45)(24, 37)(25, 35)(26, 41)(27, 33)(28, 40)(29, 48)(30, 42)(31, 44)(32, 36)(49, 52)(50, 55)(51, 56)(53, 62)(54, 61)(57, 60)(58, 63)(59, 64)(81, 83)(82, 89)(84, 88)(85, 96)(86, 90)(87, 92)(91, 94)(93, 95) MAP : A3.1141 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 66)(2, 70)(3, 78)(4, 71)(5, 79)(6, 75)(7, 77)(8, 69)(9, 67)(10, 73)(11, 65)(12, 72)(13, 80)(14, 74)(15, 76)(16, 68)(17, 48)(18, 36)(19, 44)(20, 43)(21, 35)(22, 39)(23, 33)(24, 41)(25, 47)(26, 37)(27, 45)(28, 42)(29, 34)(30, 40)(31, 46)(32, 38)(49, 61)(50, 64)(51, 63)(52, 54)(53, 57)(55, 59)(56, 58)(60, 62)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.1142 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 66)(2, 70)(3, 78)(4, 71)(5, 79)(6, 75)(7, 77)(8, 69)(9, 67)(10, 73)(11, 65)(12, 72)(13, 80)(14, 74)(15, 76)(16, 68)(17, 39)(18, 45)(19, 37)(20, 34)(21, 42)(22, 48)(23, 38)(24, 46)(25, 40)(26, 44)(27, 36)(28, 35)(29, 43)(30, 47)(31, 41)(32, 33)(49, 52)(50, 55)(51, 56)(53, 62)(54, 61)(57, 60)(58, 63)(59, 64)(81, 88)(82, 92)(83, 84)(85, 91)(86, 95)(87, 89)(90, 93)(94, 96) MAP : A3.1143 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, (x.2 * x.3)^2, x.4^4, x.4 * x.2 * x.4^-1 * x.2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 71)(2, 80)(3, 66)(4, 78)(5, 67)(6, 76)(7, 70)(8, 74)(9, 68)(10, 75)(11, 77)(12, 65)(13, 72)(14, 79)(15, 73)(16, 69)(17, 37)(18, 33)(19, 44)(20, 40)(21, 38)(22, 34)(23, 35)(24, 47)(25, 45)(26, 41)(27, 36)(28, 48)(29, 46)(30, 42)(31, 43)(32, 39)(49, 64)(50, 60)(51, 54)(52, 61)(53, 55)(56, 62)(57, 59)(58, 63)(81, 84)(82, 91)(83, 93)(85, 88)(86, 95)(87, 89)(90, 96)(92, 94) MAP : A3.1144 NOTES : type I, chiral, isomorphic to A3.1077. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, (x.2 * x.3)^2, x.4^4, x.4 * x.2 * x.4^-1 * x.2, x.3^4 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 74)(2, 78)(3, 79)(4, 67)(5, 73)(6, 77)(7, 72)(8, 76)(9, 66)(10, 70)(11, 71)(12, 75)(13, 65)(14, 69)(15, 80)(16, 68)(17, 34)(18, 38)(19, 39)(20, 43)(21, 33)(22, 37)(23, 48)(24, 36)(25, 42)(26, 46)(27, 47)(28, 35)(29, 41)(30, 45)(31, 40)(32, 44)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(81, 84)(82, 91)(83, 93)(85, 88)(86, 95)(87, 89)(90, 96)(92, 94) MAP : A3.1145 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 66)(2, 70)(3, 78)(4, 71)(5, 79)(6, 75)(7, 77)(8, 69)(9, 67)(10, 73)(11, 65)(12, 72)(13, 80)(14, 74)(15, 76)(16, 68)(17, 48)(18, 36)(19, 44)(20, 43)(21, 35)(22, 39)(23, 33)(24, 41)(25, 47)(26, 37)(27, 45)(28, 42)(29, 34)(30, 40)(31, 46)(32, 38)(49, 61)(50, 64)(51, 63)(52, 54)(53, 57)(55, 59)(56, 58)(60, 62)(81, 85)(82, 88)(83, 87)(84, 94)(86, 92)(89, 93)(90, 96)(91, 95) MAP : A3.1146 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 66)(2, 70)(3, 78)(4, 71)(5, 79)(6, 75)(7, 77)(8, 69)(9, 67)(10, 73)(11, 65)(12, 72)(13, 80)(14, 74)(15, 76)(16, 68)(17, 39)(18, 45)(19, 37)(20, 34)(21, 42)(22, 48)(23, 38)(24, 46)(25, 40)(26, 44)(27, 36)(28, 35)(29, 43)(30, 47)(31, 41)(32, 33)(49, 52)(50, 55)(51, 56)(53, 62)(54, 61)(57, 60)(58, 63)(59, 64)(81, 85)(82, 88)(83, 87)(84, 94)(86, 92)(89, 93)(90, 96)(91, 95) MAP : A3.1147 NOTES : type I, chiral, isomorphic to A3.1076. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^4, (u.3^-1 * u.2)^2 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.3 * x.1 * x.4^-1, x.4^4, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^4, (x.4 * x.2)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2) LOCAL TYPE : (3, 3, 4, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 71)(2, 77)(3, 69)(4, 66)(5, 74)(6, 80)(7, 70)(8, 78)(9, 72)(10, 76)(11, 68)(12, 67)(13, 75)(14, 79)(15, 73)(16, 65)(17, 43)(18, 33)(19, 41)(20, 48)(21, 40)(22, 34)(23, 36)(24, 44)(25, 42)(26, 46)(27, 38)(28, 47)(29, 39)(30, 35)(31, 37)(32, 45)(49, 61)(50, 64)(51, 63)(52, 54)(53, 57)(55, 59)(56, 58)(60, 62)(81, 85)(82, 88)(83, 87)(84, 94)(86, 92)(89, 93)(90, 96)(91, 95) MAP : A3.1148 NOTES : type I, non-Cayley, reflexible, representative. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 3, 4 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 54, 6, 51, 3, 49)(2, 58, 10, 85, 37, 50)(4, 57, 9, 88, 40, 52)(5, 61, 13, 82, 34, 53)(7, 94, 46, 60, 12, 55)(8, 64, 16, 84, 36, 56)(11, 78, 30, 71, 23, 59)(14, 75, 27, 92, 44, 62)(15, 81, 33, 67, 19, 63)(17, 79, 31, 86, 38, 65)(18, 77, 29, 90, 42, 66)(20, 80, 32, 89, 41, 68)(21, 74, 26, 93, 45, 69)(22, 95, 47, 83, 35, 70)(24, 73, 25, 96, 48, 72)(28, 91, 43, 87, 39, 76) L = (1, 53)(2, 49)(3, 76)(4, 65)(5, 67)(6, 52)(7, 51)(8, 54)(9, 85)(10, 59)(11, 66)(12, 69)(13, 60)(14, 61)(15, 96)(16, 77)(17, 56)(18, 87)(19, 50)(20, 74)(21, 62)(22, 55)(23, 88)(24, 82)(25, 71)(26, 57)(27, 79)(28, 70)(29, 72)(30, 81)(31, 78)(32, 91)(33, 75)(34, 64)(35, 89)(36, 92)(37, 68)(38, 93)(39, 58)(40, 94)(41, 63)(42, 86)(43, 84)(44, 80)(45, 95)(46, 73)(47, 90)(48, 83) MAP : A3.1149 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 3, 4 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 54, 6, 51, 3, 49)(2, 58, 10, 85, 37, 50)(4, 57, 9, 88, 40, 52)(5, 61, 13, 82, 34, 53)(7, 94, 46, 60, 12, 55)(8, 64, 16, 84, 36, 56)(11, 78, 30, 71, 23, 59)(14, 75, 27, 92, 44, 62)(15, 81, 33, 67, 19, 63)(17, 79, 31, 86, 38, 65)(18, 77, 29, 90, 42, 66)(20, 80, 32, 89, 41, 68)(21, 74, 26, 93, 45, 69)(22, 95, 47, 83, 35, 70)(24, 73, 25, 96, 48, 72)(28, 91, 43, 87, 39, 76) L = (1, 92)(2, 84)(3, 68)(4, 62)(5, 80)(6, 69)(7, 85)(8, 60)(9, 81)(10, 65)(11, 56)(12, 89)(13, 83)(14, 96)(15, 66)(16, 70)(17, 61)(18, 54)(19, 91)(20, 79)(21, 63)(22, 57)(23, 49)(24, 51)(25, 50)(26, 78)(27, 77)(28, 74)(29, 55)(30, 82)(31, 72)(32, 90)(33, 64)(34, 76)(35, 58)(36, 93)(37, 75)(38, 94)(39, 52)(40, 53)(41, 59)(42, 88)(43, 86)(44, 95)(45, 73)(46, 67)(47, 71)(48, 87) MAP : A3.1150 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 21)(2, 17)(3, 28)(4, 31)(5, 24)(6, 20)(7, 19)(8, 18)(9, 22)(10, 23)(11, 32)(12, 26)(13, 27)(14, 29)(15, 25)(16, 30)(33, 60)(34, 51)(35, 64)(36, 56)(37, 58)(38, 53)(39, 59)(40, 55)(41, 49)(42, 61)(43, 52)(44, 62)(45, 54)(46, 57)(47, 50)(48, 63)(65, 95)(66, 84)(67, 88)(68, 93)(69, 89)(70, 94)(71, 85)(72, 86)(73, 96)(74, 81)(75, 90)(76, 82)(77, 92)(78, 83)(79, 91)(80, 87) MAP : A3.1151 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 32)(2, 27)(3, 20)(4, 26)(5, 30)(6, 28)(7, 22)(8, 29)(9, 19)(10, 25)(11, 21)(12, 31)(13, 17)(14, 18)(15, 23)(16, 24)(33, 55)(34, 58)(35, 61)(36, 49)(37, 51)(38, 50)(39, 62)(40, 60)(41, 56)(42, 64)(43, 57)(44, 59)(45, 63)(46, 52)(47, 53)(48, 54)(65, 83)(66, 87)(67, 91)(68, 85)(69, 92)(70, 81)(71, 93)(72, 90)(73, 82)(74, 94)(75, 86)(76, 96)(77, 89)(78, 95)(79, 88)(80, 84) MAP : A3.1152 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 21)(2, 17)(3, 28)(4, 31)(5, 24)(6, 20)(7, 19)(8, 18)(9, 22)(10, 23)(11, 32)(12, 26)(13, 27)(14, 29)(15, 25)(16, 30)(33, 58)(34, 60)(35, 62)(36, 50)(37, 55)(38, 56)(39, 64)(40, 51)(41, 53)(42, 59)(43, 63)(44, 61)(45, 52)(46, 54)(47, 49)(48, 57)(65, 84)(66, 86)(67, 85)(68, 94)(69, 95)(70, 96)(71, 81)(72, 89)(73, 91)(74, 82)(75, 92)(76, 88)(77, 83)(78, 87)(79, 93)(80, 90) MAP : A3.1153 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 4, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^3, (u.1 * u.2)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^3, (x.1 * x.2^-1)^3, (x.1 * x.2)^4 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 55, 7, 61, 13, 49)(2, 57, 9, 54, 6, 50)(3, 56, 8, 91, 43, 51)(4, 71, 23, 79, 31, 52)(5, 72, 24, 63, 15, 53)(10, 67, 19, 78, 30, 58)(11, 73, 25, 77, 29, 59)(12, 88, 40, 74, 26, 60)(14, 84, 36, 82, 34, 62)(16, 65, 17, 90, 42, 64)(18, 95, 47, 76, 28, 66)(20, 83, 35, 93, 45, 68)(21, 86, 38, 75, 27, 69)(22, 96, 48, 94, 46, 70)(32, 85, 37, 87, 39, 80)(33, 89, 41, 92, 44, 81) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73) MAP : A3.1154 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 21)(2, 17)(3, 28)(4, 31)(5, 24)(6, 20)(7, 19)(8, 18)(9, 22)(10, 23)(11, 32)(12, 26)(13, 27)(14, 29)(15, 25)(16, 30)(33, 57)(34, 63)(35, 50)(36, 59)(37, 54)(38, 61)(39, 56)(40, 52)(41, 62)(42, 53)(43, 55)(44, 49)(45, 58)(46, 60)(47, 64)(48, 51)(65, 83)(66, 87)(67, 91)(68, 85)(69, 92)(70, 81)(71, 93)(72, 90)(73, 82)(74, 94)(75, 86)(76, 96)(77, 89)(78, 95)(79, 88)(80, 84) MAP : A3.1155 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 3, 4 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 51, 3, 54, 6, 49)(2, 85, 37, 58, 10, 50)(4, 88, 40, 57, 9, 52)(5, 82, 34, 61, 13, 53)(7, 60, 12, 94, 46, 55)(8, 84, 36, 64, 16, 56)(11, 71, 23, 78, 30, 59)(14, 92, 44, 75, 27, 62)(15, 67, 19, 81, 33, 63)(17, 86, 38, 79, 31, 65)(18, 90, 42, 77, 29, 66)(20, 89, 41, 80, 32, 68)(21, 93, 45, 74, 26, 69)(22, 83, 35, 95, 47, 70)(24, 96, 48, 73, 25, 72)(28, 87, 39, 91, 43, 76) L = (1, 71)(2, 73)(3, 72)(4, 87)(5, 88)(6, 66)(7, 77)(8, 59)(9, 70)(10, 83)(11, 89)(12, 56)(13, 65)(14, 52)(15, 69)(16, 81)(17, 58)(18, 63)(19, 94)(20, 51)(21, 54)(22, 64)(23, 95)(24, 79)(25, 93)(26, 76)(27, 85)(28, 82)(29, 75)(30, 74)(31, 68)(32, 53)(33, 57)(34, 78)(35, 61)(36, 50)(37, 55)(38, 91)(39, 96)(40, 90)(41, 60)(42, 80)(43, 67)(44, 49)(45, 84)(46, 86)(47, 92)(48, 62) MAP : A3.1156 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 26)(2, 28)(3, 30)(4, 18)(5, 23)(6, 24)(7, 32)(8, 19)(9, 21)(10, 27)(11, 31)(12, 29)(13, 20)(14, 22)(15, 17)(16, 25)(33, 52)(34, 54)(35, 53)(36, 62)(37, 63)(38, 64)(39, 49)(40, 57)(41, 59)(42, 50)(43, 60)(44, 56)(45, 51)(46, 55)(47, 61)(48, 58)(65, 85)(66, 81)(67, 92)(68, 95)(69, 88)(70, 84)(71, 83)(72, 82)(73, 86)(74, 87)(75, 96)(76, 90)(77, 91)(78, 93)(79, 89)(80, 94) MAP : A3.1157 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 3, 4 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 51, 3, 54, 6, 49)(2, 85, 37, 58, 10, 50)(4, 88, 40, 57, 9, 52)(5, 82, 34, 61, 13, 53)(7, 60, 12, 94, 46, 55)(8, 84, 36, 64, 16, 56)(11, 71, 23, 78, 30, 59)(14, 92, 44, 75, 27, 62)(15, 67, 19, 81, 33, 63)(17, 86, 38, 79, 31, 65)(18, 90, 42, 77, 29, 66)(20, 89, 41, 80, 32, 68)(21, 93, 45, 74, 26, 69)(22, 83, 35, 95, 47, 70)(24, 96, 48, 73, 25, 72)(28, 87, 39, 91, 43, 76) L = (1, 53)(2, 49)(3, 76)(4, 65)(5, 67)(6, 52)(7, 51)(8, 54)(9, 85)(10, 59)(11, 66)(12, 69)(13, 60)(14, 61)(15, 96)(16, 77)(17, 56)(18, 87)(19, 50)(20, 74)(21, 62)(22, 55)(23, 88)(24, 82)(25, 71)(26, 57)(27, 79)(28, 70)(29, 72)(30, 81)(31, 78)(32, 91)(33, 75)(34, 64)(35, 89)(36, 92)(37, 68)(38, 93)(39, 58)(40, 94)(41, 63)(42, 86)(43, 84)(44, 80)(45, 95)(46, 73)(47, 90)(48, 83) MAP : A3.1158 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 19)(2, 23)(3, 27)(4, 21)(5, 28)(6, 17)(7, 29)(8, 26)(9, 18)(10, 30)(11, 22)(12, 32)(13, 25)(14, 31)(15, 24)(16, 20)(33, 64)(34, 59)(35, 52)(36, 58)(37, 62)(38, 60)(39, 54)(40, 61)(41, 51)(42, 57)(43, 53)(44, 63)(45, 49)(46, 50)(47, 55)(48, 56)(65, 87)(66, 90)(67, 93)(68, 81)(69, 83)(70, 82)(71, 94)(72, 92)(73, 88)(74, 96)(75, 89)(76, 91)(77, 95)(78, 84)(79, 85)(80, 86) MAP : A3.1159 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 4, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^3, (u.1 * u.2)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^3, (x.1 * x.2^-1)^3, (x.1 * x.2)^4 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 59, 11, 68, 20, 49)(2, 96, 48, 75, 27, 50)(3, 73, 25, 69, 21, 51)(4, 76, 28, 53, 5, 52)(6, 77, 29, 92, 44, 54)(7, 90, 42, 89, 41, 55)(8, 78, 30, 93, 45, 56)(9, 95, 47, 62, 14, 57)(10, 70, 22, 84, 36, 58)(12, 64, 16, 67, 19, 60)(13, 79, 31, 80, 32, 61)(15, 74, 26, 91, 43, 63)(17, 85, 37, 94, 46, 65)(18, 81, 33, 88, 40, 66)(23, 83, 35, 82, 34, 71)(24, 86, 38, 87, 39, 72) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72) MAP : A3.1160 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 4, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^3, (u.1 * u.2)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^3, (x.1 * x.2^-1)^3, (x.1 * x.2)^4 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 68, 20, 59, 11, 49)(2, 75, 27, 96, 48, 50)(3, 69, 21, 73, 25, 51)(4, 53, 5, 76, 28, 52)(6, 92, 44, 77, 29, 54)(7, 89, 41, 90, 42, 55)(8, 93, 45, 78, 30, 56)(9, 62, 14, 95, 47, 57)(10, 84, 36, 70, 22, 58)(12, 67, 19, 64, 16, 60)(13, 80, 32, 79, 31, 61)(15, 91, 43, 74, 26, 63)(17, 94, 46, 85, 37, 65)(18, 88, 40, 81, 33, 66)(23, 82, 34, 83, 35, 71)(24, 87, 39, 86, 38, 72) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73) MAP : A3.1161 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 4, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^3, (u.1 * u.2)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^3, (x.1 * x.2^-1)^3, (x.1 * x.2)^4 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 78, 30, 69, 21, 49)(2, 72, 24, 65, 17, 50)(3, 96, 48, 92, 44, 51)(4, 91, 43, 81, 33, 52)(5, 57, 9, 83, 35, 53)(6, 90, 42, 68, 20, 54)(7, 66, 18, 67, 19, 55)(8, 71, 23, 70, 22, 56)(10, 95, 47, 75, 27, 58)(11, 80, 32, 82, 34, 59)(12, 84, 36, 85, 37, 60)(13, 86, 38, 76, 28, 61)(14, 88, 40, 77, 29, 62)(15, 93, 45, 64, 16, 63)(25, 74, 26, 87, 39, 73)(31, 89, 41, 94, 46, 79) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73) MAP : A3.1162 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 3, 4 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 54, 6, 51, 3, 49)(2, 58, 10, 85, 37, 50)(4, 57, 9, 88, 40, 52)(5, 61, 13, 82, 34, 53)(7, 94, 46, 60, 12, 55)(8, 64, 16, 84, 36, 56)(11, 78, 30, 71, 23, 59)(14, 75, 27, 92, 44, 62)(15, 81, 33, 67, 19, 63)(17, 79, 31, 86, 38, 65)(18, 77, 29, 90, 42, 66)(20, 80, 32, 89, 41, 68)(21, 74, 26, 93, 45, 69)(22, 95, 47, 83, 35, 70)(24, 73, 25, 96, 48, 72)(28, 91, 43, 87, 39, 76) L = (1, 71)(2, 73)(3, 72)(4, 87)(5, 88)(6, 66)(7, 77)(8, 59)(9, 70)(10, 83)(11, 89)(12, 56)(13, 65)(14, 52)(15, 69)(16, 81)(17, 58)(18, 63)(19, 94)(20, 51)(21, 54)(22, 64)(23, 95)(24, 79)(25, 93)(26, 76)(27, 85)(28, 82)(29, 75)(30, 74)(31, 68)(32, 53)(33, 57)(34, 78)(35, 61)(36, 50)(37, 55)(38, 91)(39, 96)(40, 90)(41, 60)(42, 80)(43, 67)(44, 49)(45, 84)(46, 86)(47, 92)(48, 62) MAP : A3.1163 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 4, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^3, (u.1 * u.2)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^3, (x.1 * x.2^-1)^3, (x.1 * x.2)^4 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 61, 13, 55, 7, 49)(2, 54, 6, 57, 9, 50)(3, 91, 43, 56, 8, 51)(4, 79, 31, 71, 23, 52)(5, 63, 15, 72, 24, 53)(10, 78, 30, 67, 19, 58)(11, 77, 29, 73, 25, 59)(12, 74, 26, 88, 40, 60)(14, 82, 34, 84, 36, 62)(16, 90, 42, 65, 17, 64)(18, 76, 28, 95, 47, 66)(20, 93, 45, 83, 35, 68)(21, 75, 27, 86, 38, 69)(22, 94, 46, 96, 48, 70)(32, 87, 39, 85, 37, 80)(33, 92, 44, 89, 41, 81) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72) MAP : A3.1164 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 3, 4 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 54, 6, 51, 3, 49)(2, 58, 10, 85, 37, 50)(4, 57, 9, 88, 40, 52)(5, 61, 13, 82, 34, 53)(7, 94, 46, 60, 12, 55)(8, 64, 16, 84, 36, 56)(11, 78, 30, 71, 23, 59)(14, 75, 27, 92, 44, 62)(15, 81, 33, 67, 19, 63)(17, 79, 31, 86, 38, 65)(18, 77, 29, 90, 42, 66)(20, 80, 32, 89, 41, 68)(21, 74, 26, 93, 45, 69)(22, 95, 47, 83, 35, 70)(24, 73, 25, 96, 48, 72)(28, 91, 43, 87, 39, 76) L = (1, 50)(2, 67)(3, 55)(4, 54)(5, 49)(6, 56)(7, 70)(8, 65)(9, 74)(10, 87)(11, 58)(12, 61)(13, 62)(14, 69)(15, 89)(16, 82)(17, 52)(18, 59)(19, 53)(20, 85)(21, 60)(22, 76)(23, 73)(24, 77)(25, 94)(26, 68)(27, 81)(28, 51)(29, 64)(30, 79)(31, 75)(32, 92)(33, 78)(34, 72)(35, 96)(36, 91)(37, 57)(38, 90)(39, 66)(40, 71)(41, 83)(42, 95)(43, 80)(44, 84)(45, 86)(46, 88)(47, 93)(48, 63) MAP : A3.1165 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 3, 4 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 51, 3, 54, 6, 49)(2, 85, 37, 58, 10, 50)(4, 88, 40, 57, 9, 52)(5, 82, 34, 61, 13, 53)(7, 60, 12, 94, 46, 55)(8, 84, 36, 64, 16, 56)(11, 71, 23, 78, 30, 59)(14, 92, 44, 75, 27, 62)(15, 67, 19, 81, 33, 63)(17, 86, 38, 79, 31, 65)(18, 90, 42, 77, 29, 66)(20, 89, 41, 80, 32, 68)(21, 93, 45, 74, 26, 69)(22, 83, 35, 95, 47, 70)(24, 96, 48, 73, 25, 72)(28, 87, 39, 91, 43, 76) L = (1, 50)(2, 67)(3, 55)(4, 54)(5, 49)(6, 56)(7, 70)(8, 65)(9, 74)(10, 87)(11, 58)(12, 61)(13, 62)(14, 69)(15, 89)(16, 82)(17, 52)(18, 59)(19, 53)(20, 85)(21, 60)(22, 76)(23, 73)(24, 77)(25, 94)(26, 68)(27, 81)(28, 51)(29, 64)(30, 79)(31, 75)(32, 92)(33, 78)(34, 72)(35, 96)(36, 91)(37, 57)(38, 90)(39, 66)(40, 71)(41, 83)(42, 95)(43, 80)(44, 84)(45, 86)(46, 88)(47, 93)(48, 63) MAP : A3.1166 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 4, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^3, (u.1 * u.2)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^3, (x.1 * x.2^-1)^3, (x.1 * x.2)^4 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 82, 34, 56, 8, 49)(2, 51, 3, 87, 39, 50)(4, 86, 38, 74, 26, 52)(5, 81, 33, 62, 14, 53)(6, 88, 40, 55, 7, 54)(9, 58, 10, 71, 23, 57)(11, 90, 42, 79, 31, 59)(12, 93, 45, 70, 22, 60)(13, 94, 46, 72, 24, 61)(15, 73, 25, 78, 30, 63)(16, 66, 18, 91, 43, 64)(17, 84, 36, 75, 27, 65)(19, 85, 37, 89, 41, 67)(20, 69, 21, 92, 44, 68)(28, 83, 35, 80, 32, 76)(29, 96, 48, 95, 47, 77) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73) MAP : A3.1167 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 32)(2, 27)(3, 20)(4, 26)(5, 30)(6, 28)(7, 22)(8, 29)(9, 19)(10, 25)(11, 21)(12, 31)(13, 17)(14, 18)(15, 23)(16, 24)(33, 57)(34, 63)(35, 50)(36, 59)(37, 54)(38, 61)(39, 56)(40, 52)(41, 62)(42, 53)(43, 55)(44, 49)(45, 58)(46, 60)(47, 64)(48, 51)(65, 86)(66, 89)(67, 81)(68, 96)(69, 84)(70, 91)(71, 82)(72, 95)(73, 93)(74, 88)(75, 83)(76, 85)(77, 87)(78, 90)(79, 94)(80, 92) MAP : A3.1168 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 32)(2, 27)(3, 20)(4, 26)(5, 30)(6, 28)(7, 22)(8, 29)(9, 19)(10, 25)(11, 21)(12, 31)(13, 17)(14, 18)(15, 23)(16, 24)(33, 60)(34, 51)(35, 64)(36, 56)(37, 58)(38, 53)(39, 59)(40, 55)(41, 49)(42, 61)(43, 52)(44, 62)(45, 54)(46, 57)(47, 50)(48, 63)(65, 90)(66, 92)(67, 94)(68, 82)(69, 87)(70, 88)(71, 96)(72, 83)(73, 85)(74, 91)(75, 95)(76, 93)(77, 84)(78, 86)(79, 81)(80, 89) MAP : A3.1169 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 32)(2, 27)(3, 20)(4, 26)(5, 30)(6, 28)(7, 22)(8, 29)(9, 19)(10, 25)(11, 21)(12, 31)(13, 17)(14, 18)(15, 23)(16, 24)(33, 58)(34, 60)(35, 62)(36, 50)(37, 55)(38, 56)(39, 64)(40, 51)(41, 53)(42, 59)(43, 63)(44, 61)(45, 52)(46, 54)(47, 49)(48, 57)(65, 92)(66, 83)(67, 96)(68, 88)(69, 90)(70, 85)(71, 91)(72, 87)(73, 81)(74, 93)(75, 84)(76, 94)(77, 86)(78, 89)(79, 82)(80, 95) MAP : A3.1170 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 21)(2, 17)(3, 28)(4, 31)(5, 24)(6, 20)(7, 19)(8, 18)(9, 22)(10, 23)(11, 32)(12, 26)(13, 27)(14, 29)(15, 25)(16, 30)(33, 52)(34, 54)(35, 53)(36, 62)(37, 63)(38, 64)(39, 49)(40, 57)(41, 59)(42, 50)(43, 60)(44, 56)(45, 51)(46, 55)(47, 61)(48, 58)(65, 90)(66, 92)(67, 94)(68, 82)(69, 87)(70, 88)(71, 96)(72, 83)(73, 85)(74, 91)(75, 95)(76, 93)(77, 84)(78, 86)(79, 81)(80, 89) MAP : A3.1171 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 3, 4 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^4, (x.2^-1 * x.1^-1)^3, (x.1 * x.2^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 51, 3, 54, 6, 49)(2, 85, 37, 58, 10, 50)(4, 88, 40, 57, 9, 52)(5, 82, 34, 61, 13, 53)(7, 60, 12, 94, 46, 55)(8, 84, 36, 64, 16, 56)(11, 71, 23, 78, 30, 59)(14, 92, 44, 75, 27, 62)(15, 67, 19, 81, 33, 63)(17, 86, 38, 79, 31, 65)(18, 90, 42, 77, 29, 66)(20, 89, 41, 80, 32, 68)(21, 93, 45, 74, 26, 69)(22, 83, 35, 95, 47, 70)(24, 96, 48, 73, 25, 72)(28, 87, 39, 91, 43, 76) L = (1, 92)(2, 84)(3, 68)(4, 62)(5, 80)(6, 69)(7, 85)(8, 60)(9, 81)(10, 65)(11, 56)(12, 89)(13, 83)(14, 96)(15, 66)(16, 70)(17, 61)(18, 54)(19, 91)(20, 79)(21, 63)(22, 57)(23, 49)(24, 51)(25, 50)(26, 78)(27, 77)(28, 74)(29, 55)(30, 82)(31, 72)(32, 90)(33, 64)(34, 76)(35, 58)(36, 93)(37, 75)(38, 94)(39, 52)(40, 53)(41, 59)(42, 88)(43, 86)(44, 95)(45, 73)(46, 67)(47, 71)(48, 87) MAP : A3.1172 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 29)(2, 30)(3, 25)(4, 19)(5, 27)(6, 23)(7, 31)(8, 32)(9, 26)(10, 20)(11, 18)(12, 22)(13, 24)(14, 21)(15, 28)(16, 17)(33, 57)(34, 63)(35, 50)(36, 59)(37, 54)(38, 61)(39, 56)(40, 52)(41, 62)(42, 53)(43, 55)(44, 49)(45, 58)(46, 60)(47, 64)(48, 51)(65, 95)(66, 84)(67, 88)(68, 93)(69, 89)(70, 94)(71, 85)(72, 86)(73, 96)(74, 81)(75, 90)(76, 82)(77, 92)(78, 83)(79, 91)(80, 87) MAP : A3.1173 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 29)(2, 30)(3, 25)(4, 19)(5, 27)(6, 23)(7, 31)(8, 32)(9, 26)(10, 20)(11, 18)(12, 22)(13, 24)(14, 21)(15, 28)(16, 17)(33, 60)(34, 51)(35, 64)(36, 56)(37, 58)(38, 53)(39, 59)(40, 55)(41, 49)(42, 61)(43, 52)(44, 62)(45, 54)(46, 57)(47, 50)(48, 63)(65, 83)(66, 87)(67, 91)(68, 85)(69, 92)(70, 81)(71, 93)(72, 90)(73, 82)(74, 94)(75, 86)(76, 96)(77, 89)(78, 95)(79, 88)(80, 84) MAP : A3.1174 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 32)(2, 27)(3, 20)(4, 26)(5, 30)(6, 28)(7, 22)(8, 29)(9, 19)(10, 25)(11, 21)(12, 31)(13, 17)(14, 18)(15, 23)(16, 24)(33, 63)(34, 52)(35, 56)(36, 61)(37, 57)(38, 62)(39, 53)(40, 54)(41, 64)(42, 49)(43, 58)(44, 50)(45, 60)(46, 51)(47, 59)(48, 55)(65, 84)(66, 86)(67, 85)(68, 94)(69, 95)(70, 96)(71, 81)(72, 89)(73, 91)(74, 82)(75, 92)(76, 88)(77, 83)(78, 87)(79, 93)(80, 90) MAP : A3.1175 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 4, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^3, (u.1 * u.2)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^3, (x.1 * x.2^-1)^3, (x.1 * x.2)^4 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 56, 8, 82, 34, 49)(2, 87, 39, 51, 3, 50)(4, 74, 26, 86, 38, 52)(5, 62, 14, 81, 33, 53)(6, 55, 7, 88, 40, 54)(9, 71, 23, 58, 10, 57)(11, 79, 31, 90, 42, 59)(12, 70, 22, 93, 45, 60)(13, 72, 24, 94, 46, 61)(15, 78, 30, 73, 25, 63)(16, 91, 43, 66, 18, 64)(17, 75, 27, 84, 36, 65)(19, 89, 41, 85, 37, 67)(20, 92, 44, 69, 21, 68)(28, 80, 32, 83, 35, 76)(29, 95, 47, 96, 48, 77) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72) MAP : A3.1176 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 19)(2, 23)(3, 27)(4, 21)(5, 28)(6, 17)(7, 29)(8, 26)(9, 18)(10, 30)(11, 22)(12, 32)(13, 25)(14, 31)(15, 24)(16, 20)(33, 61)(34, 62)(35, 57)(36, 51)(37, 59)(38, 55)(39, 63)(40, 64)(41, 58)(42, 52)(43, 50)(44, 54)(45, 56)(46, 53)(47, 60)(48, 49)(65, 92)(66, 83)(67, 96)(68, 88)(69, 90)(70, 85)(71, 91)(72, 87)(73, 81)(74, 93)(75, 84)(76, 94)(77, 86)(78, 89)(79, 82)(80, 95) MAP : A3.1177 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 28)(2, 19)(3, 32)(4, 24)(5, 26)(6, 21)(7, 27)(8, 23)(9, 17)(10, 29)(11, 20)(12, 30)(13, 22)(14, 25)(15, 18)(16, 31)(33, 61)(34, 62)(35, 57)(36, 51)(37, 59)(38, 55)(39, 63)(40, 64)(41, 58)(42, 52)(43, 50)(44, 54)(45, 56)(46, 53)(47, 60)(48, 49)(65, 83)(66, 87)(67, 91)(68, 85)(69, 92)(70, 81)(71, 93)(72, 90)(73, 82)(74, 94)(75, 86)(76, 96)(77, 89)(78, 95)(79, 88)(80, 84) MAP : A3.1178 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 28)(2, 19)(3, 32)(4, 24)(5, 26)(6, 21)(7, 27)(8, 23)(9, 17)(10, 29)(11, 20)(12, 30)(13, 22)(14, 25)(15, 18)(16, 31)(33, 64)(34, 59)(35, 52)(36, 58)(37, 62)(38, 60)(39, 54)(40, 61)(41, 51)(42, 57)(43, 53)(44, 63)(45, 49)(46, 50)(47, 55)(48, 56)(65, 90)(66, 92)(67, 94)(68, 82)(69, 87)(70, 88)(71, 96)(72, 83)(73, 85)(74, 91)(75, 95)(76, 93)(77, 84)(78, 86)(79, 81)(80, 89) MAP : A3.1179 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 26)(2, 28)(3, 30)(4, 18)(5, 23)(6, 24)(7, 32)(8, 19)(9, 21)(10, 27)(11, 31)(12, 29)(13, 20)(14, 22)(15, 17)(16, 25)(33, 50)(34, 56)(35, 55)(36, 54)(37, 49)(38, 57)(39, 58)(40, 53)(41, 63)(42, 60)(43, 61)(44, 51)(45, 62)(46, 64)(47, 52)(48, 59)(65, 89)(66, 95)(67, 82)(68, 91)(69, 86)(70, 93)(71, 88)(72, 84)(73, 94)(74, 85)(75, 87)(76, 81)(77, 90)(78, 92)(79, 96)(80, 83) MAP : A3.1180 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 26)(2, 28)(3, 30)(4, 18)(5, 23)(6, 24)(7, 32)(8, 19)(9, 21)(10, 27)(11, 31)(12, 29)(13, 20)(14, 22)(15, 17)(16, 25)(33, 53)(34, 49)(35, 60)(36, 63)(37, 56)(38, 52)(39, 51)(40, 50)(41, 54)(42, 55)(43, 64)(44, 58)(45, 59)(46, 61)(47, 57)(48, 62)(65, 84)(66, 86)(67, 85)(68, 94)(69, 95)(70, 96)(71, 81)(72, 89)(73, 91)(74, 82)(75, 92)(76, 88)(77, 83)(78, 87)(79, 93)(80, 90) MAP : A3.1181 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 9)(2, 3)(4, 8)(5, 7)(6, 10)(11, 12) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 2, 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1, u.1 * u.2^-1 * u.3^-1, u.4 * u.5^-1 * u.6^-1, (u.5 * u.1^-1)^2, u.2^4, u.6^4, (u.3 * u.4^-1)^2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.2 * x.3, x.6^-1 * x.3^-1, x.6 * x.2^-1, x.4 * x.5 * x.2^-1, x.3 * x.5 * x.4, x.4 * x.5^-1 * x.6^-1, (x.5 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.2^4, x.6^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 24)(10, 21)(11, 20)(12, 18)(13, 19)(14, 23)(15, 17)(16, 22)(25, 63)(26, 60)(27, 61)(28, 59)(29, 58)(30, 64)(31, 62)(32, 57)(33, 52)(34, 55)(35, 56)(36, 54)(37, 49)(38, 53)(39, 51)(40, 50)(41, 75)(42, 78)(43, 73)(44, 80)(45, 79)(46, 74)(47, 77)(48, 76)(81, 96)(82, 93)(83, 92)(84, 90)(85, 91)(86, 95)(87, 89)(88, 94) MAP : A3.1182 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 26)(2, 28)(3, 30)(4, 18)(5, 23)(6, 24)(7, 32)(8, 19)(9, 21)(10, 27)(11, 31)(12, 29)(13, 20)(14, 22)(15, 17)(16, 25)(33, 55)(34, 58)(35, 61)(36, 49)(37, 51)(38, 50)(39, 62)(40, 60)(41, 56)(42, 64)(43, 57)(44, 59)(45, 63)(46, 52)(47, 53)(48, 54)(65, 93)(66, 94)(67, 89)(68, 83)(69, 91)(70, 87)(71, 95)(72, 96)(73, 90)(74, 84)(75, 82)(76, 86)(77, 88)(78, 85)(79, 92)(80, 81) MAP : A3.1183 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 26)(2, 28)(3, 30)(4, 18)(5, 23)(6, 24)(7, 32)(8, 19)(9, 21)(10, 27)(11, 31)(12, 29)(13, 20)(14, 22)(15, 17)(16, 25)(33, 57)(34, 63)(35, 50)(36, 59)(37, 54)(38, 61)(39, 56)(40, 52)(41, 62)(42, 53)(43, 55)(44, 49)(45, 58)(46, 60)(47, 64)(48, 51)(65, 82)(66, 88)(67, 87)(68, 86)(69, 81)(70, 89)(71, 90)(72, 85)(73, 95)(74, 92)(75, 93)(76, 83)(77, 94)(78, 96)(79, 84)(80, 91) MAP : A3.1184 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 26)(2, 28)(3, 30)(4, 18)(5, 23)(6, 24)(7, 32)(8, 19)(9, 21)(10, 27)(11, 31)(12, 29)(13, 20)(14, 22)(15, 17)(16, 25)(33, 60)(34, 51)(35, 64)(36, 56)(37, 58)(38, 53)(39, 59)(40, 55)(41, 49)(42, 61)(43, 52)(44, 62)(45, 54)(46, 57)(47, 50)(48, 63)(65, 96)(66, 91)(67, 84)(68, 90)(69, 94)(70, 92)(71, 86)(72, 93)(73, 83)(74, 89)(75, 85)(76, 95)(77, 81)(78, 82)(79, 87)(80, 88) MAP : A3.1185 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 19)(2, 23)(3, 27)(4, 21)(5, 28)(6, 17)(7, 29)(8, 26)(9, 18)(10, 30)(11, 22)(12, 32)(13, 25)(14, 31)(15, 24)(16, 20)(33, 52)(34, 54)(35, 53)(36, 62)(37, 63)(38, 64)(39, 49)(40, 57)(41, 59)(42, 50)(43, 60)(44, 56)(45, 51)(46, 55)(47, 61)(48, 58)(65, 82)(66, 88)(67, 87)(68, 86)(69, 81)(70, 89)(71, 90)(72, 85)(73, 95)(74, 92)(75, 93)(76, 83)(77, 94)(78, 96)(79, 84)(80, 91) MAP : A3.1186 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 19)(2, 23)(3, 27)(4, 21)(5, 28)(6, 17)(7, 29)(8, 26)(9, 18)(10, 30)(11, 22)(12, 32)(13, 25)(14, 31)(15, 24)(16, 20)(33, 55)(34, 58)(35, 61)(36, 49)(37, 51)(38, 50)(39, 62)(40, 60)(41, 56)(42, 64)(43, 57)(44, 59)(45, 63)(46, 52)(47, 53)(48, 54)(65, 96)(66, 91)(67, 84)(68, 90)(69, 94)(70, 92)(71, 86)(72, 93)(73, 83)(74, 89)(75, 85)(76, 95)(77, 81)(78, 82)(79, 87)(80, 88) MAP : A3.1187 NOTES : type I, non-Cayley, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 3 ], faces: [ 4, 3 ] UNIGROUP : < u.1, u.2 | u.2^3, u.1^3, (u.1 * u.2)^4 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.2^3, x.1^3, (x.1 * x.2^-1)^3, (x.1 * x.2)^4 > SCHREIER VEC. : (x.1, x.1^-1)^3 LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 69, 21, 78, 30, 49)(2, 65, 17, 72, 24, 50)(3, 92, 44, 96, 48, 51)(4, 81, 33, 91, 43, 52)(5, 83, 35, 57, 9, 53)(6, 68, 20, 90, 42, 54)(7, 67, 19, 66, 18, 55)(8, 70, 22, 71, 23, 56)(10, 75, 27, 95, 47, 58)(11, 82, 34, 80, 32, 59)(12, 85, 37, 84, 36, 60)(13, 76, 28, 86, 38, 61)(14, 77, 29, 88, 40, 62)(15, 64, 16, 93, 45, 63)(25, 87, 39, 74, 26, 73)(31, 94, 46, 89, 41, 79) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72) MAP : A3.1188 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 20)(2, 22)(3, 21)(4, 30)(5, 31)(6, 32)(7, 17)(8, 25)(9, 27)(10, 18)(11, 28)(12, 24)(13, 19)(14, 23)(15, 29)(16, 26)(33, 51)(34, 55)(35, 59)(36, 53)(37, 60)(38, 49)(39, 61)(40, 58)(41, 50)(42, 62)(43, 54)(44, 64)(45, 57)(46, 63)(47, 56)(48, 52)(65, 82)(66, 88)(67, 87)(68, 86)(69, 81)(70, 89)(71, 90)(72, 85)(73, 95)(74, 92)(75, 93)(76, 83)(77, 94)(78, 96)(79, 84)(80, 91) MAP : A3.1189 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 20)(2, 22)(3, 21)(4, 30)(5, 31)(6, 32)(7, 17)(8, 25)(9, 27)(10, 18)(11, 28)(12, 24)(13, 19)(14, 23)(15, 29)(16, 26)(33, 54)(34, 57)(35, 49)(36, 64)(37, 52)(38, 59)(39, 50)(40, 63)(41, 61)(42, 56)(43, 51)(44, 53)(45, 55)(46, 58)(47, 62)(48, 60)(65, 93)(66, 94)(67, 89)(68, 83)(69, 91)(70, 87)(71, 95)(72, 96)(73, 90)(74, 84)(75, 82)(76, 86)(77, 88)(78, 85)(79, 92)(80, 81) MAP : A3.1190 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 20)(2, 22)(3, 21)(4, 30)(5, 31)(6, 32)(7, 17)(8, 25)(9, 27)(10, 18)(11, 28)(12, 24)(13, 19)(14, 23)(15, 29)(16, 26)(33, 58)(34, 60)(35, 62)(36, 50)(37, 55)(38, 56)(39, 64)(40, 51)(41, 53)(42, 59)(43, 63)(44, 61)(45, 52)(46, 54)(47, 49)(48, 57)(65, 85)(66, 81)(67, 92)(68, 95)(69, 88)(70, 84)(71, 83)(72, 82)(73, 86)(74, 87)(75, 96)(76, 90)(77, 91)(78, 93)(79, 89)(80, 94) MAP : A3.1191 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 20)(2, 22)(3, 21)(4, 30)(5, 31)(6, 32)(7, 17)(8, 25)(9, 27)(10, 18)(11, 28)(12, 24)(13, 19)(14, 23)(15, 29)(16, 26)(33, 63)(34, 52)(35, 56)(36, 61)(37, 57)(38, 62)(39, 53)(40, 54)(41, 64)(42, 49)(43, 58)(44, 50)(45, 60)(46, 51)(47, 59)(48, 55)(65, 96)(66, 91)(67, 84)(68, 90)(69, 94)(70, 92)(71, 86)(72, 93)(73, 83)(74, 89)(75, 85)(76, 95)(77, 81)(78, 82)(79, 87)(80, 88) MAP : A3.1192 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 20)(2, 22)(3, 21)(4, 30)(5, 31)(6, 32)(7, 17)(8, 25)(9, 27)(10, 18)(11, 28)(12, 24)(13, 19)(14, 23)(15, 29)(16, 26)(33, 61)(34, 62)(35, 57)(36, 51)(37, 59)(38, 55)(39, 63)(40, 64)(41, 58)(42, 52)(43, 50)(44, 54)(45, 56)(46, 53)(47, 60)(48, 49)(65, 86)(66, 89)(67, 81)(68, 96)(69, 84)(70, 91)(71, 82)(72, 95)(73, 93)(74, 88)(75, 83)(76, 85)(77, 87)(78, 90)(79, 94)(80, 92) MAP : A3.1193 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 20)(2, 22)(3, 21)(4, 30)(5, 31)(6, 32)(7, 17)(8, 25)(9, 27)(10, 18)(11, 28)(12, 24)(13, 19)(14, 23)(15, 29)(16, 26)(33, 64)(34, 59)(35, 52)(36, 58)(37, 62)(38, 60)(39, 54)(40, 61)(41, 51)(42, 57)(43, 53)(44, 63)(45, 49)(46, 50)(47, 55)(48, 56)(65, 95)(66, 84)(67, 88)(68, 93)(69, 89)(70, 94)(71, 85)(72, 86)(73, 96)(74, 81)(75, 90)(76, 82)(77, 92)(78, 83)(79, 91)(80, 87) MAP : A3.1194 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 23)(2, 26)(3, 29)(4, 17)(5, 19)(6, 18)(7, 30)(8, 28)(9, 24)(10, 32)(11, 25)(12, 27)(13, 31)(14, 20)(15, 21)(16, 22)(33, 50)(34, 56)(35, 55)(36, 54)(37, 49)(38, 57)(39, 58)(40, 53)(41, 63)(42, 60)(43, 61)(44, 51)(45, 62)(46, 64)(47, 52)(48, 59)(65, 95)(66, 84)(67, 88)(68, 93)(69, 89)(70, 94)(71, 85)(72, 86)(73, 96)(74, 81)(75, 90)(76, 82)(77, 92)(78, 83)(79, 91)(80, 87) MAP : A3.1195 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 23)(2, 26)(3, 29)(4, 17)(5, 19)(6, 18)(7, 30)(8, 28)(9, 24)(10, 32)(11, 25)(12, 27)(13, 31)(14, 20)(15, 21)(16, 22)(33, 53)(34, 49)(35, 60)(36, 63)(37, 56)(38, 52)(39, 51)(40, 50)(41, 54)(42, 55)(43, 64)(44, 58)(45, 59)(46, 61)(47, 57)(48, 62)(65, 86)(66, 89)(67, 81)(68, 96)(69, 84)(70, 91)(71, 82)(72, 95)(73, 93)(74, 88)(75, 83)(76, 85)(77, 87)(78, 90)(79, 94)(80, 92) MAP : A3.1196 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 18)(2, 24)(3, 23)(4, 22)(5, 17)(6, 25)(7, 26)(8, 21)(9, 31)(10, 28)(11, 29)(12, 19)(13, 30)(14, 32)(15, 20)(16, 27)(33, 51)(34, 55)(35, 59)(36, 53)(37, 60)(38, 49)(39, 61)(40, 58)(41, 50)(42, 62)(43, 54)(44, 64)(45, 57)(46, 63)(47, 56)(48, 52)(65, 84)(66, 86)(67, 85)(68, 94)(69, 95)(70, 96)(71, 81)(72, 89)(73, 91)(74, 82)(75, 92)(76, 88)(77, 83)(78, 87)(79, 93)(80, 90) MAP : A3.1197 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 18)(2, 24)(3, 23)(4, 22)(5, 17)(6, 25)(7, 26)(8, 21)(9, 31)(10, 28)(11, 29)(12, 19)(13, 30)(14, 32)(15, 20)(16, 27)(33, 54)(34, 57)(35, 49)(36, 64)(37, 52)(38, 59)(39, 50)(40, 63)(41, 61)(42, 56)(43, 51)(44, 53)(45, 55)(46, 58)(47, 62)(48, 60)(65, 92)(66, 83)(67, 96)(68, 88)(69, 90)(70, 85)(71, 91)(72, 87)(73, 81)(74, 93)(75, 84)(76, 94)(77, 86)(78, 89)(79, 82)(80, 95) MAP : A3.1198 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 18)(2, 24)(3, 23)(4, 22)(5, 17)(6, 25)(7, 26)(8, 21)(9, 31)(10, 28)(11, 29)(12, 19)(13, 30)(14, 32)(15, 20)(16, 27)(33, 52)(34, 54)(35, 53)(36, 62)(37, 63)(38, 64)(39, 49)(40, 57)(41, 59)(42, 50)(43, 60)(44, 56)(45, 51)(46, 55)(47, 61)(48, 58)(65, 83)(66, 87)(67, 91)(68, 85)(69, 92)(70, 81)(71, 93)(72, 90)(73, 82)(74, 94)(75, 86)(76, 96)(77, 89)(78, 95)(79, 88)(80, 84) MAP : A3.1199 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 18)(2, 24)(3, 23)(4, 22)(5, 17)(6, 25)(7, 26)(8, 21)(9, 31)(10, 28)(11, 29)(12, 19)(13, 30)(14, 32)(15, 20)(16, 27)(33, 55)(34, 58)(35, 61)(36, 49)(37, 51)(38, 50)(39, 62)(40, 60)(41, 56)(42, 64)(43, 57)(44, 59)(45, 63)(46, 52)(47, 53)(48, 54)(65, 95)(66, 84)(67, 88)(68, 93)(69, 89)(70, 94)(71, 85)(72, 86)(73, 96)(74, 81)(75, 90)(76, 82)(77, 92)(78, 83)(79, 91)(80, 87) MAP : A3.1200 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 18)(2, 24)(3, 23)(4, 22)(5, 17)(6, 25)(7, 26)(8, 21)(9, 31)(10, 28)(11, 29)(12, 19)(13, 30)(14, 32)(15, 20)(16, 27)(33, 57)(34, 63)(35, 50)(36, 59)(37, 54)(38, 61)(39, 56)(40, 52)(41, 62)(42, 53)(43, 55)(44, 49)(45, 58)(46, 60)(47, 64)(48, 51)(65, 90)(66, 92)(67, 94)(68, 82)(69, 87)(70, 88)(71, 96)(72, 83)(73, 85)(74, 91)(75, 95)(76, 93)(77, 84)(78, 86)(79, 81)(80, 89) MAP : A3.1201 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 18)(2, 24)(3, 23)(4, 22)(5, 17)(6, 25)(7, 26)(8, 21)(9, 31)(10, 28)(11, 29)(12, 19)(13, 30)(14, 32)(15, 20)(16, 27)(33, 60)(34, 51)(35, 64)(36, 56)(37, 58)(38, 53)(39, 59)(40, 55)(41, 49)(42, 61)(43, 52)(44, 62)(45, 54)(46, 57)(47, 50)(48, 63)(65, 86)(66, 89)(67, 81)(68, 96)(69, 84)(70, 91)(71, 82)(72, 95)(73, 93)(74, 88)(75, 83)(76, 85)(77, 87)(78, 90)(79, 94)(80, 92) MAP : A3.1202 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 18)(2, 24)(3, 23)(4, 22)(5, 17)(6, 25)(7, 26)(8, 21)(9, 31)(10, 28)(11, 29)(12, 19)(13, 30)(14, 32)(15, 20)(16, 27)(33, 58)(34, 60)(35, 62)(36, 50)(37, 55)(38, 56)(39, 64)(40, 51)(41, 53)(42, 59)(43, 63)(44, 61)(45, 52)(46, 54)(47, 49)(48, 57)(65, 89)(66, 95)(67, 82)(68, 91)(69, 86)(70, 93)(71, 88)(72, 84)(73, 94)(74, 85)(75, 87)(76, 81)(77, 90)(78, 92)(79, 96)(80, 83) MAP : A3.1203 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 18)(2, 24)(3, 23)(4, 22)(5, 17)(6, 25)(7, 26)(8, 21)(9, 31)(10, 28)(11, 29)(12, 19)(13, 30)(14, 32)(15, 20)(16, 27)(33, 63)(34, 52)(35, 56)(36, 61)(37, 57)(38, 62)(39, 53)(40, 54)(41, 64)(42, 49)(43, 58)(44, 50)(45, 60)(46, 51)(47, 59)(48, 55)(65, 87)(66, 90)(67, 93)(68, 81)(69, 83)(70, 82)(71, 94)(72, 92)(73, 88)(74, 96)(75, 89)(76, 91)(77, 95)(78, 84)(79, 85)(80, 86) MAP : A3.1204 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 21)(2, 17)(3, 28)(4, 31)(5, 24)(6, 20)(7, 19)(8, 18)(9, 22)(10, 23)(11, 32)(12, 26)(13, 27)(14, 29)(15, 25)(16, 30)(33, 51)(34, 55)(35, 59)(36, 53)(37, 60)(38, 49)(39, 61)(40, 58)(41, 50)(42, 62)(43, 54)(44, 64)(45, 57)(46, 63)(47, 56)(48, 52)(65, 89)(66, 95)(67, 82)(68, 91)(69, 86)(70, 93)(71, 88)(72, 84)(73, 94)(74, 85)(75, 87)(76, 81)(77, 90)(78, 92)(79, 96)(80, 83) MAP : A3.1205 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 21)(2, 17)(3, 28)(4, 31)(5, 24)(6, 20)(7, 19)(8, 18)(9, 22)(10, 23)(11, 32)(12, 26)(13, 27)(14, 29)(15, 25)(16, 30)(33, 54)(34, 57)(35, 49)(36, 64)(37, 52)(38, 59)(39, 50)(40, 63)(41, 61)(42, 56)(43, 51)(44, 53)(45, 55)(46, 58)(47, 62)(48, 60)(65, 87)(66, 90)(67, 93)(68, 81)(69, 83)(70, 82)(71, 94)(72, 92)(73, 88)(74, 96)(75, 89)(76, 91)(77, 95)(78, 84)(79, 85)(80, 86) MAP : A3.1206 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 25)(2, 31)(3, 18)(4, 27)(5, 22)(6, 29)(7, 24)(8, 20)(9, 30)(10, 21)(11, 23)(12, 17)(13, 26)(14, 28)(15, 32)(16, 19)(33, 51)(34, 55)(35, 59)(36, 53)(37, 60)(38, 49)(39, 61)(40, 58)(41, 50)(42, 62)(43, 54)(44, 64)(45, 57)(46, 63)(47, 56)(48, 52)(65, 85)(66, 81)(67, 92)(68, 95)(69, 88)(70, 84)(71, 83)(72, 82)(73, 86)(74, 87)(75, 96)(76, 90)(77, 91)(78, 93)(79, 89)(80, 94) MAP : A3.1207 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 21)(2, 17)(3, 28)(4, 31)(5, 24)(6, 20)(7, 19)(8, 18)(9, 22)(10, 23)(11, 32)(12, 26)(13, 27)(14, 29)(15, 25)(16, 30)(33, 55)(34, 58)(35, 61)(36, 49)(37, 51)(38, 50)(39, 62)(40, 60)(41, 56)(42, 64)(43, 57)(44, 59)(45, 63)(46, 52)(47, 53)(48, 54)(65, 86)(66, 89)(67, 81)(68, 96)(69, 84)(70, 91)(71, 82)(72, 95)(73, 93)(74, 88)(75, 83)(76, 85)(77, 87)(78, 90)(79, 94)(80, 92) MAP : A3.1208 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 25)(2, 31)(3, 18)(4, 27)(5, 22)(6, 29)(7, 24)(8, 20)(9, 30)(10, 21)(11, 23)(12, 17)(13, 26)(14, 28)(15, 32)(16, 19)(33, 58)(34, 60)(35, 62)(36, 50)(37, 55)(38, 56)(39, 64)(40, 51)(41, 53)(42, 59)(43, 63)(44, 61)(45, 52)(46, 54)(47, 49)(48, 57)(65, 82)(66, 88)(67, 87)(68, 86)(69, 81)(70, 89)(71, 90)(72, 85)(73, 95)(74, 92)(75, 93)(76, 83)(77, 94)(78, 96)(79, 84)(80, 91) MAP : A3.1209 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 25)(2, 31)(3, 18)(4, 27)(5, 22)(6, 29)(7, 24)(8, 20)(9, 30)(10, 21)(11, 23)(12, 17)(13, 26)(14, 28)(15, 32)(16, 19)(33, 63)(34, 52)(35, 56)(36, 61)(37, 57)(38, 62)(39, 53)(40, 54)(41, 64)(42, 49)(43, 58)(44, 50)(45, 60)(46, 51)(47, 59)(48, 55)(65, 93)(66, 94)(67, 89)(68, 83)(69, 91)(70, 87)(71, 95)(72, 96)(73, 90)(74, 84)(75, 82)(76, 86)(77, 88)(78, 85)(79, 92)(80, 81) MAP : A3.1210 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 25)(2, 31)(3, 18)(4, 27)(5, 22)(6, 29)(7, 24)(8, 20)(9, 30)(10, 21)(11, 23)(12, 17)(13, 26)(14, 28)(15, 32)(16, 19)(33, 61)(34, 62)(35, 57)(36, 51)(37, 59)(38, 55)(39, 63)(40, 64)(41, 58)(42, 52)(43, 50)(44, 54)(45, 56)(46, 53)(47, 60)(48, 49)(65, 95)(66, 84)(67, 88)(68, 93)(69, 89)(70, 94)(71, 85)(72, 86)(73, 96)(74, 81)(75, 90)(76, 82)(77, 92)(78, 83)(79, 91)(80, 87) MAP : A3.1211 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 21)(2, 17)(3, 28)(4, 31)(5, 24)(6, 20)(7, 19)(8, 18)(9, 22)(10, 23)(11, 32)(12, 26)(13, 27)(14, 29)(15, 25)(16, 30)(33, 63)(34, 52)(35, 56)(36, 61)(37, 57)(38, 62)(39, 53)(40, 54)(41, 64)(42, 49)(43, 58)(44, 50)(45, 60)(46, 51)(47, 59)(48, 55)(65, 92)(66, 83)(67, 96)(68, 88)(69, 90)(70, 85)(71, 91)(72, 87)(73, 81)(74, 93)(75, 84)(76, 94)(77, 86)(78, 89)(79, 82)(80, 95) MAP : A3.1212 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 19)(2, 23)(3, 27)(4, 21)(5, 28)(6, 17)(7, 29)(8, 26)(9, 18)(10, 30)(11, 22)(12, 32)(13, 25)(14, 31)(15, 24)(16, 20)(33, 50)(34, 56)(35, 55)(36, 54)(37, 49)(38, 57)(39, 58)(40, 53)(41, 63)(42, 60)(43, 61)(44, 51)(45, 62)(46, 64)(47, 52)(48, 59)(65, 84)(66, 86)(67, 85)(68, 94)(69, 95)(70, 96)(71, 81)(72, 89)(73, 91)(74, 82)(75, 92)(76, 88)(77, 83)(78, 87)(79, 93)(80, 90) MAP : A3.1213 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 19)(2, 23)(3, 27)(4, 21)(5, 28)(6, 17)(7, 29)(8, 26)(9, 18)(10, 30)(11, 22)(12, 32)(13, 25)(14, 31)(15, 24)(16, 20)(33, 53)(34, 49)(35, 60)(36, 63)(37, 56)(38, 52)(39, 51)(40, 50)(41, 54)(42, 55)(43, 64)(44, 58)(45, 59)(46, 61)(47, 57)(48, 62)(65, 89)(66, 95)(67, 82)(68, 91)(69, 86)(70, 93)(71, 88)(72, 84)(73, 94)(74, 85)(75, 87)(76, 81)(77, 90)(78, 92)(79, 96)(80, 83) MAP : A3.1214 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 28)(2, 19)(3, 32)(4, 24)(5, 26)(6, 21)(7, 27)(8, 23)(9, 17)(10, 29)(11, 20)(12, 30)(13, 22)(14, 25)(15, 18)(16, 31)(33, 51)(34, 55)(35, 59)(36, 53)(37, 60)(38, 49)(39, 61)(40, 58)(41, 50)(42, 62)(43, 54)(44, 64)(45, 57)(46, 63)(47, 56)(48, 52)(65, 93)(66, 94)(67, 89)(68, 83)(69, 91)(70, 87)(71, 95)(72, 96)(73, 90)(74, 84)(75, 82)(76, 86)(77, 88)(78, 85)(79, 92)(80, 81) MAP : A3.1215 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 28)(2, 19)(3, 32)(4, 24)(5, 26)(6, 21)(7, 27)(8, 23)(9, 17)(10, 29)(11, 20)(12, 30)(13, 22)(14, 25)(15, 18)(16, 31)(33, 54)(34, 57)(35, 49)(36, 64)(37, 52)(38, 59)(39, 50)(40, 63)(41, 61)(42, 56)(43, 51)(44, 53)(45, 55)(46, 58)(47, 62)(48, 60)(65, 82)(66, 88)(67, 87)(68, 86)(69, 81)(70, 89)(71, 90)(72, 85)(73, 95)(74, 92)(75, 93)(76, 83)(77, 94)(78, 96)(79, 84)(80, 91) MAP : A3.1216 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 19)(2, 23)(3, 27)(4, 21)(5, 28)(6, 17)(7, 29)(8, 26)(9, 18)(10, 30)(11, 22)(12, 32)(13, 25)(14, 31)(15, 24)(16, 20)(33, 57)(34, 63)(35, 50)(36, 59)(37, 54)(38, 61)(39, 56)(40, 52)(41, 62)(42, 53)(43, 55)(44, 49)(45, 58)(46, 60)(47, 64)(48, 51)(65, 85)(66, 81)(67, 92)(68, 95)(69, 88)(70, 84)(71, 83)(72, 82)(73, 86)(74, 87)(75, 96)(76, 90)(77, 91)(78, 93)(79, 89)(80, 94) MAP : A3.1217 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 19)(2, 23)(3, 27)(4, 21)(5, 28)(6, 17)(7, 29)(8, 26)(9, 18)(10, 30)(11, 22)(12, 32)(13, 25)(14, 31)(15, 24)(16, 20)(33, 60)(34, 51)(35, 64)(36, 56)(37, 58)(38, 53)(39, 59)(40, 55)(41, 49)(42, 61)(43, 52)(44, 62)(45, 54)(46, 57)(47, 50)(48, 63)(65, 93)(66, 94)(67, 89)(68, 83)(69, 91)(70, 87)(71, 95)(72, 96)(73, 90)(74, 84)(75, 82)(76, 86)(77, 88)(78, 85)(79, 92)(80, 81) MAP : A3.1218 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 9)(2, 3)(4, 8)(5, 7)(6, 10)(11, 12) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 2, 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1, u.1 * u.2^-1 * u.3^-1, u.4 * u.5^-1 * u.6^-1, (u.5 * u.1^-1)^2, u.2^4, u.6^4, (u.3 * u.4^-1)^2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.2 * x.3, x.6^-1 * x.3^-1, x.6 * x.2^-1, x.4 * x.5 * x.2^-1, x.3 * x.5 * x.4, x.4 * x.5^-1 * x.6^-1, (x.5 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.2^4, x.6^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 21)(10, 24)(11, 23)(12, 17)(13, 22)(14, 20)(15, 18)(16, 19)(25, 60)(26, 63)(27, 64)(28, 62)(29, 57)(30, 61)(31, 59)(32, 58)(33, 55)(34, 52)(35, 53)(36, 51)(37, 50)(38, 56)(39, 54)(40, 49)(41, 75)(42, 78)(43, 73)(44, 80)(45, 79)(46, 74)(47, 77)(48, 76)(81, 93)(82, 96)(83, 95)(84, 89)(85, 94)(86, 92)(87, 90)(88, 91) MAP : A3.1219 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 9)(2, 3)(4, 8)(5, 7)(6, 10)(11, 12) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 2, 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1, u.1 * u.2^-1 * u.3^-1, u.4 * u.5^-1 * u.6^-1, (u.5 * u.1^-1)^2, u.2^4, u.6^4, (u.3 * u.4^-1)^2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.2 * x.3, x.6^-1 * x.3^-1, x.6 * x.2^-1, x.4 * x.5 * x.2^-1, x.3 * x.5 * x.4, x.4 * x.5^-1 * x.6^-1, (x.5 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.2^4, x.6^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 21)(10, 24)(11, 23)(12, 17)(13, 22)(14, 20)(15, 18)(16, 19)(25, 60)(26, 63)(27, 64)(28, 62)(29, 57)(30, 61)(31, 59)(32, 58)(33, 56)(34, 53)(35, 52)(36, 50)(37, 51)(38, 55)(39, 49)(40, 54)(41, 74)(42, 73)(43, 78)(44, 79)(45, 80)(46, 75)(47, 76)(48, 77)(81, 93)(82, 96)(83, 95)(84, 89)(85, 94)(86, 92)(87, 90)(88, 91) MAP : A3.1220 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 22)(2, 25)(3, 17)(4, 32)(5, 20)(6, 27)(7, 18)(8, 31)(9, 29)(10, 24)(11, 19)(12, 21)(13, 23)(14, 26)(15, 30)(16, 28)(33, 50)(34, 56)(35, 55)(36, 54)(37, 49)(38, 57)(39, 58)(40, 53)(41, 63)(42, 60)(43, 61)(44, 51)(45, 62)(46, 64)(47, 52)(48, 59)(65, 92)(66, 83)(67, 96)(68, 88)(69, 90)(70, 85)(71, 91)(72, 87)(73, 81)(74, 93)(75, 84)(76, 94)(77, 86)(78, 89)(79, 82)(80, 95) MAP : A3.1221 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 22)(2, 25)(3, 17)(4, 32)(5, 20)(6, 27)(7, 18)(8, 31)(9, 29)(10, 24)(11, 19)(12, 21)(13, 23)(14, 26)(15, 30)(16, 28)(33, 53)(34, 49)(35, 60)(36, 63)(37, 56)(38, 52)(39, 51)(40, 50)(41, 54)(42, 55)(43, 64)(44, 58)(45, 59)(46, 61)(47, 57)(48, 62)(65, 87)(66, 90)(67, 93)(68, 81)(69, 83)(70, 82)(71, 94)(72, 92)(73, 88)(74, 96)(75, 89)(76, 91)(77, 95)(78, 84)(79, 85)(80, 86) MAP : A3.1222 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 22)(2, 25)(3, 17)(4, 32)(5, 20)(6, 27)(7, 18)(8, 31)(9, 29)(10, 24)(11, 19)(12, 21)(13, 23)(14, 26)(15, 30)(16, 28)(33, 52)(34, 54)(35, 53)(36, 62)(37, 63)(38, 64)(39, 49)(40, 57)(41, 59)(42, 50)(43, 60)(44, 56)(45, 51)(46, 55)(47, 61)(48, 58)(65, 93)(66, 94)(67, 89)(68, 83)(69, 91)(70, 87)(71, 95)(72, 96)(73, 90)(74, 84)(75, 82)(76, 86)(77, 88)(78, 85)(79, 92)(80, 81) MAP : A3.1223 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 22)(2, 25)(3, 17)(4, 32)(5, 20)(6, 27)(7, 18)(8, 31)(9, 29)(10, 24)(11, 19)(12, 21)(13, 23)(14, 26)(15, 30)(16, 28)(33, 55)(34, 58)(35, 61)(36, 49)(37, 51)(38, 50)(39, 62)(40, 60)(41, 56)(42, 64)(43, 57)(44, 59)(45, 63)(46, 52)(47, 53)(48, 54)(65, 85)(66, 81)(67, 92)(68, 95)(69, 88)(70, 84)(71, 83)(72, 82)(73, 86)(74, 87)(75, 96)(76, 90)(77, 91)(78, 93)(79, 89)(80, 94) MAP : A3.1224 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 22)(2, 25)(3, 17)(4, 32)(5, 20)(6, 27)(7, 18)(8, 31)(9, 29)(10, 24)(11, 19)(12, 21)(13, 23)(14, 26)(15, 30)(16, 28)(33, 57)(34, 63)(35, 50)(36, 59)(37, 54)(38, 61)(39, 56)(40, 52)(41, 62)(42, 53)(43, 55)(44, 49)(45, 58)(46, 60)(47, 64)(48, 51)(65, 96)(66, 91)(67, 84)(68, 90)(69, 94)(70, 92)(71, 86)(72, 93)(73, 83)(74, 89)(75, 85)(76, 95)(77, 81)(78, 82)(79, 87)(80, 88) MAP : A3.1225 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 22)(2, 25)(3, 17)(4, 32)(5, 20)(6, 27)(7, 18)(8, 31)(9, 29)(10, 24)(11, 19)(12, 21)(13, 23)(14, 26)(15, 30)(16, 28)(33, 60)(34, 51)(35, 64)(36, 56)(37, 58)(38, 53)(39, 59)(40, 55)(41, 49)(42, 61)(43, 52)(44, 62)(45, 54)(46, 57)(47, 50)(48, 63)(65, 82)(66, 88)(67, 87)(68, 86)(69, 81)(70, 89)(71, 90)(72, 85)(73, 95)(74, 92)(75, 93)(76, 83)(77, 94)(78, 96)(79, 84)(80, 91) MAP : A3.1226 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 22)(2, 25)(3, 17)(4, 32)(5, 20)(6, 27)(7, 18)(8, 31)(9, 29)(10, 24)(11, 19)(12, 21)(13, 23)(14, 26)(15, 30)(16, 28)(33, 61)(34, 62)(35, 57)(36, 51)(37, 59)(38, 55)(39, 63)(40, 64)(41, 58)(42, 52)(43, 50)(44, 54)(45, 56)(46, 53)(47, 60)(48, 49)(65, 84)(66, 86)(67, 85)(68, 94)(69, 95)(70, 96)(71, 81)(72, 89)(73, 91)(74, 82)(75, 92)(76, 88)(77, 83)(78, 87)(79, 93)(80, 90) MAP : A3.1227 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 22)(2, 25)(3, 17)(4, 32)(5, 20)(6, 27)(7, 18)(8, 31)(9, 29)(10, 24)(11, 19)(12, 21)(13, 23)(14, 26)(15, 30)(16, 28)(33, 64)(34, 59)(35, 52)(36, 58)(37, 62)(38, 60)(39, 54)(40, 61)(41, 51)(42, 57)(43, 53)(44, 63)(45, 49)(46, 50)(47, 55)(48, 56)(65, 89)(66, 95)(67, 82)(68, 91)(69, 86)(70, 93)(71, 88)(72, 84)(73, 94)(74, 85)(75, 87)(76, 81)(77, 90)(78, 92)(79, 96)(80, 83) MAP : A3.1228 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 20)(2, 22)(3, 21)(4, 30)(5, 31)(6, 32)(7, 17)(8, 25)(9, 27)(10, 18)(11, 28)(12, 24)(13, 19)(14, 23)(15, 29)(16, 26)(33, 50)(34, 56)(35, 55)(36, 54)(37, 49)(38, 57)(39, 58)(40, 53)(41, 63)(42, 60)(43, 61)(44, 51)(45, 62)(46, 64)(47, 52)(48, 59)(65, 83)(66, 87)(67, 91)(68, 85)(69, 92)(70, 81)(71, 93)(72, 90)(73, 82)(74, 94)(75, 86)(76, 96)(77, 89)(78, 95)(79, 88)(80, 84) MAP : A3.1229 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 20)(2, 22)(3, 21)(4, 30)(5, 31)(6, 32)(7, 17)(8, 25)(9, 27)(10, 18)(11, 28)(12, 24)(13, 19)(14, 23)(15, 29)(16, 26)(33, 53)(34, 49)(35, 60)(36, 63)(37, 56)(38, 52)(39, 51)(40, 50)(41, 54)(42, 55)(43, 64)(44, 58)(45, 59)(46, 61)(47, 57)(48, 62)(65, 90)(66, 92)(67, 94)(68, 82)(69, 87)(70, 88)(71, 96)(72, 83)(73, 85)(74, 91)(75, 95)(76, 93)(77, 84)(78, 86)(79, 81)(80, 89) MAP : A3.1230 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 31)(2, 20)(3, 24)(4, 29)(5, 25)(6, 30)(7, 21)(8, 22)(9, 32)(10, 17)(11, 26)(12, 18)(13, 28)(14, 19)(15, 27)(16, 23)(33, 52)(34, 54)(35, 53)(36, 62)(37, 63)(38, 64)(39, 49)(40, 57)(41, 59)(42, 50)(43, 60)(44, 56)(45, 51)(46, 55)(47, 61)(48, 58)(65, 96)(66, 91)(67, 84)(68, 90)(69, 94)(70, 92)(71, 86)(72, 93)(73, 83)(74, 89)(75, 85)(76, 95)(77, 81)(78, 82)(79, 87)(80, 88) MAP : A3.1231 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 31)(2, 20)(3, 24)(4, 29)(5, 25)(6, 30)(7, 21)(8, 22)(9, 32)(10, 17)(11, 26)(12, 18)(13, 28)(14, 19)(15, 27)(16, 23)(33, 55)(34, 58)(35, 61)(36, 49)(37, 51)(38, 50)(39, 62)(40, 60)(41, 56)(42, 64)(43, 57)(44, 59)(45, 63)(46, 52)(47, 53)(48, 54)(65, 82)(66, 88)(67, 87)(68, 86)(69, 81)(70, 89)(71, 90)(72, 85)(73, 95)(74, 92)(75, 93)(76, 83)(77, 94)(78, 96)(79, 84)(80, 91) MAP : A3.1232 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 31)(2, 20)(3, 24)(4, 29)(5, 25)(6, 30)(7, 21)(8, 22)(9, 32)(10, 17)(11, 26)(12, 18)(13, 28)(14, 19)(15, 27)(16, 23)(33, 57)(34, 63)(35, 50)(36, 59)(37, 54)(38, 61)(39, 56)(40, 52)(41, 62)(42, 53)(43, 55)(44, 49)(45, 58)(46, 60)(47, 64)(48, 51)(65, 93)(66, 94)(67, 89)(68, 83)(69, 91)(70, 87)(71, 95)(72, 96)(73, 90)(74, 84)(75, 82)(76, 86)(77, 88)(78, 85)(79, 92)(80, 81) MAP : A3.1233 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 31)(2, 20)(3, 24)(4, 29)(5, 25)(6, 30)(7, 21)(8, 22)(9, 32)(10, 17)(11, 26)(12, 18)(13, 28)(14, 19)(15, 27)(16, 23)(33, 60)(34, 51)(35, 64)(36, 56)(37, 58)(38, 53)(39, 59)(40, 55)(41, 49)(42, 61)(43, 52)(44, 62)(45, 54)(46, 57)(47, 50)(48, 63)(65, 85)(66, 81)(67, 92)(68, 95)(69, 88)(70, 84)(71, 83)(72, 82)(73, 86)(74, 87)(75, 96)(76, 90)(77, 91)(78, 93)(79, 89)(80, 94) MAP : A3.1234 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 31)(2, 20)(3, 24)(4, 29)(5, 25)(6, 30)(7, 21)(8, 22)(9, 32)(10, 17)(11, 26)(12, 18)(13, 28)(14, 19)(15, 27)(16, 23)(33, 61)(34, 62)(35, 57)(36, 51)(37, 59)(38, 55)(39, 63)(40, 64)(41, 58)(42, 52)(43, 50)(44, 54)(45, 56)(46, 53)(47, 60)(48, 49)(65, 89)(66, 95)(67, 82)(68, 91)(69, 86)(70, 93)(71, 88)(72, 84)(73, 94)(74, 85)(75, 87)(76, 81)(77, 90)(78, 92)(79, 96)(80, 83) MAP : A3.1235 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 31)(2, 20)(3, 24)(4, 29)(5, 25)(6, 30)(7, 21)(8, 22)(9, 32)(10, 17)(11, 26)(12, 18)(13, 28)(14, 19)(15, 27)(16, 23)(33, 64)(34, 59)(35, 52)(36, 58)(37, 62)(38, 60)(39, 54)(40, 61)(41, 51)(42, 57)(43, 53)(44, 63)(45, 49)(46, 50)(47, 55)(48, 56)(65, 84)(66, 86)(67, 85)(68, 94)(69, 95)(70, 96)(71, 81)(72, 89)(73, 91)(74, 82)(75, 92)(76, 88)(77, 83)(78, 87)(79, 93)(80, 90) MAP : A3.1236 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 29)(2, 30)(3, 25)(4, 19)(5, 27)(6, 23)(7, 31)(8, 32)(9, 26)(10, 20)(11, 18)(12, 22)(13, 24)(14, 21)(15, 28)(16, 17)(33, 51)(34, 55)(35, 59)(36, 53)(37, 60)(38, 49)(39, 61)(40, 58)(41, 50)(42, 62)(43, 54)(44, 64)(45, 57)(46, 63)(47, 56)(48, 52)(65, 92)(66, 83)(67, 96)(68, 88)(69, 90)(70, 85)(71, 91)(72, 87)(73, 81)(74, 93)(75, 84)(76, 94)(77, 86)(78, 89)(79, 82)(80, 95) MAP : A3.1237 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 29)(2, 30)(3, 25)(4, 19)(5, 27)(6, 23)(7, 31)(8, 32)(9, 26)(10, 20)(11, 18)(12, 22)(13, 24)(14, 21)(15, 28)(16, 17)(33, 54)(34, 57)(35, 49)(36, 64)(37, 52)(38, 59)(39, 50)(40, 63)(41, 61)(42, 56)(43, 51)(44, 53)(45, 55)(46, 58)(47, 62)(48, 60)(65, 84)(66, 86)(67, 85)(68, 94)(69, 95)(70, 96)(71, 81)(72, 89)(73, 91)(74, 82)(75, 92)(76, 88)(77, 83)(78, 87)(79, 93)(80, 90) MAP : A3.1238 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 23)(2, 26)(3, 29)(4, 17)(5, 19)(6, 18)(7, 30)(8, 28)(9, 24)(10, 32)(11, 25)(12, 27)(13, 31)(14, 20)(15, 21)(16, 22)(33, 51)(34, 55)(35, 59)(36, 53)(37, 60)(38, 49)(39, 61)(40, 58)(41, 50)(42, 62)(43, 54)(44, 64)(45, 57)(46, 63)(47, 56)(48, 52)(65, 96)(66, 91)(67, 84)(68, 90)(69, 94)(70, 92)(71, 86)(72, 93)(73, 83)(74, 89)(75, 85)(76, 95)(77, 81)(78, 82)(79, 87)(80, 88) MAP : A3.1239 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 23)(2, 26)(3, 29)(4, 17)(5, 19)(6, 18)(7, 30)(8, 28)(9, 24)(10, 32)(11, 25)(12, 27)(13, 31)(14, 20)(15, 21)(16, 22)(33, 54)(34, 57)(35, 49)(36, 64)(37, 52)(38, 59)(39, 50)(40, 63)(41, 61)(42, 56)(43, 51)(44, 53)(45, 55)(46, 58)(47, 62)(48, 60)(65, 85)(66, 81)(67, 92)(68, 95)(69, 88)(70, 84)(71, 83)(72, 82)(73, 86)(74, 87)(75, 96)(76, 90)(77, 91)(78, 93)(79, 89)(80, 94) MAP : A3.1240 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 23)(2, 26)(3, 29)(4, 17)(5, 19)(6, 18)(7, 30)(8, 28)(9, 24)(10, 32)(11, 25)(12, 27)(13, 31)(14, 20)(15, 21)(16, 22)(33, 58)(34, 60)(35, 62)(36, 50)(37, 55)(38, 56)(39, 64)(40, 51)(41, 53)(42, 59)(43, 63)(44, 61)(45, 52)(46, 54)(47, 49)(48, 57)(65, 93)(66, 94)(67, 89)(68, 83)(69, 91)(70, 87)(71, 95)(72, 96)(73, 90)(74, 84)(75, 82)(76, 86)(77, 88)(78, 85)(79, 92)(80, 81) MAP : A3.1241 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 23)(2, 26)(3, 29)(4, 17)(5, 19)(6, 18)(7, 30)(8, 28)(9, 24)(10, 32)(11, 25)(12, 27)(13, 31)(14, 20)(15, 21)(16, 22)(33, 63)(34, 52)(35, 56)(36, 61)(37, 57)(38, 62)(39, 53)(40, 54)(41, 64)(42, 49)(43, 58)(44, 50)(45, 60)(46, 51)(47, 59)(48, 55)(65, 82)(66, 88)(67, 87)(68, 86)(69, 81)(70, 89)(71, 90)(72, 85)(73, 95)(74, 92)(75, 93)(76, 83)(77, 94)(78, 96)(79, 84)(80, 91) MAP : A3.1242 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 23)(2, 26)(3, 29)(4, 17)(5, 19)(6, 18)(7, 30)(8, 28)(9, 24)(10, 32)(11, 25)(12, 27)(13, 31)(14, 20)(15, 21)(16, 22)(33, 61)(34, 62)(35, 57)(36, 51)(37, 59)(38, 55)(39, 63)(40, 64)(41, 58)(42, 52)(43, 50)(44, 54)(45, 56)(46, 53)(47, 60)(48, 49)(65, 90)(66, 92)(67, 94)(68, 82)(69, 87)(70, 88)(71, 96)(72, 83)(73, 85)(74, 91)(75, 95)(76, 93)(77, 84)(78, 86)(79, 81)(80, 89) MAP : A3.1243 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 23)(2, 26)(3, 29)(4, 17)(5, 19)(6, 18)(7, 30)(8, 28)(9, 24)(10, 32)(11, 25)(12, 27)(13, 31)(14, 20)(15, 21)(16, 22)(33, 64)(34, 59)(35, 52)(36, 58)(37, 62)(38, 60)(39, 54)(40, 61)(41, 51)(42, 57)(43, 53)(44, 63)(45, 49)(46, 50)(47, 55)(48, 56)(65, 83)(66, 87)(67, 91)(68, 85)(69, 92)(70, 81)(71, 93)(72, 90)(73, 82)(74, 94)(75, 86)(76, 96)(77, 89)(78, 95)(79, 88)(80, 84) MAP : A3.1244 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 25)(2, 31)(3, 18)(4, 27)(5, 22)(6, 29)(7, 24)(8, 20)(9, 30)(10, 21)(11, 23)(12, 17)(13, 26)(14, 28)(15, 32)(16, 19)(33, 50)(34, 56)(35, 55)(36, 54)(37, 49)(38, 57)(39, 58)(40, 53)(41, 63)(42, 60)(43, 61)(44, 51)(45, 62)(46, 64)(47, 52)(48, 59)(65, 90)(66, 92)(67, 94)(68, 82)(69, 87)(70, 88)(71, 96)(72, 83)(73, 85)(74, 91)(75, 95)(76, 93)(77, 84)(78, 86)(79, 81)(80, 89) MAP : A3.1245 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 25)(2, 31)(3, 18)(4, 27)(5, 22)(6, 29)(7, 24)(8, 20)(9, 30)(10, 21)(11, 23)(12, 17)(13, 26)(14, 28)(15, 32)(16, 19)(33, 53)(34, 49)(35, 60)(36, 63)(37, 56)(38, 52)(39, 51)(40, 50)(41, 54)(42, 55)(43, 64)(44, 58)(45, 59)(46, 61)(47, 57)(48, 62)(65, 83)(66, 87)(67, 91)(68, 85)(69, 92)(70, 81)(71, 93)(72, 90)(73, 82)(74, 94)(75, 86)(76, 96)(77, 89)(78, 95)(79, 88)(80, 84) MAP : A3.1246 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 32)(2, 27)(3, 20)(4, 26)(5, 30)(6, 28)(7, 22)(8, 29)(9, 19)(10, 25)(11, 21)(12, 31)(13, 17)(14, 18)(15, 23)(16, 24)(33, 52)(34, 54)(35, 53)(36, 62)(37, 63)(38, 64)(39, 49)(40, 57)(41, 59)(42, 50)(43, 60)(44, 56)(45, 51)(46, 55)(47, 61)(48, 58)(65, 95)(66, 84)(67, 88)(68, 93)(69, 89)(70, 94)(71, 85)(72, 86)(73, 96)(74, 81)(75, 90)(76, 82)(77, 92)(78, 83)(79, 91)(80, 87) MAP : A3.1247 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 25)(2, 31)(3, 18)(4, 27)(5, 22)(6, 29)(7, 24)(8, 20)(9, 30)(10, 21)(11, 23)(12, 17)(13, 26)(14, 28)(15, 32)(16, 19)(33, 54)(34, 57)(35, 49)(36, 64)(37, 52)(38, 59)(39, 50)(40, 63)(41, 61)(42, 56)(43, 51)(44, 53)(45, 55)(46, 58)(47, 62)(48, 60)(65, 96)(66, 91)(67, 84)(68, 90)(69, 94)(70, 92)(71, 86)(72, 93)(73, 83)(74, 89)(75, 85)(76, 95)(77, 81)(78, 82)(79, 87)(80, 88) MAP : A3.1248 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 9)(2, 3)(4, 8)(5, 7)(6, 10)(11, 12) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 2, 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1, u.1 * u.2^-1 * u.3^-1, u.4 * u.5^-1 * u.6^-1, (u.5 * u.1^-1)^2, u.2^4, u.6^4, (u.3 * u.4^-1)^2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.2 * x.3, x.6^-1 * x.3^-1, x.6 * x.2^-1, x.4 * x.5 * x.2^-1, x.3 * x.5 * x.4, x.4 * x.5^-1 * x.6^-1, (x.5 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.2^4, x.6^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 20)(10, 23)(11, 24)(12, 22)(13, 17)(14, 21)(15, 19)(16, 18)(25, 61)(26, 64)(27, 63)(28, 57)(29, 62)(30, 60)(31, 58)(32, 59)(33, 56)(34, 53)(35, 52)(36, 50)(37, 51)(38, 55)(39, 49)(40, 54)(41, 75)(42, 78)(43, 73)(44, 80)(45, 79)(46, 74)(47, 77)(48, 76)(81, 92)(82, 95)(83, 96)(84, 94)(85, 89)(86, 93)(87, 91)(88, 90) MAP : A3.1249 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 28)(2, 19)(3, 32)(4, 24)(5, 26)(6, 21)(7, 27)(8, 23)(9, 17)(10, 29)(11, 20)(12, 30)(13, 22)(14, 25)(15, 18)(16, 31)(33, 53)(34, 49)(35, 60)(36, 63)(37, 56)(38, 52)(39, 51)(40, 50)(41, 54)(42, 55)(43, 64)(44, 58)(45, 59)(46, 61)(47, 57)(48, 62)(65, 95)(66, 84)(67, 88)(68, 93)(69, 89)(70, 94)(71, 85)(72, 86)(73, 96)(74, 81)(75, 90)(76, 82)(77, 92)(78, 83)(79, 91)(80, 87) MAP : A3.1250 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 9)(2, 3)(4, 8)(5, 7)(6, 10)(11, 12) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 2, 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1, u.1 * u.2^-1 * u.3^-1, u.4 * u.5^-1 * u.6^-1, (u.5 * u.1^-1)^2, u.2^4, u.6^4, (u.3 * u.4^-1)^2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.2 * x.3, x.6^-1 * x.3^-1, x.6 * x.2^-1, x.4 * x.5 * x.2^-1, x.3 * x.5 * x.4, x.4 * x.5^-1 * x.6^-1, (x.5 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.2^4, x.6^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 24)(10, 21)(11, 20)(12, 18)(13, 19)(14, 23)(15, 17)(16, 22)(25, 63)(26, 60)(27, 61)(28, 59)(29, 58)(30, 64)(31, 62)(32, 57)(33, 53)(34, 56)(35, 55)(36, 49)(37, 54)(38, 52)(39, 50)(40, 51)(41, 74)(42, 73)(43, 78)(44, 79)(45, 80)(46, 75)(47, 76)(48, 77)(81, 96)(82, 93)(83, 92)(84, 90)(85, 91)(86, 95)(87, 89)(88, 94) MAP : A3.1251 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 25)(2, 31)(3, 18)(4, 27)(5, 22)(6, 29)(7, 24)(8, 20)(9, 30)(10, 21)(11, 23)(12, 17)(13, 26)(14, 28)(15, 32)(16, 19)(33, 64)(34, 59)(35, 52)(36, 58)(37, 62)(38, 60)(39, 54)(40, 61)(41, 51)(42, 57)(43, 53)(44, 63)(45, 49)(46, 50)(47, 55)(48, 56)(65, 86)(66, 89)(67, 81)(68, 96)(69, 84)(70, 91)(71, 82)(72, 95)(73, 93)(74, 88)(75, 83)(76, 85)(77, 87)(78, 90)(79, 94)(80, 92) MAP : A3.1252 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 28)(2, 19)(3, 32)(4, 24)(5, 26)(6, 21)(7, 27)(8, 23)(9, 17)(10, 29)(11, 20)(12, 30)(13, 22)(14, 25)(15, 18)(16, 31)(33, 50)(34, 56)(35, 55)(36, 54)(37, 49)(38, 57)(39, 58)(40, 53)(41, 63)(42, 60)(43, 61)(44, 51)(45, 62)(46, 64)(47, 52)(48, 59)(65, 86)(66, 89)(67, 81)(68, 96)(69, 84)(70, 91)(71, 82)(72, 95)(73, 93)(74, 88)(75, 83)(76, 85)(77, 87)(78, 90)(79, 94)(80, 92) MAP : A3.1253 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 28)(2, 19)(3, 32)(4, 24)(5, 26)(6, 21)(7, 27)(8, 23)(9, 17)(10, 29)(11, 20)(12, 30)(13, 22)(14, 25)(15, 18)(16, 31)(33, 63)(34, 52)(35, 56)(36, 61)(37, 57)(38, 62)(39, 53)(40, 54)(41, 64)(42, 49)(43, 58)(44, 50)(45, 60)(46, 51)(47, 59)(48, 55)(65, 85)(66, 81)(67, 92)(68, 95)(69, 88)(70, 84)(71, 83)(72, 82)(73, 86)(74, 87)(75, 96)(76, 90)(77, 91)(78, 93)(79, 89)(80, 94) MAP : A3.1254 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 26)(2, 28)(3, 30)(4, 18)(5, 23)(6, 24)(7, 32)(8, 19)(9, 21)(10, 27)(11, 31)(12, 29)(13, 20)(14, 22)(15, 17)(16, 25)(33, 64)(34, 59)(35, 52)(36, 58)(37, 62)(38, 60)(39, 54)(40, 61)(41, 51)(42, 57)(43, 53)(44, 63)(45, 49)(46, 50)(47, 55)(48, 56)(65, 92)(66, 83)(67, 96)(68, 88)(69, 90)(70, 85)(71, 91)(72, 87)(73, 81)(74, 93)(75, 84)(76, 94)(77, 86)(78, 89)(79, 82)(80, 95) MAP : A3.1255 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 31)(2, 20)(3, 24)(4, 29)(5, 25)(6, 30)(7, 21)(8, 22)(9, 32)(10, 17)(11, 26)(12, 18)(13, 28)(14, 19)(15, 27)(16, 23)(33, 50)(34, 56)(35, 55)(36, 54)(37, 49)(38, 57)(39, 58)(40, 53)(41, 63)(42, 60)(43, 61)(44, 51)(45, 62)(46, 64)(47, 52)(48, 59)(65, 87)(66, 90)(67, 93)(68, 81)(69, 83)(70, 82)(71, 94)(72, 92)(73, 88)(74, 96)(75, 89)(76, 91)(77, 95)(78, 84)(79, 85)(80, 86) MAP : A3.1256 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 28)(2, 19)(3, 32)(4, 24)(5, 26)(6, 21)(7, 27)(8, 23)(9, 17)(10, 29)(11, 20)(12, 30)(13, 22)(14, 25)(15, 18)(16, 31)(33, 58)(34, 60)(35, 62)(36, 50)(37, 55)(38, 56)(39, 64)(40, 51)(41, 53)(42, 59)(43, 63)(44, 61)(45, 52)(46, 54)(47, 49)(48, 57)(65, 96)(66, 91)(67, 84)(68, 90)(69, 94)(70, 92)(71, 86)(72, 93)(73, 83)(74, 89)(75, 85)(76, 95)(77, 81)(78, 82)(79, 87)(80, 88) MAP : A3.1257 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 9)(2, 3)(4, 8)(5, 7)(6, 10)(11, 12) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 2, 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1, u.1 * u.2^-1 * u.3^-1, u.4 * u.5^-1 * u.6^-1, (u.5 * u.1^-1)^2, u.2^4, u.6^4, (u.3 * u.4^-1)^2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.2 * x.3, x.6^-1 * x.3^-1, x.6 * x.2^-1, x.4 * x.5 * x.2^-1, x.3 * x.5 * x.4, x.4 * x.5^-1 * x.6^-1, (x.5 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.2^4, x.6^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 23)(10, 20)(11, 21)(12, 19)(13, 18)(14, 24)(15, 22)(16, 17)(25, 64)(26, 61)(27, 60)(28, 58)(29, 59)(30, 63)(31, 57)(32, 62)(33, 53)(34, 56)(35, 55)(36, 49)(37, 54)(38, 52)(39, 50)(40, 51)(41, 75)(42, 78)(43, 73)(44, 80)(45, 79)(46, 74)(47, 77)(48, 76)(81, 95)(82, 92)(83, 93)(84, 91)(85, 90)(86, 96)(87, 94)(88, 89) MAP : A3.1258 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 32)(2, 27)(3, 20)(4, 26)(5, 30)(6, 28)(7, 22)(8, 29)(9, 19)(10, 25)(11, 21)(12, 31)(13, 17)(14, 18)(15, 23)(16, 24)(33, 51)(34, 55)(35, 59)(36, 53)(37, 60)(38, 49)(39, 61)(40, 58)(41, 50)(42, 62)(43, 54)(44, 64)(45, 57)(46, 63)(47, 56)(48, 52)(65, 87)(66, 90)(67, 93)(68, 81)(69, 83)(70, 82)(71, 94)(72, 92)(73, 88)(74, 96)(75, 89)(76, 91)(77, 95)(78, 84)(79, 85)(80, 86) MAP : A3.1259 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 32)(2, 27)(3, 20)(4, 26)(5, 30)(6, 28)(7, 22)(8, 29)(9, 19)(10, 25)(11, 21)(12, 31)(13, 17)(14, 18)(15, 23)(16, 24)(33, 54)(34, 57)(35, 49)(36, 64)(37, 52)(38, 59)(39, 50)(40, 63)(41, 61)(42, 56)(43, 51)(44, 53)(45, 55)(46, 58)(47, 62)(48, 60)(65, 89)(66, 95)(67, 82)(68, 91)(69, 86)(70, 93)(71, 88)(72, 84)(73, 94)(74, 85)(75, 87)(76, 81)(77, 90)(78, 92)(79, 96)(80, 83) MAP : A3.1260 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 9)(2, 3)(4, 8)(5, 7)(6, 10)(11, 12) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 2, 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1, u.1 * u.2^-1 * u.3^-1, u.4 * u.5^-1 * u.6^-1, (u.5 * u.1^-1)^2, u.2^4, u.6^4, (u.3 * u.4^-1)^2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.2 * x.3, x.6^-1 * x.3^-1, x.6 * x.2^-1, x.4 * x.5 * x.2^-1, x.3 * x.5 * x.4, x.4 * x.5^-1 * x.6^-1, (x.5 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.2^4, x.6^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 20)(10, 23)(11, 24)(12, 22)(13, 17)(14, 21)(15, 19)(16, 18)(25, 61)(26, 64)(27, 63)(28, 57)(29, 62)(30, 60)(31, 58)(32, 59)(33, 55)(34, 52)(35, 53)(36, 51)(37, 50)(38, 56)(39, 54)(40, 49)(41, 74)(42, 73)(43, 78)(44, 79)(45, 80)(46, 75)(47, 76)(48, 77)(81, 92)(82, 95)(83, 96)(84, 94)(85, 89)(86, 93)(87, 91)(88, 90) MAP : A3.1261 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 31)(2, 20)(3, 24)(4, 29)(5, 25)(6, 30)(7, 21)(8, 22)(9, 32)(10, 17)(11, 26)(12, 18)(13, 28)(14, 19)(15, 27)(16, 23)(33, 53)(34, 49)(35, 60)(36, 63)(37, 56)(38, 52)(39, 51)(40, 50)(41, 54)(42, 55)(43, 64)(44, 58)(45, 59)(46, 61)(47, 57)(48, 62)(65, 92)(66, 83)(67, 96)(68, 88)(69, 90)(70, 85)(71, 91)(72, 87)(73, 81)(74, 93)(75, 84)(76, 94)(77, 86)(78, 89)(79, 82)(80, 95) MAP : A3.1262 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 26)(2, 28)(3, 30)(4, 18)(5, 23)(6, 24)(7, 32)(8, 19)(9, 21)(10, 27)(11, 31)(12, 29)(13, 20)(14, 22)(15, 17)(16, 25)(33, 61)(34, 62)(35, 57)(36, 51)(37, 59)(38, 55)(39, 63)(40, 64)(41, 58)(42, 52)(43, 50)(44, 54)(45, 56)(46, 53)(47, 60)(48, 49)(65, 87)(66, 90)(67, 93)(68, 81)(69, 83)(70, 82)(71, 94)(72, 92)(73, 88)(74, 96)(75, 89)(76, 91)(77, 95)(78, 84)(79, 85)(80, 86) MAP : A3.1263 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 29)(2, 30)(3, 25)(4, 19)(5, 27)(6, 23)(7, 31)(8, 32)(9, 26)(10, 20)(11, 18)(12, 22)(13, 24)(14, 21)(15, 28)(16, 17)(33, 55)(34, 58)(35, 61)(36, 49)(37, 51)(38, 50)(39, 62)(40, 60)(41, 56)(42, 64)(43, 57)(44, 59)(45, 63)(46, 52)(47, 53)(48, 54)(65, 90)(66, 92)(67, 94)(68, 82)(69, 87)(70, 88)(71, 96)(72, 83)(73, 85)(74, 91)(75, 95)(76, 93)(77, 84)(78, 86)(79, 81)(80, 89) MAP : A3.1264 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 9)(2, 3)(4, 8)(5, 7)(6, 10)(11, 12) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 2, 2, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1, u.1 * u.2^-1 * u.3^-1, u.4 * u.5^-1 * u.6^-1, (u.5 * u.1^-1)^2, u.2^4, u.6^4, (u.3 * u.4^-1)^2 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.2 * x.3, x.6^-1 * x.3^-1, x.6 * x.2^-1, x.4 * x.5 * x.2^-1, x.3 * x.5 * x.4, x.4 * x.5^-1 * x.6^-1, (x.5 * x.1^-1)^2, (x.3 * x.4^-1)^2, x.2^4, x.6^4 > SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 9, 17, 25, 33, 41)(2, 10, 18, 26, 34, 42)(3, 11, 19, 27, 35, 43)(4, 12, 20, 28, 36, 44)(5, 13, 21, 29, 37, 45)(6, 14, 22, 30, 38, 46)(7, 15, 23, 31, 39, 47)(8, 16, 24, 32, 40, 48)(49, 57, 65, 73, 81, 89)(50, 58, 66, 74, 82, 90)(51, 59, 67, 75, 83, 91)(52, 60, 68, 76, 84, 92)(53, 61, 69, 77, 85, 93)(54, 62, 70, 78, 86, 94)(55, 63, 71, 79, 87, 95)(56, 64, 72, 80, 88, 96) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 23)(10, 20)(11, 21)(12, 19)(13, 18)(14, 24)(15, 22)(16, 17)(25, 64)(26, 61)(27, 60)(28, 58)(29, 59)(30, 63)(31, 57)(32, 62)(33, 52)(34, 55)(35, 56)(36, 54)(37, 49)(38, 53)(39, 51)(40, 50)(41, 74)(42, 73)(43, 78)(44, 79)(45, 80)(46, 75)(47, 76)(48, 77)(81, 95)(82, 92)(83, 93)(84, 91)(85, 90)(86, 96)(87, 94)(88, 89) MAP : A3.1265 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 29)(2, 30)(3, 25)(4, 19)(5, 27)(6, 23)(7, 31)(8, 32)(9, 26)(10, 20)(11, 18)(12, 22)(13, 24)(14, 21)(15, 28)(16, 17)(33, 63)(34, 52)(35, 56)(36, 61)(37, 57)(38, 62)(39, 53)(40, 54)(41, 64)(42, 49)(43, 58)(44, 50)(45, 60)(46, 51)(47, 59)(48, 55)(65, 89)(66, 95)(67, 82)(68, 91)(69, 86)(70, 93)(71, 88)(72, 84)(73, 94)(74, 85)(75, 87)(76, 81)(77, 90)(78, 92)(79, 96)(80, 83) MAP : A3.1266 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 29)(2, 30)(3, 25)(4, 19)(5, 27)(6, 23)(7, 31)(8, 32)(9, 26)(10, 20)(11, 18)(12, 22)(13, 24)(14, 21)(15, 28)(16, 17)(33, 52)(34, 54)(35, 53)(36, 62)(37, 63)(38, 64)(39, 49)(40, 57)(41, 59)(42, 50)(43, 60)(44, 56)(45, 51)(46, 55)(47, 61)(48, 58)(65, 86)(66, 89)(67, 81)(68, 96)(69, 84)(70, 91)(71, 82)(72, 95)(73, 93)(74, 88)(75, 83)(76, 85)(77, 87)(78, 90)(79, 94)(80, 92) MAP : A3.1267 NOTES : type I, reflexible, isomorphic to A3.1148. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6) ORBIFOLD : O(0, {4, 4, 4}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 4, 4, 1 ] UNIGROUP : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^4 > CTG (small) : <16, 2> CTG (fp) : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.3 * x.1, x.1^4, x.2^4, x.3^4 > SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1) LOCAL TYPE : (3, 4, 3, 4, 3, 4) #DARTS : 96 R = (1, 17, 33, 49, 65, 81)(2, 18, 34, 50, 66, 82)(3, 19, 35, 51, 67, 83)(4, 20, 36, 52, 68, 84)(5, 21, 37, 53, 69, 85)(6, 22, 38, 54, 70, 86)(7, 23, 39, 55, 71, 87)(8, 24, 40, 56, 72, 88)(9, 25, 41, 57, 73, 89)(10, 26, 42, 58, 74, 90)(11, 27, 43, 59, 75, 91)(12, 28, 44, 60, 76, 92)(13, 29, 45, 61, 77, 93)(14, 30, 46, 62, 78, 94)(15, 31, 47, 63, 79, 95)(16, 32, 48, 64, 80, 96) L = (1, 29)(2, 30)(3, 25)(4, 19)(5, 27)(6, 23)(7, 31)(8, 32)(9, 26)(10, 20)(11, 18)(12, 22)(13, 24)(14, 21)(15, 28)(16, 17)(33, 58)(34, 60)(35, 62)(36, 50)(37, 55)(38, 56)(39, 64)(40, 51)(41, 53)(42, 59)(43, 63)(44, 61)(45, 52)(46, 54)(47, 49)(48, 57)(65, 87)(66, 90)(67, 93)(68, 81)(69, 83)(70, 82)(71, 94)(72, 92)(73, 88)(74, 96)(75, 89)(76, 91)(77, 95)(78, 84)(79, 85)(80, 86) MAP : A3.1268 NOTES : type I, non-Cayley, reflexible, representative. QUOTIENT : R = (1, 2, 3) L = (2, 3) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 3, 2 ] UNIGROUP : < u.1, u.2, u.3 | u.3^2, u.1^2, u.2^3, (u.1 * u.3 * u.2^-1)^2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3 | x.3^2, x.1^2, x.2^3, x.1 * x.3 * x.2 * x.3 * x.2, x.1 * x.2^-1 * x.3 * x.2^-1 * x.3, (x.1 * x.3 * x.2^-1)^2, (x.2 * x.1)^3 > SCHREIER VEC. : (x.1, x.2, x.2^-1)^2 LOCAL TYPE : (3, 4, 4, 3, 4, 4) #DARTS : 72 R = (1, 40, 64, 16, 25, 49)(2, 48, 72, 24, 26, 50)(3, 32, 56, 8, 27, 51)(4, 31, 55, 7, 28, 52)(5, 36, 60, 12, 29, 53)(6, 44, 68, 20, 30, 54)(9, 47, 71, 23, 33, 57)(10, 45, 69, 21, 34, 58)(11, 46, 70, 22, 35, 59)(13, 43, 67, 19, 37, 61)(14, 41, 65, 17, 38, 62)(15, 42, 66, 18, 39, 63) L = (1, 18)(2, 19)(3, 17)(4, 10)(5, 15)(6, 13)(7, 14)(8, 21)(9, 20)(11, 12)(16, 22)(23, 24)(25, 50)(26, 51)(27, 49)(28, 66)(29, 55)(30, 53)(31, 54)(32, 61)(33, 52)(34, 60)(35, 68)(36, 67)(37, 70)(38, 71)(39, 69)(40, 62)(41, 59)(42, 57)(43, 58)(44, 65)(45, 72)(46, 56)(47, 64)(48, 63) MAP : A3.1269 NOTES : type I, reflexible, isomorphic to A3.1268. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(4, 5) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^3, u.4^3, u.3^-1 * u.1 * u.4^-1 * u.2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.4^3, x.1 * x.4 * x.3, x.2 * x.4^-1 * x.3^-1, x.3^-1 * x.1 * x.4^-1 * x.2, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.4, x.4^-1, x.2) LOCAL TYPE : (3, 4, 4, 3, 4, 4) #DARTS : 72 R = (1, 13, 25, 37, 49, 61)(2, 14, 26, 38, 50, 62)(3, 15, 27, 39, 51, 63)(4, 16, 28, 40, 52, 64)(5, 17, 29, 41, 53, 65)(6, 18, 30, 42, 54, 66)(7, 19, 31, 43, 55, 67)(8, 20, 32, 44, 56, 68)(9, 21, 33, 45, 57, 69)(10, 22, 34, 46, 58, 70)(11, 23, 35, 47, 59, 71)(12, 24, 36, 48, 60, 72) L = (1, 14)(2, 15)(3, 13)(4, 18)(5, 23)(6, 21)(7, 22)(8, 17)(9, 16)(10, 24)(11, 20)(12, 19)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(37, 53)(38, 54)(39, 55)(40, 56)(41, 57)(42, 58)(43, 59)(44, 60)(45, 49)(46, 50)(47, 51)(48, 52)(61, 71)(62, 69)(63, 70)(64, 65)(66, 72)(67, 68) MAP : A3.1270 NOTES : type I, reflexible, isomorphic to A3.1268. QUOTIENT : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(4, 5) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2^2, u.3^3, u.4^3, u.3^-1 * u.1 * u.4^-1 * u.2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.4^3, x.1 * x.4 * x.3, x.2 * x.4^-1 * x.3^-1, x.3^-1 * x.1 * x.4^-1 * x.2, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.4, x.4^-1, x.2) LOCAL TYPE : (3, 4, 4, 3, 4, 4) #DARTS : 72 R = (1, 13, 25, 37, 49, 61)(2, 14, 26, 38, 50, 62)(3, 15, 27, 39, 51, 63)(4, 16, 28, 40, 52, 64)(5, 17, 29, 41, 53, 65)(6, 18, 30, 42, 54, 66)(7, 19, 31, 43, 55, 67)(8, 20, 32, 44, 56, 68)(9, 21, 33, 45, 57, 69)(10, 22, 34, 46, 58, 70)(11, 23, 35, 47, 59, 71)(12, 24, 36, 48, 60, 72) L = (1, 15)(2, 13)(3, 14)(4, 21)(5, 20)(6, 16)(7, 24)(8, 23)(9, 18)(10, 19)(11, 17)(12, 22)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(37, 55)(38, 53)(39, 54)(40, 49)(41, 60)(42, 56)(43, 52)(44, 51)(45, 58)(46, 59)(47, 57)(48, 50)(61, 72)(62, 68)(63, 64)(65, 70)(66, 71)(67, 69) MAP : A3.1271 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.5^3, u.4 * u.5^-1 * u.3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.5^3, x.4 * x.5^-1 * x.3, x.5^-1 * x.1 * x.3 * x.2, x.4^4, x.3 * x.4^-1 * x.5 * x.1 * x.5 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 18)(2, 19)(3, 17)(4, 10)(5, 15)(6, 13)(7, 14)(8, 21)(9, 20)(11, 12)(16, 22)(23, 24)(25, 31)(26, 29)(27, 30)(28, 37)(32, 42)(33, 46)(34, 47)(35, 45)(36, 38)(39, 44)(40, 43)(41, 48)(49, 158)(50, 159)(51, 157)(52, 150)(53, 163)(54, 161)(55, 162)(56, 145)(57, 160)(58, 168)(59, 152)(60, 151)(61, 154)(62, 155)(63, 153)(64, 146)(65, 167)(66, 165)(67, 166)(68, 149)(69, 156)(70, 164)(71, 148)(72, 147)(73, 115)(74, 113)(75, 114)(76, 97)(77, 110)(78, 111)(79, 109)(80, 102)(81, 106)(82, 107)(83, 105)(84, 98)(85, 112)(86, 120)(87, 104)(88, 103)(89, 108)(90, 116)(91, 100)(92, 99)(93, 119)(94, 117)(95, 118)(96, 101)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1272 NOTES : type I, reflexible, isomorphic to Dual({3,7}), representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.5^3, u.4 * u.5^-1 * u.3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.5^3, x.4 * x.5^-1 * x.3, x.5 * x.4 * x.3 * x.2, (x.5 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 7)(2, 5)(3, 6)(4, 13)(8, 18)(9, 22)(10, 23)(11, 21)(12, 14)(15, 20)(16, 19)(17, 24)(25, 36)(26, 44)(27, 28)(29, 40)(30, 48)(31, 32)(33, 43)(34, 41)(35, 42)(37, 47)(38, 45)(39, 46)(49, 158)(50, 159)(51, 157)(52, 150)(53, 163)(54, 161)(55, 162)(56, 145)(57, 160)(58, 168)(59, 152)(60, 151)(61, 154)(62, 155)(63, 153)(64, 146)(65, 167)(66, 165)(67, 166)(68, 149)(69, 156)(70, 164)(71, 148)(72, 147)(73, 115)(74, 113)(75, 114)(76, 97)(77, 110)(78, 111)(79, 109)(80, 102)(81, 106)(82, 107)(83, 105)(84, 98)(85, 112)(86, 120)(87, 104)(88, 103)(89, 108)(90, 116)(91, 100)(92, 99)(93, 119)(94, 117)(95, 118)(96, 101)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1273 NOTES : type I, non-Cayley, reflexible, isomorphic to Dual({3,7}), isomorphic to A3.1272. QUOTIENT : R = Id($) L = Id($) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 7 ], faces: [ 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2)^3, u.2^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2)^3, x.2^7, x.1 * x.2^-2 * x.1 * x.2 * x.1 * x.2^-2 * x.1 * x.2^-3 * x.1 * x.2^-3 > SCHREIER VEC. : (x.1)^7 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 136, 5, 38, 159, 34, 92)(2, 133, 8, 39, 158, 33, 75)(3, 24, 22, 36, 95, 17, 77)(4, 131, 157, 102, 168, 49, 74)(6, 129, 140, 109, 96, 42, 59)(7, 130, 155, 112, 93, 41, 76)(9, 150, 72, 135, 156, 35, 90)(10, 151, 69, 134, 163, 52, 89)(11, 148, 160, 103, 165, 50, 73)(12, 46, 67, 120, 162, 55, 105)(13, 146, 142, 100, 32, 51, 57)(14, 53, 65, 104, 147, 71, 98)(15, 56, 66, 101, 164, 70, 97)(16, 145, 143, 107, 29, 44, 58)(18, 80, 20, 21, 23, 19, 94)(25, 79, 62, 132, 154, 37, 91)(26, 78, 63, 115, 153, 40, 108)(27, 47, 60, 117, 161, 54, 106)(28, 64, 118, 114, 137, 141, 111)(30, 48, 125, 123, 122, 124, 127)(31, 45, 128, 116, 121, 139, 126)(43, 61, 119, 113, 138, 144, 110)(68, 99, 167, 88, 81, 86, 149)(82, 87, 152, 83, 84, 166, 85) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168) MAP : A3.1274 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.5^3, u.4 * u.5^-1 * u.3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^3, x.1 * x.2 * x.4^-1, x.5^3, x.4 * x.5^-1 * x.3, (x.5 * x.1)^2, x.1 * x.3 * x.2 * x.3 * x.5^-1 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 7)(2, 5)(3, 6)(4, 13)(8, 18)(9, 22)(10, 23)(11, 21)(12, 14)(15, 20)(16, 19)(17, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(49, 146)(50, 147)(51, 145)(52, 162)(53, 151)(54, 149)(55, 150)(56, 157)(57, 148)(58, 156)(59, 164)(60, 163)(61, 166)(62, 167)(63, 165)(64, 158)(65, 155)(66, 153)(67, 154)(68, 161)(69, 168)(70, 152)(71, 160)(72, 159)(73, 115)(74, 113)(75, 114)(76, 97)(77, 110)(78, 111)(79, 109)(80, 102)(81, 106)(82, 107)(83, 105)(84, 98)(85, 112)(86, 120)(87, 104)(88, 103)(89, 108)(90, 116)(91, 100)(92, 99)(93, 119)(94, 117)(95, 118)(96, 101)(121, 138)(122, 139)(123, 137)(124, 130)(125, 135)(126, 133)(127, 134)(128, 141)(129, 140)(131, 132)(136, 142)(143, 144) MAP : A3.1275 NOTES : type I, non-Cayley, reflexible, isomorphic to Dual({3,7}), isomorphic to A3.1272. QUOTIENT : R = Id($) L = Id($) ORBIFOLD : O(0, {7, 3, 2}) EMBEDDING : vertices: [ 7 ], faces: [ 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2)^3, u.2^7 > CTG (small) : <168, 42> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2)^3, x.2^7, x.1 * x.2^-2 * x.1 * x.2 * x.1 * x.2^-2 * x.1 * x.2^-3 * x.1 * x.2^-3 > SCHREIER VEC. : (x.1)^7 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 92, 34, 159, 38, 5, 136)(2, 75, 33, 158, 39, 8, 133)(3, 77, 17, 95, 36, 22, 24)(4, 74, 49, 168, 102, 157, 131)(6, 59, 42, 96, 109, 140, 129)(7, 76, 41, 93, 112, 155, 130)(9, 90, 35, 156, 135, 72, 150)(10, 89, 52, 163, 134, 69, 151)(11, 73, 50, 165, 103, 160, 148)(12, 105, 55, 162, 120, 67, 46)(13, 57, 51, 32, 100, 142, 146)(14, 98, 71, 147, 104, 65, 53)(15, 97, 70, 164, 101, 66, 56)(16, 58, 44, 29, 107, 143, 145)(18, 94, 19, 23, 21, 20, 80)(25, 91, 37, 154, 132, 62, 79)(26, 108, 40, 153, 115, 63, 78)(27, 106, 54, 161, 117, 60, 47)(28, 111, 141, 137, 114, 118, 64)(30, 127, 124, 122, 123, 125, 48)(31, 126, 139, 121, 116, 128, 45)(43, 110, 144, 138, 113, 119, 61)(68, 149, 86, 81, 88, 167, 99)(82, 85, 166, 84, 83, 152, 87) L = (1, 2)(3, 9)(4, 17)(5, 25)(6, 34)(7, 33)(8, 26)(10, 20)(11, 18)(12, 23)(13, 19)(14, 95)(15, 94)(16, 36)(21, 104)(22, 27)(24, 101)(28, 157)(29, 159)(30, 140)(31, 155)(32, 158)(35, 119)(37, 116)(38, 120)(39, 117)(40, 123)(41, 72)(42, 69)(43, 160)(44, 67)(45, 142)(46, 65)(47, 66)(48, 143)(49, 62)(50, 63)(51, 60)(52, 118)(53, 58)(54, 125)(55, 128)(56, 57)(59, 88)(61, 70)(64, 71)(68, 78)(73, 149)(74, 152)(75, 166)(76, 85)(77, 87)(79, 83)(80, 86)(81, 151)(82, 150)(84, 136)(89, 147)(90, 164)(91, 162)(92, 167)(93, 163)(96, 156)(97, 148)(98, 131)(99, 133)(100, 130)(102, 115)(103, 132)(105, 146)(106, 145)(107, 129)(108, 161)(109, 113)(110, 154)(111, 153)(112, 114)(121, 144)(122, 141)(124, 139)(126, 137)(127, 138)(134, 135)(165, 168) MAP : A3.1276 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.6^3, u.8^3, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.7 * x.3^-1 * x.2, x.6^3, x.8^3, x.5 * x.6^-1 * x.7^-1, x.4 * x.2 * x.6^-1, x.3 * x.4^-1 * x.8^-1, x.1 * x.6 * x.4^-1, x.4 * x.1 * x.5^-1, x.2 * x.8 * x.6, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 13, 25, 37, 49, 61, 73)(2, 14, 26, 38, 50, 62, 74)(3, 15, 27, 39, 51, 63, 75)(4, 16, 28, 40, 52, 64, 76)(5, 17, 29, 41, 53, 65, 77)(6, 18, 30, 42, 54, 66, 78)(7, 19, 31, 43, 55, 67, 79)(8, 20, 32, 44, 56, 68, 80)(9, 21, 33, 45, 57, 69, 81)(10, 22, 34, 46, 58, 70, 82)(11, 23, 35, 47, 59, 71, 83)(12, 24, 36, 48, 60, 72, 84)(85, 97, 109, 121, 133, 145, 157)(86, 98, 110, 122, 134, 146, 158)(87, 99, 111, 123, 135, 147, 159)(88, 100, 112, 124, 136, 148, 160)(89, 101, 113, 125, 137, 149, 161)(90, 102, 114, 126, 138, 150, 162)(91, 103, 115, 127, 139, 151, 163)(92, 104, 116, 128, 140, 152, 164)(93, 105, 117, 129, 141, 153, 165)(94, 106, 118, 130, 142, 154, 166)(95, 107, 119, 131, 143, 155, 167)(96, 108, 120, 132, 144, 156, 168) L = (1, 133)(2, 134)(3, 135)(4, 136)(5, 137)(6, 138)(7, 139)(8, 140)(9, 141)(10, 142)(11, 143)(12, 144)(13, 98)(14, 99)(15, 97)(16, 102)(17, 107)(18, 105)(19, 106)(20, 101)(21, 100)(22, 108)(23, 104)(24, 103)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(37, 93)(38, 94)(39, 95)(40, 96)(41, 85)(42, 86)(43, 87)(44, 88)(45, 89)(46, 90)(47, 91)(48, 92)(49, 67)(50, 65)(51, 66)(52, 61)(53, 72)(54, 68)(55, 64)(56, 63)(57, 70)(58, 71)(59, 69)(60, 62)(73, 168)(74, 164)(75, 160)(76, 159)(77, 166)(78, 167)(79, 165)(80, 158)(81, 163)(82, 161)(83, 162)(84, 157)(109, 123)(110, 121)(111, 122)(112, 129)(113, 128)(114, 124)(115, 132)(116, 131)(117, 126)(118, 127)(119, 125)(120, 130)(145, 156)(146, 152)(147, 148)(149, 154)(150, 155)(151, 153) MAP : A3.1277 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.5^3, u.4 * u.5^-1 * u.3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.5^3, x.4 * x.5^-1 * x.3, x.5 * x.3 * x.5^-1 * x.1, (x.3 * x.2)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 21)(2, 22)(3, 23)(4, 24)(5, 9)(6, 10)(7, 11)(8, 12)(13, 17)(14, 18)(15, 19)(16, 20)(25, 42)(26, 43)(27, 41)(28, 34)(29, 39)(30, 37)(31, 38)(32, 45)(33, 44)(35, 36)(40, 46)(47, 48)(49, 158)(50, 159)(51, 157)(52, 150)(53, 163)(54, 161)(55, 162)(56, 145)(57, 160)(58, 168)(59, 152)(60, 151)(61, 154)(62, 155)(63, 153)(64, 146)(65, 167)(66, 165)(67, 166)(68, 149)(69, 156)(70, 164)(71, 148)(72, 147)(73, 115)(74, 113)(75, 114)(76, 97)(77, 110)(78, 111)(79, 109)(80, 102)(81, 106)(82, 107)(83, 105)(84, 98)(85, 112)(86, 120)(87, 104)(88, 103)(89, 108)(90, 116)(91, 100)(92, 99)(93, 119)(94, 117)(95, 118)(96, 101)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1278 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.5^3, u.4 * u.5^-1 * u.3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.5^3, x.4 * x.5^-1 * x.3, x.4^-1 * x.5^-1 * x.1 * x.3, x.5 * x.3 * x.5^-1 * x.2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 12)(2, 20)(3, 4)(5, 16)(6, 24)(7, 8)(9, 19)(10, 17)(11, 18)(13, 23)(14, 21)(15, 22)(25, 45)(26, 46)(27, 47)(28, 48)(29, 33)(30, 34)(31, 35)(32, 36)(37, 41)(38, 42)(39, 43)(40, 44)(49, 158)(50, 159)(51, 157)(52, 150)(53, 163)(54, 161)(55, 162)(56, 145)(57, 160)(58, 168)(59, 152)(60, 151)(61, 154)(62, 155)(63, 153)(64, 146)(65, 167)(66, 165)(67, 166)(68, 149)(69, 156)(70, 164)(71, 148)(72, 147)(73, 115)(74, 113)(75, 114)(76, 97)(77, 110)(78, 111)(79, 109)(80, 102)(81, 106)(82, 107)(83, 105)(84, 98)(85, 112)(86, 120)(87, 104)(88, 103)(89, 108)(90, 116)(91, 100)(92, 99)(93, 119)(94, 117)(95, 118)(96, 101)(121, 126)(122, 127)(123, 125)(124, 142)(128, 129)(130, 136)(131, 144)(132, 143)(133, 138)(134, 139)(135, 137)(140, 141) MAP : A3.1279 NOTES : type I, chiral, isomorphic to A3.1271. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^3, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^3, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, (x.4 * x.1)^2, x.5^4, x.1 * x.4^-1 * x.5 * x.3 * x.5^-1, x.1 * x.3 * x.4 * x.5 * x.3 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 26)(2, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(49, 128)(50, 136)(51, 144)(52, 143)(53, 140)(54, 124)(55, 132)(56, 131)(57, 135)(58, 133)(59, 134)(60, 141)(61, 123)(62, 121)(63, 122)(64, 129)(65, 126)(66, 127)(67, 125)(68, 142)(69, 138)(70, 139)(71, 137)(72, 130)(73, 79)(74, 77)(75, 78)(76, 85)(80, 90)(81, 94)(82, 95)(83, 93)(84, 86)(87, 92)(88, 91)(89, 96)(97, 108)(98, 116)(99, 100)(101, 112)(102, 120)(103, 104)(105, 115)(106, 113)(107, 114)(109, 119)(110, 117)(111, 118)(145, 160)(146, 168)(147, 152)(148, 151)(149, 156)(150, 164)(153, 167)(154, 165)(155, 166)(157, 163)(158, 161)(159, 162) MAP : A3.1280 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^3, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.5^3, x.4^3, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.4^-1 * x.2 * x.4 * x.1, (x.3 * x.1)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 26)(2, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(49, 137)(50, 138)(51, 139)(52, 140)(53, 133)(54, 134)(55, 135)(56, 136)(57, 121)(58, 122)(59, 123)(60, 124)(61, 141)(62, 142)(63, 143)(64, 144)(65, 129)(66, 130)(67, 131)(68, 132)(69, 125)(70, 126)(71, 127)(72, 128)(73, 85)(74, 86)(75, 87)(76, 88)(77, 89)(78, 90)(79, 91)(80, 92)(81, 93)(82, 94)(83, 95)(84, 96)(97, 117)(98, 118)(99, 119)(100, 120)(101, 105)(102, 106)(103, 107)(104, 108)(109, 113)(110, 114)(111, 115)(112, 116)(145, 162)(146, 163)(147, 161)(148, 154)(149, 159)(150, 157)(151, 158)(152, 165)(153, 164)(155, 156)(160, 166)(167, 168) MAP : A3.1281 NOTES : type I, reflexible, isomorphic to Dual({3,7}), isomorphic to A3.1272. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^3, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^3, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.5 * x.3 * x.1 * x.4^-1, (x.4 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 26)(2, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(49, 128)(50, 136)(51, 144)(52, 143)(53, 140)(54, 124)(55, 132)(56, 131)(57, 135)(58, 133)(59, 134)(60, 141)(61, 123)(62, 121)(63, 122)(64, 129)(65, 126)(66, 127)(67, 125)(68, 142)(69, 138)(70, 139)(71, 137)(72, 130)(73, 90)(74, 91)(75, 89)(76, 82)(77, 87)(78, 85)(79, 86)(80, 93)(81, 92)(83, 84)(88, 94)(95, 96)(97, 103)(98, 101)(99, 102)(100, 109)(104, 114)(105, 118)(106, 119)(107, 117)(108, 110)(111, 116)(112, 115)(113, 120)(145, 160)(146, 168)(147, 152)(148, 151)(149, 156)(150, 164)(153, 167)(154, 165)(155, 166)(157, 163)(158, 161)(159, 162) MAP : A3.1282 NOTES : type II, reflexible, isomorphic to A3.1276. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.6^3, u.8^3, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.7 * x.3^-1 * x.2, x.6^3, x.8^3, x.5 * x.6^-1 * x.7^-1, x.4 * x.2 * x.6^-1, x.3 * x.4^-1 * x.8^-1, x.1 * x.6 * x.4^-1, x.4 * x.1 * x.5^-1, x.2 * x.8 * x.6, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 13, 25, 37, 49, 61, 73)(2, 14, 26, 38, 50, 62, 74)(3, 15, 27, 39, 51, 63, 75)(4, 16, 28, 40, 52, 64, 76)(5, 17, 29, 41, 53, 65, 77)(6, 18, 30, 42, 54, 66, 78)(7, 19, 31, 43, 55, 67, 79)(8, 20, 32, 44, 56, 68, 80)(9, 21, 33, 45, 57, 69, 81)(10, 22, 34, 46, 58, 70, 82)(11, 23, 35, 47, 59, 71, 83)(12, 24, 36, 48, 60, 72, 84)(85, 97, 109, 121, 133, 145, 157)(86, 98, 110, 122, 134, 146, 158)(87, 99, 111, 123, 135, 147, 159)(88, 100, 112, 124, 136, 148, 160)(89, 101, 113, 125, 137, 149, 161)(90, 102, 114, 126, 138, 150, 162)(91, 103, 115, 127, 139, 151, 163)(92, 104, 116, 128, 140, 152, 164)(93, 105, 117, 129, 141, 153, 165)(94, 106, 118, 130, 142, 154, 166)(95, 107, 119, 131, 143, 155, 167)(96, 108, 120, 132, 144, 156, 168) L = (1, 133)(2, 134)(3, 135)(4, 136)(5, 137)(6, 138)(7, 139)(8, 140)(9, 141)(10, 142)(11, 143)(12, 144)(13, 99)(14, 97)(15, 98)(16, 105)(17, 104)(18, 100)(19, 108)(20, 107)(21, 102)(22, 103)(23, 101)(24, 106)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(37, 88)(38, 96)(39, 92)(40, 91)(41, 86)(42, 87)(43, 85)(44, 90)(45, 95)(46, 93)(47, 94)(48, 89)(49, 65)(50, 66)(51, 67)(52, 68)(53, 69)(54, 70)(55, 71)(56, 72)(57, 61)(58, 62)(59, 63)(60, 64)(73, 167)(74, 165)(75, 166)(76, 161)(77, 160)(78, 168)(79, 164)(80, 163)(81, 158)(82, 159)(83, 157)(84, 162)(109, 122)(110, 123)(111, 121)(112, 126)(113, 131)(114, 129)(115, 130)(116, 125)(117, 124)(118, 132)(119, 128)(120, 127)(145, 155)(146, 153)(147, 154)(148, 149)(150, 156)(151, 152) MAP : A3.1283 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^3, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.5^3, x.4^3, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, (x.4 * x.1)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 26)(2, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(49, 137)(50, 138)(51, 139)(52, 140)(53, 133)(54, 134)(55, 135)(56, 136)(57, 121)(58, 122)(59, 123)(60, 124)(61, 141)(62, 142)(63, 143)(64, 144)(65, 129)(66, 130)(67, 131)(68, 132)(69, 125)(70, 126)(71, 127)(72, 128)(73, 77)(74, 78)(75, 79)(76, 80)(81, 85)(82, 86)(83, 87)(84, 88)(89, 93)(90, 94)(91, 95)(92, 96)(97, 109)(98, 110)(99, 111)(100, 112)(101, 113)(102, 114)(103, 115)(104, 116)(105, 117)(106, 118)(107, 119)(108, 120)(145, 162)(146, 163)(147, 161)(148, 154)(149, 159)(150, 157)(151, 158)(152, 165)(153, 164)(155, 156)(160, 166)(167, 168) MAP : A3.1284 NOTES : type I, chiral, isomorphic to A3.1283. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.5^3, u.4 * u.5^-1 * u.3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^3, x.1 * x.2 * x.4^-1, x.5^3, x.4 * x.5^-1 * x.3, x.5^-1 * x.1 * x.3 * x.2 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 6)(2, 7)(3, 5)(4, 22)(8, 9)(10, 16)(11, 24)(12, 23)(13, 18)(14, 19)(15, 17)(20, 21)(25, 31)(26, 29)(27, 30)(28, 37)(32, 42)(33, 46)(34, 47)(35, 45)(36, 38)(39, 44)(40, 43)(41, 48)(49, 146)(50, 147)(51, 145)(52, 162)(53, 151)(54, 149)(55, 150)(56, 157)(57, 148)(58, 156)(59, 164)(60, 163)(61, 166)(62, 167)(63, 165)(64, 158)(65, 155)(66, 153)(67, 154)(68, 161)(69, 168)(70, 152)(71, 160)(72, 159)(73, 115)(74, 113)(75, 114)(76, 97)(77, 110)(78, 111)(79, 109)(80, 102)(81, 106)(82, 107)(83, 105)(84, 98)(85, 112)(86, 120)(87, 104)(88, 103)(89, 108)(90, 116)(91, 100)(92, 99)(93, 119)(94, 117)(95, 118)(96, 101)(121, 138)(122, 139)(123, 137)(124, 130)(125, 135)(126, 133)(127, 134)(128, 141)(129, 140)(131, 132)(136, 142)(143, 144) MAP : A3.1285 NOTES : type I, chiral, isomorphic to A3.1280. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.5^3, u.4 * u.5^-1 * u.3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^3, x.1 * x.2 * x.4^-1, x.5^3, x.4 * x.5^-1 * x.3, x.5^-1 * x.2 * x.5 * x.1, (x.3 * x.2)^2 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 30)(26, 31)(27, 29)(28, 46)(32, 33)(34, 40)(35, 48)(36, 47)(37, 42)(38, 43)(39, 41)(44, 45)(49, 146)(50, 147)(51, 145)(52, 162)(53, 151)(54, 149)(55, 150)(56, 157)(57, 148)(58, 156)(59, 164)(60, 163)(61, 166)(62, 167)(63, 165)(64, 158)(65, 155)(66, 153)(67, 154)(68, 161)(69, 168)(70, 152)(71, 160)(72, 159)(73, 115)(74, 113)(75, 114)(76, 97)(77, 110)(78, 111)(79, 109)(80, 102)(81, 106)(82, 107)(83, 105)(84, 98)(85, 112)(86, 120)(87, 104)(88, 103)(89, 108)(90, 116)(91, 100)(92, 99)(93, 119)(94, 117)(95, 118)(96, 101)(121, 138)(122, 139)(123, 137)(124, 130)(125, 135)(126, 133)(127, 134)(128, 141)(129, 140)(131, 132)(136, 142)(143, 144) MAP : A3.1286 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^3, u.7^3, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.5, x.1^2, x.2^2, x.4 * x.6, x.3^3, x.7^3, x.5 * x.6^-1 * x.8, x.3^-1 * x.4^-1 * x.1, x.2 * x.7 * x.3^-1, x.1 * x.6 * x.7^-1, x.7 * x.2 * x.8^-1, (x.2 * x.1)^2, x.3 * x.6 * x.7 * x.1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 13, 25, 37, 49, 61, 73)(2, 14, 26, 38, 50, 62, 74)(3, 15, 27, 39, 51, 63, 75)(4, 16, 28, 40, 52, 64, 76)(5, 17, 29, 41, 53, 65, 77)(6, 18, 30, 42, 54, 66, 78)(7, 19, 31, 43, 55, 67, 79)(8, 20, 32, 44, 56, 68, 80)(9, 21, 33, 45, 57, 69, 81)(10, 22, 34, 46, 58, 70, 82)(11, 23, 35, 47, 59, 71, 83)(12, 24, 36, 48, 60, 72, 84)(85, 97, 109, 121, 133, 145, 157)(86, 98, 110, 122, 134, 146, 158)(87, 99, 111, 123, 135, 147, 159)(88, 100, 112, 124, 136, 148, 160)(89, 101, 113, 125, 137, 149, 161)(90, 102, 114, 126, 138, 150, 162)(91, 103, 115, 127, 139, 151, 163)(92, 104, 116, 128, 140, 152, 164)(93, 105, 117, 129, 141, 153, 165)(94, 106, 118, 130, 142, 154, 166)(95, 107, 119, 131, 143, 155, 167)(96, 108, 120, 132, 144, 156, 168) L = (1, 15)(2, 13)(3, 14)(4, 21)(5, 20)(6, 16)(7, 24)(8, 23)(9, 18)(10, 19)(11, 17)(12, 22)(25, 67)(26, 65)(27, 66)(28, 61)(29, 72)(30, 68)(31, 64)(32, 63)(33, 70)(34, 71)(35, 69)(36, 62)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 136)(50, 144)(51, 140)(52, 139)(53, 134)(54, 135)(55, 133)(56, 138)(57, 143)(58, 141)(59, 142)(60, 137)(73, 78)(74, 79)(75, 77)(76, 82)(80, 81)(83, 84)(85, 166)(86, 167)(87, 165)(88, 158)(89, 163)(90, 161)(91, 162)(92, 157)(93, 168)(94, 164)(95, 160)(96, 159)(97, 107)(98, 105)(99, 106)(100, 101)(102, 108)(103, 104)(109, 148)(110, 156)(111, 152)(112, 151)(113, 146)(114, 147)(115, 145)(116, 150)(117, 155)(118, 153)(119, 154)(120, 149) MAP : A3.1287 NOTES : type I, chiral, isomorphic to A3.1277. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^3, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^3, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.4 * x.2 * x.4^-1 * x.3, (x.3 * x.1)^2, x.5^4 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 26)(2, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(49, 128)(50, 136)(51, 144)(52, 143)(53, 140)(54, 124)(55, 132)(56, 131)(57, 135)(58, 133)(59, 134)(60, 141)(61, 123)(62, 121)(63, 122)(64, 129)(65, 126)(66, 127)(67, 125)(68, 142)(69, 138)(70, 139)(71, 137)(72, 130)(73, 84)(74, 92)(75, 76)(77, 88)(78, 96)(79, 80)(81, 91)(82, 89)(83, 90)(85, 95)(86, 93)(87, 94)(97, 117)(98, 118)(99, 119)(100, 120)(101, 105)(102, 106)(103, 107)(104, 108)(109, 113)(110, 114)(111, 115)(112, 116)(145, 160)(146, 168)(147, 152)(148, 151)(149, 156)(150, 164)(153, 167)(154, 165)(155, 166)(157, 163)(158, 161)(159, 162) MAP : A3.1288 NOTES : type I, chiral, isomorphic to A3.1274. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^3, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.5^3, x.4^3, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, (x.4 * x.2)^2, x.1 * x.3 * x.2 * x.4^-1 * x.3, x.1 * x.4 * x.1 * x.5 * x.4^-1 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 26)(2, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(49, 137)(50, 138)(51, 139)(52, 140)(53, 133)(54, 134)(55, 135)(56, 136)(57, 121)(58, 122)(59, 123)(60, 124)(61, 141)(62, 142)(63, 143)(64, 144)(65, 129)(66, 130)(67, 131)(68, 132)(69, 125)(70, 126)(71, 127)(72, 128)(73, 93)(74, 94)(75, 95)(76, 96)(77, 81)(78, 82)(79, 83)(80, 84)(85, 89)(86, 90)(87, 91)(88, 92)(97, 101)(98, 102)(99, 103)(100, 104)(105, 109)(106, 110)(107, 111)(108, 112)(113, 117)(114, 118)(115, 119)(116, 120)(145, 162)(146, 163)(147, 161)(148, 154)(149, 159)(150, 157)(151, 158)(152, 165)(153, 164)(155, 156)(160, 166)(167, 168) MAP : A3.1289 NOTES : type II, reflexible, isomorphic to A3.1286. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 3, 3, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^3, u.7^3, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.5, x.1^2, x.2^2, x.4 * x.6, x.3^3, x.7^3, x.5 * x.6^-1 * x.8, x.3^-1 * x.4^-1 * x.1, x.2 * x.7 * x.3^-1, x.1 * x.6 * x.7^-1, x.7 * x.2 * x.8^-1, (x.2 * x.1)^2, x.3 * x.6 * x.7 * x.1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 13, 25, 37, 49, 61, 73)(2, 14, 26, 38, 50, 62, 74)(3, 15, 27, 39, 51, 63, 75)(4, 16, 28, 40, 52, 64, 76)(5, 17, 29, 41, 53, 65, 77)(6, 18, 30, 42, 54, 66, 78)(7, 19, 31, 43, 55, 67, 79)(8, 20, 32, 44, 56, 68, 80)(9, 21, 33, 45, 57, 69, 81)(10, 22, 34, 46, 58, 70, 82)(11, 23, 35, 47, 59, 71, 83)(12, 24, 36, 48, 60, 72, 84)(85, 97, 109, 121, 133, 145, 157)(86, 98, 110, 122, 134, 146, 158)(87, 99, 111, 123, 135, 147, 159)(88, 100, 112, 124, 136, 148, 160)(89, 101, 113, 125, 137, 149, 161)(90, 102, 114, 126, 138, 150, 162)(91, 103, 115, 127, 139, 151, 163)(92, 104, 116, 128, 140, 152, 164)(93, 105, 117, 129, 141, 153, 165)(94, 106, 118, 130, 142, 154, 166)(95, 107, 119, 131, 143, 155, 167)(96, 108, 120, 132, 144, 156, 168) L = (1, 14)(2, 15)(3, 13)(4, 18)(5, 23)(6, 21)(7, 22)(8, 17)(9, 16)(10, 24)(11, 20)(12, 19)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 61)(34, 62)(35, 63)(36, 64)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 141)(50, 142)(51, 143)(52, 144)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(73, 78)(74, 79)(75, 77)(76, 82)(80, 81)(83, 84)(85, 164)(86, 160)(87, 168)(88, 167)(89, 162)(90, 163)(91, 161)(92, 166)(93, 159)(94, 157)(95, 158)(96, 165)(97, 108)(98, 104)(99, 100)(101, 106)(102, 107)(103, 105)(109, 153)(110, 154)(111, 155)(112, 156)(113, 145)(114, 146)(115, 147)(116, 148)(117, 149)(118, 150)(119, 151)(120, 152) MAP : A3.1290 NOTES : type I, chiral, isomorphic to A3.1278. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^3, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^3, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.1 * x.4 * x.5^-1 * x.4, x.4^-1 * x.1 * x.2 * x.3, x.5 * x.4^-2 * x.3, x.5^4 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3) #DARTS : 168 R = (1, 25, 49, 73, 97, 121, 145)(2, 26, 50, 74, 98, 122, 146)(3, 27, 51, 75, 99, 123, 147)(4, 28, 52, 76, 100, 124, 148)(5, 29, 53, 77, 101, 125, 149)(6, 30, 54, 78, 102, 126, 150)(7, 31, 55, 79, 103, 127, 151)(8, 32, 56, 80, 104, 128, 152)(9, 33, 57, 81, 105, 129, 153)(10, 34, 58, 82, 106, 130, 154)(11, 35, 59, 83, 107, 131, 155)(12, 36, 60, 84, 108, 132, 156)(13, 37, 61, 85, 109, 133, 157)(14, 38, 62, 86, 110, 134, 158)(15, 39, 63, 87, 111, 135, 159)(16, 40, 64, 88, 112, 136, 160)(17, 41, 65, 89, 113, 137, 161)(18, 42, 66, 90, 114, 138, 162)(19, 43, 67, 91, 115, 139, 163)(20, 44, 68, 92, 116, 140, 164)(21, 45, 69, 93, 117, 141, 165)(22, 46, 70, 94, 118, 142, 166)(23, 47, 71, 95, 119, 143, 167)(24, 48, 72, 96, 120, 144, 168) L = (1, 26)(2, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(49, 128)(50, 136)(51, 144)(52, 143)(53, 140)(54, 124)(55, 132)(56, 131)(57, 135)(58, 133)(59, 134)(60, 141)(61, 123)(62, 121)(63, 122)(64, 129)(65, 126)(66, 127)(67, 125)(68, 142)(69, 138)(70, 139)(71, 137)(72, 130)(73, 93)(74, 94)(75, 95)(76, 96)(77, 81)(78, 82)(79, 83)(80, 84)(85, 89)(86, 90)(87, 91)(88, 92)(97, 114)(98, 115)(99, 113)(100, 106)(101, 111)(102, 109)(103, 110)(104, 117)(105, 116)(107, 108)(112, 118)(119, 120)(145, 160)(146, 168)(147, 152)(148, 151)(149, 156)(150, 164)(153, 167)(154, 165)(155, 166)(157, 163)(158, 161)(159, 162) MAP : A3.1291 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 8)(2, 12)(3, 4)(5, 11)(6, 15)(7, 9)(10, 13)(14, 16)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 66)(50, 70)(51, 78)(52, 71)(53, 79)(54, 75)(55, 77)(56, 69)(57, 67)(58, 73)(59, 65)(60, 72)(61, 80)(62, 74)(63, 76)(64, 68)(81, 84)(82, 87)(83, 88)(85, 94)(86, 93)(89, 92)(90, 95)(91, 96) MAP : A3.1292 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 3)(2, 9)(4, 8)(5, 16)(6, 10)(7, 12)(11, 14)(13, 15)(17, 28)(18, 31)(19, 32)(20, 25)(21, 22)(23, 26)(24, 27)(29, 30)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 66)(50, 70)(51, 78)(52, 71)(53, 79)(54, 75)(55, 77)(56, 69)(57, 67)(58, 73)(59, 65)(60, 72)(61, 80)(62, 74)(63, 76)(64, 68)(81, 84)(82, 87)(83, 88)(85, 94)(86, 93)(89, 92)(90, 95)(91, 96) MAP : A3.1293 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 31)(18, 21)(19, 29)(20, 26)(22, 24)(23, 30)(25, 32)(27, 28)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 66)(50, 70)(51, 78)(52, 71)(53, 79)(54, 75)(55, 77)(56, 69)(57, 67)(58, 73)(59, 65)(60, 72)(61, 80)(62, 74)(63, 76)(64, 68)(81, 84)(82, 87)(83, 88)(85, 94)(86, 93)(89, 92)(90, 95)(91, 96) MAP : A3.1294 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 5)(2, 8)(3, 7)(4, 14)(6, 12)(9, 13)(10, 16)(11, 15)(17, 19)(18, 25)(20, 24)(21, 32)(22, 26)(23, 28)(27, 30)(29, 31)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 66)(50, 70)(51, 78)(52, 71)(53, 79)(54, 75)(55, 77)(56, 69)(57, 67)(58, 73)(59, 65)(60, 72)(61, 80)(62, 74)(63, 76)(64, 68)(81, 84)(82, 87)(83, 88)(85, 94)(86, 93)(89, 92)(90, 95)(91, 96) MAP : A3.1295 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 26)(18, 30)(19, 22)(20, 31)(21, 23)(24, 29)(25, 27)(28, 32)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 71)(50, 77)(51, 69)(52, 66)(53, 74)(54, 80)(55, 70)(56, 78)(57, 72)(58, 76)(59, 68)(60, 67)(61, 75)(62, 79)(63, 73)(64, 65)(81, 84)(82, 87)(83, 88)(85, 94)(86, 93)(89, 92)(90, 95)(91, 96) MAP : A3.1296 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, x.3 * x.1 * x.5^-1 * x.2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 4)(2, 11)(3, 13)(5, 8)(6, 15)(7, 9)(10, 16)(12, 14)(17, 19)(18, 23)(20, 26)(21, 28)(22, 32)(24, 25)(27, 30)(29, 31)(33, 109)(34, 105)(35, 100)(36, 112)(37, 110)(38, 106)(39, 107)(40, 103)(41, 101)(42, 97)(43, 108)(44, 104)(45, 102)(46, 98)(47, 99)(48, 111)(49, 69)(50, 65)(51, 76)(52, 72)(53, 70)(54, 66)(55, 67)(56, 79)(57, 77)(58, 73)(59, 68)(60, 80)(61, 78)(62, 74)(63, 75)(64, 71)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.1297 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 26)(18, 30)(19, 22)(20, 31)(21, 23)(24, 29)(25, 27)(28, 32)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 80)(50, 68)(51, 76)(52, 75)(53, 67)(54, 71)(55, 65)(56, 73)(57, 79)(58, 69)(59, 77)(60, 74)(61, 66)(62, 72)(63, 78)(64, 70)(81, 93)(82, 96)(83, 95)(84, 86)(85, 89)(87, 91)(88, 90)(92, 94) MAP : A3.1298 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 8)(2, 12)(3, 4)(5, 11)(6, 15)(7, 9)(10, 13)(14, 16)(17, 28)(18, 31)(19, 32)(20, 25)(21, 22)(23, 26)(24, 27)(29, 30)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 71)(50, 77)(51, 69)(52, 66)(53, 74)(54, 80)(55, 70)(56, 78)(57, 72)(58, 76)(59, 68)(60, 67)(61, 75)(62, 79)(63, 73)(64, 65)(81, 84)(82, 87)(83, 88)(85, 94)(86, 93)(89, 92)(90, 95)(91, 96) MAP : A3.1299 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 23)(2, 29)(3, 21)(4, 18)(5, 26)(6, 32)(7, 22)(8, 30)(9, 24)(10, 28)(11, 20)(12, 19)(13, 27)(14, 31)(15, 25)(16, 17)(33, 91)(34, 81)(35, 89)(36, 96)(37, 88)(38, 82)(39, 84)(40, 92)(41, 90)(42, 94)(43, 86)(44, 95)(45, 87)(46, 83)(47, 85)(48, 93)(49, 53)(50, 56)(51, 55)(52, 62)(54, 60)(57, 61)(58, 64)(59, 63)(65, 72)(66, 76)(67, 68)(69, 75)(70, 79)(71, 73)(74, 77)(78, 80)(97, 100)(98, 103)(99, 104)(101, 110)(102, 109)(105, 108)(106, 111)(107, 112) MAP : A3.1300 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 23)(2, 29)(3, 21)(4, 18)(5, 26)(6, 32)(7, 22)(8, 30)(9, 24)(10, 28)(11, 20)(12, 19)(13, 27)(14, 31)(15, 25)(16, 17)(33, 91)(34, 81)(35, 89)(36, 96)(37, 88)(38, 82)(39, 84)(40, 92)(41, 90)(42, 94)(43, 86)(44, 95)(45, 87)(46, 83)(47, 85)(48, 93)(49, 56)(50, 60)(51, 52)(53, 59)(54, 63)(55, 57)(58, 61)(62, 64)(65, 76)(66, 79)(67, 80)(68, 73)(69, 70)(71, 74)(72, 75)(77, 78)(97, 100)(98, 103)(99, 104)(101, 110)(102, 109)(105, 108)(106, 111)(107, 112) MAP : A3.1301 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 23)(2, 29)(3, 21)(4, 18)(5, 26)(6, 32)(7, 22)(8, 30)(9, 24)(10, 28)(11, 20)(12, 19)(13, 27)(14, 31)(15, 25)(16, 17)(33, 91)(34, 81)(35, 89)(36, 96)(37, 88)(38, 82)(39, 84)(40, 92)(41, 90)(42, 94)(43, 86)(44, 95)(45, 87)(46, 83)(47, 85)(48, 93)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 74)(66, 78)(67, 70)(68, 79)(69, 71)(72, 77)(73, 75)(76, 80)(97, 100)(98, 103)(99, 104)(101, 110)(102, 109)(105, 108)(106, 111)(107, 112) MAP : A3.1302 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 3)(2, 9)(4, 8)(5, 16)(6, 10)(7, 12)(11, 14)(13, 15)(17, 28)(18, 31)(19, 32)(20, 25)(21, 22)(23, 26)(24, 27)(29, 30)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 75)(50, 65)(51, 73)(52, 80)(53, 72)(54, 66)(55, 68)(56, 76)(57, 74)(58, 78)(59, 70)(60, 79)(61, 71)(62, 67)(63, 69)(64, 77)(81, 93)(82, 96)(83, 95)(84, 86)(85, 89)(87, 91)(88, 90)(92, 94) MAP : A3.1303 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 18)(2, 22)(3, 30)(4, 23)(5, 31)(6, 27)(7, 29)(8, 21)(9, 19)(10, 25)(11, 17)(12, 24)(13, 32)(14, 26)(15, 28)(16, 20)(33, 96)(34, 84)(35, 92)(36, 91)(37, 83)(38, 87)(39, 81)(40, 89)(41, 95)(42, 85)(43, 93)(44, 90)(45, 82)(46, 88)(47, 94)(48, 86)(49, 51)(50, 57)(52, 56)(53, 64)(54, 58)(55, 60)(59, 62)(61, 63)(65, 76)(66, 79)(67, 80)(68, 73)(69, 70)(71, 74)(72, 75)(77, 78)(97, 100)(98, 103)(99, 104)(101, 110)(102, 109)(105, 108)(106, 111)(107, 112) MAP : A3.1304 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 18)(2, 22)(3, 30)(4, 23)(5, 31)(6, 27)(7, 29)(8, 21)(9, 19)(10, 25)(11, 17)(12, 24)(13, 32)(14, 26)(15, 28)(16, 20)(33, 96)(34, 84)(35, 92)(36, 91)(37, 83)(38, 87)(39, 81)(40, 89)(41, 95)(42, 85)(43, 93)(44, 90)(45, 82)(46, 88)(47, 94)(48, 86)(49, 53)(50, 56)(51, 55)(52, 62)(54, 60)(57, 61)(58, 64)(59, 63)(65, 67)(66, 73)(68, 72)(69, 80)(70, 74)(71, 76)(75, 78)(77, 79)(97, 100)(98, 103)(99, 104)(101, 110)(102, 109)(105, 108)(106, 111)(107, 112) MAP : A3.1305 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 18)(2, 22)(3, 30)(4, 23)(5, 31)(6, 27)(7, 29)(8, 21)(9, 19)(10, 25)(11, 17)(12, 24)(13, 32)(14, 26)(15, 28)(16, 20)(33, 96)(34, 84)(35, 92)(36, 91)(37, 83)(38, 87)(39, 81)(40, 89)(41, 95)(42, 85)(43, 93)(44, 90)(45, 82)(46, 88)(47, 94)(48, 86)(49, 56)(50, 60)(51, 52)(53, 59)(54, 63)(55, 57)(58, 61)(62, 64)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80)(97, 100)(98, 103)(99, 104)(101, 110)(102, 109)(105, 108)(106, 111)(107, 112) MAP : A3.1306 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.7^-1 * x.3^-1, x.4 * x.5^-1 * x.6, x.1 * x.3 * x.6^-1, x.1 * x.7 * x.4^-1, x.5 * x.6^-1 * x.8, x.7 * x.2 * x.8^-1, x.7^4, x.3^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 12)(2, 15)(3, 16)(4, 14)(5, 9)(6, 13)(7, 11)(8, 10)(17, 47)(18, 44)(19, 45)(20, 43)(21, 42)(22, 48)(23, 46)(24, 41)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 96)(34, 93)(35, 92)(36, 90)(37, 91)(38, 95)(39, 89)(40, 94)(49, 51)(50, 54)(52, 56)(53, 55)(57, 109)(58, 112)(59, 111)(60, 105)(61, 110)(62, 108)(63, 106)(64, 107)(65, 66)(67, 70)(68, 71)(69, 72)(73, 104)(74, 101)(75, 100)(76, 98)(77, 99)(78, 103)(79, 97)(80, 102) MAP : A3.1307 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 18)(2, 22)(3, 30)(4, 23)(5, 31)(6, 27)(7, 29)(8, 21)(9, 19)(10, 25)(11, 17)(12, 24)(13, 32)(14, 26)(15, 28)(16, 20)(33, 87)(34, 93)(35, 85)(36, 82)(37, 90)(38, 96)(39, 86)(40, 94)(41, 88)(42, 92)(43, 84)(44, 83)(45, 91)(46, 95)(47, 89)(48, 81)(49, 51)(50, 57)(52, 56)(53, 64)(54, 58)(55, 60)(59, 62)(61, 63)(65, 69)(66, 72)(67, 71)(68, 78)(70, 76)(73, 77)(74, 80)(75, 79)(97, 109)(98, 112)(99, 111)(100, 102)(101, 105)(103, 107)(104, 106)(108, 110) MAP : A3.1308 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 18)(2, 22)(3, 30)(4, 23)(5, 31)(6, 27)(7, 29)(8, 21)(9, 19)(10, 25)(11, 17)(12, 24)(13, 32)(14, 26)(15, 28)(16, 20)(33, 87)(34, 93)(35, 85)(36, 82)(37, 90)(38, 96)(39, 86)(40, 94)(41, 88)(42, 92)(43, 84)(44, 83)(45, 91)(46, 95)(47, 89)(48, 81)(49, 53)(50, 56)(51, 55)(52, 62)(54, 60)(57, 61)(58, 64)(59, 63)(65, 74)(66, 78)(67, 70)(68, 79)(69, 71)(72, 77)(73, 75)(76, 80)(97, 109)(98, 112)(99, 111)(100, 102)(101, 105)(103, 107)(104, 106)(108, 110) MAP : A3.1309 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 18)(2, 22)(3, 30)(4, 23)(5, 31)(6, 27)(7, 29)(8, 21)(9, 19)(10, 25)(11, 17)(12, 24)(13, 32)(14, 26)(15, 28)(16, 20)(33, 87)(34, 93)(35, 85)(36, 82)(37, 90)(38, 96)(39, 86)(40, 94)(41, 88)(42, 92)(43, 84)(44, 83)(45, 91)(46, 95)(47, 89)(48, 81)(49, 56)(50, 60)(51, 52)(53, 59)(54, 63)(55, 57)(58, 61)(62, 64)(65, 78)(66, 67)(68, 69)(70, 73)(71, 72)(74, 75)(76, 77)(79, 80)(97, 109)(98, 112)(99, 111)(100, 102)(101, 105)(103, 107)(104, 106)(108, 110) MAP : A3.1310 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 18)(2, 22)(3, 30)(4, 23)(5, 31)(6, 27)(7, 29)(8, 21)(9, 19)(10, 25)(11, 17)(12, 24)(13, 32)(14, 26)(15, 28)(16, 20)(33, 96)(34, 84)(35, 92)(36, 91)(37, 83)(38, 87)(39, 81)(40, 89)(41, 95)(42, 85)(43, 93)(44, 90)(45, 82)(46, 88)(47, 94)(48, 86)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 79)(66, 69)(67, 77)(68, 74)(70, 72)(71, 78)(73, 80)(75, 76)(97, 100)(98, 103)(99, 104)(101, 110)(102, 109)(105, 108)(106, 111)(107, 112) MAP : A3.1311 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, x.4 * x.1 * x.4^-1 * x.1 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 21)(2, 17)(3, 28)(4, 24)(5, 22)(6, 18)(7, 19)(8, 31)(9, 29)(10, 25)(11, 20)(12, 32)(13, 30)(14, 26)(15, 27)(16, 23)(33, 87)(34, 96)(35, 82)(36, 94)(37, 83)(38, 92)(39, 86)(40, 90)(41, 84)(42, 91)(43, 93)(44, 81)(45, 88)(46, 95)(47, 89)(48, 85)(49, 52)(50, 59)(51, 61)(53, 56)(54, 63)(55, 57)(58, 64)(60, 62)(65, 78)(66, 77)(67, 72)(68, 71)(69, 74)(70, 73)(75, 80)(76, 79)(97, 99)(98, 103)(100, 106)(101, 108)(102, 112)(104, 105)(107, 110)(109, 111) MAP : A3.1312 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, x.4 * x.1 * x.4^-1 * x.1 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 21)(2, 17)(3, 28)(4, 24)(5, 22)(6, 18)(7, 19)(8, 31)(9, 29)(10, 25)(11, 20)(12, 32)(13, 30)(14, 26)(15, 27)(16, 23)(33, 87)(34, 96)(35, 82)(36, 94)(37, 83)(38, 92)(39, 86)(40, 90)(41, 84)(42, 91)(43, 93)(44, 81)(45, 88)(46, 95)(47, 89)(48, 85)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 68)(66, 75)(67, 77)(69, 72)(70, 79)(71, 73)(74, 80)(76, 78)(97, 99)(98, 103)(100, 106)(101, 108)(102, 112)(104, 105)(107, 110)(109, 111) MAP : A3.1313 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, x.4 * x.1 * x.4^-1 * x.1 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 21)(2, 17)(3, 28)(4, 24)(5, 22)(6, 18)(7, 19)(8, 31)(9, 29)(10, 25)(11, 20)(12, 32)(13, 30)(14, 26)(15, 27)(16, 23)(33, 91)(34, 95)(35, 89)(36, 82)(37, 84)(38, 88)(39, 90)(40, 81)(41, 96)(42, 92)(43, 86)(44, 93)(45, 87)(46, 83)(47, 85)(48, 94)(49, 51)(50, 55)(52, 58)(53, 60)(54, 64)(56, 57)(59, 62)(61, 63)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80)(97, 100)(98, 107)(99, 109)(101, 104)(102, 111)(103, 105)(106, 112)(108, 110) MAP : A3.1314 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, x.4 * x.1 * x.4^-1 * x.1 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 21)(2, 17)(3, 28)(4, 24)(5, 22)(6, 18)(7, 19)(8, 31)(9, 29)(10, 25)(11, 20)(12, 32)(13, 30)(14, 26)(15, 27)(16, 23)(33, 91)(34, 95)(35, 89)(36, 82)(37, 84)(38, 88)(39, 90)(40, 81)(41, 96)(42, 92)(43, 86)(44, 93)(45, 87)(46, 83)(47, 85)(48, 94)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 80)(66, 76)(67, 70)(68, 77)(69, 71)(72, 78)(73, 75)(74, 79)(97, 100)(98, 107)(99, 109)(101, 104)(102, 111)(103, 105)(106, 112)(108, 110) MAP : A3.1315 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 23)(2, 29)(3, 21)(4, 18)(5, 26)(6, 32)(7, 22)(8, 30)(9, 24)(10, 28)(11, 20)(12, 19)(13, 27)(14, 31)(15, 25)(16, 17)(33, 82)(34, 86)(35, 94)(36, 87)(37, 95)(38, 91)(39, 93)(40, 85)(41, 83)(42, 89)(43, 81)(44, 88)(45, 96)(46, 90)(47, 92)(48, 84)(49, 51)(50, 57)(52, 56)(53, 64)(54, 58)(55, 60)(59, 62)(61, 63)(65, 78)(66, 67)(68, 69)(70, 73)(71, 72)(74, 75)(76, 77)(79, 80)(97, 109)(98, 112)(99, 111)(100, 102)(101, 105)(103, 107)(104, 106)(108, 110) MAP : A3.1316 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 23)(2, 29)(3, 21)(4, 18)(5, 26)(6, 32)(7, 22)(8, 30)(9, 24)(10, 28)(11, 20)(12, 19)(13, 27)(14, 31)(15, 25)(16, 17)(33, 82)(34, 86)(35, 94)(36, 87)(37, 95)(38, 91)(39, 93)(40, 85)(41, 83)(42, 89)(43, 81)(44, 88)(45, 96)(46, 90)(47, 92)(48, 84)(49, 53)(50, 56)(51, 55)(52, 62)(54, 60)(57, 61)(58, 64)(59, 63)(65, 79)(66, 69)(67, 77)(68, 74)(70, 72)(71, 78)(73, 80)(75, 76)(97, 109)(98, 112)(99, 111)(100, 102)(101, 105)(103, 107)(104, 106)(108, 110) MAP : A3.1317 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 23)(2, 29)(3, 21)(4, 18)(5, 26)(6, 32)(7, 22)(8, 30)(9, 24)(10, 28)(11, 20)(12, 19)(13, 27)(14, 31)(15, 25)(16, 17)(33, 82)(34, 86)(35, 94)(36, 87)(37, 95)(38, 91)(39, 93)(40, 85)(41, 83)(42, 89)(43, 81)(44, 88)(45, 96)(46, 90)(47, 92)(48, 84)(49, 56)(50, 60)(51, 52)(53, 59)(54, 63)(55, 57)(58, 61)(62, 64)(65, 69)(66, 72)(67, 71)(68, 78)(70, 76)(73, 77)(74, 80)(75, 79)(97, 109)(98, 112)(99, 111)(100, 102)(101, 105)(103, 107)(104, 106)(108, 110) MAP : A3.1318 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 23)(2, 29)(3, 21)(4, 18)(5, 26)(6, 32)(7, 22)(8, 30)(9, 24)(10, 28)(11, 20)(12, 19)(13, 27)(14, 31)(15, 25)(16, 17)(33, 82)(34, 86)(35, 94)(36, 87)(37, 95)(38, 91)(39, 93)(40, 85)(41, 83)(42, 89)(43, 81)(44, 88)(45, 96)(46, 90)(47, 92)(48, 84)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 67)(66, 73)(68, 72)(69, 80)(70, 74)(71, 76)(75, 78)(77, 79)(97, 109)(98, 112)(99, 111)(100, 102)(101, 105)(103, 107)(104, 106)(108, 110) MAP : A3.1319 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, x.4 * x.1 * x.4^-1 * x.1 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 18)(2, 22)(3, 23)(4, 27)(5, 17)(6, 21)(7, 32)(8, 20)(9, 26)(10, 30)(11, 31)(12, 19)(13, 25)(14, 29)(15, 24)(16, 28)(33, 92)(34, 83)(35, 85)(36, 89)(37, 96)(38, 87)(39, 81)(40, 93)(41, 95)(42, 88)(43, 90)(44, 86)(45, 91)(46, 84)(47, 94)(48, 82)(49, 52)(50, 59)(51, 61)(53, 56)(54, 63)(55, 57)(58, 64)(60, 62)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80)(97, 99)(98, 103)(100, 106)(101, 108)(102, 112)(104, 105)(107, 110)(109, 111) MAP : A3.1320 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, x.4 * x.1 * x.4^-1 * x.1 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 18)(2, 22)(3, 23)(4, 27)(5, 17)(6, 21)(7, 32)(8, 20)(9, 26)(10, 30)(11, 31)(12, 19)(13, 25)(14, 29)(15, 24)(16, 28)(33, 88)(34, 84)(35, 94)(36, 85)(37, 95)(38, 91)(39, 93)(40, 86)(41, 83)(42, 87)(43, 81)(44, 90)(45, 92)(46, 96)(47, 82)(48, 89)(49, 51)(50, 55)(52, 58)(53, 60)(54, 64)(56, 57)(59, 62)(61, 63)(65, 78)(66, 77)(67, 72)(68, 71)(69, 74)(70, 73)(75, 80)(76, 79)(97, 100)(98, 107)(99, 109)(101, 104)(102, 111)(103, 105)(106, 112)(108, 110) MAP : A3.1321 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, x.4 * x.1 * x.4^-1 * x.1 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 18)(2, 22)(3, 23)(4, 27)(5, 17)(6, 21)(7, 32)(8, 20)(9, 26)(10, 30)(11, 31)(12, 19)(13, 25)(14, 29)(15, 24)(16, 28)(33, 88)(34, 84)(35, 94)(36, 85)(37, 95)(38, 91)(39, 93)(40, 86)(41, 83)(42, 87)(43, 81)(44, 90)(45, 92)(46, 96)(47, 82)(48, 89)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 67)(66, 71)(68, 74)(69, 76)(70, 80)(72, 73)(75, 78)(77, 79)(97, 100)(98, 107)(99, 109)(101, 104)(102, 111)(103, 105)(106, 112)(108, 110) MAP : A3.1322 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, x.4 * x.1 * x.4^-1 * x.1 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 18)(2, 22)(3, 23)(4, 27)(5, 17)(6, 21)(7, 32)(8, 20)(9, 26)(10, 30)(11, 31)(12, 19)(13, 25)(14, 29)(15, 24)(16, 28)(33, 93)(34, 89)(35, 84)(36, 96)(37, 94)(38, 90)(39, 91)(40, 87)(41, 85)(42, 81)(43, 92)(44, 88)(45, 86)(46, 82)(47, 83)(48, 95)(49, 51)(50, 55)(52, 58)(53, 60)(54, 64)(56, 57)(59, 62)(61, 63)(65, 68)(66, 75)(67, 77)(69, 72)(70, 79)(71, 73)(74, 80)(76, 78)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.1323 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, x.4 * x.1 * x.4^-1 * x.1 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 18)(2, 22)(3, 23)(4, 27)(5, 17)(6, 21)(7, 32)(8, 20)(9, 26)(10, 30)(11, 31)(12, 19)(13, 25)(14, 29)(15, 24)(16, 28)(33, 93)(34, 89)(35, 84)(36, 96)(37, 94)(38, 90)(39, 91)(40, 87)(41, 85)(42, 81)(43, 92)(44, 88)(45, 86)(46, 82)(47, 83)(48, 95)(49, 52)(50, 59)(51, 61)(53, 56)(54, 63)(55, 57)(58, 64)(60, 62)(65, 80)(66, 76)(67, 70)(68, 77)(69, 71)(72, 78)(73, 75)(74, 79)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.1324 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 3)(2, 9)(4, 8)(5, 16)(6, 10)(7, 12)(11, 14)(13, 15)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 71)(50, 77)(51, 69)(52, 66)(53, 74)(54, 80)(55, 70)(56, 78)(57, 72)(58, 76)(59, 68)(60, 67)(61, 75)(62, 79)(63, 73)(64, 65)(81, 84)(82, 87)(83, 88)(85, 94)(86, 93)(89, 92)(90, 95)(91, 96) MAP : A3.1325 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 5)(2, 8)(3, 7)(4, 14)(6, 12)(9, 13)(10, 16)(11, 15)(17, 24)(18, 28)(19, 20)(21, 27)(22, 31)(23, 25)(26, 29)(30, 32)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 71)(50, 77)(51, 69)(52, 66)(53, 74)(54, 80)(55, 70)(56, 78)(57, 72)(58, 76)(59, 68)(60, 67)(61, 75)(62, 79)(63, 73)(64, 65)(81, 84)(82, 87)(83, 88)(85, 94)(86, 93)(89, 92)(90, 95)(91, 96) MAP : A3.1326 NOTES : type II, reflexible, isomorphic to A3.1306. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.7^-1 * x.3^-1, x.4 * x.5^-1 * x.6, x.1 * x.3 * x.6^-1, x.1 * x.7 * x.4^-1, x.5 * x.6^-1 * x.8, x.7 * x.2 * x.8^-1, x.7^4, x.3^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 15)(2, 12)(3, 13)(4, 11)(5, 10)(6, 16)(7, 14)(8, 9)(17, 45)(18, 48)(19, 47)(20, 41)(21, 46)(22, 44)(23, 42)(24, 43)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 92)(34, 95)(35, 96)(36, 94)(37, 89)(38, 93)(39, 91)(40, 90)(49, 50)(51, 54)(52, 55)(53, 56)(57, 112)(58, 109)(59, 108)(60, 106)(61, 107)(62, 111)(63, 105)(64, 110)(65, 67)(66, 70)(68, 72)(69, 71)(73, 100)(74, 103)(75, 104)(76, 102)(77, 97)(78, 101)(79, 99)(80, 98) MAP : A3.1327 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.5, x.1^2, x.2^2, x.4 * x.6, x.2 * x.1, x.7 * x.3^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.6^-1, x.7 * x.2 * x.8^-1, x.5 * x.6^-1 * x.8, x.3^4, x.7^4, x.4 * x.3^-1 * x.6^-1 * x.3^-1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 16)(2, 13)(3, 12)(4, 10)(5, 11)(6, 15)(7, 9)(8, 14)(17, 44)(18, 47)(19, 48)(20, 46)(21, 41)(22, 45)(23, 43)(24, 42)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 93)(34, 96)(35, 95)(36, 89)(37, 94)(38, 92)(39, 90)(40, 91)(49, 50)(51, 54)(52, 55)(53, 56)(57, 112)(58, 109)(59, 108)(60, 106)(61, 107)(62, 111)(63, 105)(64, 110)(65, 66)(67, 70)(68, 71)(69, 72)(73, 101)(74, 104)(75, 103)(76, 97)(77, 102)(78, 100)(79, 98)(80, 99) MAP : A3.1328 NOTES : type II, reflexible, isomorphic to A3.1306. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.7^-1 * x.3^-1, x.4 * x.5^-1 * x.6, x.1 * x.3 * x.6^-1, x.1 * x.7 * x.4^-1, x.5 * x.6^-1 * x.8, x.7 * x.2 * x.8^-1, x.7^4, x.3^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 16)(2, 13)(3, 12)(4, 10)(5, 11)(6, 15)(7, 9)(8, 14)(17, 44)(18, 47)(19, 48)(20, 46)(21, 41)(22, 45)(23, 43)(24, 42)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 93)(34, 96)(35, 95)(36, 89)(37, 94)(38, 92)(39, 90)(40, 91)(49, 50)(51, 54)(52, 55)(53, 56)(57, 111)(58, 108)(59, 109)(60, 107)(61, 106)(62, 112)(63, 110)(64, 105)(65, 67)(66, 70)(68, 72)(69, 71)(73, 101)(74, 104)(75, 103)(76, 97)(77, 102)(78, 100)(79, 98)(80, 99) MAP : A3.1329 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, x.3 * x.1 * x.5^-1 * x.2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 4)(2, 11)(3, 13)(5, 8)(6, 15)(7, 9)(10, 16)(12, 14)(17, 30)(18, 29)(19, 24)(20, 23)(21, 26)(22, 25)(27, 32)(28, 31)(33, 108)(34, 99)(35, 101)(36, 105)(37, 112)(38, 103)(39, 97)(40, 109)(41, 111)(42, 104)(43, 106)(44, 102)(45, 107)(46, 100)(47, 110)(48, 98)(49, 69)(50, 65)(51, 76)(52, 72)(53, 70)(54, 66)(55, 67)(56, 79)(57, 77)(58, 73)(59, 68)(60, 80)(61, 78)(62, 74)(63, 75)(64, 71)(81, 83)(82, 87)(84, 90)(85, 92)(86, 96)(88, 89)(91, 94)(93, 95) MAP : A3.1330 NOTES : type II, reflexible, isomorphic to A3.1327. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.5, x.1^2, x.2^2, x.4 * x.6, x.2 * x.1, x.7 * x.3^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.6^-1, x.7 * x.2 * x.8^-1, x.5 * x.6^-1 * x.8, x.3^4, x.7^4, x.4 * x.3^-1 * x.6^-1 * x.3^-1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 12)(2, 15)(3, 16)(4, 14)(5, 9)(6, 13)(7, 11)(8, 10)(17, 47)(18, 44)(19, 45)(20, 43)(21, 42)(22, 48)(23, 46)(24, 41)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 96)(34, 93)(35, 92)(36, 90)(37, 91)(38, 95)(39, 89)(40, 94)(49, 51)(50, 54)(52, 56)(53, 55)(57, 108)(58, 111)(59, 112)(60, 110)(61, 105)(62, 109)(63, 107)(64, 106)(65, 67)(66, 70)(68, 72)(69, 71)(73, 104)(74, 101)(75, 100)(76, 98)(77, 99)(78, 103)(79, 97)(80, 102) MAP : A3.1331 NOTES : type II, reflexible, isomorphic to A3.1306. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.7^-1 * x.3^-1, x.4 * x.5^-1 * x.6, x.1 * x.3 * x.6^-1, x.1 * x.7 * x.4^-1, x.5 * x.6^-1 * x.8, x.7 * x.2 * x.8^-1, x.7^4, x.3^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 13)(2, 16)(3, 15)(4, 9)(5, 14)(6, 12)(7, 10)(8, 11)(17, 48)(18, 45)(19, 44)(20, 42)(21, 43)(22, 47)(23, 41)(24, 46)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 95)(34, 92)(35, 93)(36, 91)(37, 90)(38, 96)(39, 94)(40, 89)(49, 51)(50, 54)(52, 56)(53, 55)(57, 108)(58, 111)(59, 112)(60, 110)(61, 105)(62, 109)(63, 107)(64, 106)(65, 66)(67, 70)(68, 71)(69, 72)(73, 103)(74, 100)(75, 101)(76, 99)(77, 98)(78, 104)(79, 102)(80, 97) MAP : A3.1332 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 3)(2, 9)(4, 8)(5, 16)(6, 10)(7, 12)(11, 14)(13, 15)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 80)(50, 68)(51, 76)(52, 75)(53, 67)(54, 71)(55, 65)(56, 73)(57, 79)(58, 69)(59, 77)(60, 74)(61, 66)(62, 72)(63, 78)(64, 70)(81, 93)(82, 96)(83, 95)(84, 86)(85, 89)(87, 91)(88, 90)(92, 94) MAP : A3.1333 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 5)(2, 8)(3, 7)(4, 14)(6, 12)(9, 13)(10, 16)(11, 15)(17, 24)(18, 28)(19, 20)(21, 27)(22, 31)(23, 25)(26, 29)(30, 32)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 80)(50, 68)(51, 76)(52, 75)(53, 67)(54, 71)(55, 65)(56, 73)(57, 79)(58, 69)(59, 77)(60, 74)(61, 66)(62, 72)(63, 78)(64, 70)(81, 93)(82, 96)(83, 95)(84, 86)(85, 89)(87, 91)(88, 90)(92, 94) MAP : A3.1334 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 8)(2, 12)(3, 4)(5, 11)(6, 15)(7, 9)(10, 13)(14, 16)(17, 28)(18, 31)(19, 32)(20, 25)(21, 22)(23, 26)(24, 27)(29, 30)(33, 98)(34, 102)(35, 110)(36, 103)(37, 111)(38, 107)(39, 109)(40, 101)(41, 99)(42, 105)(43, 97)(44, 104)(45, 112)(46, 106)(47, 108)(48, 100)(49, 80)(50, 68)(51, 76)(52, 75)(53, 67)(54, 71)(55, 65)(56, 73)(57, 79)(58, 69)(59, 77)(60, 74)(61, 66)(62, 72)(63, 78)(64, 70)(81, 93)(82, 96)(83, 95)(84, 86)(85, 89)(87, 91)(88, 90)(92, 94) MAP : A3.1335 NOTES : type II, reflexible, isomorphic to A3.1306. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.7^-1 * x.3^-1, x.4 * x.5^-1 * x.6, x.1 * x.3 * x.6^-1, x.1 * x.7 * x.4^-1, x.5 * x.6^-1 * x.8, x.7 * x.2 * x.8^-1, x.7^4, x.3^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 16)(2, 13)(3, 12)(4, 10)(5, 11)(6, 15)(7, 9)(8, 14)(17, 45)(18, 48)(19, 47)(20, 41)(21, 46)(22, 44)(23, 42)(24, 43)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 92)(34, 95)(35, 96)(36, 94)(37, 89)(38, 93)(39, 91)(40, 90)(49, 51)(50, 54)(52, 56)(53, 55)(57, 111)(58, 108)(59, 109)(60, 107)(61, 106)(62, 112)(63, 110)(64, 105)(65, 66)(67, 70)(68, 71)(69, 72)(73, 100)(74, 103)(75, 104)(76, 102)(77, 97)(78, 101)(79, 99)(80, 98) MAP : A3.1336 NOTES : type II, reflexible, isomorphic to A3.1327. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.5, x.1^2, x.2^2, x.4 * x.6, x.2 * x.1, x.7 * x.3^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.6^-1, x.7 * x.2 * x.8^-1, x.5 * x.6^-1 * x.8, x.3^4, x.7^4, x.4 * x.3^-1 * x.6^-1 * x.3^-1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 16)(2, 13)(3, 12)(4, 10)(5, 11)(6, 15)(7, 9)(8, 14)(17, 45)(18, 48)(19, 47)(20, 41)(21, 46)(22, 44)(23, 42)(24, 43)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 92)(34, 95)(35, 96)(36, 94)(37, 89)(38, 93)(39, 91)(40, 90)(49, 51)(50, 54)(52, 56)(53, 55)(57, 112)(58, 109)(59, 108)(60, 106)(61, 107)(62, 111)(63, 105)(64, 110)(65, 67)(66, 70)(68, 72)(69, 71)(73, 100)(74, 103)(75, 104)(76, 102)(77, 97)(78, 101)(79, 99)(80, 98) MAP : A3.1337 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 18)(2, 22)(3, 30)(4, 23)(5, 31)(6, 27)(7, 29)(8, 21)(9, 19)(10, 25)(11, 17)(12, 24)(13, 32)(14, 26)(15, 28)(16, 20)(33, 87)(34, 93)(35, 85)(36, 82)(37, 90)(38, 96)(39, 86)(40, 94)(41, 88)(42, 92)(43, 84)(44, 83)(45, 91)(46, 95)(47, 89)(48, 81)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 72)(66, 76)(67, 68)(69, 75)(70, 79)(71, 73)(74, 77)(78, 80)(97, 109)(98, 112)(99, 111)(100, 102)(101, 105)(103, 107)(104, 106)(108, 110) MAP : A3.1338 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, (x.5 * x.4^-1)^2, (x.3 * x.1)^2, (x.4^-1 * x.2)^2 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 23)(2, 29)(3, 21)(4, 18)(5, 26)(6, 32)(7, 22)(8, 30)(9, 24)(10, 28)(11, 20)(12, 19)(13, 27)(14, 31)(15, 25)(16, 17)(33, 91)(34, 81)(35, 89)(36, 96)(37, 88)(38, 82)(39, 84)(40, 92)(41, 90)(42, 94)(43, 86)(44, 95)(45, 87)(46, 83)(47, 85)(48, 93)(49, 51)(50, 57)(52, 56)(53, 64)(54, 58)(55, 60)(59, 62)(61, 63)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80)(97, 100)(98, 103)(99, 104)(101, 110)(102, 109)(105, 108)(106, 111)(107, 112) MAP : A3.1339 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 31)(18, 21)(19, 29)(20, 26)(22, 24)(23, 30)(25, 32)(27, 28)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 75)(50, 65)(51, 73)(52, 80)(53, 72)(54, 66)(55, 68)(56, 76)(57, 74)(58, 78)(59, 70)(60, 79)(61, 71)(62, 67)(63, 69)(64, 77)(81, 93)(82, 96)(83, 95)(84, 86)(85, 89)(87, 91)(88, 90)(92, 94) MAP : A3.1340 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, x.3 * x.1 * x.5^-1 * x.2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 4)(2, 11)(3, 13)(5, 8)(6, 15)(7, 9)(10, 16)(12, 14)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 66)(50, 70)(51, 71)(52, 75)(53, 65)(54, 69)(55, 80)(56, 68)(57, 74)(58, 78)(59, 79)(60, 67)(61, 73)(62, 77)(63, 72)(64, 76)(81, 83)(82, 87)(84, 90)(85, 92)(86, 96)(88, 89)(91, 94)(93, 95) MAP : A3.1341 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, x.3 * x.1 * x.5^-1 * x.2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 31)(18, 24)(19, 26)(20, 22)(21, 27)(23, 30)(25, 28)(29, 32)(33, 103)(34, 112)(35, 98)(36, 110)(37, 99)(38, 108)(39, 102)(40, 106)(41, 100)(42, 107)(43, 109)(44, 97)(45, 104)(46, 111)(47, 105)(48, 101)(49, 66)(50, 70)(51, 71)(52, 75)(53, 65)(54, 69)(55, 80)(56, 68)(57, 74)(58, 78)(59, 79)(60, 67)(61, 73)(62, 77)(63, 72)(64, 76)(81, 83)(82, 87)(84, 90)(85, 92)(86, 96)(88, 89)(91, 94)(93, 95) MAP : A3.1342 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, x.4 * x.1 * x.4^-1 * x.1 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 21)(2, 17)(3, 28)(4, 24)(5, 22)(6, 18)(7, 19)(8, 31)(9, 29)(10, 25)(11, 20)(12, 32)(13, 30)(14, 26)(15, 27)(16, 23)(33, 90)(34, 94)(35, 95)(36, 83)(37, 89)(38, 93)(39, 88)(40, 92)(41, 82)(42, 86)(43, 87)(44, 91)(45, 81)(46, 85)(47, 96)(48, 84)(49, 51)(50, 55)(52, 58)(53, 60)(54, 64)(56, 57)(59, 62)(61, 63)(65, 79)(66, 72)(67, 74)(68, 70)(69, 75)(71, 78)(73, 76)(77, 80)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.1343 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, x.3 * x.1 * x.5^-1 * x.2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 20)(18, 27)(19, 29)(21, 24)(22, 31)(23, 25)(26, 32)(28, 30)(33, 108)(34, 99)(35, 101)(36, 105)(37, 112)(38, 103)(39, 97)(40, 109)(41, 111)(42, 104)(43, 106)(44, 102)(45, 107)(46, 100)(47, 110)(48, 98)(49, 69)(50, 65)(51, 76)(52, 72)(53, 70)(54, 66)(55, 67)(56, 79)(57, 77)(58, 73)(59, 68)(60, 80)(61, 78)(62, 74)(63, 75)(64, 71)(81, 83)(82, 87)(84, 90)(85, 92)(86, 96)(88, 89)(91, 94)(93, 95) MAP : A3.1344 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, x.3 * x.1 * x.5^-1 * x.2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 3)(2, 7)(4, 10)(5, 12)(6, 16)(8, 9)(11, 14)(13, 15)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 69)(50, 65)(51, 76)(52, 72)(53, 70)(54, 66)(55, 67)(56, 79)(57, 77)(58, 73)(59, 68)(60, 80)(61, 78)(62, 74)(63, 75)(64, 71)(81, 84)(82, 91)(83, 93)(85, 88)(86, 95)(87, 89)(90, 96)(92, 94) MAP : A3.1345 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, x.3 * x.1 * x.5^-1 * x.2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 32)(18, 28)(19, 22)(20, 29)(21, 23)(24, 30)(25, 27)(26, 31)(33, 104)(34, 100)(35, 110)(36, 101)(37, 111)(38, 107)(39, 109)(40, 102)(41, 99)(42, 103)(43, 97)(44, 106)(45, 108)(46, 112)(47, 98)(48, 105)(49, 69)(50, 65)(51, 76)(52, 72)(53, 70)(54, 66)(55, 67)(56, 79)(57, 77)(58, 73)(59, 68)(60, 80)(61, 78)(62, 74)(63, 75)(64, 71)(81, 84)(82, 91)(83, 93)(85, 88)(86, 95)(87, 89)(90, 96)(92, 94) MAP : A3.1346 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, x.3 * x.1 * x.5^-1 * x.2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 3)(2, 7)(4, 10)(5, 12)(6, 16)(8, 9)(11, 14)(13, 15)(17, 30)(18, 29)(19, 24)(20, 23)(21, 26)(22, 25)(27, 32)(28, 31)(33, 107)(34, 111)(35, 105)(36, 98)(37, 100)(38, 104)(39, 106)(40, 97)(41, 112)(42, 108)(43, 102)(44, 109)(45, 103)(46, 99)(47, 101)(48, 110)(49, 66)(50, 70)(51, 71)(52, 75)(53, 65)(54, 69)(55, 80)(56, 68)(57, 74)(58, 78)(59, 79)(60, 67)(61, 73)(62, 77)(63, 72)(64, 76)(81, 84)(82, 91)(83, 93)(85, 88)(86, 95)(87, 89)(90, 96)(92, 94) MAP : A3.1347 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, x.3 * x.1 * x.5^-1 * x.2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 19)(18, 23)(20, 26)(21, 28)(22, 32)(24, 25)(27, 30)(29, 31)(33, 107)(34, 111)(35, 105)(36, 98)(37, 100)(38, 104)(39, 106)(40, 97)(41, 112)(42, 108)(43, 102)(44, 109)(45, 103)(46, 99)(47, 101)(48, 110)(49, 66)(50, 70)(51, 71)(52, 75)(53, 65)(54, 69)(55, 80)(56, 68)(57, 74)(58, 78)(59, 79)(60, 67)(61, 73)(62, 77)(63, 72)(64, 76)(81, 84)(82, 91)(83, 93)(85, 88)(86, 95)(87, 89)(90, 96)(92, 94) MAP : A3.1348 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, x.3 * x.1 * x.5^-1 * x.2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 3)(2, 7)(4, 10)(5, 12)(6, 16)(8, 9)(11, 14)(13, 15)(17, 20)(18, 27)(19, 29)(21, 24)(22, 31)(23, 25)(26, 32)(28, 30)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 66)(50, 70)(51, 71)(52, 75)(53, 65)(54, 69)(55, 80)(56, 68)(57, 74)(58, 78)(59, 79)(60, 67)(61, 73)(62, 77)(63, 72)(64, 76)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.1349 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, x.3 * x.1 * x.5^-1 * x.2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 4)(2, 11)(3, 13)(5, 8)(6, 15)(7, 9)(10, 16)(12, 14)(17, 32)(18, 28)(19, 22)(20, 29)(21, 23)(24, 30)(25, 27)(26, 31)(33, 106)(34, 110)(35, 111)(36, 99)(37, 105)(38, 109)(39, 104)(40, 108)(41, 98)(42, 102)(43, 103)(44, 107)(45, 97)(46, 101)(47, 112)(48, 100)(49, 66)(50, 70)(51, 71)(52, 75)(53, 65)(54, 69)(55, 80)(56, 68)(57, 74)(58, 78)(59, 79)(60, 67)(61, 73)(62, 77)(63, 72)(64, 76)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.1350 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, x.3 * x.1 * x.5^-1 * x.2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 3)(2, 7)(4, 10)(5, 12)(6, 16)(8, 9)(11, 14)(13, 15)(17, 31)(18, 24)(19, 26)(20, 22)(21, 27)(23, 30)(25, 28)(29, 32)(33, 109)(34, 105)(35, 100)(36, 112)(37, 110)(38, 106)(39, 107)(40, 103)(41, 101)(42, 97)(43, 108)(44, 104)(45, 102)(46, 98)(47, 99)(48, 111)(49, 69)(50, 65)(51, 76)(52, 72)(53, 70)(54, 66)(55, 67)(56, 79)(57, 77)(58, 73)(59, 68)(60, 80)(61, 78)(62, 74)(63, 75)(64, 71)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96) MAP : A3.1351 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.6^-1 * x.4^-1, x.8 * x.6^-1, x.7 * x.3^-1 * x.2, x.5 * x.6^-1 * x.7^-1, x.1 * x.6 * x.5, x.1 * x.6^-1 * x.5^-1, x.4 * x.1 * x.5^-1, x.3 * x.4^-1 * x.8^-1, x.8^4, x.6^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 72)(10, 69)(11, 68)(12, 66)(13, 67)(14, 71)(15, 65)(16, 70)(17, 18)(19, 22)(20, 23)(21, 24)(25, 61)(26, 64)(27, 63)(28, 57)(29, 62)(30, 60)(31, 58)(32, 59)(33, 47)(34, 44)(35, 45)(36, 43)(37, 42)(38, 48)(39, 46)(40, 41)(49, 107)(50, 110)(51, 105)(52, 112)(53, 111)(54, 106)(55, 109)(56, 108)(73, 87)(74, 84)(75, 85)(76, 83)(77, 82)(78, 88)(79, 86)(80, 81)(97, 99)(98, 102)(100, 104)(101, 103) MAP : A3.1352 NOTES : type II, reflexible, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.1 * x.2, x.6^-1 * x.8^-1, x.6 * x.4^-1, x.3 * x.4^-1 * x.8^-1, x.7 * x.3^-1 * x.2, x.8 * x.1 * x.5, x.5 * x.6^-1 * x.7^-1, x.4 * x.2 * x.5^-1, x.8^4, x.6^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 72)(10, 69)(11, 68)(12, 66)(13, 67)(14, 71)(15, 65)(16, 70)(17, 18)(19, 22)(20, 23)(21, 24)(25, 61)(26, 64)(27, 63)(28, 57)(29, 62)(30, 60)(31, 58)(32, 59)(33, 48)(34, 45)(35, 44)(36, 42)(37, 43)(38, 47)(39, 41)(40, 46)(49, 106)(50, 105)(51, 110)(52, 111)(53, 112)(54, 107)(55, 108)(56, 109)(73, 87)(74, 84)(75, 85)(76, 83)(77, 82)(78, 88)(79, 86)(80, 81)(97, 98)(99, 102)(100, 103)(101, 104) MAP : A3.1353 NOTES : type II, reflexible, isomorphic to A3.1351. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.6^-1 * x.4^-1, x.8 * x.6^-1, x.7 * x.3^-1 * x.2, x.5 * x.6^-1 * x.7^-1, x.1 * x.6 * x.5, x.1 * x.6^-1 * x.5^-1, x.4 * x.1 * x.5^-1, x.3 * x.4^-1 * x.8^-1, x.8^4, x.6^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 72)(10, 69)(11, 68)(12, 66)(13, 67)(14, 71)(15, 65)(16, 70)(17, 19)(18, 22)(20, 24)(21, 23)(25, 60)(26, 63)(27, 64)(28, 62)(29, 57)(30, 61)(31, 59)(32, 58)(33, 47)(34, 44)(35, 45)(36, 43)(37, 42)(38, 48)(39, 46)(40, 41)(49, 106)(50, 105)(51, 110)(52, 111)(53, 112)(54, 107)(55, 108)(56, 109)(73, 87)(74, 84)(75, 85)(76, 83)(77, 82)(78, 88)(79, 86)(80, 81)(97, 98)(99, 102)(100, 103)(101, 104) MAP : A3.1354 NOTES : type II, reflexible, isomorphic to A3.1352. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.1 * x.2, x.6^-1 * x.8^-1, x.6 * x.4^-1, x.3 * x.4^-1 * x.8^-1, x.7 * x.3^-1 * x.2, x.8 * x.1 * x.5, x.5 * x.6^-1 * x.7^-1, x.4 * x.2 * x.5^-1, x.8^4, x.6^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 72)(10, 69)(11, 68)(12, 66)(13, 67)(14, 71)(15, 65)(16, 70)(17, 19)(18, 22)(20, 24)(21, 23)(25, 60)(26, 63)(27, 64)(28, 62)(29, 57)(30, 61)(31, 59)(32, 58)(33, 48)(34, 45)(35, 44)(36, 42)(37, 43)(38, 47)(39, 41)(40, 46)(49, 107)(50, 110)(51, 105)(52, 112)(53, 111)(54, 106)(55, 109)(56, 108)(73, 87)(74, 84)(75, 85)(76, 83)(77, 82)(78, 88)(79, 86)(80, 81)(97, 99)(98, 102)(100, 104)(101, 103) MAP : A3.1355 NOTES : type II, reflexible, isomorphic to A3.1352. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.1 * x.2, x.6^-1 * x.8^-1, x.6 * x.4^-1, x.3 * x.4^-1 * x.8^-1, x.7 * x.3^-1 * x.2, x.8 * x.1 * x.5, x.5 * x.6^-1 * x.7^-1, x.4 * x.2 * x.5^-1, x.8^4, x.6^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 68)(10, 71)(11, 72)(12, 70)(13, 65)(14, 69)(15, 67)(16, 66)(17, 19)(18, 22)(20, 24)(21, 23)(25, 64)(26, 61)(27, 60)(28, 58)(29, 59)(30, 63)(31, 57)(32, 62)(33, 44)(34, 47)(35, 48)(36, 46)(37, 41)(38, 45)(39, 43)(40, 42)(49, 107)(50, 110)(51, 105)(52, 112)(53, 111)(54, 106)(55, 109)(56, 108)(73, 85)(74, 88)(75, 87)(76, 81)(77, 86)(78, 84)(79, 82)(80, 83)(97, 99)(98, 102)(100, 104)(101, 103) MAP : A3.1356 NOTES : type I, chiral, isomorphic to A3.1296. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.4^-1 * u.5^-1 * u.3, u.5 * u.1 * u.2, u.4^4 > CTG (small) : <16, 13> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.4^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.3 * x.4 * x.5, x.4^4, x.4 * x.1 * x.4^-1 * x.1 > SCHREIER VEC. : (x.4, x.4^-1, x.5, x.1, x.2, x.5^-1, x.3) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 21)(2, 17)(3, 28)(4, 24)(5, 22)(6, 18)(7, 19)(8, 31)(9, 29)(10, 25)(11, 20)(12, 32)(13, 30)(14, 26)(15, 27)(16, 23)(33, 90)(34, 94)(35, 95)(36, 83)(37, 89)(38, 93)(39, 88)(40, 92)(41, 82)(42, 86)(43, 87)(44, 91)(45, 81)(46, 85)(47, 96)(48, 84)(49, 52)(50, 59)(51, 61)(53, 56)(54, 63)(55, 57)(58, 64)(60, 62)(65, 67)(66, 71)(68, 74)(69, 76)(70, 80)(72, 73)(75, 78)(77, 79)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112) MAP : A3.1357 NOTES : type II, reflexible, isomorphic to A3.1351. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.6^-1 * x.4^-1, x.8 * x.6^-1, x.7 * x.3^-1 * x.2, x.5 * x.6^-1 * x.7^-1, x.1 * x.6 * x.5, x.1 * x.6^-1 * x.5^-1, x.4 * x.1 * x.5^-1, x.3 * x.4^-1 * x.8^-1, x.8^4, x.6^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 69)(10, 72)(11, 71)(12, 65)(13, 70)(14, 68)(15, 66)(16, 67)(17, 18)(19, 22)(20, 23)(21, 24)(25, 64)(26, 61)(27, 60)(28, 58)(29, 59)(30, 63)(31, 57)(32, 62)(33, 44)(34, 47)(35, 48)(36, 46)(37, 41)(38, 45)(39, 43)(40, 42)(49, 107)(50, 110)(51, 105)(52, 112)(53, 111)(54, 106)(55, 109)(56, 108)(73, 84)(74, 87)(75, 88)(76, 86)(77, 81)(78, 85)(79, 83)(80, 82)(97, 99)(98, 102)(100, 104)(101, 103) MAP : A3.1358 NOTES : type II, reflexible, isomorphic to A3.1352. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.1 * x.2, x.6^-1 * x.8^-1, x.6 * x.4^-1, x.3 * x.4^-1 * x.8^-1, x.7 * x.3^-1 * x.2, x.8 * x.1 * x.5, x.5 * x.6^-1 * x.7^-1, x.4 * x.2 * x.5^-1, x.8^4, x.6^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 69)(10, 72)(11, 71)(12, 65)(13, 70)(14, 68)(15, 66)(16, 67)(17, 18)(19, 22)(20, 23)(21, 24)(25, 64)(26, 61)(27, 60)(28, 58)(29, 59)(30, 63)(31, 57)(32, 62)(33, 45)(34, 48)(35, 47)(36, 41)(37, 46)(38, 44)(39, 42)(40, 43)(49, 106)(50, 105)(51, 110)(52, 111)(53, 112)(54, 107)(55, 108)(56, 109)(73, 84)(74, 87)(75, 88)(76, 86)(77, 81)(78, 85)(79, 83)(80, 82)(97, 98)(99, 102)(100, 103)(101, 104) MAP : A3.1359 NOTES : type II, reflexible, isomorphic to A3.1327. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.5, x.1^2, x.2^2, x.4 * x.6, x.2 * x.1, x.7 * x.3^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.6^-1, x.7 * x.2 * x.8^-1, x.5 * x.6^-1 * x.8, x.3^4, x.7^4, x.4 * x.3^-1 * x.6^-1 * x.3^-1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 13)(2, 16)(3, 15)(4, 9)(5, 14)(6, 12)(7, 10)(8, 11)(17, 48)(18, 45)(19, 44)(20, 42)(21, 43)(22, 47)(23, 41)(24, 46)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 95)(34, 92)(35, 93)(36, 91)(37, 90)(38, 96)(39, 94)(40, 89)(49, 51)(50, 54)(52, 56)(53, 55)(57, 109)(58, 112)(59, 111)(60, 105)(61, 110)(62, 108)(63, 106)(64, 107)(65, 67)(66, 70)(68, 72)(69, 71)(73, 103)(74, 100)(75, 101)(76, 99)(77, 98)(78, 104)(79, 102)(80, 97) MAP : A3.1360 NOTES : type II, reflexible, isomorphic to A3.1306. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.7^-1 * x.3^-1, x.4 * x.5^-1 * x.6, x.1 * x.3 * x.6^-1, x.1 * x.7 * x.4^-1, x.5 * x.6^-1 * x.8, x.7 * x.2 * x.8^-1, x.7^4, x.3^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 15)(2, 12)(3, 13)(4, 11)(5, 10)(6, 16)(7, 14)(8, 9)(17, 44)(18, 47)(19, 48)(20, 46)(21, 41)(22, 45)(23, 43)(24, 42)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 93)(34, 96)(35, 95)(36, 89)(37, 94)(38, 92)(39, 90)(40, 91)(49, 51)(50, 54)(52, 56)(53, 55)(57, 112)(58, 109)(59, 108)(60, 106)(61, 107)(62, 111)(63, 105)(64, 110)(65, 66)(67, 70)(68, 71)(69, 72)(73, 101)(74, 104)(75, 103)(76, 97)(77, 102)(78, 100)(79, 98)(80, 99) MAP : A3.1361 NOTES : type II, reflexible, isomorphic to A3.1327. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.5, x.1^2, x.2^2, x.4 * x.6, x.2 * x.1, x.7 * x.3^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.6^-1, x.7 * x.2 * x.8^-1, x.5 * x.6^-1 * x.8, x.3^4, x.7^4, x.4 * x.3^-1 * x.6^-1 * x.3^-1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 12)(2, 15)(3, 16)(4, 14)(5, 9)(6, 13)(7, 11)(8, 10)(17, 48)(18, 45)(19, 44)(20, 42)(21, 43)(22, 47)(23, 41)(24, 46)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 95)(34, 92)(35, 93)(36, 91)(37, 90)(38, 96)(39, 94)(40, 89)(49, 50)(51, 54)(52, 55)(53, 56)(57, 108)(58, 111)(59, 112)(60, 110)(61, 105)(62, 109)(63, 107)(64, 106)(65, 66)(67, 70)(68, 71)(69, 72)(73, 103)(74, 100)(75, 101)(76, 99)(77, 98)(78, 104)(79, 102)(80, 97) MAP : A3.1362 NOTES : type II, reflexible, isomorphic to A3.1306. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.7^-1 * x.3^-1, x.4 * x.5^-1 * x.6, x.1 * x.3 * x.6^-1, x.1 * x.7 * x.4^-1, x.5 * x.6^-1 * x.8, x.7 * x.2 * x.8^-1, x.7^4, x.3^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 12)(2, 15)(3, 16)(4, 14)(5, 9)(6, 13)(7, 11)(8, 10)(17, 48)(18, 45)(19, 44)(20, 42)(21, 43)(22, 47)(23, 41)(24, 46)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 95)(34, 92)(35, 93)(36, 91)(37, 90)(38, 96)(39, 94)(40, 89)(49, 50)(51, 54)(52, 55)(53, 56)(57, 109)(58, 112)(59, 111)(60, 105)(61, 110)(62, 108)(63, 106)(64, 107)(65, 67)(66, 70)(68, 72)(69, 71)(73, 103)(74, 100)(75, 101)(76, 99)(77, 98)(78, 104)(79, 102)(80, 97) MAP : A3.1363 NOTES : type II, reflexible, isomorphic to A3.1327. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.5, x.1^2, x.2^2, x.4 * x.6, x.2 * x.1, x.7 * x.3^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.6^-1, x.7 * x.2 * x.8^-1, x.5 * x.6^-1 * x.8, x.3^4, x.7^4, x.4 * x.3^-1 * x.6^-1 * x.3^-1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 13)(2, 16)(3, 15)(4, 9)(5, 14)(6, 12)(7, 10)(8, 11)(17, 47)(18, 44)(19, 45)(20, 43)(21, 42)(22, 48)(23, 46)(24, 41)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 96)(34, 93)(35, 92)(36, 90)(37, 91)(38, 95)(39, 89)(40, 94)(49, 50)(51, 54)(52, 55)(53, 56)(57, 109)(58, 112)(59, 111)(60, 105)(61, 110)(62, 108)(63, 106)(64, 107)(65, 66)(67, 70)(68, 71)(69, 72)(73, 104)(74, 101)(75, 100)(76, 98)(77, 99)(78, 103)(79, 97)(80, 102) MAP : A3.1364 NOTES : type II, reflexible, isomorphic to A3.1306. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.1^2, x.2^2, x.7^-1 * x.3^-1, x.4 * x.5^-1 * x.6, x.1 * x.3 * x.6^-1, x.1 * x.7 * x.4^-1, x.5 * x.6^-1 * x.8, x.7 * x.2 * x.8^-1, x.7^4, x.3^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 13)(2, 16)(3, 15)(4, 9)(5, 14)(6, 12)(7, 10)(8, 11)(17, 47)(18, 44)(19, 45)(20, 43)(21, 42)(22, 48)(23, 46)(24, 41)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 96)(34, 93)(35, 92)(36, 90)(37, 91)(38, 95)(39, 89)(40, 94)(49, 50)(51, 54)(52, 55)(53, 56)(57, 108)(58, 111)(59, 112)(60, 110)(61, 105)(62, 109)(63, 107)(64, 106)(65, 67)(66, 70)(68, 72)(69, 71)(73, 104)(74, 101)(75, 100)(76, 98)(77, 99)(78, 103)(79, 97)(80, 102) MAP : A3.1365 NOTES : type II, reflexible, isomorphic to A3.1327. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.5, x.1^2, x.2^2, x.4 * x.6, x.2 * x.1, x.7 * x.3^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.6^-1, x.7 * x.2 * x.8^-1, x.5 * x.6^-1 * x.8, x.3^4, x.7^4, x.4 * x.3^-1 * x.6^-1 * x.3^-1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 15)(2, 12)(3, 13)(4, 11)(5, 10)(6, 16)(7, 14)(8, 9)(17, 45)(18, 48)(19, 47)(20, 41)(21, 46)(22, 44)(23, 42)(24, 43)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 92)(34, 95)(35, 96)(36, 94)(37, 89)(38, 93)(39, 91)(40, 90)(49, 50)(51, 54)(52, 55)(53, 56)(57, 111)(58, 108)(59, 109)(60, 107)(61, 106)(62, 112)(63, 110)(64, 105)(65, 66)(67, 70)(68, 71)(69, 72)(73, 100)(74, 103)(75, 104)(76, 102)(77, 97)(78, 101)(79, 99)(80, 98) MAP : A3.1366 NOTES : type II, reflexible, isomorphic to A3.1352. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.1 * x.2, x.6^-1 * x.8^-1, x.6 * x.4^-1, x.3 * x.4^-1 * x.8^-1, x.7 * x.3^-1 * x.2, x.8 * x.1 * x.5, x.5 * x.6^-1 * x.7^-1, x.4 * x.2 * x.5^-1, x.8^4, x.6^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 68)(10, 71)(11, 72)(12, 70)(13, 65)(14, 69)(15, 67)(16, 66)(17, 18)(19, 22)(20, 23)(21, 24)(25, 63)(26, 60)(27, 61)(28, 59)(29, 58)(30, 64)(31, 62)(32, 57)(33, 44)(34, 47)(35, 48)(36, 46)(37, 41)(38, 45)(39, 43)(40, 42)(49, 106)(50, 105)(51, 110)(52, 111)(53, 112)(54, 107)(55, 108)(56, 109)(73, 85)(74, 88)(75, 87)(76, 81)(77, 86)(78, 84)(79, 82)(80, 83)(97, 98)(99, 102)(100, 103)(101, 104) MAP : A3.1367 NOTES : type II, reflexible, isomorphic to A3.1351. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.6^-1 * x.4^-1, x.8 * x.6^-1, x.7 * x.3^-1 * x.2, x.5 * x.6^-1 * x.7^-1, x.1 * x.6 * x.5, x.1 * x.6^-1 * x.5^-1, x.4 * x.1 * x.5^-1, x.3 * x.4^-1 * x.8^-1, x.8^4, x.6^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 68)(10, 71)(11, 72)(12, 70)(13, 65)(14, 69)(15, 67)(16, 66)(17, 18)(19, 22)(20, 23)(21, 24)(25, 63)(26, 60)(27, 61)(28, 59)(29, 58)(30, 64)(31, 62)(32, 57)(33, 45)(34, 48)(35, 47)(36, 41)(37, 46)(38, 44)(39, 42)(40, 43)(49, 107)(50, 110)(51, 105)(52, 112)(53, 111)(54, 106)(55, 109)(56, 108)(73, 85)(74, 88)(75, 87)(76, 81)(77, 86)(78, 84)(79, 82)(80, 83)(97, 99)(98, 102)(100, 104)(101, 103) MAP : A3.1368 NOTES : type II, reflexible, isomorphic to A3.1351. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.6^-1 * x.4^-1, x.8 * x.6^-1, x.7 * x.3^-1 * x.2, x.5 * x.6^-1 * x.7^-1, x.1 * x.6 * x.5, x.1 * x.6^-1 * x.5^-1, x.4 * x.1 * x.5^-1, x.3 * x.4^-1 * x.8^-1, x.8^4, x.6^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 69)(10, 72)(11, 71)(12, 65)(13, 70)(14, 68)(15, 66)(16, 67)(17, 19)(18, 22)(20, 24)(21, 23)(25, 63)(26, 60)(27, 61)(28, 59)(29, 58)(30, 64)(31, 62)(32, 57)(33, 44)(34, 47)(35, 48)(36, 46)(37, 41)(38, 45)(39, 43)(40, 42)(49, 106)(50, 105)(51, 110)(52, 111)(53, 112)(54, 107)(55, 108)(56, 109)(73, 84)(74, 87)(75, 88)(76, 86)(77, 81)(78, 85)(79, 83)(80, 82)(97, 98)(99, 102)(100, 103)(101, 104) MAP : A3.1369 NOTES : type II, reflexible, isomorphic to A3.1351. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.6^-1 * x.4^-1, x.8 * x.6^-1, x.7 * x.3^-1 * x.2, x.5 * x.6^-1 * x.7^-1, x.1 * x.6 * x.5, x.1 * x.6^-1 * x.5^-1, x.4 * x.1 * x.5^-1, x.3 * x.4^-1 * x.8^-1, x.8^4, x.6^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 68)(10, 71)(11, 72)(12, 70)(13, 65)(14, 69)(15, 67)(16, 66)(17, 19)(18, 22)(20, 24)(21, 23)(25, 64)(26, 61)(27, 60)(28, 58)(29, 59)(30, 63)(31, 57)(32, 62)(33, 45)(34, 48)(35, 47)(36, 41)(37, 46)(38, 44)(39, 42)(40, 43)(49, 106)(50, 105)(51, 110)(52, 111)(53, 112)(54, 107)(55, 108)(56, 109)(73, 85)(74, 88)(75, 87)(76, 81)(77, 86)(78, 84)(79, 82)(80, 83)(97, 98)(99, 102)(100, 103)(101, 104) MAP : A3.1370 NOTES : type II, reflexible, isomorphic to A3.1327. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 6)(4, 11)(5, 12)(8, 14)(10, 13) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.5, u.1^2, u.2^2, u.4 * u.5^-1 * u.6, u.3^-1 * u.4^-1 * u.1, u.5 * u.6^-1 * u.8, u.7 * u.2 * u.8^-1, u.3^4, u.7^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.5, x.5, x.1^2, x.2^2, x.4 * x.6, x.2 * x.1, x.7 * x.3^-1, x.3^-1 * x.4^-1 * x.1, x.1 * x.3 * x.6^-1, x.7 * x.2 * x.8^-1, x.5 * x.6^-1 * x.8, x.3^4, x.7^4, x.4 * x.3^-1 * x.6^-1 * x.3^-1 > SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.6, x.4^-1, x.1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 15)(2, 12)(3, 13)(4, 11)(5, 10)(6, 16)(7, 14)(8, 9)(17, 44)(18, 47)(19, 48)(20, 46)(21, 41)(22, 45)(23, 43)(24, 42)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 93)(34, 96)(35, 95)(36, 89)(37, 94)(38, 92)(39, 90)(40, 91)(49, 51)(50, 54)(52, 56)(53, 55)(57, 111)(58, 108)(59, 109)(60, 107)(61, 106)(62, 112)(63, 110)(64, 105)(65, 67)(66, 70)(68, 72)(69, 71)(73, 101)(74, 104)(75, 103)(76, 97)(77, 102)(78, 100)(79, 98)(80, 99) MAP : A3.1371 NOTES : type II, reflexible, isomorphic to A3.1351. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.6^-1 * x.4^-1, x.8 * x.6^-1, x.7 * x.3^-1 * x.2, x.5 * x.6^-1 * x.7^-1, x.1 * x.6 * x.5, x.1 * x.6^-1 * x.5^-1, x.4 * x.1 * x.5^-1, x.3 * x.4^-1 * x.8^-1, x.8^4, x.6^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 71)(10, 68)(11, 69)(12, 67)(13, 66)(14, 72)(15, 70)(16, 65)(17, 18)(19, 22)(20, 23)(21, 24)(25, 60)(26, 63)(27, 64)(28, 62)(29, 57)(30, 61)(31, 59)(32, 58)(33, 48)(34, 45)(35, 44)(36, 42)(37, 43)(38, 47)(39, 41)(40, 46)(49, 107)(50, 110)(51, 105)(52, 112)(53, 111)(54, 106)(55, 109)(56, 108)(73, 88)(74, 85)(75, 84)(76, 82)(77, 83)(78, 87)(79, 81)(80, 86)(97, 99)(98, 102)(100, 104)(101, 103) MAP : A3.1372 NOTES : type II, reflexible, isomorphic to A3.1352. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.1 * x.2, x.6^-1 * x.8^-1, x.6 * x.4^-1, x.3 * x.4^-1 * x.8^-1, x.7 * x.3^-1 * x.2, x.8 * x.1 * x.5, x.5 * x.6^-1 * x.7^-1, x.4 * x.2 * x.5^-1, x.8^4, x.6^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 71)(10, 68)(11, 69)(12, 67)(13, 66)(14, 72)(15, 70)(16, 65)(17, 19)(18, 22)(20, 24)(21, 23)(25, 61)(26, 64)(27, 63)(28, 57)(29, 62)(30, 60)(31, 58)(32, 59)(33, 47)(34, 44)(35, 45)(36, 43)(37, 42)(38, 48)(39, 46)(40, 41)(49, 107)(50, 110)(51, 105)(52, 112)(53, 111)(54, 106)(55, 109)(56, 108)(73, 88)(74, 85)(75, 84)(76, 82)(77, 83)(78, 87)(79, 81)(80, 86)(97, 99)(98, 102)(100, 104)(101, 103) MAP : A3.1373 NOTES : type II, reflexible, isomorphic to A3.1352. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.1 * x.2, x.6^-1 * x.8^-1, x.6 * x.4^-1, x.3 * x.4^-1 * x.8^-1, x.7 * x.3^-1 * x.2, x.8 * x.1 * x.5, x.5 * x.6^-1 * x.7^-1, x.4 * x.2 * x.5^-1, x.8^4, x.6^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 69)(10, 72)(11, 71)(12, 65)(13, 70)(14, 68)(15, 66)(16, 67)(17, 19)(18, 22)(20, 24)(21, 23)(25, 63)(26, 60)(27, 61)(28, 59)(29, 58)(30, 64)(31, 62)(32, 57)(33, 45)(34, 48)(35, 47)(36, 41)(37, 46)(38, 44)(39, 42)(40, 43)(49, 107)(50, 110)(51, 105)(52, 112)(53, 111)(54, 106)(55, 109)(56, 108)(73, 84)(74, 87)(75, 88)(76, 86)(77, 81)(78, 85)(79, 83)(80, 82)(97, 99)(98, 102)(100, 104)(101, 103) MAP : A3.1374 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 8)(2, 12)(3, 4)(5, 11)(6, 15)(7, 9)(10, 13)(14, 16)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 75)(50, 65)(51, 73)(52, 80)(53, 72)(54, 66)(55, 68)(56, 76)(57, 74)(58, 78)(59, 70)(60, 79)(61, 71)(62, 67)(63, 69)(64, 77)(81, 93)(82, 96)(83, 95)(84, 86)(85, 89)(87, 91)(88, 90)(92, 94) MAP : A3.1375 NOTES : type II, reflexible, isomorphic to A3.1352. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.1 * x.2, x.6^-1 * x.8^-1, x.6 * x.4^-1, x.3 * x.4^-1 * x.8^-1, x.7 * x.3^-1 * x.2, x.8 * x.1 * x.5, x.5 * x.6^-1 * x.7^-1, x.4 * x.2 * x.5^-1, x.8^4, x.6^4 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 71)(10, 68)(11, 69)(12, 67)(13, 66)(14, 72)(15, 70)(16, 65)(17, 18)(19, 22)(20, 23)(21, 24)(25, 60)(26, 63)(27, 64)(28, 62)(29, 57)(30, 61)(31, 59)(32, 58)(33, 47)(34, 44)(35, 45)(36, 43)(37, 42)(38, 48)(39, 46)(40, 41)(49, 106)(50, 105)(51, 110)(52, 111)(53, 112)(54, 107)(55, 108)(56, 109)(73, 88)(74, 85)(75, 84)(76, 82)(77, 83)(78, 87)(79, 81)(80, 86)(97, 98)(99, 102)(100, 103)(101, 104) MAP : A3.1376 NOTES : type I, chiral, isomorphic to A3.1291. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5) ORBIFOLD : O(0, {4, 2, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 4, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^2, u.1 * u.2 * u.4^-1, u.4 * u.5^-1 * u.3, u.5^4 > CTG (small) : <16, 11> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.1 * x.2 * x.4^-1, x.4 * x.5^-1 * x.3, x.3 * x.4^-1 * x.5, x.5^4, (x.5 * x.1)^2, (x.3 * x.1)^2, x.4^4 > SCHREIER VEC. : (x.1, x.2, x.4, x.5, x.5^-1, x.3, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 17, 33, 49, 65, 81, 97)(2, 18, 34, 50, 66, 82, 98)(3, 19, 35, 51, 67, 83, 99)(4, 20, 36, 52, 68, 84, 100)(5, 21, 37, 53, 69, 85, 101)(6, 22, 38, 54, 70, 86, 102)(7, 23, 39, 55, 71, 87, 103)(8, 24, 40, 56, 72, 88, 104)(9, 25, 41, 57, 73, 89, 105)(10, 26, 42, 58, 74, 90, 106)(11, 27, 43, 59, 75, 91, 107)(12, 28, 44, 60, 76, 92, 108)(13, 29, 45, 61, 77, 93, 109)(14, 30, 46, 62, 78, 94, 110)(15, 31, 47, 63, 79, 95, 111)(16, 32, 48, 64, 80, 96, 112) L = (1, 5)(2, 8)(3, 7)(4, 14)(6, 12)(9, 13)(10, 16)(11, 15)(17, 19)(18, 25)(20, 24)(21, 32)(22, 26)(23, 28)(27, 30)(29, 31)(33, 103)(34, 109)(35, 101)(36, 98)(37, 106)(38, 112)(39, 102)(40, 110)(41, 104)(42, 108)(43, 100)(44, 99)(45, 107)(46, 111)(47, 105)(48, 97)(49, 75)(50, 65)(51, 73)(52, 80)(53, 72)(54, 66)(55, 68)(56, 76)(57, 74)(58, 78)(59, 70)(60, 79)(61, 71)(62, 67)(63, 69)(64, 77)(81, 93)(82, 96)(83, 95)(84, 86)(85, 89)(87, 91)(88, 90)(92, 94) MAP : A3.1377 NOTES : type II, reflexible, isomorphic to A3.1351. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 12)(2, 9)(4, 8)(5, 6)(7, 14)(10, 11) ORBIFOLD : O(0, {4, 4, 2, 2}) EMBEDDING : vertices: [ 1, 1 ], faces: [ 4, 4, 1, 1, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.3, u.1^2, u.2^2, u.7 * u.3^-1 * u.2, u.3 * u.4^-1 * u.8^-1, u.4 * u.1 * u.5^-1, u.5 * u.6^-1 * u.7^-1, u.6^4, u.8^4 > CTG (small) : <8, 2> CTG (fp) : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.1^2, x.2^2, x.6^-1 * x.4^-1, x.8 * x.6^-1, x.7 * x.3^-1 * x.2, x.5 * x.6^-1 * x.7^-1, x.1 * x.6 * x.5, x.1 * x.6^-1 * x.5^-1, x.4 * x.1 * x.5^-1, x.3 * x.4^-1 * x.8^-1, x.8^4, x.6^4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.6, x.6^-1, x.7) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 4) #DARTS : 112 R = (1, 9, 17, 25, 33, 41, 49)(2, 10, 18, 26, 34, 42, 50)(3, 11, 19, 27, 35, 43, 51)(4, 12, 20, 28, 36, 44, 52)(5, 13, 21, 29, 37, 45, 53)(6, 14, 22, 30, 38, 46, 54)(7, 15, 23, 31, 39, 47, 55)(8, 16, 24, 32, 40, 48, 56)(57, 65, 73, 81, 89, 97, 105)(58, 66, 74, 82, 90, 98, 106)(59, 67, 75, 83, 91, 99, 107)(60, 68, 76, 84, 92, 100, 108)(61, 69, 77, 85, 93, 101, 109)(62, 70, 78, 86, 94, 102, 110)(63, 71, 79, 87, 95, 103, 111)(64, 72, 80, 88, 96, 104, 112) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 71)(10, 68)(11, 69)(12, 67)(13, 66)(14, 72)(15, 70)(16, 65)(17, 19)(18, 22)(20, 24)(21, 23)(25, 61)(26, 64)(27, 63)(28, 57)(29, 62)(30, 60)(31, 58)(32, 59)(33, 48)(34, 45)(35, 44)(36, 42)(37, 43)(38, 47)(39, 41)(40, 46)(49, 106)(50, 105)(51, 110)(52, 111)(53, 112)(54, 107)(55, 108)(56, 109)(73, 88)(74, 85)(75, 84)(76, 82)(77, 83)(78, 87)(79, 81)(80, 86)(97, 98)(99, 102)(100, 103)(101, 104) MAP : A3.1378 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 5)(3, 4) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2 * u.3^-1 * u.1, u.4^3, u.2^3, (u.3 * u.4^-1)^2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.1, x.4^3, x.2^3, x.1 * x.2^-1 * x.4, x.3^3, x.2 * x.4 * x.3, (x.3 * x.4^-1)^2 > SCHREIER VEC. : (x.2, x.3, x.4, x.4^-1, x.3^-1, x.1, x.2^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 3, 4) #DARTS : 84 R = (1, 13, 25, 37, 49, 61, 73)(2, 14, 26, 38, 50, 62, 74)(3, 15, 27, 39, 51, 63, 75)(4, 16, 28, 40, 52, 64, 76)(5, 17, 29, 41, 53, 65, 77)(6, 18, 30, 42, 54, 66, 78)(7, 19, 31, 43, 55, 67, 79)(8, 20, 32, 44, 56, 68, 80)(9, 21, 33, 45, 57, 69, 81)(10, 22, 34, 46, 58, 70, 82)(11, 23, 35, 47, 59, 71, 83)(12, 24, 36, 48, 60, 72, 84) L = (1, 77)(2, 78)(3, 79)(4, 80)(5, 81)(6, 82)(7, 83)(8, 84)(9, 73)(10, 74)(11, 75)(12, 76)(13, 51)(14, 49)(15, 50)(16, 57)(17, 56)(18, 52)(19, 60)(20, 59)(21, 54)(22, 55)(23, 53)(24, 58)(25, 46)(26, 47)(27, 45)(28, 38)(29, 43)(30, 41)(31, 42)(32, 37)(33, 48)(34, 44)(35, 40)(36, 39)(61, 66)(62, 67)(63, 65)(64, 70)(68, 69)(71, 72) MAP : A3.1379 NOTES : type I, chiral, isomorphic to A3.1378. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 5)(3, 4) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2 * u.3^-1 * u.1, u.4^3, u.2^3, (u.3 * u.4^-1)^2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.1, x.4^3, x.2^3, x.1 * x.2^-1 * x.4, x.3^3, x.2 * x.4 * x.3, (x.3 * x.4^-1)^2 > SCHREIER VEC. : (x.2, x.3, x.4, x.4^-1, x.3^-1, x.1, x.2^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 3, 4) #DARTS : 84 R = (1, 13, 25, 37, 49, 61, 73)(2, 14, 26, 38, 50, 62, 74)(3, 15, 27, 39, 51, 63, 75)(4, 16, 28, 40, 52, 64, 76)(5, 17, 29, 41, 53, 65, 77)(6, 18, 30, 42, 54, 66, 78)(7, 19, 31, 43, 55, 67, 79)(8, 20, 32, 44, 56, 68, 80)(9, 21, 33, 45, 57, 69, 81)(10, 22, 34, 46, 58, 70, 82)(11, 23, 35, 47, 59, 71, 83)(12, 24, 36, 48, 60, 72, 84) L = (1, 79)(2, 77)(3, 78)(4, 73)(5, 84)(6, 80)(7, 76)(8, 75)(9, 82)(10, 83)(11, 81)(12, 74)(13, 50)(14, 51)(15, 49)(16, 54)(17, 59)(18, 57)(19, 58)(20, 53)(21, 52)(22, 60)(23, 56)(24, 55)(25, 44)(26, 40)(27, 48)(28, 47)(29, 42)(30, 43)(31, 41)(32, 46)(33, 39)(34, 37)(35, 38)(36, 45)(61, 66)(62, 67)(63, 65)(64, 70)(68, 69)(71, 72) MAP : A3.1380 NOTES : type I, chiral, isomorphic to A3.1378. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 5)(2, 3)(6, 7) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2 * u.3^-1 * u.1, u.3^3, u.4^3, (u.2^-1 * u.4^-1)^2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.4^-1 * x.2 * x.3, x.2 * x.3^-1 * x.1, x.3^3, x.4^3, x.1 * x.4 * x.3, x.2^3, (x.2^-1 * x.4^-1)^2 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.1, x.2^-1, x.4, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 3, 4) #DARTS : 84 R = (1, 13, 25, 37, 49, 61, 73)(2, 14, 26, 38, 50, 62, 74)(3, 15, 27, 39, 51, 63, 75)(4, 16, 28, 40, 52, 64, 76)(5, 17, 29, 41, 53, 65, 77)(6, 18, 30, 42, 54, 66, 78)(7, 19, 31, 43, 55, 67, 79)(8, 20, 32, 44, 56, 68, 80)(9, 21, 33, 45, 57, 69, 81)(10, 22, 34, 46, 58, 70, 82)(11, 23, 35, 47, 59, 71, 83)(12, 24, 36, 48, 60, 72, 84) L = (1, 50)(2, 51)(3, 49)(4, 54)(5, 59)(6, 57)(7, 58)(8, 53)(9, 52)(10, 60)(11, 56)(12, 55)(13, 31)(14, 29)(15, 30)(16, 25)(17, 36)(18, 32)(19, 28)(20, 27)(21, 34)(22, 35)(23, 33)(24, 26)(37, 42)(38, 43)(39, 41)(40, 46)(44, 45)(47, 48)(61, 82)(62, 83)(63, 81)(64, 74)(65, 79)(66, 77)(67, 78)(68, 73)(69, 84)(70, 80)(71, 76)(72, 75) MAP : A3.1381 NOTES : type I, chiral, isomorphic to A3.1378. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 5)(2, 3)(6, 7) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 2, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.1^2, u.2 * u.3^-1 * u.1, u.3^3, u.4^3, (u.2^-1 * u.4^-1)^2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4 | x.1^2, x.4^-1 * x.2 * x.3, x.2 * x.3^-1 * x.1, x.3^3, x.4^3, x.1 * x.4 * x.3, x.2^3, (x.2^-1 * x.4^-1)^2 > SCHREIER VEC. : (x.2, x.3, x.3^-1, x.1, x.2^-1, x.4, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 4, 3, 4) #DARTS : 84 R = (1, 13, 25, 37, 49, 61, 73)(2, 14, 26, 38, 50, 62, 74)(3, 15, 27, 39, 51, 63, 75)(4, 16, 28, 40, 52, 64, 76)(5, 17, 29, 41, 53, 65, 77)(6, 18, 30, 42, 54, 66, 78)(7, 19, 31, 43, 55, 67, 79)(8, 20, 32, 44, 56, 68, 80)(9, 21, 33, 45, 57, 69, 81)(10, 22, 34, 46, 58, 70, 82)(11, 23, 35, 47, 59, 71, 83)(12, 24, 36, 48, 60, 72, 84) L = (1, 51)(2, 49)(3, 50)(4, 57)(5, 56)(6, 52)(7, 60)(8, 59)(9, 54)(10, 55)(11, 53)(12, 58)(13, 29)(14, 30)(15, 31)(16, 32)(17, 33)(18, 34)(19, 35)(20, 36)(21, 25)(22, 26)(23, 27)(24, 28)(37, 42)(38, 43)(39, 41)(40, 46)(44, 45)(47, 48)(61, 80)(62, 76)(63, 84)(64, 83)(65, 78)(66, 79)(67, 77)(68, 82)(69, 75)(70, 73)(71, 74)(72, 81) MAP : A3.1382 NOTES : type I, non-biCayley, reflexible, isomorphic to Dual({3,8}), representative. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 8)(2, 5)(3, 4)(6, 7) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 2, 2 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1, u.5^2, u.6^2, u.3^3, u.4^3, u.1 * u.2^-1 * u.4^-1, u.2 * u.3^-1 * u.5 * u.1^-1 * u.6 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.5^2, x.6^2, x.4 * x.2^-2, x.3^3, x.4^3, x.1 * x.2^-1 * x.4^-1, x.4 * x.3 * x.5, x.2 * x.5 * x.3^-1, x.4 * x.3^-1 * x.6 * x.3^-1, x.5 * x.2 * x.6 * x.2^-1, x.2 * x.3^-1 * x.5 * x.1^-1 * x.6 > SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1)^2 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 13, 25, 37, 11, 23, 35, 47)(2, 14, 26, 38, 9, 21, 33, 45)(3, 15, 27, 39, 10, 22, 34, 46)(4, 16, 28, 40, 5, 17, 29, 41)(6, 18, 30, 42, 12, 24, 36, 48)(7, 19, 31, 43, 8, 20, 32, 44)(49, 61, 73, 85, 54, 66, 78, 90)(50, 62, 74, 86, 55, 67, 79, 91)(51, 63, 75, 87, 53, 65, 77, 89)(52, 64, 76, 88, 58, 70, 82, 94)(56, 68, 80, 92, 57, 69, 81, 93)(59, 71, 83, 95, 60, 72, 84, 96) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 50)(14, 51)(15, 49)(16, 54)(17, 59)(18, 57)(19, 58)(20, 53)(21, 52)(22, 60)(23, 56)(24, 55)(25, 44)(26, 40)(27, 48)(28, 47)(29, 42)(30, 43)(31, 41)(32, 46)(33, 39)(34, 37)(35, 38)(36, 45)(61, 75)(62, 73)(63, 74)(64, 81)(65, 80)(66, 76)(67, 84)(68, 83)(69, 78)(70, 79)(71, 77)(72, 82) MAP : A3.1383 NOTES : type I, non-Cayley, reflexible, isomorphic to Dual({3,8}), isomorphic to A3.1382. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 4 ], faces: [ 3, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^4 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 71, 23, 95, 47, 92, 44, 49)(2, 73, 25, 93, 45, 84, 36, 50)(3, 72, 24, 79, 31, 68, 20, 51)(4, 87, 39, 96, 48, 62, 14, 52)(5, 88, 40, 90, 42, 80, 32, 53)(6, 66, 18, 63, 15, 69, 21, 54)(7, 77, 29, 75, 27, 85, 37, 55)(8, 59, 11, 89, 41, 60, 12, 56)(9, 70, 22, 64, 16, 81, 33, 57)(10, 83, 35, 61, 13, 65, 17, 58)(19, 94, 46, 86, 38, 91, 43, 67)(26, 76, 28, 82, 34, 78, 30, 74) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72) MAP : A3.1384 NOTES : type I, non-Cayley, chiral, representative. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.4^2, u.1^2, u.2^2, u.3^-1 * u.1 * u.2, (u.3 * u.4)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.4^2, x.1^2, x.2^2, x.3^-1 * x.1 * x.2, x.3^4, x.3 * x.4 * x.2 * x.4 * x.3, (x.3 * x.4)^3 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.2)^2 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 30, 54, 78, 6, 25, 49, 73)(2, 31, 55, 79, 7, 26, 50, 74)(3, 29, 53, 77, 5, 27, 51, 75)(4, 46, 70, 94, 22, 28, 52, 76)(8, 33, 57, 81, 9, 32, 56, 80)(10, 40, 64, 88, 16, 34, 58, 82)(11, 48, 72, 96, 24, 35, 59, 83)(12, 47, 71, 95, 23, 36, 60, 84)(13, 42, 66, 90, 18, 37, 61, 85)(14, 43, 67, 91, 19, 38, 62, 86)(15, 41, 65, 89, 17, 39, 63, 87)(20, 45, 69, 93, 21, 44, 68, 92) L = (1, 38)(2, 39)(3, 37)(4, 30)(5, 43)(6, 41)(7, 42)(8, 25)(9, 40)(10, 48)(11, 32)(12, 31)(13, 34)(14, 35)(15, 33)(16, 26)(17, 47)(18, 45)(19, 46)(20, 29)(21, 36)(22, 44)(23, 28)(24, 27)(49, 55)(50, 53)(51, 54)(52, 61)(56, 66)(57, 70)(58, 71)(59, 69)(60, 62)(63, 68)(64, 67)(65, 72)(73, 84)(74, 92)(75, 76)(77, 88)(78, 96)(79, 80)(81, 91)(82, 89)(83, 90)(85, 95)(86, 93)(87, 94) MAP : A3.1385 NOTES : type I, non-biCayley, reflexible, isomorphic to Dual({3,8}), isomorphic to A3.1382. QUOTIENT : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 8)(2, 5)(3, 4)(6, 7) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 2, 2 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1, u.5^2, u.6^2, u.3^3, u.4^3, u.1 * u.2^-1 * u.4^-1, u.2 * u.3^-1 * u.5 * u.1^-1 * u.6 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.5^2, x.6^2, x.4 * x.2^-2, x.3^3, x.4^3, x.1 * x.2^-1 * x.4^-1, x.4 * x.3 * x.5, x.2 * x.5 * x.3^-1, x.4 * x.3^-1 * x.6 * x.3^-1, x.5 * x.2 * x.6 * x.2^-1, x.2 * x.3^-1 * x.5 * x.1^-1 * x.6 > SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1)^2 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 13, 25, 37, 12, 24, 36, 48)(2, 14, 26, 38, 8, 20, 32, 44)(3, 15, 27, 39, 4, 16, 28, 40)(5, 17, 29, 41, 10, 22, 34, 46)(6, 18, 30, 42, 11, 23, 35, 47)(7, 19, 31, 43, 9, 21, 33, 45)(49, 61, 73, 85, 54, 66, 78, 90)(50, 62, 74, 86, 55, 67, 79, 91)(51, 63, 75, 87, 53, 65, 77, 89)(52, 64, 76, 88, 58, 70, 82, 94)(56, 68, 80, 92, 57, 69, 81, 93)(59, 71, 83, 95, 60, 72, 84, 96) L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 51)(14, 49)(15, 50)(16, 57)(17, 56)(18, 52)(19, 60)(20, 59)(21, 54)(22, 55)(23, 53)(24, 58)(25, 46)(26, 47)(27, 45)(28, 38)(29, 43)(30, 41)(31, 42)(32, 37)(33, 48)(34, 44)(35, 40)(36, 39)(61, 74)(62, 75)(63, 73)(64, 78)(65, 83)(66, 81)(67, 82)(68, 77)(69, 76)(70, 84)(71, 80)(72, 79) MAP : A3.1386 NOTES : type I, non-Cayley, reflexible, isomorphic to Dual({3,8}), isomorphic to A3.1382. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 4 ], faces: [ 3, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^4 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 92, 44, 95, 47, 71, 23, 49)(2, 84, 36, 93, 45, 73, 25, 50)(3, 68, 20, 79, 31, 72, 24, 51)(4, 62, 14, 96, 48, 87, 39, 52)(5, 80, 32, 90, 42, 88, 40, 53)(6, 69, 21, 63, 15, 66, 18, 54)(7, 85, 37, 75, 27, 77, 29, 55)(8, 60, 12, 89, 41, 59, 11, 56)(9, 81, 33, 64, 16, 70, 22, 57)(10, 65, 17, 61, 13, 83, 35, 58)(19, 91, 43, 86, 38, 94, 46, 67)(26, 78, 30, 82, 34, 76, 28, 74) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72) MAP : A3.1387 NOTES : type I, non-Cayley, chiral, isomorphic to A3.1384. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.4^2, u.1^2, u.2^2, u.3^-1 * u.1 * u.2, (u.3 * u.4)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.4^2, x.1^2, x.2^2, x.3^-1 * x.1 * x.2, x.3^4, x.4 * x.1 * x.4 * x.3^2, (x.3 * x.4)^3 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.2)^2 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 30, 54, 78, 6, 25, 49, 73)(2, 31, 55, 79, 7, 26, 50, 74)(3, 29, 53, 77, 5, 27, 51, 75)(4, 46, 70, 94, 22, 28, 52, 76)(8, 33, 57, 81, 9, 32, 56, 80)(10, 40, 64, 88, 16, 34, 58, 82)(11, 48, 72, 96, 24, 35, 59, 83)(12, 47, 71, 95, 23, 36, 60, 84)(13, 42, 66, 90, 18, 37, 61, 85)(14, 43, 67, 91, 19, 38, 62, 86)(15, 41, 65, 89, 17, 39, 63, 87)(20, 45, 69, 93, 21, 44, 68, 92) L = (1, 38)(2, 39)(3, 37)(4, 30)(5, 43)(6, 41)(7, 42)(8, 25)(9, 40)(10, 48)(11, 32)(12, 31)(13, 34)(14, 35)(15, 33)(16, 26)(17, 47)(18, 45)(19, 46)(20, 29)(21, 36)(22, 44)(23, 28)(24, 27)(49, 60)(50, 68)(51, 52)(53, 64)(54, 72)(55, 56)(57, 67)(58, 65)(59, 66)(61, 71)(62, 69)(63, 70)(73, 93)(74, 94)(75, 95)(76, 96)(77, 81)(78, 82)(79, 83)(80, 84)(85, 89)(86, 90)(87, 91)(88, 92) MAP : A3.1388 NOTES : type I, non-Cayley, reflexible, isomorphic to Dual({3,8}), isomorphic to A3.1382. QUOTIENT : R = Id($) L = Id($) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 8 ], faces: [ 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2)^3, u.2^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2^-1)^3, x.2^8, x.2^2 * x.1 * x.2^-1 * x.1 * x.2^2 * x.1 * x.2^3 * x.1, (x.2^2 * x.1 * x.2^-3 * x.1)^2 > SCHREIER VEC. : (x.1)^8 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 18, 69, 68, 73, 10, 6, 3)(2, 21, 65, 72, 78, 11, 7, 4)(5, 17, 66, 67, 77, 15, 12, 8)(9, 37, 20, 50, 71, 61, 16, 44)(13, 34, 19, 49, 70, 62, 96, 39)(14, 33, 24, 53, 76, 57, 80, 38)(22, 51, 74, 47, 91, 40, 30, 81)(23, 52, 75, 42, 95, 35, 29, 82)(25, 85, 28, 56, 79, 43, 90, 36)(26, 54, 89, 32, 92, 45, 63, 83)(27, 55, 94, 48, 86, 41, 58, 84)(31, 60, 93, 64, 87, 46, 59, 88) L = (1, 4)(2, 8)(3, 5)(6, 34)(7, 37)(9, 18)(10, 81)(11, 82)(12, 33)(13, 17)(14, 21)(15, 85)(16, 53)(19, 30)(20, 29)(22, 63)(23, 58)(24, 25)(26, 48)(27, 64)(28, 59)(31, 32)(35, 39)(36, 44)(38, 40)(41, 43)(42, 45)(46, 47)(49, 80)(50, 96)(51, 75)(52, 79)(54, 76)(55, 70)(56, 74)(57, 94)(60, 71)(61, 89)(62, 93)(65, 91)(66, 95)(67, 92)(68, 86)(69, 90)(72, 87)(73, 83)(77, 88)(78, 84) MAP : A3.1389 NOTES : type I, non-Cayley, reflexible, isomorphic to Dual({3,8}), isomorphic to A3.1382. QUOTIENT : R = Id($) L = Id($) ORBIFOLD : O(0, {8, 3, 2}) EMBEDDING : vertices: [ 8 ], faces: [ 3 ] UNIGROUP : < u.1, u.2 | u.1^2, (u.1 * u.2)^3, u.2^8 > CTG (small) : <96, 64> CTG (fp) : < x.1, x.2 | x.1^2, (x.1 * x.2^-1)^3, x.2^8, x.2^2 * x.1 * x.2^-1 * x.1 * x.2^2 * x.1 * x.2^3 * x.1, (x.2^2 * x.1 * x.2^-3 * x.1)^2 > SCHREIER VEC. : (x.1)^8 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 68, 6, 18, 73, 3, 69, 10)(2, 72, 7, 21, 78, 4, 65, 11)(5, 67, 12, 17, 77, 8, 66, 15)(9, 50, 16, 37, 71, 44, 20, 61)(13, 49, 96, 34, 70, 39, 19, 62)(14, 53, 80, 33, 76, 38, 24, 57)(22, 47, 30, 51, 91, 81, 74, 40)(23, 42, 29, 52, 95, 82, 75, 35)(25, 56, 90, 85, 79, 36, 28, 43)(26, 32, 63, 54, 92, 83, 89, 45)(27, 48, 58, 55, 86, 84, 94, 41)(31, 64, 59, 60, 87, 88, 93, 46) L = (1, 4)(2, 8)(3, 5)(6, 34)(7, 37)(9, 18)(10, 81)(11, 82)(12, 33)(13, 17)(14, 21)(15, 85)(16, 53)(19, 30)(20, 29)(22, 63)(23, 58)(24, 25)(26, 48)(27, 64)(28, 59)(31, 32)(35, 39)(36, 44)(38, 40)(41, 43)(42, 45)(46, 47)(49, 80)(50, 96)(51, 75)(52, 79)(54, 76)(55, 70)(56, 74)(57, 94)(60, 71)(61, 89)(62, 93)(65, 91)(66, 95)(67, 92)(68, 86)(69, 90)(72, 87)(73, 83)(77, 88)(78, 84) MAP : A3.1390 NOTES : type I, non-Cayley, reflexible, isomorphic to Dual({3,8}), isomorphic to A3.1382. QUOTIENT : R = (1, 2, 3, 4) L = (1, 2) ORBIFOLD : O(0, {3, 2, 2, 2}) EMBEDDING : vertices: [ 2 ], faces: [ 3, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4 | u.4^2, u.1^2, u.2^2, u.3^-1 * u.1 * u.2, (u.3 * u.4)^3 > CTG (small) : <24, 12> CTG (fp) : < x.1, x.2, x.3, x.4 | x.4^2, x.1^2, x.2^2, x.3^3, x.3^-1 * x.1 * x.2, x.3 * x.1 * x.3^-1 * x.2, (x.3 * x.4)^3, x.3 * x.4 * x.3 * x.1 * x.4 * x.2 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.2)^2 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 42, 66, 90, 18, 25, 49, 73)(2, 43, 67, 91, 19, 26, 50, 74)(3, 41, 65, 89, 17, 27, 51, 75)(4, 34, 58, 82, 10, 28, 52, 76)(5, 39, 63, 87, 15, 29, 53, 77)(6, 37, 61, 85, 13, 30, 54, 78)(7, 38, 62, 86, 14, 31, 55, 79)(8, 45, 69, 93, 21, 32, 56, 80)(9, 44, 68, 92, 20, 33, 57, 81)(11, 36, 60, 84, 12, 35, 59, 83)(16, 46, 70, 94, 22, 40, 64, 88)(23, 48, 72, 96, 24, 47, 71, 95) L = (1, 26)(2, 27)(3, 25)(4, 42)(5, 31)(6, 29)(7, 30)(8, 37)(9, 28)(10, 36)(11, 44)(12, 43)(13, 46)(14, 47)(15, 45)(16, 38)(17, 35)(18, 33)(19, 34)(20, 41)(21, 48)(22, 32)(23, 40)(24, 39)(49, 55)(50, 53)(51, 54)(52, 61)(56, 66)(57, 70)(58, 71)(59, 69)(60, 62)(63, 68)(64, 67)(65, 72)(73, 77)(74, 78)(75, 79)(76, 80)(81, 85)(82, 86)(83, 87)(84, 88)(89, 93)(90, 94)(91, 95)(92, 96) MAP : A3.1391 NOTES : type I, non-Cayley, reflexible, isomorphic to Dual({3,8}), isomorphic to A3.1382. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 4 ], faces: [ 3, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^4 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 53, 5, 67, 19, 50, 2, 49)(3, 76, 28, 70, 22, 55, 7, 51)(4, 65, 17, 56, 8, 54, 6, 52)(9, 85, 37, 68, 20, 74, 26, 57)(10, 59, 11, 66, 18, 87, 39, 58)(12, 69, 21, 62, 14, 61, 13, 60)(15, 96, 48, 83, 35, 89, 41, 63)(16, 77, 29, 72, 24, 82, 34, 64)(23, 88, 40, 94, 46, 73, 25, 71)(27, 79, 31, 78, 30, 81, 33, 75)(32, 91, 43, 84, 36, 92, 44, 80)(38, 93, 45, 95, 47, 90, 42, 86) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73) MAP : A3.1392 NOTES : type I, non-Cayley, reflexible, isomorphic to Dual({3,8}), isomorphic to A3.1382. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 4 ], faces: [ 3, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^4 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 50, 2, 67, 19, 53, 5, 49)(3, 55, 7, 70, 22, 76, 28, 51)(4, 54, 6, 56, 8, 65, 17, 52)(9, 74, 26, 68, 20, 85, 37, 57)(10, 87, 39, 66, 18, 59, 11, 58)(12, 61, 13, 62, 14, 69, 21, 60)(15, 89, 41, 83, 35, 96, 48, 63)(16, 82, 34, 72, 24, 77, 29, 64)(23, 73, 25, 94, 46, 88, 40, 71)(27, 81, 33, 78, 30, 79, 31, 75)(32, 92, 44, 84, 36, 91, 43, 80)(38, 90, 42, 95, 47, 93, 45, 86) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73) MAP : A3.1393 NOTES : type I, non-Cayley, reflexible, isomorphic to Dual({3,8}), isomorphic to A3.1382. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 4 ], faces: [ 3, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^4 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 92, 44, 95, 47, 71, 23, 49)(2, 84, 36, 93, 45, 73, 25, 50)(3, 68, 20, 79, 31, 72, 24, 51)(4, 62, 14, 96, 48, 87, 39, 52)(5, 80, 32, 90, 42, 88, 40, 53)(6, 69, 21, 63, 15, 66, 18, 54)(7, 85, 37, 75, 27, 77, 29, 55)(8, 60, 12, 89, 41, 59, 11, 56)(9, 81, 33, 64, 16, 70, 22, 57)(10, 65, 17, 61, 13, 83, 35, 58)(19, 91, 43, 86, 38, 94, 46, 67)(26, 78, 30, 82, 34, 76, 28, 74) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73) MAP : A3.1394 NOTES : type I, non-Cayley, reflexible, isomorphic to Dual({3,8}), isomorphic to A3.1382. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 4 ], faces: [ 3, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^4 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 71, 23, 95, 47, 92, 44, 49)(2, 73, 25, 93, 45, 84, 36, 50)(3, 72, 24, 79, 31, 68, 20, 51)(4, 87, 39, 96, 48, 62, 14, 52)(5, 88, 40, 90, 42, 80, 32, 53)(6, 66, 18, 63, 15, 69, 21, 54)(7, 77, 29, 75, 27, 85, 37, 55)(8, 59, 11, 89, 41, 60, 12, 56)(9, 70, 22, 64, 16, 81, 33, 57)(10, 83, 35, 61, 13, 65, 17, 58)(19, 94, 46, 86, 38, 91, 43, 67)(26, 76, 28, 82, 34, 78, 30, 74) L = (1, 51)(2, 85)(3, 54)(4, 88)(5, 82)(6, 49)(7, 60)(8, 84)(9, 52)(10, 50)(11, 71)(12, 94)(13, 53)(14, 92)(15, 67)(16, 56)(17, 86)(18, 90)(19, 81)(20, 89)(21, 93)(22, 83)(23, 78)(24, 96)(25, 72)(26, 69)(27, 62)(28, 87)(29, 66)(30, 59)(31, 65)(32, 68)(33, 63)(34, 61)(35, 95)(36, 64)(37, 58)(38, 79)(39, 91)(40, 57)(41, 80)(42, 77)(43, 76)(44, 75)(45, 74)(46, 55)(47, 70)(48, 73) MAP : A3.1395 NOTES : type I, non-Cayley, reflexible, isomorphic to Dual({3,8}), isomorphic to A3.1382. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 4 ], faces: [ 3, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^4 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 53, 5, 67, 19, 50, 2, 49)(3, 76, 28, 70, 22, 55, 7, 51)(4, 65, 17, 56, 8, 54, 6, 52)(9, 85, 37, 68, 20, 74, 26, 57)(10, 59, 11, 66, 18, 87, 39, 58)(12, 69, 21, 62, 14, 61, 13, 60)(15, 96, 48, 83, 35, 89, 41, 63)(16, 77, 29, 72, 24, 82, 34, 64)(23, 88, 40, 94, 46, 73, 25, 71)(27, 79, 31, 78, 30, 81, 33, 75)(32, 91, 43, 84, 36, 92, 44, 80)(38, 93, 45, 95, 47, 90, 42, 86) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72) MAP : A3.1396 NOTES : type I, non-Cayley, reflexible, isomorphic to Dual({3,8}), isomorphic to A3.1382. QUOTIENT : R = (1, 2) L = (1, 2) ORBIFOLD : O(0, {4, 3, 3}) EMBEDDING : vertices: [ 4 ], faces: [ 3, 3 ] UNIGROUP : < u.1, u.2 | u.1^3, u.2^4, (u.1 * u.2)^3 > CTG (small) : <48, 3> CTG (fp) : < x.1, x.2 | x.1^3, x.2^4, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3 > SCHREIER VEC. : (x.1, x.1^-1)^4 LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 50, 2, 67, 19, 53, 5, 49)(3, 55, 7, 70, 22, 76, 28, 51)(4, 54, 6, 56, 8, 65, 17, 52)(9, 74, 26, 68, 20, 85, 37, 57)(10, 87, 39, 66, 18, 59, 11, 58)(12, 61, 13, 62, 14, 69, 21, 60)(15, 89, 41, 83, 35, 96, 48, 63)(16, 82, 34, 72, 24, 77, 29, 64)(23, 73, 25, 94, 46, 88, 40, 71)(27, 81, 33, 78, 30, 79, 31, 75)(32, 92, 44, 84, 36, 91, 43, 80)(38, 90, 42, 95, 47, 93, 45, 86) L = (1, 54)(2, 58)(3, 49)(4, 57)(5, 61)(6, 51)(7, 94)(8, 64)(9, 88)(10, 85)(11, 78)(12, 55)(13, 82)(14, 75)(15, 81)(16, 84)(17, 79)(18, 77)(19, 63)(20, 80)(21, 74)(22, 95)(23, 59)(24, 73)(25, 96)(26, 93)(27, 92)(28, 91)(29, 90)(30, 71)(31, 86)(32, 89)(33, 67)(34, 53)(35, 70)(36, 56)(37, 50)(38, 65)(39, 76)(40, 52)(41, 68)(42, 66)(43, 87)(44, 62)(45, 69)(46, 60)(47, 83)(48, 72) MAP : A3.1397 NOTES : type I, chiral, representative. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 5)(2, 3)(7, 8) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, u.5^3, u.3^-1 * u.2 * u.5^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.4^3, x.5^3, x.3^-1 * x.2 * x.5^-1, x.3 * x.1 * x.5, x.2 * x.5 * x.4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2, x.5, x.5^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 13, 25, 37, 49, 61, 73, 85)(2, 14, 26, 38, 50, 62, 74, 86)(3, 15, 27, 39, 51, 63, 75, 87)(4, 16, 28, 40, 52, 64, 76, 88)(5, 17, 29, 41, 53, 65, 77, 89)(6, 18, 30, 42, 54, 66, 78, 90)(7, 19, 31, 43, 55, 67, 79, 91)(8, 20, 32, 44, 56, 68, 80, 92)(9, 21, 33, 45, 57, 69, 81, 93)(10, 22, 34, 46, 58, 70, 82, 94)(11, 23, 35, 47, 59, 71, 83, 95)(12, 24, 36, 48, 60, 72, 84, 96) L = (1, 50)(2, 51)(3, 49)(4, 54)(5, 59)(6, 57)(7, 58)(8, 53)(9, 52)(10, 60)(11, 56)(12, 55)(13, 32)(14, 28)(15, 36)(16, 35)(17, 30)(18, 31)(19, 29)(20, 34)(21, 27)(22, 25)(23, 26)(24, 33)(37, 48)(38, 44)(39, 40)(41, 46)(42, 47)(43, 45)(61, 66)(62, 67)(63, 65)(64, 70)(68, 69)(71, 72)(73, 88)(74, 96)(75, 92)(76, 91)(77, 86)(78, 87)(79, 85)(80, 90)(81, 95)(82, 93)(83, 94)(84, 89) MAP : A3.1398 NOTES : type I, chiral, isomorphic to A3.1397. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 5)(2, 3)(7, 8) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, u.5^3, u.3^-1 * u.2 * u.5^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.4^3, x.5^3, x.3^-1 * x.2 * x.5^-1, x.3 * x.2 * x.4^-1, x.1 * x.5 * x.4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2, x.5, x.5^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 13, 25, 37, 49, 61, 73, 85)(2, 14, 26, 38, 50, 62, 74, 86)(3, 15, 27, 39, 51, 63, 75, 87)(4, 16, 28, 40, 52, 64, 76, 88)(5, 17, 29, 41, 53, 65, 77, 89)(6, 18, 30, 42, 54, 66, 78, 90)(7, 19, 31, 43, 55, 67, 79, 91)(8, 20, 32, 44, 56, 68, 80, 92)(9, 21, 33, 45, 57, 69, 81, 93)(10, 22, 34, 46, 58, 70, 82, 94)(11, 23, 35, 47, 59, 71, 83, 95)(12, 24, 36, 48, 60, 72, 84, 96) L = (1, 50)(2, 51)(3, 49)(4, 54)(5, 59)(6, 57)(7, 58)(8, 53)(9, 52)(10, 60)(11, 56)(12, 55)(13, 33)(14, 34)(15, 35)(16, 36)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)(37, 47)(38, 45)(39, 46)(40, 41)(42, 48)(43, 44)(61, 66)(62, 67)(63, 65)(64, 70)(68, 69)(71, 72)(73, 88)(74, 96)(75, 92)(76, 91)(77, 86)(78, 87)(79, 85)(80, 90)(81, 95)(82, 93)(83, 94)(84, 89) MAP : A3.1399 NOTES : type I, chiral, isomorphic to A3.1397. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 5)(2, 3)(7, 8) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, u.5^3, u.3^-1 * u.2 * u.5^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.4^3, x.5^3, x.3^-1 * x.2 * x.5^-1, x.3 * x.2 * x.4^-1, x.1 * x.5 * x.4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2, x.5, x.5^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 13, 25, 37, 49, 61, 73, 85)(2, 14, 26, 38, 50, 62, 74, 86)(3, 15, 27, 39, 51, 63, 75, 87)(4, 16, 28, 40, 52, 64, 76, 88)(5, 17, 29, 41, 53, 65, 77, 89)(6, 18, 30, 42, 54, 66, 78, 90)(7, 19, 31, 43, 55, 67, 79, 91)(8, 20, 32, 44, 56, 68, 80, 92)(9, 21, 33, 45, 57, 69, 81, 93)(10, 22, 34, 46, 58, 70, 82, 94)(11, 23, 35, 47, 59, 71, 83, 95)(12, 24, 36, 48, 60, 72, 84, 96) L = (1, 51)(2, 49)(3, 50)(4, 57)(5, 56)(6, 52)(7, 60)(8, 59)(9, 54)(10, 55)(11, 53)(12, 58)(13, 28)(14, 36)(15, 32)(16, 31)(17, 26)(18, 27)(19, 25)(20, 30)(21, 35)(22, 33)(23, 34)(24, 29)(37, 48)(38, 44)(39, 40)(41, 46)(42, 47)(43, 45)(61, 66)(62, 67)(63, 65)(64, 70)(68, 69)(71, 72)(73, 93)(74, 94)(75, 95)(76, 96)(77, 85)(78, 86)(79, 87)(80, 88)(81, 89)(82, 90)(83, 91)(84, 92) MAP : A3.1400 NOTES : type I, chiral, isomorphic to A3.1397. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 5)(2, 3)(7, 8) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3 * u.4^-1 * u.1, u.4^3, u.5^3, u.3^-1 * u.2 * u.5^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.4^3, x.5^3, x.3^-1 * x.2 * x.5^-1, x.3 * x.1 * x.5, x.2 * x.5 * x.4, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2, x.5, x.5^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 13, 25, 37, 49, 61, 73, 85)(2, 14, 26, 38, 50, 62, 74, 86)(3, 15, 27, 39, 51, 63, 75, 87)(4, 16, 28, 40, 52, 64, 76, 88)(5, 17, 29, 41, 53, 65, 77, 89)(6, 18, 30, 42, 54, 66, 78, 90)(7, 19, 31, 43, 55, 67, 79, 91)(8, 20, 32, 44, 56, 68, 80, 92)(9, 21, 33, 45, 57, 69, 81, 93)(10, 22, 34, 46, 58, 70, 82, 94)(11, 23, 35, 47, 59, 71, 83, 95)(12, 24, 36, 48, 60, 72, 84, 96) L = (1, 51)(2, 49)(3, 50)(4, 57)(5, 56)(6, 52)(7, 60)(8, 59)(9, 54)(10, 55)(11, 53)(12, 58)(13, 34)(14, 35)(15, 33)(16, 26)(17, 31)(18, 29)(19, 30)(20, 25)(21, 36)(22, 32)(23, 28)(24, 27)(37, 47)(38, 45)(39, 46)(40, 41)(42, 48)(43, 44)(61, 66)(62, 67)(63, 65)(64, 70)(68, 69)(71, 72)(73, 93)(74, 94)(75, 95)(76, 96)(77, 85)(78, 86)(79, 87)(80, 88)(81, 89)(82, 90)(83, 91)(84, 92) MAP : A3.1401 NOTES : type I, chiral, isomorphic to A3.1384. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 2)(4, 8)(5, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^3, u.5^3, u.3^-1 * u.1 * u.4^-1, u.4 * u.5^-1 * u.2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^3, x.5^3, x.3^-1 * x.1 * x.4^-1, x.4 * x.5^-1 * x.2, x.1 * x.5 * x.3, x.2 * x.3 * x.5, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.4, x.5, x.5^-1, x.2, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 13, 25, 37, 49, 61, 73, 85)(2, 14, 26, 38, 50, 62, 74, 86)(3, 15, 27, 39, 51, 63, 75, 87)(4, 16, 28, 40, 52, 64, 76, 88)(5, 17, 29, 41, 53, 65, 77, 89)(6, 18, 30, 42, 54, 66, 78, 90)(7, 19, 31, 43, 55, 67, 79, 91)(8, 20, 32, 44, 56, 68, 80, 92)(9, 21, 33, 45, 57, 69, 81, 93)(10, 22, 34, 46, 58, 70, 82, 94)(11, 23, 35, 47, 59, 71, 83, 95)(12, 24, 36, 48, 60, 72, 84, 96) L = (1, 14)(2, 15)(3, 13)(4, 18)(5, 23)(6, 21)(7, 22)(8, 17)(9, 16)(10, 24)(11, 20)(12, 19)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(37, 88)(38, 96)(39, 92)(40, 91)(41, 86)(42, 87)(43, 85)(44, 90)(45, 95)(46, 93)(47, 94)(48, 89)(49, 65)(50, 66)(51, 67)(52, 68)(53, 69)(54, 70)(55, 71)(56, 72)(57, 61)(58, 62)(59, 63)(60, 64)(73, 83)(74, 81)(75, 82)(76, 77)(78, 84)(79, 80) MAP : A3.1402 NOTES : type I, chiral, isomorphic to A3.1384. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 2)(4, 8)(5, 6) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3^3, u.5^3, u.3^-1 * u.1 * u.4^-1, u.4 * u.5^-1 * u.2 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^3, x.5^3, x.3^-1 * x.1 * x.4^-1, x.4 * x.5^-1 * x.2, x.1 * x.5 * x.3, x.2 * x.3 * x.5, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.3^-1, x.1, x.4, x.5, x.5^-1, x.2, x.4^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 13, 25, 37, 49, 61, 73, 85)(2, 14, 26, 38, 50, 62, 74, 86)(3, 15, 27, 39, 51, 63, 75, 87)(4, 16, 28, 40, 52, 64, 76, 88)(5, 17, 29, 41, 53, 65, 77, 89)(6, 18, 30, 42, 54, 66, 78, 90)(7, 19, 31, 43, 55, 67, 79, 91)(8, 20, 32, 44, 56, 68, 80, 92)(9, 21, 33, 45, 57, 69, 81, 93)(10, 22, 34, 46, 58, 70, 82, 94)(11, 23, 35, 47, 59, 71, 83, 95)(12, 24, 36, 48, 60, 72, 84, 96) L = (1, 15)(2, 13)(3, 14)(4, 21)(5, 20)(6, 16)(7, 24)(8, 23)(9, 18)(10, 19)(11, 17)(12, 22)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(37, 93)(38, 94)(39, 95)(40, 96)(41, 85)(42, 86)(43, 87)(44, 88)(45, 89)(46, 90)(47, 91)(48, 92)(49, 67)(50, 65)(51, 66)(52, 61)(53, 72)(54, 68)(55, 64)(56, 63)(57, 70)(58, 71)(59, 69)(60, 62)(73, 84)(74, 80)(75, 76)(77, 82)(78, 83)(79, 81) MAP : A3.1403 NOTES : type I, chiral, isomorphic to A3.1384. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 8)(2, 6)(4, 5) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3 * u.4^-1 * u.2, u.5^3, u.3^3, u.4 * u.1 * u.5^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.2, x.5^3, x.3^3, x.4 * x.1 * x.5^-1, x.3 * x.2 * x.5^-1, x.1 * x.3 * x.5^-1, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.5^-1, x.4^-1, x.2, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 13, 25, 37, 49, 61, 73, 85)(2, 14, 26, 38, 50, 62, 74, 86)(3, 15, 27, 39, 51, 63, 75, 87)(4, 16, 28, 40, 52, 64, 76, 88)(5, 17, 29, 41, 53, 65, 77, 89)(6, 18, 30, 42, 54, 66, 78, 90)(7, 19, 31, 43, 55, 67, 79, 91)(8, 20, 32, 44, 56, 68, 80, 92)(9, 21, 33, 45, 57, 69, 81, 93)(10, 22, 34, 46, 58, 70, 82, 94)(11, 23, 35, 47, 59, 71, 83, 95)(12, 24, 36, 48, 60, 72, 84, 96) L = (1, 92)(2, 88)(3, 96)(4, 95)(5, 90)(6, 91)(7, 89)(8, 94)(9, 87)(10, 85)(11, 86)(12, 93)(13, 62)(14, 63)(15, 61)(16, 66)(17, 71)(18, 69)(19, 70)(20, 65)(21, 64)(22, 72)(23, 68)(24, 67)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(37, 57)(38, 58)(39, 59)(40, 60)(41, 49)(42, 50)(43, 51)(44, 52)(45, 53)(46, 54)(47, 55)(48, 56)(73, 84)(74, 80)(75, 76)(77, 82)(78, 83)(79, 81) MAP : A3.1404 NOTES : type I, chiral, isomorphic to A3.1384. QUOTIENT : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 8)(2, 6)(4, 5) ORBIFOLD : O(0, {3, 3, 2, 2}) EMBEDDING : vertices: [ 1 ], faces: [ 3, 3, 1, 1 ] UNIGROUP : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^2, u.3 * u.4^-1 * u.2, u.5^3, u.3^3, u.4 * u.1 * u.5^-1 > CTG (small) : <12, 3> CTG (fp) : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.2, x.5^3, x.3^3, x.4 * x.1 * x.5^-1, x.3 * x.2 * x.5^-1, x.1 * x.3 * x.5^-1, (x.2 * x.1)^2 > SCHREIER VEC. : (x.3, x.4, x.1, x.5, x.5^-1, x.4^-1, x.2, x.3^-1) LOCAL TYPE : (3, 3, 3, 3, 3, 3, 3, 3) #DARTS : 96 R = (1, 13, 25, 37, 49, 61, 73, 85)(2, 14, 26, 38, 50, 62, 74, 86)(3, 15, 27, 39, 51, 63, 75, 87)(4, 16, 28, 40, 52, 64, 76, 88)(5, 17, 29, 41, 53, 65, 77, 89)(6, 18, 30, 42, 54, 66, 78, 90)(7, 19, 31, 43, 55, 67, 79, 91)(8, 20, 32, 44, 56, 68, 80, 92)(9, 21, 33, 45, 57, 69, 81, 93)(10, 22, 34, 46, 58, 70, 82, 94)(11, 23, 35, 47, 59, 71, 83, 95)(12, 24, 36, 48, 60, 72, 84, 96) L = (1, 94)(2, 95)(3, 93)(4, 86)(5, 91)(6, 89)(7, 90)(8, 85)(9, 96)(10, 92)(11, 88)(12, 87)(13, 63)(14, 61)(15, 62)(16, 69)(17, 68)(18, 64)(19, 72)(20, 71)(21, 66)(22, 67)(23, 65)(24, 70)(25, 30)(26, 31)(27, 29)(28, 34)(32, 33)(35, 36)(37, 52)(38, 60)(39, 56)(40, 55)(41, 50)(42, 51)(43, 49)(44, 54)(45, 59)(46, 57)(47, 58)(48, 53)(73, 83)(74, 81)(75, 82)(76, 77)(78, 84)(79, 80)