Created on Wed Sep 22 2010, 08:29:36 CEST

GENUS: 4
NUMBER OF RECORDS: 1886
NUMBER OF MAPS: 111
REFLEXIBLE MAPS: 77
CHIRAL MAPS: 34
#TYPE I: 76
#TYPE II: 35
CAYLEY MAPS: 109
NON-CAYLEY MAPS: 2
NON-CAYLEY REPRESENTATIVES: A4.656, A4.1874

ISOMORPHISMS
Representatives
[ 1, 7, 10, 16, 31, 44, 46, 100, 103, 105, 143, 161, 163, 179, 186, 205, 209, 211, 213, 247, 253, 254, 259, 279, 286, 329, 353, 356, 357, 419, 515, 517, 521, 525, 526, 655, 656, 659, 663, 667, 668, 670, 671, 673, 678, 682, 683, 720, 721, 725, 806, 810, 812, 813, 814, 816, 820, 828, 830, 831, 838, 874, 875, 879, 880, 886, 890, 918, 930, 931, 933, 934, 935, 939, 947, 951, 953, 961, 964, 965, 1111, 1211, 1212, 1221, 1242, 1244, 1246, 1248, 1249, 1250, 1251, 1254, 1267, 1277, 1282, 1292, 1489, 1493, 1494, 1495, 1496, 1497, 1504, 1506, 1510, 1868, 1872, 1874, 1875, 1876, 1883 ]
Classes
[
{@ 1, 2, 3, 4, 5, 6, 94, 95, 96, 97, 98, 99 @},
{@ 7, 8, 9, 28, 29, 30 @},
{@ 10, 11, 12, 13, 14, 15, 38, 39, 40, 41, 42, 43 @},
{@ 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93 @},
{@ 31, 32, 33, 34, 35, 36, 37 @},
{@ 44, 45, 51, 52, 53, 54, 59, 60, 71, 72, 76, 78, 79, 81 @},
{@ 46, 47, 48, 49, 50, 55, 56, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 73, 74, 75, 77, 80 @},
{@ 100, 101, 102 @},
{@ 103, 104 @},
{@ 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142 @},
{@ 143, 144, 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, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204 @},
{@ 186, 187 @},
{@ 205, 206, 207, 208 @},
{@ 209, 210, 212, 221, 225, 226, 227, 229, 230, 231, 232, 234, 236, 237, 238, 242, 243, 246 @},
{@ 211, 215, 218, 222 @},
{@ 213, 214, 216, 217, 219, 220, 223, 224, 228, 233, 235, 239, 240, 241, 244, 245 @},
{@ 247, 248, 249, 250, 251, 252, 256, 258 @},
{@ 253, 255 @},
{@ 254, 257 @},
{@ 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 280, 282, 283, 284, 285, 288, 289, 290, 293, 294, 295, 296, 297, 299, 300, 302, 304, 306, 308, 309, 310, 311, 312, 313, 315, 317, 322, 334, 338, 339, 348, 350 @},
{@ 279, 281, 291, 292, 298, 301, 303, 305, 307, 314, 316, 318, 319, 320, 321, 323, 324, 325, 326, 327, 328, 335, 336, 337, 340, 341, 342, 343, 344, 345, 346, 349 @},
{@ 286, 287 @},
{@ 329, 330, 331, 332, 333, 347, 351, 352 @},
{@ 353, 354, 355, 363, 364, 365, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 390, 391, 392, 393, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 422, 423, 424, 425, 426, 427, 428, 429, 434, 435, 436, 437, 438, 439, 440, 441, 442, 445, 447, 448, 449, 452, 454, 458, 459, 460, 462, 463, 464, 465, 466, 470, 471, 472, 473, 475, 476, 477, 478, 479, 480, 483, 484, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 498, 501, 513 @},
{@ 356, 360, 361, 368, 389, 394, 431, 432, 443, 444, 446, 450, 451, 453, 455, 467, 468, 469, 474, 481, 482, 485, 496, 497, 499, 500, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 514 @},
{@ 357, 358, 359, 362, 366, 367, 388, 395, 396, 397, 398, 399, 420, 421, 430, 433 @},
{@ 419, 456, 457, 461 @},
{@ 515, 516, 519, 520 @},
{@ 517, 518 @},
{@ 521, 522, 523, 524 @},
{@ 525, 527, 530, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 577, 578, 583, 584, 595, 596, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 637, 638, 639, 640, 641, 642, 643, 644, 646, 649, 653 @},
{@ 526, 528, 529, 531, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 579, 580, 581, 582, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 597, 598, 617, 618, 636, 645, 647, 648, 650, 651, 652, 654 @},
{@ 655 @},
{@ 656, 657, 658 @},
{@ 659, 660, 661, 662 @},
{@ 663, 664, 665, 666 @},
{@ 667 @},
{@ 668, 669 @},
{@ 670, 677 @},
{@ 671, 672, 680, 681 @},
{@ 673, 674, 675, 676, 716, 717, 718, 719 @},
{@ 678, 679 @},
{@ 682, 685, 688, 693, 694, 695, 696, 697 @},
{@ 683, 684, 686, 687, 689, 690, 691, 692, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 715 @},
{@ 720, 722, 723, 730, 732, 738, 740, 741, 746, 747, 748, 749, 750, 766, 771, 772, 776, 777, 778, 779, 780, 781, 782, 783, 787, 788, 793, 794, 797, 803 @},
{@ 721, 724, 727, 734, 735, 739, 751, 752, 753, 754, 755, 756, 757, 773, 785, 786, 789, 790, 791, 792, 798, 799, 800, 801, 804, 805 @},
{@ 725, 726, 728, 729, 731, 733, 736, 737, 742, 743, 744, 745, 758, 759, 760, 761, 762, 763, 764, 765, 767, 768, 769, 770, 774, 775, 784, 795, 796, 802 @},
{@ 806, 807, 808, 809 @},
{@ 810, 811, 822, 823 @},
{@ 812, 818 @},
{@ 813, 815, 825, 826 @},
{@ 814, 817, 824, 829 @},
{@ 816, 819, 821, 827 @},
{@ 820 @},
{@ 828 @},
{@ 830, 832, 834, 837 @},
{@ 831, 833, 835, 836 @},
{@ 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873 @},
{@ 874, 878, 882, 883 @},
{@ 875, 876, 877, 885 @},
{@ 879, 881 @},
{@ 880, 884 @},
{@ 886, 887, 888, 889 @},
{@ 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 919, 923, 924, 925, 926, 927, 928, 929 @},
{@ 918, 920, 921, 922 @},
{@ 930, 932 @},
{@ 931 @},
{@ 933, 937 @},
{@ 934, 938 @},
{@ 935, 936 @},
{@ 939, 940, 941, 942, 943, 944, 945, 946 @},
{@ 947, 948, 949, 950 @},
{@ 951, 952, 954, 957, 959 @},
{@ 953, 955, 956, 958, 960 @},
{@ 961, 962, 963, 971 @},
{@ 964, 968, 969, 972, 974, 975, 978, 982, 985, 989, 994, 996, 1000, 1001, 1005, 1008, 1011, 1014, 1018, 1019, 1022, 1023, 1027, 1030, 1032, 1036, 1037, 1041, 1044, 1047, 1050, 1054, 1055, 1059, 1063, 1065, 1068, 1069, 1072, 1074, 1079, 1081, 1086, 1090, 1094, 1098, 1100, 1105, 1106, 1108 @},
{@ 965, 966, 967, 970, 973, 976, 977, 979, 980, 981, 983, 984, 986, 987, 988, 990, 991, 992, 993, 995, 997, 998, 999, 1002, 1003, 1004, 1006, 1007, 1009, 1010, 1012, 1013, 1015, 1016, 1017, 1020, 1021, 1024, 1025, 1026, 1028, 1029, 1031, 1033, 1034, 1035, 1038, 1039, 1040, 1042, 1043, 1045, 1046, 1048, 1049, 1051, 1052, 1053, 1056, 1057, 1058, 1060, 1061, 1062, 1064, 1066, 1067, 1070, 1071, 1073, 1075, 1076, 1077, 1078, 1080, 1082, 1083, 1084, 1085, 1087, 1088, 1089, 1091, 1092, 1093, 1095, 1096, 1097, 1099, 1101, 1102, 1103, 1104, 1107, 1109, 1110 @},
{@ 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 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, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 1225, 1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233, 1234, 1235, 1237, 1238, 1239, 1240, 1241 @},
{@ 1212, 1220, 1222 @},
{@ 1221, 1223, 1224, 1236 @},
{@ 1242, 1243 @},
{@ 1244, 1245 @},
{@ 1246, 1247 @},
{@ 1248, 1252, 1253, 1264 @},
{@ 1249, 1261 @},
{@ 1250, 1260, 1262, 1265 @},
{@ 1251, 1259 @},
{@ 1254, 1255, 1256, 1257, 1258, 1263, 1266 @},
{@ 1267, 1268, 1269, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1279, 1280, 1281, 1284, 1286, 1287, 1288, 1289, 1290, 1291, 1298, 1299, 1300, 1301, 1304, 1309, 1313, 1316, 1320, 1325, 1329, 1332, 1336, 1341, 1345, 1348, 1352, 1357, 1361, 1362, 1369, 1370, 1377, 1380, 1382, 1389, 1390, 1397, 1401, 1402, 1409, 1410, 1415, 1418, 1422, 1426, 1429, 1430, 1437, 1438, 1443, 1446, 1451, 1455, 1458, 1463, 1465, 1471, 1473, 1474, 1478, 1483 @},
{@ 1277, 1278, 1283, 1285, 1303, 1305, 1307, 1308, 1311, 1312, 1315, 1317, 1319, 1321, 1323, 1324, 1326, 1328, 1330, 1333, 1334, 1337, 1338, 1340, 1342, 1344, 1346, 1349, 1351, 1353, 1355, 1356, 1358, 1360, 1363, 1365, 1366, 1368, 1372, 1373, 1374, 1376, 1378, 1381, 1383, 1385, 1386, 1387, 1391, 1393, 1394, 1395, 1398, 1400, 1404, 1405, 1406, 1408, 1412, 1413, 1414, 1417, 1419, 1421, 1423, 1425, 1427, 1431, 1434, 1435, 1439, 1440, 1442, 1444, 1447, 1449, 1450, 1453, 1454, 1457, 1459, 1461, 1462, 1466, 1467, 1469, 1470, 1472, 1475, 1476, 1479, 1480, 1482, 1484, 1486, 1487 @},
{@ 1282, 1295, 1296, 1302, 1306, 1310, 1314, 1318, 1322, 1327, 1331, 1335, 1339, 1343, 1347, 1350, 1354, 1359, 1364, 1367, 1371, 1375, 1379, 1384, 1388, 1392, 1396, 1399, 1403, 1407, 1411, 1416, 1420, 1424, 1428, 1432, 1433, 1436, 1441, 1445, 1448, 1452, 1456, 1460, 1464, 1468, 1477, 1481, 1485, 1488 @},
{@ 1292, 1293, 1294, 1297 @},
{@ 1489, 1490, 1491, 1492 @},
{@ 1493, 1540, 1541, 1543, 1544, 1546, 1547, 1549, 1550, 1552, 1553, 1555, 1556, 1557, 1559, 1560, 1562, 1563, 1565, 1566, 1568, 1569, 1571, 1572, 1574, 1576, 1577, 1579, 1580, 1582, 1583, 1584, 1586, 1588, 1589, 1590, 1592, 1593, 1595, 1596, 1598, 1599, 1600, 1602, 1604, 1605, 1606, 1608, 1610, 1612, 1613, 1614, 1616, 1618, 1619, 1620, 1622, 1623, 1625, 1626, 1628, 1629, 1630, 1632, 1634, 1635, 1638, 1640, 1641, 1642, 1644, 1645, 1647, 1649, 1650, 1652, 1653, 1655, 1656, 1658, 1659, 1661, 1662, 1664, 1665, 1666, 1668, 1669, 1671, 1672, 1674, 1675, 1677, 1678, 1680, 1681 @},
{@ 1494, 1502, 1513, 1514, 1683, 1687, 1691, 1695, 1699, 1703, 1708, 1712, 1716, 1720, 1724, 1728, 1731, 1735, 1740, 1744, 1748, 1752, 1756, 1757, 1760, 1765, 1769, 1773, 1777, 1780, 1784, 1788, 1792, 1797, 1801, 1805, 1809, 1813, 1817, 1822, 1826, 1829, 1833, 1841, 1845, 1849, 1854, 1862, 1865, 1867 @},
{@ 1495, 1503, 1516, 1517, 1518, 1519, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 1530, 1531, 1532, 1533, 1534, 1685, 1690, 1694, 1697, 1701, 1706, 1710, 1713, 1717, 1722, 1726, 1729, 1733, 1738, 1742, 1743, 1750, 1751, 1758, 1761, 1763, 1770, 1771, 1778, 1782, 1783, 1790, 1791, 1796, 1799, 1803, 1810, 1811, 1818, 1819, 1824, 1827, 1832, 1836, 1839, 1844, 1847, 1852, 1855, 1859, 1863 @},
{@ 1496, 1499, 1539, 1542, 1545, 1548, 1551, 1554, 1558, 1561, 1564, 1567, 1570, 1573, 1575, 1578, 1581, 1585, 1587, 1591, 1594, 1597, 1601, 1603, 1607, 1609, 1611, 1615, 1617, 1621, 1624, 1627, 1631, 1633, 1637, 1639, 1643, 1646, 1648, 1651, 1654, 1657, 1660, 1663, 1667, 1670, 1673, 1676, 1679, 1682 @},
{@ 1497, 1498, 1500, 1501 @},
{@ 1504, 1505, 1636, 1684, 1686, 1688, 1689, 1692, 1693, 1696, 1698, 1700, 1702, 1704, 1705, 1707, 1709, 1711, 1714, 1715, 1718, 1719, 1721, 1723, 1725, 1727, 1730, 1732, 1734, 1736, 1737, 1739, 1741, 1745, 1746, 1747, 1749, 1753, 1754, 1755, 1759, 1762, 1764, 1766, 1767, 1768, 1772, 1774, 1775, 1776, 1779, 1781, 1785, 1786, 1787, 1789, 1793, 1794, 1795, 1798, 1800, 1802, 1804, 1806, 1807, 1808, 1812, 1814, 1815, 1816, 1820, 1821, 1823, 1825, 1828, 1830, 1831, 1834, 1835, 1837, 1838, 1840, 1842, 1843, 1846, 1848, 1850, 1851, 1853, 1856, 1857, 1858, 1860, 1861, 1864, 1866 @},
{@ 1506, 1507, 1508, 1509, 1535, 1536, 1537, 1538 @},
{@ 1510, 1511, 1512, 1515 @},
{@ 1868, 1869, 1870, 1871 @},
{@ 1872, 1873 @},
{@ 1874 @},
{@ 1875, 1878, 1879, 1882 @},
{@ 1876, 1877, 1880, 1881 @},
{@ 1883, 1884, 1885, 1886 @}
]

MAP           : A4.1
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: [ 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)   : <72, 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^-1 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2^-1, x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * 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 * 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^-1 * 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^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1, x.3^-3 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2 * x.3^-3 * x.2 * x.3^-1 * x.2 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 6, 24)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 366)(74, 371)(75, 361)(76, 369)(77, 364)(78, 363)(79, 396)(80, 362)(81, 365)(82, 403)(83, 368)(84, 370)(85, 378)(86, 383)(87, 373)(88, 381)(89, 376)(90, 375)(91, 420)(92, 374)(93, 377)(94, 391)(95, 380)(96, 382)(97, 414)(98, 419)(99, 409)(100, 417)(101, 412)(102, 411)(103, 384)(104, 410)(105, 413)(106, 427)(107, 416)(108, 418)(109, 390)(110, 395)(111, 385)(112, 393)(113, 388)(114, 387)(115, 372)(116, 386)(117, 389)(118, 379)(119, 392)(120, 394)(121, 402)(122, 407)(123, 397)(124, 405)(125, 400)(126, 399)(127, 432)(128, 398)(129, 401)(130, 367)(131, 404)(132, 406)(133, 426)(134, 431)(135, 421)(136, 429)(137, 424)(138, 423)(139, 408)(140, 422)(141, 425)(142, 415)(143, 428)(144, 430)(145, 292)(146, 294)(147, 331)(148, 289)(149, 355)(150, 290)(151, 299)(152, 340)(153, 326)(154, 338)(155, 295)(156, 328)(157, 312)(158, 321)(159, 311)(160, 324)(161, 347)(162, 309)(163, 315)(164, 348)(165, 306)(166, 345)(167, 303)(168, 301)(169, 316)(170, 318)(171, 307)(172, 313)(173, 343)(174, 314)(175, 323)(176, 352)(177, 302)(178, 350)(179, 319)(180, 304)(181, 336)(182, 297)(183, 335)(184, 300)(185, 359)(186, 333)(187, 291)(188, 360)(189, 330)(190, 357)(191, 327)(192, 325)(193, 344)(194, 298)(195, 341)(196, 296)(197, 339)(198, 346)(199, 317)(200, 337)(201, 310)(202, 342)(203, 305)(204, 308)(205, 356)(206, 322)(207, 353)(208, 320)(209, 351)(210, 358)(211, 293)(212, 349)(213, 334)(214, 354)(215, 329)(216, 332)

MAP           : A4.2
NOTES         : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A4.1.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^3, x.3^-1 * x.2 * x.3^4 * x.2^-1 * x.3^-3, 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, (x.3 * x.1^-1)^12 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 6, 24)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 364)(74, 366)(75, 403)(76, 361)(77, 427)(78, 362)(79, 371)(80, 412)(81, 398)(82, 410)(83, 367)(84, 400)(85, 384)(86, 393)(87, 383)(88, 396)(89, 419)(90, 381)(91, 387)(92, 420)(93, 378)(94, 417)(95, 375)(96, 373)(97, 388)(98, 390)(99, 379)(100, 385)(101, 415)(102, 386)(103, 395)(104, 424)(105, 374)(106, 422)(107, 391)(108, 376)(109, 408)(110, 369)(111, 407)(112, 372)(113, 431)(114, 405)(115, 363)(116, 432)(117, 402)(118, 429)(119, 399)(120, 397)(121, 416)(122, 370)(123, 413)(124, 368)(125, 411)(126, 418)(127, 389)(128, 409)(129, 382)(130, 414)(131, 377)(132, 380)(133, 428)(134, 394)(135, 425)(136, 392)(137, 423)(138, 430)(139, 365)(140, 421)(141, 406)(142, 426)(143, 401)(144, 404)(145, 290)(146, 295)(147, 292)(148, 326)(149, 289)(150, 331)(151, 304)(152, 294)(153, 355)(154, 291)(155, 340)(156, 338)(157, 309)(158, 303)(159, 312)(160, 306)(161, 324)(162, 311)(163, 308)(164, 321)(165, 347)(166, 323)(167, 348)(168, 345)(169, 346)(170, 305)(171, 344)(172, 310)(173, 296)(174, 341)(175, 301)(176, 298)(177, 339)(178, 293)(179, 337)(180, 342)(181, 314)(182, 319)(183, 316)(184, 302)(185, 313)(186, 307)(187, 328)(188, 318)(189, 343)(190, 315)(191, 352)(192, 350)(193, 333)(194, 327)(195, 336)(196, 330)(197, 300)(198, 335)(199, 332)(200, 297)(201, 359)(202, 299)(203, 360)(204, 357)(205, 358)(206, 329)(207, 356)(208, 334)(209, 320)(210, 353)(211, 325)(212, 322)(213, 351)(214, 317)(215, 349)(216, 354)

MAP           : A4.3
NOTES         : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A4.1.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^3, x.3^-1 * x.2 * x.3^4 * x.2^-1 * x.3^-3, 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, (x.3 * x.1^-1)^12 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 6, 24)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 364)(74, 366)(75, 403)(76, 361)(77, 427)(78, 362)(79, 371)(80, 412)(81, 398)(82, 410)(83, 367)(84, 400)(85, 384)(86, 393)(87, 383)(88, 396)(89, 419)(90, 381)(91, 387)(92, 420)(93, 378)(94, 417)(95, 375)(96, 373)(97, 388)(98, 390)(99, 379)(100, 385)(101, 415)(102, 386)(103, 395)(104, 424)(105, 374)(106, 422)(107, 391)(108, 376)(109, 408)(110, 369)(111, 407)(112, 372)(113, 431)(114, 405)(115, 363)(116, 432)(117, 402)(118, 429)(119, 399)(120, 397)(121, 416)(122, 370)(123, 413)(124, 368)(125, 411)(126, 418)(127, 389)(128, 409)(129, 382)(130, 414)(131, 377)(132, 380)(133, 428)(134, 394)(135, 425)(136, 392)(137, 423)(138, 430)(139, 365)(140, 421)(141, 406)(142, 426)(143, 401)(144, 404)(145, 311)(146, 348)(147, 309)(148, 347)(149, 306)(150, 312)(151, 357)(152, 303)(153, 324)(154, 301)(155, 321)(156, 323)(157, 353)(158, 349)(159, 358)(160, 351)(161, 334)(162, 356)(163, 350)(164, 329)(165, 320)(166, 332)(167, 322)(168, 317)(169, 307)(170, 352)(171, 314)(172, 343)(173, 302)(174, 316)(175, 354)(176, 319)(177, 313)(178, 304)(179, 318)(180, 315)(181, 335)(182, 360)(183, 333)(184, 359)(185, 330)(186, 336)(187, 345)(188, 327)(189, 300)(190, 325)(191, 297)(192, 299)(193, 341)(194, 337)(195, 346)(196, 339)(197, 310)(198, 344)(199, 338)(200, 305)(201, 296)(202, 308)(203, 298)(204, 293)(205, 331)(206, 340)(207, 290)(208, 355)(209, 326)(210, 292)(211, 342)(212, 295)(213, 289)(214, 328)(215, 294)(216, 291)

MAP           : A4.4
NOTES         : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A4.1.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.2^-1 * x.3)^2, (x.3 * x.1^-1)^3, (x.3 * x.2^2)^3, x.3 * x.2^4 * x.3^-1 * x.2^-4, (x.1 * x.2^-1)^12 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 6, 24)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 362)(74, 367)(75, 364)(76, 398)(77, 361)(78, 403)(79, 376)(80, 366)(81, 427)(82, 363)(83, 412)(84, 410)(85, 381)(86, 375)(87, 384)(88, 378)(89, 396)(90, 383)(91, 380)(92, 393)(93, 419)(94, 395)(95, 420)(96, 417)(97, 418)(98, 377)(99, 416)(100, 382)(101, 368)(102, 413)(103, 373)(104, 370)(105, 411)(106, 365)(107, 409)(108, 414)(109, 386)(110, 391)(111, 388)(112, 374)(113, 385)(114, 379)(115, 400)(116, 390)(117, 415)(118, 387)(119, 424)(120, 422)(121, 405)(122, 399)(123, 408)(124, 402)(125, 372)(126, 407)(127, 404)(128, 369)(129, 431)(130, 371)(131, 432)(132, 429)(133, 430)(134, 401)(135, 428)(136, 406)(137, 392)(138, 425)(139, 397)(140, 394)(141, 423)(142, 389)(143, 421)(144, 426)(145, 294)(146, 299)(147, 289)(148, 297)(149, 292)(150, 291)(151, 324)(152, 290)(153, 293)(154, 331)(155, 296)(156, 298)(157, 306)(158, 311)(159, 301)(160, 309)(161, 304)(162, 303)(163, 348)(164, 302)(165, 305)(166, 319)(167, 308)(168, 310)(169, 342)(170, 347)(171, 337)(172, 345)(173, 340)(174, 339)(175, 312)(176, 338)(177, 341)(178, 355)(179, 344)(180, 346)(181, 318)(182, 323)(183, 313)(184, 321)(185, 316)(186, 315)(187, 300)(188, 314)(189, 317)(190, 307)(191, 320)(192, 322)(193, 330)(194, 335)(195, 325)(196, 333)(197, 328)(198, 327)(199, 360)(200, 326)(201, 329)(202, 295)(203, 332)(204, 334)(205, 354)(206, 359)(207, 349)(208, 357)(209, 352)(210, 351)(211, 336)(212, 350)(213, 353)(214, 343)(215, 356)(216, 358)

MAP           : A4.5
NOTES         : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A4.1.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.2^-1 * x.3)^2, (x.3 * x.1^-1)^3, (x.3 * x.2^2)^3, x.3 * x.2^4 * x.3^-1 * x.2^-4, (x.1 * x.2^-1)^12 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 6, 24)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 383)(74, 420)(75, 381)(76, 419)(77, 378)(78, 384)(79, 429)(80, 375)(81, 396)(82, 373)(83, 393)(84, 395)(85, 425)(86, 421)(87, 430)(88, 423)(89, 406)(90, 428)(91, 422)(92, 401)(93, 392)(94, 404)(95, 394)(96, 389)(97, 379)(98, 424)(99, 386)(100, 415)(101, 374)(102, 388)(103, 426)(104, 391)(105, 385)(106, 376)(107, 390)(108, 387)(109, 407)(110, 432)(111, 405)(112, 431)(113, 402)(114, 408)(115, 417)(116, 399)(117, 372)(118, 397)(119, 369)(120, 371)(121, 413)(122, 409)(123, 418)(124, 411)(125, 382)(126, 416)(127, 410)(128, 377)(129, 368)(130, 380)(131, 370)(132, 365)(133, 403)(134, 412)(135, 362)(136, 427)(137, 398)(138, 364)(139, 414)(140, 367)(141, 361)(142, 400)(143, 366)(144, 363)(145, 307)(146, 352)(147, 314)(148, 343)(149, 302)(150, 316)(151, 354)(152, 319)(153, 313)(154, 304)(155, 318)(156, 315)(157, 335)(158, 360)(159, 333)(160, 359)(161, 330)(162, 336)(163, 345)(164, 327)(165, 300)(166, 325)(167, 297)(168, 299)(169, 311)(170, 348)(171, 309)(172, 347)(173, 306)(174, 312)(175, 357)(176, 303)(177, 324)(178, 301)(179, 321)(180, 323)(181, 353)(182, 349)(183, 358)(184, 351)(185, 334)(186, 356)(187, 350)(188, 329)(189, 320)(190, 332)(191, 322)(192, 317)(193, 331)(194, 340)(195, 290)(196, 355)(197, 326)(198, 292)(199, 342)(200, 295)(201, 289)(202, 328)(203, 294)(204, 291)(205, 341)(206, 337)(207, 346)(208, 339)(209, 310)(210, 344)(211, 338)(212, 305)(213, 296)(214, 308)(215, 298)(216, 293)

MAP           : A4.6
NOTES         : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A4.1.
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)   : <72, 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^-1 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2^-1, x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3^-1 * 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 * 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^-1 * 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^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1, x.3^-3 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2 * x.3^-3 * x.2 * x.3^-1 * x.2 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 6, 24)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 363)(74, 368)(75, 366)(76, 365)(77, 369)(78, 361)(79, 418)(80, 371)(81, 364)(82, 372)(83, 362)(84, 403)(85, 375)(86, 380)(87, 378)(88, 377)(89, 381)(90, 373)(91, 406)(92, 383)(93, 376)(94, 384)(95, 374)(96, 391)(97, 399)(98, 404)(99, 402)(100, 401)(101, 405)(102, 397)(103, 382)(104, 407)(105, 400)(106, 408)(107, 398)(108, 367)(109, 411)(110, 416)(111, 414)(112, 413)(113, 417)(114, 409)(115, 370)(116, 419)(117, 412)(118, 420)(119, 410)(120, 427)(121, 387)(122, 392)(123, 390)(124, 389)(125, 393)(126, 385)(127, 430)(128, 395)(129, 388)(130, 396)(131, 386)(132, 379)(133, 423)(134, 428)(135, 426)(136, 425)(137, 429)(138, 421)(139, 394)(140, 431)(141, 424)(142, 432)(143, 422)(144, 415)(145, 292)(146, 294)(147, 331)(148, 289)(149, 355)(150, 290)(151, 299)(152, 340)(153, 326)(154, 338)(155, 295)(156, 328)(157, 312)(158, 321)(159, 311)(160, 324)(161, 347)(162, 309)(163, 315)(164, 348)(165, 306)(166, 345)(167, 303)(168, 301)(169, 316)(170, 318)(171, 307)(172, 313)(173, 343)(174, 314)(175, 323)(176, 352)(177, 302)(178, 350)(179, 319)(180, 304)(181, 336)(182, 297)(183, 335)(184, 300)(185, 359)(186, 333)(187, 291)(188, 360)(189, 330)(190, 357)(191, 327)(192, 325)(193, 344)(194, 298)(195, 341)(196, 296)(197, 339)(198, 346)(199, 317)(200, 337)(201, 310)(202, 342)(203, 305)(204, 308)(205, 356)(206, 322)(207, 353)(208, 320)(209, 351)(210, 358)(211, 293)(212, 349)(213, 334)(214, 354)(215, 329)(216, 332)

MAP           : A4.7
NOTES         : type II, reflexible, isomorphic to DBar({4,5}), representative.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^4, (x.2^-1 * x.3)^2, (x.3 * x.1^-1)^4, (x.2^-1 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1)^2, (x.1 * x.2^-1)^5, x.3^2 * x.2^-1 * x.3^-1 * x.2^2 * x.3^-1 * x.2^-1 * x.3^-2 * x.2^-2 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 10)
#DARTS        : 720
R = (1, 121, 241)(2, 122, 242)(3, 123, 243)(4, 124, 244)(5, 125, 245)(6, 126, 246)(7, 127, 247)(8, 128, 248)(9, 129, 249)(10, 130, 250)(11, 131, 251)(12, 132, 252)(13, 133, 253)(14, 134, 254)(15, 135, 255)(16, 136, 256)(17, 137, 257)(18, 138, 258)(19, 139, 259)(20, 140, 260)(21, 141, 261)(22, 142, 262)(23, 143, 263)(24, 144, 264)(25, 145, 265)(26, 146, 266)(27, 147, 267)(28, 148, 268)(29, 149, 269)(30, 150, 270)(31, 151, 271)(32, 152, 272)(33, 153, 273)(34, 154, 274)(35, 155, 275)(36, 156, 276)(37, 157, 277)(38, 158, 278)(39, 159, 279)(40, 160, 280)(41, 161, 281)(42, 162, 282)(43, 163, 283)(44, 164, 284)(45, 165, 285)(46, 166, 286)(47, 167, 287)(48, 168, 288)(49, 169, 289)(50, 170, 290)(51, 171, 291)(52, 172, 292)(53, 173, 293)(54, 174, 294)(55, 175, 295)(56, 176, 296)(57, 177, 297)(58, 178, 298)(59, 179, 299)(60, 180, 300)(61, 181, 301)(62, 182, 302)(63, 183, 303)(64, 184, 304)(65, 185, 305)(66, 186, 306)(67, 187, 307)(68, 188, 308)(69, 189, 309)(70, 190, 310)(71, 191, 311)(72, 192, 312)(73, 193, 313)(74, 194, 314)(75, 195, 315)(76, 196, 316)(77, 197, 317)(78, 198, 318)(79, 199, 319)(80, 200, 320)(81, 201, 321)(82, 202, 322)(83, 203, 323)(84, 204, 324)(85, 205, 325)(86, 206, 326)(87, 207, 327)(88, 208, 328)(89, 209, 329)(90, 210, 330)(91, 211, 331)(92, 212, 332)(93, 213, 333)(94, 214, 334)(95, 215, 335)(96, 216, 336)(97, 217, 337)(98, 218, 338)(99, 219, 339)(100, 220, 340)(101, 221, 341)(102, 222, 342)(103, 223, 343)(104, 224, 344)(105, 225, 345)(106, 226, 346)(107, 227, 347)(108, 228, 348)(109, 229, 349)(110, 230, 350)(111, 231, 351)(112, 232, 352)(113, 233, 353)(114, 234, 354)(115, 235, 355)(116, 236, 356)(117, 237, 357)(118, 238, 358)(119, 239, 359)(120, 240, 360)(361, 481, 601)(362, 482, 602)(363, 483, 603)(364, 484, 604)(365, 485, 605)(366, 486, 606)(367, 487, 607)(368, 488, 608)(369, 489, 609)(370, 490, 610)(371, 491, 611)(372, 492, 612)(373, 493, 613)(374, 494, 614)(375, 495, 615)(376, 496, 616)(377, 497, 617)(378, 498, 618)(379, 499, 619)(380, 500, 620)(381, 501, 621)(382, 502, 622)(383, 503, 623)(384, 504, 624)(385, 505, 625)(386, 506, 626)(387, 507, 627)(388, 508, 628)(389, 509, 629)(390, 510, 630)(391, 511, 631)(392, 512, 632)(393, 513, 633)(394, 514, 634)(395, 515, 635)(396, 516, 636)(397, 517, 637)(398, 518, 638)(399, 519, 639)(400, 520, 640)(401, 521, 641)(402, 522, 642)(403, 523, 643)(404, 524, 644)(405, 525, 645)(406, 526, 646)(407, 527, 647)(408, 528, 648)(409, 529, 649)(410, 530, 650)(411, 531, 651)(412, 532, 652)(413, 533, 653)(414, 534, 654)(415, 535, 655)(416, 536, 656)(417, 537, 657)(418, 538, 658)(419, 539, 659)(420, 540, 660)(421, 541, 661)(422, 542, 662)(423, 543, 663)(424, 544, 664)(425, 545, 665)(426, 546, 666)(427, 547, 667)(428, 548, 668)(429, 549, 669)(430, 550, 670)(431, 551, 671)(432, 552, 672)(433, 553, 673)(434, 554, 674)(435, 555, 675)(436, 556, 676)(437, 557, 677)(438, 558, 678)(439, 559, 679)(440, 560, 680)(441, 561, 681)(442, 562, 682)(443, 563, 683)(444, 564, 684)(445, 565, 685)(446, 566, 686)(447, 567, 687)(448, 568, 688)(449, 569, 689)(450, 570, 690)(451, 571, 691)(452, 572, 692)(453, 573, 693)(454, 574, 694)(455, 575, 695)(456, 576, 696)(457, 577, 697)(458, 578, 698)(459, 579, 699)(460, 580, 700)(461, 581, 701)(462, 582, 702)(463, 583, 703)(464, 584, 704)(465, 585, 705)(466, 586, 706)(467, 587, 707)(468, 588, 708)(469, 589, 709)(470, 590, 710)(471, 591, 711)(472, 592, 712)(473, 593, 713)(474, 594, 714)(475, 595, 715)(476, 596, 716)(477, 597, 717)(478, 598, 718)(479, 599, 719)(480, 600, 720)
L = (1, 361)(2, 362)(3, 363)(4, 364)(5, 365)(6, 366)(7, 367)(8, 368)(9, 369)(10, 370)(11, 371)(12, 372)(13, 373)(14, 374)(15, 375)(16, 376)(17, 377)(18, 378)(19, 379)(20, 380)(21, 381)(22, 382)(23, 383)(24, 384)(25, 385)(26, 386)(27, 387)(28, 388)(29, 389)(30, 390)(31, 391)(32, 392)(33, 393)(34, 394)(35, 395)(36, 396)(37, 397)(38, 398)(39, 399)(40, 400)(41, 401)(42, 402)(43, 403)(44, 404)(45, 405)(46, 406)(47, 407)(48, 408)(49, 409)(50, 410)(51, 411)(52, 412)(53, 413)(54, 414)(55, 415)(56, 416)(57, 417)(58, 418)(59, 419)(60, 420)(61, 421)(62, 422)(63, 423)(64, 424)(65, 425)(66, 426)(67, 427)(68, 428)(69, 429)(70, 430)(71, 431)(72, 432)(73, 433)(74, 434)(75, 435)(76, 436)(77, 437)(78, 438)(79, 439)(80, 440)(81, 441)(82, 442)(83, 443)(84, 444)(85, 445)(86, 446)(87, 447)(88, 448)(89, 449)(90, 450)(91, 451)(92, 452)(93, 453)(94, 454)(95, 455)(96, 456)(97, 457)(98, 458)(99, 459)(100, 460)(101, 461)(102, 462)(103, 463)(104, 464)(105, 465)(106, 466)(107, 467)(108, 468)(109, 469)(110, 470)(111, 471)(112, 472)(113, 473)(114, 474)(115, 475)(116, 476)(117, 477)(118, 478)(119, 479)(120, 480)(121, 604)(122, 605)(123, 602)(124, 641)(125, 640)(126, 601)(127, 719)(128, 718)(129, 677)(130, 705)(131, 708)(132, 676)(133, 612)(134, 609)(135, 636)(136, 607)(137, 608)(138, 633)(139, 716)(140, 715)(141, 703)(142, 710)(143, 709)(144, 704)(145, 717)(146, 720)(147, 712)(148, 684)(149, 681)(150, 713)(151, 686)(152, 685)(153, 673)(154, 680)(155, 679)(156, 674)(157, 687)(158, 690)(159, 682)(160, 654)(161, 651)(162, 683)(163, 689)(164, 688)(165, 647)(166, 675)(167, 678)(168, 646)(169, 702)(170, 699)(171, 606)(172, 697)(173, 698)(174, 603)(175, 694)(176, 695)(177, 692)(178, 611)(179, 610)(180, 691)(181, 657)(182, 660)(183, 652)(184, 624)(185, 621)(186, 653)(187, 672)(188, 669)(189, 696)(190, 667)(191, 668)(192, 693)(193, 656)(194, 655)(195, 643)(196, 650)(197, 649)(198, 644)(199, 664)(200, 665)(201, 662)(202, 701)(203, 700)(204, 661)(205, 659)(206, 658)(207, 617)(208, 645)(209, 648)(210, 616)(211, 629)(212, 628)(213, 707)(214, 615)(215, 618)(216, 706)(217, 626)(218, 625)(219, 613)(220, 620)(221, 619)(222, 614)(223, 634)(224, 635)(225, 632)(226, 671)(227, 670)(228, 631)(229, 627)(230, 630)(231, 622)(232, 714)(233, 711)(234, 623)(235, 642)(236, 639)(237, 666)(238, 637)(239, 638)(240, 663)(241, 563)(242, 562)(243, 533)(244, 567)(245, 570)(246, 532)(247, 560)(248, 559)(249, 565)(250, 548)(251, 547)(252, 566)(253, 592)(254, 593)(255, 590)(256, 503)(257, 502)(258, 589)(259, 561)(260, 564)(261, 550)(262, 516)(263, 513)(264, 551)(265, 600)(266, 597)(267, 492)(268, 595)(269, 596)(270, 489)(271, 556)(272, 557)(273, 554)(274, 599)(275, 598)(276, 553)(277, 521)(278, 520)(279, 485)(280, 531)(281, 534)(282, 484)(283, 546)(284, 543)(285, 594)(286, 541)(287, 542)(288, 591)(289, 518)(290, 517)(291, 529)(292, 512)(293, 511)(294, 530)(295, 519)(296, 522)(297, 514)(298, 510)(299, 507)(300, 515)(301, 494)(302, 493)(303, 481)(304, 506)(305, 505)(306, 482)(307, 495)(308, 498)(309, 508)(310, 588)(311, 585)(312, 509)(313, 497)(314, 496)(315, 581)(316, 483)(317, 486)(318, 580)(319, 528)(320, 525)(321, 558)(322, 523)(323, 524)(324, 555)(325, 538)(326, 539)(327, 536)(328, 545)(329, 544)(330, 535)(331, 573)(332, 576)(333, 586)(334, 552)(335, 549)(336, 587)(337, 504)(338, 501)(339, 540)(340, 499)(341, 500)(342, 537)(343, 572)(344, 571)(345, 577)(346, 584)(347, 583)(348, 578)(349, 490)(350, 491)(351, 488)(352, 527)(353, 526)(354, 487)(355, 575)(356, 574)(357, 569)(358, 579)(359, 582)(360, 568)

MAP           : A4.8
NOTES         : type II, reflexible, isomorphic to DBar({4,5}), isomorphic to A4.7.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 5, 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)^5 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^4, (x.3 * x.1^-1)^2, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^5, 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^-1, x.3 * x.2^-2 * x.3 * x.2^-2 * x.3 * x.2^-1 * x.3^-1 * x.2^-2 * x.3^-1 * x.2^-2 * x.3^-1 * x.2^-1, x.3 * x.2^-2 * x.3 * x.2 * x.3 * x.2^-2 * x.3^-1 * x.2^-2 * x.3^-1 * x.2 * x.3^-1 * x.2^-2, x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-2 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 10)
#DARTS        : 720
R = (1, 121, 241)(2, 122, 242)(3, 123, 243)(4, 124, 244)(5, 125, 245)(6, 126, 246)(7, 127, 247)(8, 128, 248)(9, 129, 249)(10, 130, 250)(11, 131, 251)(12, 132, 252)(13, 133, 253)(14, 134, 254)(15, 135, 255)(16, 136, 256)(17, 137, 257)(18, 138, 258)(19, 139, 259)(20, 140, 260)(21, 141, 261)(22, 142, 262)(23, 143, 263)(24, 144, 264)(25, 145, 265)(26, 146, 266)(27, 147, 267)(28, 148, 268)(29, 149, 269)(30, 150, 270)(31, 151, 271)(32, 152, 272)(33, 153, 273)(34, 154, 274)(35, 155, 275)(36, 156, 276)(37, 157, 277)(38, 158, 278)(39, 159, 279)(40, 160, 280)(41, 161, 281)(42, 162, 282)(43, 163, 283)(44, 164, 284)(45, 165, 285)(46, 166, 286)(47, 167, 287)(48, 168, 288)(49, 169, 289)(50, 170, 290)(51, 171, 291)(52, 172, 292)(53, 173, 293)(54, 174, 294)(55, 175, 295)(56, 176, 296)(57, 177, 297)(58, 178, 298)(59, 179, 299)(60, 180, 300)(61, 181, 301)(62, 182, 302)(63, 183, 303)(64, 184, 304)(65, 185, 305)(66, 186, 306)(67, 187, 307)(68, 188, 308)(69, 189, 309)(70, 190, 310)(71, 191, 311)(72, 192, 312)(73, 193, 313)(74, 194, 314)(75, 195, 315)(76, 196, 316)(77, 197, 317)(78, 198, 318)(79, 199, 319)(80, 200, 320)(81, 201, 321)(82, 202, 322)(83, 203, 323)(84, 204, 324)(85, 205, 325)(86, 206, 326)(87, 207, 327)(88, 208, 328)(89, 209, 329)(90, 210, 330)(91, 211, 331)(92, 212, 332)(93, 213, 333)(94, 214, 334)(95, 215, 335)(96, 216, 336)(97, 217, 337)(98, 218, 338)(99, 219, 339)(100, 220, 340)(101, 221, 341)(102, 222, 342)(103, 223, 343)(104, 224, 344)(105, 225, 345)(106, 226, 346)(107, 227, 347)(108, 228, 348)(109, 229, 349)(110, 230, 350)(111, 231, 351)(112, 232, 352)(113, 233, 353)(114, 234, 354)(115, 235, 355)(116, 236, 356)(117, 237, 357)(118, 238, 358)(119, 239, 359)(120, 240, 360)(361, 481, 601)(362, 482, 602)(363, 483, 603)(364, 484, 604)(365, 485, 605)(366, 486, 606)(367, 487, 607)(368, 488, 608)(369, 489, 609)(370, 490, 610)(371, 491, 611)(372, 492, 612)(373, 493, 613)(374, 494, 614)(375, 495, 615)(376, 496, 616)(377, 497, 617)(378, 498, 618)(379, 499, 619)(380, 500, 620)(381, 501, 621)(382, 502, 622)(383, 503, 623)(384, 504, 624)(385, 505, 625)(386, 506, 626)(387, 507, 627)(388, 508, 628)(389, 509, 629)(390, 510, 630)(391, 511, 631)(392, 512, 632)(393, 513, 633)(394, 514, 634)(395, 515, 635)(396, 516, 636)(397, 517, 637)(398, 518, 638)(399, 519, 639)(400, 520, 640)(401, 521, 641)(402, 522, 642)(403, 523, 643)(404, 524, 644)(405, 525, 645)(406, 526, 646)(407, 527, 647)(408, 528, 648)(409, 529, 649)(410, 530, 650)(411, 531, 651)(412, 532, 652)(413, 533, 653)(414, 534, 654)(415, 535, 655)(416, 536, 656)(417, 537, 657)(418, 538, 658)(419, 539, 659)(420, 540, 660)(421, 541, 661)(422, 542, 662)(423, 543, 663)(424, 544, 664)(425, 545, 665)(426, 546, 666)(427, 547, 667)(428, 548, 668)(429, 549, 669)(430, 550, 670)(431, 551, 671)(432, 552, 672)(433, 553, 673)(434, 554, 674)(435, 555, 675)(436, 556, 676)(437, 557, 677)(438, 558, 678)(439, 559, 679)(440, 560, 680)(441, 561, 681)(442, 562, 682)(443, 563, 683)(444, 564, 684)(445, 565, 685)(446, 566, 686)(447, 567, 687)(448, 568, 688)(449, 569, 689)(450, 570, 690)(451, 571, 691)(452, 572, 692)(453, 573, 693)(454, 574, 694)(455, 575, 695)(456, 576, 696)(457, 577, 697)(458, 578, 698)(459, 579, 699)(460, 580, 700)(461, 581, 701)(462, 582, 702)(463, 583, 703)(464, 584, 704)(465, 585, 705)(466, 586, 706)(467, 587, 707)(468, 588, 708)(469, 589, 709)(470, 590, 710)(471, 591, 711)(472, 592, 712)(473, 593, 713)(474, 594, 714)(475, 595, 715)(476, 596, 716)(477, 597, 717)(478, 598, 718)(479, 599, 719)(480, 600, 720)
L = (1, 361)(2, 362)(3, 363)(4, 364)(5, 365)(6, 366)(7, 367)(8, 368)(9, 369)(10, 370)(11, 371)(12, 372)(13, 373)(14, 374)(15, 375)(16, 376)(17, 377)(18, 378)(19, 379)(20, 380)(21, 381)(22, 382)(23, 383)(24, 384)(25, 385)(26, 386)(27, 387)(28, 388)(29, 389)(30, 390)(31, 391)(32, 392)(33, 393)(34, 394)(35, 395)(36, 396)(37, 397)(38, 398)(39, 399)(40, 400)(41, 401)(42, 402)(43, 403)(44, 404)(45, 405)(46, 406)(47, 407)(48, 408)(49, 409)(50, 410)(51, 411)(52, 412)(53, 413)(54, 414)(55, 415)(56, 416)(57, 417)(58, 418)(59, 419)(60, 420)(61, 421)(62, 422)(63, 423)(64, 424)(65, 425)(66, 426)(67, 427)(68, 428)(69, 429)(70, 430)(71, 431)(72, 432)(73, 433)(74, 434)(75, 435)(76, 436)(77, 437)(78, 438)(79, 439)(80, 440)(81, 441)(82, 442)(83, 443)(84, 444)(85, 445)(86, 446)(87, 447)(88, 448)(89, 449)(90, 450)(91, 451)(92, 452)(93, 453)(94, 454)(95, 455)(96, 456)(97, 457)(98, 458)(99, 459)(100, 460)(101, 461)(102, 462)(103, 463)(104, 464)(105, 465)(106, 466)(107, 467)(108, 468)(109, 469)(110, 470)(111, 471)(112, 472)(113, 473)(114, 474)(115, 475)(116, 476)(117, 477)(118, 478)(119, 479)(120, 480)(121, 603)(122, 606)(123, 616)(124, 702)(125, 699)(126, 617)(127, 654)(128, 651)(129, 690)(130, 649)(131, 650)(132, 687)(133, 602)(134, 601)(135, 607)(136, 614)(137, 613)(138, 608)(139, 640)(140, 641)(141, 638)(142, 677)(143, 676)(144, 637)(145, 605)(146, 604)(147, 719)(148, 609)(149, 612)(150, 718)(151, 713)(152, 712)(153, 683)(154, 717)(155, 720)(156, 682)(157, 710)(158, 709)(159, 715)(160, 698)(161, 697)(162, 716)(163, 622)(164, 623)(165, 620)(166, 653)(167, 652)(168, 619)(169, 711)(170, 714)(171, 700)(172, 666)(173, 663)(174, 701)(175, 630)(176, 627)(177, 642)(178, 625)(179, 626)(180, 639)(181, 706)(182, 707)(183, 704)(184, 629)(185, 628)(186, 703)(187, 671)(188, 670)(189, 635)(190, 681)(191, 684)(192, 634)(193, 696)(194, 693)(195, 624)(196, 691)(197, 692)(198, 621)(199, 668)(200, 667)(201, 679)(202, 662)(203, 661)(204, 680)(205, 669)(206, 672)(207, 664)(208, 660)(209, 657)(210, 665)(211, 644)(212, 643)(213, 631)(214, 656)(215, 655)(216, 632)(217, 645)(218, 648)(219, 658)(220, 618)(221, 615)(222, 659)(223, 647)(224, 646)(225, 611)(226, 633)(227, 636)(228, 610)(229, 678)(230, 675)(231, 708)(232, 673)(233, 674)(234, 705)(235, 688)(236, 689)(237, 686)(238, 695)(239, 694)(240, 685)(241, 482)(242, 481)(243, 487)(244, 494)(245, 493)(246, 488)(247, 483)(248, 486)(249, 496)(250, 582)(251, 579)(252, 497)(253, 485)(254, 484)(255, 599)(256, 489)(257, 492)(258, 598)(259, 534)(260, 531)(261, 570)(262, 529)(263, 530)(264, 567)(265, 520)(266, 521)(267, 518)(268, 557)(269, 556)(270, 517)(271, 591)(272, 594)(273, 580)(274, 546)(275, 543)(276, 581)(277, 510)(278, 507)(279, 522)(280, 505)(281, 506)(282, 519)(283, 590)(284, 589)(285, 595)(286, 578)(287, 577)(288, 596)(289, 502)(290, 503)(291, 500)(292, 533)(293, 532)(294, 499)(295, 593)(296, 592)(297, 563)(298, 597)(299, 600)(300, 562)(301, 551)(302, 550)(303, 515)(304, 561)(305, 564)(306, 514)(307, 548)(308, 547)(309, 559)(310, 542)(311, 541)(312, 560)(313, 586)(314, 587)(315, 584)(316, 509)(317, 508)(318, 583)(319, 549)(320, 552)(321, 544)(322, 540)(323, 537)(324, 545)(325, 576)(326, 573)(327, 504)(328, 571)(329, 572)(330, 501)(331, 568)(332, 569)(333, 566)(334, 575)(335, 574)(336, 565)(337, 527)(338, 526)(339, 491)(340, 513)(341, 516)(342, 490)(343, 558)(344, 555)(345, 588)(346, 553)(347, 554)(348, 585)(349, 524)(350, 523)(351, 511)(352, 536)(353, 535)(354, 512)(355, 525)(356, 528)(357, 538)(358, 498)(359, 495)(360, 539)

MAP           : A4.9
NOTES         : type II, reflexible, isomorphic to DBar({4,5}), isomorphic to A4.7.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 4, 5 ]
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)^5 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^4, (x.1 * x.2^-1)^2, x.2^-1 * x.3^-1 * x.2^2 * x.3 * x.2^-1, x.3 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2 * x.3 * x.2, (x.3 * x.1^-1)^5, x.3 * x.2^-1 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2, x.3^-1 * x.2 * x.3^2 * x.2 * x.3^-2 * x.2^-1 * x.3^2 * x.2^-1 * x.3^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 10)
#DARTS        : 720
R = (1, 121, 241)(2, 122, 242)(3, 123, 243)(4, 124, 244)(5, 125, 245)(6, 126, 246)(7, 127, 247)(8, 128, 248)(9, 129, 249)(10, 130, 250)(11, 131, 251)(12, 132, 252)(13, 133, 253)(14, 134, 254)(15, 135, 255)(16, 136, 256)(17, 137, 257)(18, 138, 258)(19, 139, 259)(20, 140, 260)(21, 141, 261)(22, 142, 262)(23, 143, 263)(24, 144, 264)(25, 145, 265)(26, 146, 266)(27, 147, 267)(28, 148, 268)(29, 149, 269)(30, 150, 270)(31, 151, 271)(32, 152, 272)(33, 153, 273)(34, 154, 274)(35, 155, 275)(36, 156, 276)(37, 157, 277)(38, 158, 278)(39, 159, 279)(40, 160, 280)(41, 161, 281)(42, 162, 282)(43, 163, 283)(44, 164, 284)(45, 165, 285)(46, 166, 286)(47, 167, 287)(48, 168, 288)(49, 169, 289)(50, 170, 290)(51, 171, 291)(52, 172, 292)(53, 173, 293)(54, 174, 294)(55, 175, 295)(56, 176, 296)(57, 177, 297)(58, 178, 298)(59, 179, 299)(60, 180, 300)(61, 181, 301)(62, 182, 302)(63, 183, 303)(64, 184, 304)(65, 185, 305)(66, 186, 306)(67, 187, 307)(68, 188, 308)(69, 189, 309)(70, 190, 310)(71, 191, 311)(72, 192, 312)(73, 193, 313)(74, 194, 314)(75, 195, 315)(76, 196, 316)(77, 197, 317)(78, 198, 318)(79, 199, 319)(80, 200, 320)(81, 201, 321)(82, 202, 322)(83, 203, 323)(84, 204, 324)(85, 205, 325)(86, 206, 326)(87, 207, 327)(88, 208, 328)(89, 209, 329)(90, 210, 330)(91, 211, 331)(92, 212, 332)(93, 213, 333)(94, 214, 334)(95, 215, 335)(96, 216, 336)(97, 217, 337)(98, 218, 338)(99, 219, 339)(100, 220, 340)(101, 221, 341)(102, 222, 342)(103, 223, 343)(104, 224, 344)(105, 225, 345)(106, 226, 346)(107, 227, 347)(108, 228, 348)(109, 229, 349)(110, 230, 350)(111, 231, 351)(112, 232, 352)(113, 233, 353)(114, 234, 354)(115, 235, 355)(116, 236, 356)(117, 237, 357)(118, 238, 358)(119, 239, 359)(120, 240, 360)(361, 481, 601)(362, 482, 602)(363, 483, 603)(364, 484, 604)(365, 485, 605)(366, 486, 606)(367, 487, 607)(368, 488, 608)(369, 489, 609)(370, 490, 610)(371, 491, 611)(372, 492, 612)(373, 493, 613)(374, 494, 614)(375, 495, 615)(376, 496, 616)(377, 497, 617)(378, 498, 618)(379, 499, 619)(380, 500, 620)(381, 501, 621)(382, 502, 622)(383, 503, 623)(384, 504, 624)(385, 505, 625)(386, 506, 626)(387, 507, 627)(388, 508, 628)(389, 509, 629)(390, 510, 630)(391, 511, 631)(392, 512, 632)(393, 513, 633)(394, 514, 634)(395, 515, 635)(396, 516, 636)(397, 517, 637)(398, 518, 638)(399, 519, 639)(400, 520, 640)(401, 521, 641)(402, 522, 642)(403, 523, 643)(404, 524, 644)(405, 525, 645)(406, 526, 646)(407, 527, 647)(408, 528, 648)(409, 529, 649)(410, 530, 650)(411, 531, 651)(412, 532, 652)(413, 533, 653)(414, 534, 654)(415, 535, 655)(416, 536, 656)(417, 537, 657)(418, 538, 658)(419, 539, 659)(420, 540, 660)(421, 541, 661)(422, 542, 662)(423, 543, 663)(424, 544, 664)(425, 545, 665)(426, 546, 666)(427, 547, 667)(428, 548, 668)(429, 549, 669)(430, 550, 670)(431, 551, 671)(432, 552, 672)(433, 553, 673)(434, 554, 674)(435, 555, 675)(436, 556, 676)(437, 557, 677)(438, 558, 678)(439, 559, 679)(440, 560, 680)(441, 561, 681)(442, 562, 682)(443, 563, 683)(444, 564, 684)(445, 565, 685)(446, 566, 686)(447, 567, 687)(448, 568, 688)(449, 569, 689)(450, 570, 690)(451, 571, 691)(452, 572, 692)(453, 573, 693)(454, 574, 694)(455, 575, 695)(456, 576, 696)(457, 577, 697)(458, 578, 698)(459, 579, 699)(460, 580, 700)(461, 581, 701)(462, 582, 702)(463, 583, 703)(464, 584, 704)(465, 585, 705)(466, 586, 706)(467, 587, 707)(468, 588, 708)(469, 589, 709)(470, 590, 710)(471, 591, 711)(472, 592, 712)(473, 593, 713)(474, 594, 714)(475, 595, 715)(476, 596, 716)(477, 597, 717)(478, 598, 718)(479, 599, 719)(480, 600, 720)
L = (1, 361)(2, 362)(3, 363)(4, 364)(5, 365)(6, 366)(7, 367)(8, 368)(9, 369)(10, 370)(11, 371)(12, 372)(13, 373)(14, 374)(15, 375)(16, 376)(17, 377)(18, 378)(19, 379)(20, 380)(21, 381)(22, 382)(23, 383)(24, 384)(25, 385)(26, 386)(27, 387)(28, 388)(29, 389)(30, 390)(31, 391)(32, 392)(33, 393)(34, 394)(35, 395)(36, 396)(37, 397)(38, 398)(39, 399)(40, 400)(41, 401)(42, 402)(43, 403)(44, 404)(45, 405)(46, 406)(47, 407)(48, 408)(49, 409)(50, 410)(51, 411)(52, 412)(53, 413)(54, 414)(55, 415)(56, 416)(57, 417)(58, 418)(59, 419)(60, 420)(61, 421)(62, 422)(63, 423)(64, 424)(65, 425)(66, 426)(67, 427)(68, 428)(69, 429)(70, 430)(71, 431)(72, 432)(73, 433)(74, 434)(75, 435)(76, 436)(77, 437)(78, 438)(79, 439)(80, 440)(81, 441)(82, 442)(83, 443)(84, 444)(85, 445)(86, 446)(87, 447)(88, 448)(89, 449)(90, 450)(91, 451)(92, 452)(93, 453)(94, 454)(95, 455)(96, 456)(97, 457)(98, 458)(99, 459)(100, 460)(101, 461)(102, 462)(103, 463)(104, 464)(105, 465)(106, 466)(107, 467)(108, 468)(109, 469)(110, 470)(111, 471)(112, 472)(113, 473)(114, 474)(115, 475)(116, 476)(117, 477)(118, 478)(119, 479)(120, 480)(121, 602)(122, 601)(123, 607)(124, 614)(125, 613)(126, 608)(127, 603)(128, 606)(129, 616)(130, 702)(131, 699)(132, 617)(133, 605)(134, 604)(135, 719)(136, 609)(137, 612)(138, 718)(139, 654)(140, 651)(141, 690)(142, 649)(143, 650)(144, 687)(145, 640)(146, 641)(147, 638)(148, 677)(149, 676)(150, 637)(151, 711)(152, 714)(153, 700)(154, 666)(155, 663)(156, 701)(157, 630)(158, 627)(159, 642)(160, 625)(161, 626)(162, 639)(163, 710)(164, 709)(165, 715)(166, 698)(167, 697)(168, 716)(169, 622)(170, 623)(171, 620)(172, 653)(173, 652)(174, 619)(175, 713)(176, 712)(177, 683)(178, 717)(179, 720)(180, 682)(181, 671)(182, 670)(183, 635)(184, 681)(185, 684)(186, 634)(187, 668)(188, 667)(189, 679)(190, 662)(191, 661)(192, 680)(193, 706)(194, 707)(195, 704)(196, 629)(197, 628)(198, 703)(199, 669)(200, 672)(201, 664)(202, 660)(203, 657)(204, 665)(205, 696)(206, 693)(207, 624)(208, 691)(209, 692)(210, 621)(211, 688)(212, 689)(213, 686)(214, 695)(215, 694)(216, 685)(217, 647)(218, 646)(219, 611)(220, 633)(221, 636)(222, 610)(223, 678)(224, 675)(225, 708)(226, 673)(227, 674)(228, 705)(229, 644)(230, 643)(231, 631)(232, 656)(233, 655)(234, 632)(235, 645)(236, 648)(237, 658)(238, 618)(239, 615)(240, 659)(241, 484)(242, 485)(243, 482)(244, 521)(245, 520)(246, 481)(247, 599)(248, 598)(249, 557)(250, 585)(251, 588)(252, 556)(253, 492)(254, 489)(255, 516)(256, 487)(257, 488)(258, 513)(259, 596)(260, 595)(261, 583)(262, 590)(263, 589)(264, 584)(265, 597)(266, 600)(267, 592)(268, 564)(269, 561)(270, 593)(271, 566)(272, 565)(273, 553)(274, 560)(275, 559)(276, 554)(277, 567)(278, 570)(279, 562)(280, 534)(281, 531)(282, 563)(283, 569)(284, 568)(285, 527)(286, 555)(287, 558)(288, 526)(289, 582)(290, 579)(291, 486)(292, 577)(293, 578)(294, 483)(295, 574)(296, 575)(297, 572)(298, 491)(299, 490)(300, 571)(301, 537)(302, 540)(303, 532)(304, 504)(305, 501)(306, 533)(307, 552)(308, 549)(309, 576)(310, 547)(311, 548)(312, 573)(313, 536)(314, 535)(315, 523)(316, 530)(317, 529)(318, 524)(319, 544)(320, 545)(321, 542)(322, 581)(323, 580)(324, 541)(325, 539)(326, 538)(327, 497)(328, 525)(329, 528)(330, 496)(331, 509)(332, 508)(333, 587)(334, 495)(335, 498)(336, 586)(337, 506)(338, 505)(339, 493)(340, 500)(341, 499)(342, 494)(343, 514)(344, 515)(345, 512)(346, 551)(347, 550)(348, 511)(349, 507)(350, 510)(351, 502)(352, 594)(353, 591)(354, 503)(355, 522)(356, 519)(357, 546)(358, 517)(359, 518)(360, 543)

MAP           : A4.10
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: [ 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)   : <72, 40>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.3 * x.2 * x.3^2 * x.2 * x.3 * x.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        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 362)(74, 365)(75, 368)(76, 363)(77, 426)(78, 369)(79, 416)(80, 419)(81, 422)(82, 417)(83, 372)(84, 423)(85, 420)(86, 411)(87, 414)(88, 425)(89, 406)(90, 377)(91, 366)(92, 393)(93, 396)(94, 371)(95, 388)(96, 431)(97, 364)(98, 391)(99, 394)(100, 379)(101, 392)(102, 385)(103, 382)(104, 373)(105, 376)(106, 361)(107, 374)(108, 367)(109, 402)(110, 429)(111, 432)(112, 407)(113, 424)(114, 395)(115, 400)(116, 427)(117, 430)(118, 415)(119, 428)(120, 421)(121, 418)(122, 409)(123, 412)(124, 397)(125, 410)(126, 403)(127, 398)(128, 401)(129, 404)(130, 399)(131, 390)(132, 405)(133, 380)(134, 383)(135, 386)(136, 381)(137, 408)(138, 387)(139, 384)(140, 375)(141, 378)(142, 389)(143, 370)(144, 413)(145, 330)(146, 357)(147, 360)(148, 335)(149, 352)(150, 323)(151, 328)(152, 355)(153, 358)(154, 343)(155, 356)(156, 349)(157, 346)(158, 337)(159, 340)(160, 325)(161, 338)(162, 331)(163, 326)(164, 329)(165, 332)(166, 327)(167, 318)(168, 333)(169, 308)(170, 311)(171, 314)(172, 309)(173, 336)(174, 315)(175, 312)(176, 303)(177, 306)(178, 317)(179, 298)(180, 341)(181, 290)(182, 293)(183, 296)(184, 291)(185, 354)(186, 297)(187, 344)(188, 347)(189, 350)(190, 345)(191, 300)(192, 351)(193, 348)(194, 339)(195, 342)(196, 353)(197, 334)(198, 305)(199, 294)(200, 321)(201, 324)(202, 299)(203, 316)(204, 359)(205, 292)(206, 319)(207, 322)(208, 307)(209, 320)(210, 313)(211, 310)(212, 301)(213, 304)(214, 289)(215, 302)(216, 295)

MAP           : A4.11
NOTES         : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A4.10.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^4, x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 12)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 364)(74, 391)(75, 394)(76, 379)(77, 392)(78, 385)(79, 366)(80, 393)(81, 396)(82, 371)(83, 388)(84, 431)(85, 362)(86, 365)(87, 368)(88, 363)(89, 426)(90, 369)(91, 382)(92, 373)(93, 376)(94, 361)(95, 374)(96, 367)(97, 384)(98, 375)(99, 378)(100, 389)(101, 370)(102, 413)(103, 380)(104, 383)(105, 386)(106, 381)(107, 408)(108, 387)(109, 418)(110, 409)(111, 412)(112, 397)(113, 410)(114, 403)(115, 420)(116, 411)(117, 414)(118, 425)(119, 406)(120, 377)(121, 416)(122, 419)(123, 422)(124, 417)(125, 372)(126, 423)(127, 400)(128, 427)(129, 430)(130, 415)(131, 428)(132, 421)(133, 402)(134, 429)(135, 432)(136, 407)(137, 424)(138, 395)(139, 398)(140, 401)(141, 404)(142, 399)(143, 390)(144, 405)(145, 354)(146, 315)(147, 318)(148, 347)(149, 322)(150, 311)(151, 352)(152, 313)(153, 316)(154, 355)(155, 314)(156, 319)(157, 358)(158, 325)(159, 328)(160, 349)(161, 326)(162, 343)(163, 350)(164, 353)(165, 344)(166, 351)(167, 294)(168, 345)(169, 296)(170, 299)(171, 290)(172, 297)(173, 348)(174, 291)(175, 300)(176, 333)(177, 336)(178, 293)(179, 340)(180, 329)(181, 302)(182, 305)(183, 338)(184, 303)(185, 324)(186, 339)(187, 356)(188, 359)(189, 320)(190, 357)(191, 342)(192, 321)(193, 360)(194, 327)(195, 330)(196, 323)(197, 346)(198, 335)(199, 306)(200, 309)(201, 312)(202, 341)(203, 292)(204, 317)(205, 304)(206, 307)(207, 310)(208, 295)(209, 308)(210, 289)(211, 298)(212, 331)(213, 334)(214, 301)(215, 332)(216, 337)

MAP           : A4.12
NOTES         : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A4.10.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^4, (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^-1)^2, (x.2^-1 * x.3^-1)^4, (x.3 * x.1^-1)^6, x.3^-2 * x.2 * x.3^-2 * x.2 * x.3^2 * x.2^-1 * x.3^2 * x.2^-1, x.3^2 * x.2 * x.3^2 * x.2 * x.3^-2 * x.2^-1 * x.3^-2 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 12)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 426)(74, 387)(75, 390)(76, 419)(77, 394)(78, 383)(79, 424)(80, 385)(81, 388)(82, 427)(83, 386)(84, 391)(85, 430)(86, 397)(87, 400)(88, 421)(89, 398)(90, 415)(91, 422)(92, 425)(93, 416)(94, 423)(95, 366)(96, 417)(97, 368)(98, 371)(99, 362)(100, 369)(101, 420)(102, 363)(103, 372)(104, 405)(105, 408)(106, 365)(107, 412)(108, 401)(109, 374)(110, 377)(111, 410)(112, 375)(113, 396)(114, 411)(115, 428)(116, 431)(117, 392)(118, 429)(119, 414)(120, 393)(121, 432)(122, 399)(123, 402)(124, 395)(125, 418)(126, 407)(127, 378)(128, 381)(129, 384)(130, 413)(131, 364)(132, 389)(133, 376)(134, 379)(135, 382)(136, 367)(137, 380)(138, 361)(139, 370)(140, 403)(141, 406)(142, 373)(143, 404)(144, 409)(145, 299)(146, 348)(147, 353)(148, 290)(149, 339)(150, 344)(151, 359)(152, 342)(153, 305)(154, 320)(155, 345)(156, 338)(157, 321)(158, 316)(159, 319)(160, 324)(161, 349)(162, 322)(163, 291)(164, 310)(165, 289)(166, 294)(167, 301)(168, 292)(169, 297)(170, 304)(171, 295)(172, 300)(173, 307)(174, 298)(175, 293)(176, 354)(177, 347)(178, 296)(179, 315)(180, 350)(181, 335)(182, 312)(183, 317)(184, 326)(185, 303)(186, 308)(187, 323)(188, 306)(189, 341)(190, 356)(191, 309)(192, 302)(193, 357)(194, 352)(195, 355)(196, 360)(197, 313)(198, 358)(199, 327)(200, 346)(201, 325)(202, 330)(203, 337)(204, 328)(205, 333)(206, 340)(207, 331)(208, 336)(209, 343)(210, 334)(211, 329)(212, 318)(213, 311)(214, 332)(215, 351)(216, 314)

MAP           : A4.13
NOTES         : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A4.10.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^4, (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^-1)^2, (x.2^-1 * x.3^-1)^4, (x.3 * x.1^-1)^6, x.3^-2 * x.2 * x.3^-2 * x.2 * x.3^2 * x.2^-1 * x.3^2 * x.2^-1, x.3^2 * x.2 * x.3^2 * x.2 * x.3^-2 * x.2^-1 * x.3^-2 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 12)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 363)(74, 382)(75, 361)(76, 366)(77, 373)(78, 364)(79, 369)(80, 376)(81, 367)(82, 372)(83, 379)(84, 370)(85, 365)(86, 426)(87, 419)(88, 368)(89, 387)(90, 422)(91, 371)(92, 420)(93, 425)(94, 362)(95, 411)(96, 416)(97, 431)(98, 414)(99, 377)(100, 392)(101, 417)(102, 410)(103, 393)(104, 388)(105, 391)(106, 396)(107, 421)(108, 394)(109, 399)(110, 418)(111, 397)(112, 402)(113, 409)(114, 400)(115, 405)(116, 412)(117, 403)(118, 408)(119, 415)(120, 406)(121, 401)(122, 390)(123, 383)(124, 404)(125, 423)(126, 386)(127, 407)(128, 384)(129, 389)(130, 398)(131, 375)(132, 380)(133, 395)(134, 378)(135, 413)(136, 428)(137, 381)(138, 374)(139, 429)(140, 424)(141, 427)(142, 432)(143, 385)(144, 430)(145, 290)(146, 293)(147, 296)(148, 291)(149, 354)(150, 297)(151, 344)(152, 347)(153, 350)(154, 345)(155, 300)(156, 351)(157, 348)(158, 339)(159, 342)(160, 353)(161, 334)(162, 305)(163, 294)(164, 321)(165, 324)(166, 299)(167, 316)(168, 359)(169, 292)(170, 319)(171, 322)(172, 307)(173, 320)(174, 313)(175, 310)(176, 301)(177, 304)(178, 289)(179, 302)(180, 295)(181, 330)(182, 357)(183, 360)(184, 335)(185, 352)(186, 323)(187, 328)(188, 355)(189, 358)(190, 343)(191, 356)(192, 349)(193, 346)(194, 337)(195, 340)(196, 325)(197, 338)(198, 331)(199, 326)(200, 329)(201, 332)(202, 327)(203, 318)(204, 333)(205, 308)(206, 311)(207, 314)(208, 309)(209, 336)(210, 315)(211, 312)(212, 303)(213, 306)(214, 317)(215, 298)(216, 341)

MAP           : A4.14
NOTES         : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A4.10.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.3 * x.2 * x.3^2 * x.2 * x.3 * x.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        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 371)(74, 420)(75, 425)(76, 362)(77, 411)(78, 416)(79, 431)(80, 414)(81, 377)(82, 392)(83, 417)(84, 410)(85, 393)(86, 388)(87, 391)(88, 396)(89, 421)(90, 394)(91, 363)(92, 382)(93, 361)(94, 366)(95, 373)(96, 364)(97, 369)(98, 376)(99, 367)(100, 372)(101, 379)(102, 370)(103, 365)(104, 426)(105, 419)(106, 368)(107, 387)(108, 422)(109, 407)(110, 384)(111, 389)(112, 398)(113, 375)(114, 380)(115, 395)(116, 378)(117, 413)(118, 428)(119, 381)(120, 374)(121, 429)(122, 424)(123, 427)(124, 432)(125, 385)(126, 430)(127, 399)(128, 418)(129, 397)(130, 402)(131, 409)(132, 400)(133, 405)(134, 412)(135, 403)(136, 408)(137, 415)(138, 406)(139, 401)(140, 390)(141, 383)(142, 404)(143, 423)(144, 386)(145, 314)(146, 317)(147, 308)(148, 315)(149, 330)(150, 309)(151, 332)(152, 335)(153, 326)(154, 333)(155, 312)(156, 327)(157, 336)(158, 297)(159, 300)(160, 329)(161, 304)(162, 293)(163, 318)(164, 351)(165, 354)(166, 311)(167, 358)(168, 347)(169, 316)(170, 349)(171, 352)(172, 319)(173, 350)(174, 355)(175, 322)(176, 289)(177, 292)(178, 313)(179, 290)(180, 307)(181, 342)(182, 345)(183, 348)(184, 305)(185, 328)(186, 353)(187, 340)(188, 343)(189, 346)(190, 331)(191, 344)(192, 325)(193, 334)(194, 295)(195, 298)(196, 337)(197, 296)(198, 301)(199, 338)(200, 341)(201, 302)(202, 339)(203, 360)(204, 303)(205, 320)(206, 323)(207, 356)(208, 321)(209, 306)(210, 357)(211, 324)(212, 291)(213, 294)(214, 359)(215, 310)(216, 299)

MAP           : A4.15
NOTES         : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A4.10.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^4, x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2 * x.3^-1 * x.2^-1, (x.1 * x.2^-1)^4, (x.2 * x.3^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 12)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 364)(74, 391)(75, 394)(76, 379)(77, 392)(78, 385)(79, 366)(80, 393)(81, 396)(82, 371)(83, 388)(84, 431)(85, 362)(86, 365)(87, 368)(88, 363)(89, 426)(90, 369)(91, 382)(92, 373)(93, 376)(94, 361)(95, 374)(96, 367)(97, 384)(98, 375)(99, 378)(100, 389)(101, 370)(102, 413)(103, 380)(104, 383)(105, 386)(106, 381)(107, 408)(108, 387)(109, 418)(110, 409)(111, 412)(112, 397)(113, 410)(114, 403)(115, 420)(116, 411)(117, 414)(118, 425)(119, 406)(120, 377)(121, 416)(122, 419)(123, 422)(124, 417)(125, 372)(126, 423)(127, 400)(128, 427)(129, 430)(130, 415)(131, 428)(132, 421)(133, 402)(134, 429)(135, 432)(136, 407)(137, 424)(138, 395)(139, 398)(140, 401)(141, 404)(142, 399)(143, 390)(144, 405)(145, 291)(146, 310)(147, 289)(148, 294)(149, 301)(150, 292)(151, 297)(152, 304)(153, 295)(154, 300)(155, 307)(156, 298)(157, 293)(158, 354)(159, 347)(160, 296)(161, 315)(162, 350)(163, 299)(164, 348)(165, 353)(166, 290)(167, 339)(168, 344)(169, 359)(170, 342)(171, 305)(172, 320)(173, 345)(174, 338)(175, 321)(176, 316)(177, 319)(178, 324)(179, 349)(180, 322)(181, 327)(182, 346)(183, 325)(184, 330)(185, 337)(186, 328)(187, 333)(188, 340)(189, 331)(190, 336)(191, 343)(192, 334)(193, 329)(194, 318)(195, 311)(196, 332)(197, 351)(198, 314)(199, 335)(200, 312)(201, 317)(202, 326)(203, 303)(204, 308)(205, 323)(206, 306)(207, 341)(208, 356)(209, 309)(210, 302)(211, 357)(212, 352)(213, 355)(214, 360)(215, 313)(216, 358)

MAP           : A4.16
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), representative.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 10, 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)^10 >
CTG (small)   : <40, 8>
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)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 20)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 203)(42, 208)(43, 227)(44, 207)(45, 212)(46, 231)(47, 226)(48, 223)(49, 206)(50, 216)(51, 235)(52, 228)(53, 211)(54, 220)(55, 239)(56, 232)(57, 215)(58, 219)(59, 240)(60, 236)(61, 204)(62, 201)(63, 225)(64, 209)(65, 202)(66, 221)(67, 222)(68, 230)(69, 213)(70, 205)(71, 224)(72, 234)(73, 217)(74, 210)(75, 229)(76, 238)(77, 218)(78, 214)(79, 233)(80, 237)(81, 167)(82, 163)(83, 162)(84, 166)(85, 168)(86, 164)(87, 161)(88, 165)(89, 171)(90, 172)(91, 169)(92, 170)(93, 175)(94, 176)(95, 173)(96, 174)(97, 179)(98, 180)(99, 177)(100, 178)(101, 187)(102, 183)(103, 182)(104, 186)(105, 188)(106, 184)(107, 181)(108, 185)(109, 191)(110, 192)(111, 189)(112, 190)(113, 195)(114, 196)(115, 193)(116, 194)(117, 199)(118, 200)(119, 197)(120, 198)

MAP           : A4.17
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 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)^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2^-1)^2, (x.2 * x.3^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 20)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 213)(42, 209)(43, 234)(44, 217)(45, 204)(46, 225)(47, 230)(48, 238)(49, 218)(50, 201)(51, 222)(52, 237)(53, 214)(54, 202)(55, 221)(56, 233)(57, 210)(58, 205)(59, 224)(60, 229)(61, 212)(62, 216)(63, 231)(64, 208)(65, 220)(66, 239)(67, 235)(68, 226)(69, 203)(70, 219)(71, 240)(72, 227)(73, 207)(74, 215)(75, 236)(76, 223)(77, 206)(78, 211)(79, 232)(80, 228)(81, 163)(82, 168)(83, 187)(84, 167)(85, 172)(86, 191)(87, 186)(88, 183)(89, 166)(90, 176)(91, 195)(92, 188)(93, 171)(94, 180)(95, 199)(96, 192)(97, 175)(98, 179)(99, 200)(100, 196)(101, 164)(102, 161)(103, 185)(104, 169)(105, 162)(106, 181)(107, 182)(108, 190)(109, 173)(110, 165)(111, 184)(112, 194)(113, 177)(114, 170)(115, 189)(116, 198)(117, 178)(118, 174)(119, 193)(120, 197)

MAP           : A4.18
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 4, 10 ]
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)^10 >
CTG (small)   : <40, 8>
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.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3, (x.3 * x.1^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 20)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 207)(42, 203)(43, 202)(44, 206)(45, 208)(46, 204)(47, 201)(48, 205)(49, 211)(50, 212)(51, 209)(52, 210)(53, 215)(54, 216)(55, 213)(56, 214)(57, 219)(58, 220)(59, 217)(60, 218)(61, 227)(62, 223)(63, 222)(64, 226)(65, 228)(66, 224)(67, 221)(68, 225)(69, 231)(70, 232)(71, 229)(72, 230)(73, 235)(74, 236)(75, 233)(76, 234)(77, 239)(78, 240)(79, 237)(80, 238)(81, 162)(82, 165)(83, 181)(84, 161)(85, 170)(86, 189)(87, 184)(88, 182)(89, 164)(90, 174)(91, 193)(92, 185)(93, 169)(94, 178)(95, 197)(96, 190)(97, 173)(98, 177)(99, 198)(100, 194)(101, 166)(102, 167)(103, 188)(104, 171)(105, 163)(106, 187)(107, 183)(108, 192)(109, 175)(110, 168)(111, 186)(112, 196)(113, 179)(114, 172)(115, 191)(116, 200)(117, 180)(118, 176)(119, 195)(120, 199)

MAP           : A4.19
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 4, 10 ]
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)^10 >
CTG (small)   : <40, 8>
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.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3, (x.3 * x.1^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 20)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 207)(42, 203)(43, 202)(44, 206)(45, 208)(46, 204)(47, 201)(48, 205)(49, 211)(50, 212)(51, 209)(52, 210)(53, 215)(54, 216)(55, 213)(56, 214)(57, 219)(58, 220)(59, 217)(60, 218)(61, 227)(62, 223)(63, 222)(64, 226)(65, 228)(66, 224)(67, 221)(68, 225)(69, 231)(70, 232)(71, 229)(72, 230)(73, 235)(74, 236)(75, 233)(76, 234)(77, 239)(78, 240)(79, 237)(80, 238)(81, 170)(82, 174)(83, 189)(84, 165)(85, 178)(86, 197)(87, 193)(88, 184)(89, 162)(90, 177)(91, 198)(92, 181)(93, 161)(94, 173)(95, 194)(96, 182)(97, 164)(98, 169)(99, 190)(100, 185)(101, 175)(102, 171)(103, 196)(104, 179)(105, 166)(106, 188)(107, 192)(108, 200)(109, 180)(110, 167)(111, 183)(112, 199)(113, 176)(114, 163)(115, 187)(116, 195)(117, 172)(118, 168)(119, 186)(120, 191)

MAP           : A4.20
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 10, 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)^10 >
CTG (small)   : <40, 8>
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)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 20)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 203)(42, 208)(43, 227)(44, 207)(45, 212)(46, 231)(47, 226)(48, 223)(49, 206)(50, 216)(51, 235)(52, 228)(53, 211)(54, 220)(55, 239)(56, 232)(57, 215)(58, 219)(59, 240)(60, 236)(61, 204)(62, 201)(63, 225)(64, 209)(65, 202)(66, 221)(67, 222)(68, 230)(69, 213)(70, 205)(71, 224)(72, 234)(73, 217)(74, 210)(75, 229)(76, 238)(77, 218)(78, 214)(79, 233)(80, 237)(81, 176)(82, 180)(83, 173)(84, 172)(85, 179)(86, 178)(87, 177)(88, 169)(89, 168)(90, 175)(91, 174)(92, 164)(93, 163)(94, 171)(95, 170)(96, 161)(97, 167)(98, 166)(99, 165)(100, 162)(101, 199)(102, 195)(103, 198)(104, 200)(105, 191)(106, 190)(107, 194)(108, 197)(109, 196)(110, 186)(111, 185)(112, 193)(113, 192)(114, 187)(115, 182)(116, 189)(117, 188)(118, 183)(119, 181)(120, 184)

MAP           : A4.21
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 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)^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2^-1)^2, (x.2 * x.3^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 20)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 204)(42, 201)(43, 225)(44, 209)(45, 202)(46, 221)(47, 222)(48, 230)(49, 213)(50, 205)(51, 224)(52, 234)(53, 217)(54, 210)(55, 229)(56, 238)(57, 218)(58, 214)(59, 233)(60, 237)(61, 203)(62, 208)(63, 227)(64, 207)(65, 212)(66, 231)(67, 226)(68, 223)(69, 206)(70, 216)(71, 235)(72, 228)(73, 211)(74, 220)(75, 239)(76, 232)(77, 215)(78, 219)(79, 240)(80, 236)(81, 163)(82, 168)(83, 187)(84, 167)(85, 172)(86, 191)(87, 186)(88, 183)(89, 166)(90, 176)(91, 195)(92, 188)(93, 171)(94, 180)(95, 199)(96, 192)(97, 175)(98, 179)(99, 200)(100, 196)(101, 164)(102, 161)(103, 185)(104, 169)(105, 162)(106, 181)(107, 182)(108, 190)(109, 173)(110, 165)(111, 184)(112, 194)(113, 177)(114, 170)(115, 189)(116, 198)(117, 178)(118, 174)(119, 193)(120, 197)

MAP           : A4.22
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 10, 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)^10 >
CTG (small)   : <40, 8>
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)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 20)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 203)(42, 208)(43, 227)(44, 207)(45, 212)(46, 231)(47, 226)(48, 223)(49, 206)(50, 216)(51, 235)(52, 228)(53, 211)(54, 220)(55, 239)(56, 232)(57, 215)(58, 219)(59, 240)(60, 236)(61, 204)(62, 201)(63, 225)(64, 209)(65, 202)(66, 221)(67, 222)(68, 230)(69, 213)(70, 205)(71, 224)(72, 234)(73, 217)(74, 210)(75, 229)(76, 238)(77, 218)(78, 214)(79, 233)(80, 237)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200)(101, 161)(102, 162)(103, 163)(104, 164)(105, 165)(106, 166)(107, 167)(108, 168)(109, 169)(110, 170)(111, 171)(112, 172)(113, 173)(114, 174)(115, 175)(116, 176)(117, 177)(118, 178)(119, 179)(120, 180)

MAP           : A4.23
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 4, 10 ]
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)^10 >
CTG (small)   : <40, 8>
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.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3, (x.3 * x.1^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 20)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 207)(42, 203)(43, 202)(44, 206)(45, 208)(46, 204)(47, 201)(48, 205)(49, 211)(50, 212)(51, 209)(52, 210)(53, 215)(54, 216)(55, 213)(56, 214)(57, 219)(58, 220)(59, 217)(60, 218)(61, 227)(62, 223)(63, 222)(64, 226)(65, 228)(66, 224)(67, 221)(68, 225)(69, 231)(70, 232)(71, 229)(72, 230)(73, 235)(74, 236)(75, 233)(76, 234)(77, 239)(78, 240)(79, 237)(80, 238)(81, 173)(82, 169)(83, 194)(84, 177)(85, 164)(86, 185)(87, 190)(88, 198)(89, 178)(90, 161)(91, 182)(92, 197)(93, 174)(94, 162)(95, 181)(96, 193)(97, 170)(98, 165)(99, 184)(100, 189)(101, 172)(102, 176)(103, 191)(104, 168)(105, 180)(106, 199)(107, 195)(108, 186)(109, 163)(110, 179)(111, 200)(112, 187)(113, 167)(114, 175)(115, 196)(116, 183)(117, 166)(118, 171)(119, 192)(120, 188)

MAP           : A4.24
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 10, 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)^10 >
CTG (small)   : <40, 8>
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)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 20)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 203)(42, 208)(43, 227)(44, 207)(45, 212)(46, 231)(47, 226)(48, 223)(49, 206)(50, 216)(51, 235)(52, 228)(53, 211)(54, 220)(55, 239)(56, 232)(57, 215)(58, 219)(59, 240)(60, 236)(61, 204)(62, 201)(63, 225)(64, 209)(65, 202)(66, 221)(67, 222)(68, 230)(69, 213)(70, 205)(71, 224)(72, 234)(73, 217)(74, 210)(75, 229)(76, 238)(77, 218)(78, 214)(79, 233)(80, 237)(81, 171)(82, 166)(83, 170)(84, 175)(85, 167)(86, 162)(87, 165)(88, 174)(89, 179)(90, 163)(91, 161)(92, 178)(93, 180)(94, 168)(95, 164)(96, 177)(97, 176)(98, 172)(99, 169)(100, 173)(101, 188)(102, 192)(103, 184)(104, 183)(105, 196)(106, 193)(107, 189)(108, 181)(109, 187)(110, 200)(111, 197)(112, 182)(113, 186)(114, 199)(115, 198)(116, 185)(117, 191)(118, 195)(119, 194)(120, 190)

MAP           : A4.25
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 4, 10 ]
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)^10 >
CTG (small)   : <40, 8>
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.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3, (x.3 * x.1^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 20)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 207)(42, 203)(43, 202)(44, 206)(45, 208)(46, 204)(47, 201)(48, 205)(49, 211)(50, 212)(51, 209)(52, 210)(53, 215)(54, 216)(55, 213)(56, 214)(57, 219)(58, 220)(59, 217)(60, 218)(61, 227)(62, 223)(63, 222)(64, 226)(65, 228)(66, 224)(67, 221)(68, 225)(69, 231)(70, 232)(71, 229)(72, 230)(73, 235)(74, 236)(75, 233)(76, 234)(77, 239)(78, 240)(79, 237)(80, 238)(81, 164)(82, 161)(83, 185)(84, 169)(85, 162)(86, 181)(87, 182)(88, 190)(89, 173)(90, 165)(91, 184)(92, 194)(93, 177)(94, 170)(95, 189)(96, 198)(97, 178)(98, 174)(99, 193)(100, 197)(101, 163)(102, 168)(103, 187)(104, 167)(105, 172)(106, 191)(107, 186)(108, 183)(109, 166)(110, 176)(111, 195)(112, 188)(113, 171)(114, 180)(115, 199)(116, 192)(117, 175)(118, 179)(119, 200)(120, 196)

MAP           : A4.26
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 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)^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2^-1)^2, (x.2 * x.3^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 20)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 202)(42, 205)(43, 221)(44, 201)(45, 210)(46, 229)(47, 224)(48, 222)(49, 204)(50, 214)(51, 233)(52, 225)(53, 209)(54, 218)(55, 237)(56, 230)(57, 213)(58, 217)(59, 238)(60, 234)(61, 206)(62, 207)(63, 228)(64, 211)(65, 203)(66, 227)(67, 223)(68, 232)(69, 215)(70, 208)(71, 226)(72, 236)(73, 219)(74, 212)(75, 231)(76, 240)(77, 220)(78, 216)(79, 235)(80, 239)(81, 163)(82, 168)(83, 187)(84, 167)(85, 172)(86, 191)(87, 186)(88, 183)(89, 166)(90, 176)(91, 195)(92, 188)(93, 171)(94, 180)(95, 199)(96, 192)(97, 175)(98, 179)(99, 200)(100, 196)(101, 164)(102, 161)(103, 185)(104, 169)(105, 162)(106, 181)(107, 182)(108, 190)(109, 173)(110, 165)(111, 184)(112, 194)(113, 177)(114, 170)(115, 189)(116, 198)(117, 178)(118, 174)(119, 193)(120, 197)

MAP           : A4.27
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 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)^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2^-1)^2, (x.2 * x.3^-1)^2, (x.3 * x.1^-1)^4, (x.1 * x.2^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 8, 20)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 210)(42, 214)(43, 229)(44, 205)(45, 218)(46, 237)(47, 233)(48, 224)(49, 202)(50, 217)(51, 238)(52, 221)(53, 201)(54, 213)(55, 234)(56, 222)(57, 204)(58, 209)(59, 230)(60, 225)(61, 215)(62, 211)(63, 236)(64, 219)(65, 206)(66, 228)(67, 232)(68, 240)(69, 220)(70, 207)(71, 223)(72, 239)(73, 216)(74, 203)(75, 227)(76, 235)(77, 212)(78, 208)(79, 226)(80, 231)(81, 163)(82, 168)(83, 187)(84, 167)(85, 172)(86, 191)(87, 186)(88, 183)(89, 166)(90, 176)(91, 195)(92, 188)(93, 171)(94, 180)(95, 199)(96, 192)(97, 175)(98, 179)(99, 200)(100, 196)(101, 164)(102, 161)(103, 185)(104, 169)(105, 162)(106, 181)(107, 182)(108, 190)(109, 173)(110, 165)(111, 184)(112, 194)(113, 177)(114, 170)(115, 189)(116, 198)(117, 178)(118, 174)(119, 193)(120, 197)

MAP           : A4.28
NOTES         : type II, reflexible, isomorphic to DBar({4,5}), isomorphic to A4.7.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^4, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^4, x.2^-1 * x.3 * x.2^-1 * x.3^-1 * x.2^2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1, (x.2 * x.3^-1)^5, x.3^-1 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1, x.3^-2 * x.2 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-2 * x.2^-1 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 10, 8)
#DARTS        : 720
R = (1, 121, 241)(2, 122, 242)(3, 123, 243)(4, 124, 244)(5, 125, 245)(6, 126, 246)(7, 127, 247)(8, 128, 248)(9, 129, 249)(10, 130, 250)(11, 131, 251)(12, 132, 252)(13, 133, 253)(14, 134, 254)(15, 135, 255)(16, 136, 256)(17, 137, 257)(18, 138, 258)(19, 139, 259)(20, 140, 260)(21, 141, 261)(22, 142, 262)(23, 143, 263)(24, 144, 264)(25, 145, 265)(26, 146, 266)(27, 147, 267)(28, 148, 268)(29, 149, 269)(30, 150, 270)(31, 151, 271)(32, 152, 272)(33, 153, 273)(34, 154, 274)(35, 155, 275)(36, 156, 276)(37, 157, 277)(38, 158, 278)(39, 159, 279)(40, 160, 280)(41, 161, 281)(42, 162, 282)(43, 163, 283)(44, 164, 284)(45, 165, 285)(46, 166, 286)(47, 167, 287)(48, 168, 288)(49, 169, 289)(50, 170, 290)(51, 171, 291)(52, 172, 292)(53, 173, 293)(54, 174, 294)(55, 175, 295)(56, 176, 296)(57, 177, 297)(58, 178, 298)(59, 179, 299)(60, 180, 300)(61, 181, 301)(62, 182, 302)(63, 183, 303)(64, 184, 304)(65, 185, 305)(66, 186, 306)(67, 187, 307)(68, 188, 308)(69, 189, 309)(70, 190, 310)(71, 191, 311)(72, 192, 312)(73, 193, 313)(74, 194, 314)(75, 195, 315)(76, 196, 316)(77, 197, 317)(78, 198, 318)(79, 199, 319)(80, 200, 320)(81, 201, 321)(82, 202, 322)(83, 203, 323)(84, 204, 324)(85, 205, 325)(86, 206, 326)(87, 207, 327)(88, 208, 328)(89, 209, 329)(90, 210, 330)(91, 211, 331)(92, 212, 332)(93, 213, 333)(94, 214, 334)(95, 215, 335)(96, 216, 336)(97, 217, 337)(98, 218, 338)(99, 219, 339)(100, 220, 340)(101, 221, 341)(102, 222, 342)(103, 223, 343)(104, 224, 344)(105, 225, 345)(106, 226, 346)(107, 227, 347)(108, 228, 348)(109, 229, 349)(110, 230, 350)(111, 231, 351)(112, 232, 352)(113, 233, 353)(114, 234, 354)(115, 235, 355)(116, 236, 356)(117, 237, 357)(118, 238, 358)(119, 239, 359)(120, 240, 360)(361, 481, 601)(362, 482, 602)(363, 483, 603)(364, 484, 604)(365, 485, 605)(366, 486, 606)(367, 487, 607)(368, 488, 608)(369, 489, 609)(370, 490, 610)(371, 491, 611)(372, 492, 612)(373, 493, 613)(374, 494, 614)(375, 495, 615)(376, 496, 616)(377, 497, 617)(378, 498, 618)(379, 499, 619)(380, 500, 620)(381, 501, 621)(382, 502, 622)(383, 503, 623)(384, 504, 624)(385, 505, 625)(386, 506, 626)(387, 507, 627)(388, 508, 628)(389, 509, 629)(390, 510, 630)(391, 511, 631)(392, 512, 632)(393, 513, 633)(394, 514, 634)(395, 515, 635)(396, 516, 636)(397, 517, 637)(398, 518, 638)(399, 519, 639)(400, 520, 640)(401, 521, 641)(402, 522, 642)(403, 523, 643)(404, 524, 644)(405, 525, 645)(406, 526, 646)(407, 527, 647)(408, 528, 648)(409, 529, 649)(410, 530, 650)(411, 531, 651)(412, 532, 652)(413, 533, 653)(414, 534, 654)(415, 535, 655)(416, 536, 656)(417, 537, 657)(418, 538, 658)(419, 539, 659)(420, 540, 660)(421, 541, 661)(422, 542, 662)(423, 543, 663)(424, 544, 664)(425, 545, 665)(426, 546, 666)(427, 547, 667)(428, 548, 668)(429, 549, 669)(430, 550, 670)(431, 551, 671)(432, 552, 672)(433, 553, 673)(434, 554, 674)(435, 555, 675)(436, 556, 676)(437, 557, 677)(438, 558, 678)(439, 559, 679)(440, 560, 680)(441, 561, 681)(442, 562, 682)(443, 563, 683)(444, 564, 684)(445, 565, 685)(446, 566, 686)(447, 567, 687)(448, 568, 688)(449, 569, 689)(450, 570, 690)(451, 571, 691)(452, 572, 692)(453, 573, 693)(454, 574, 694)(455, 575, 695)(456, 576, 696)(457, 577, 697)(458, 578, 698)(459, 579, 699)(460, 580, 700)(461, 581, 701)(462, 582, 702)(463, 583, 703)(464, 584, 704)(465, 585, 705)(466, 586, 706)(467, 587, 707)(468, 588, 708)(469, 589, 709)(470, 590, 710)(471, 591, 711)(472, 592, 712)(473, 593, 713)(474, 594, 714)(475, 595, 715)(476, 596, 716)(477, 597, 717)(478, 598, 718)(479, 599, 719)(480, 600, 720)
L = (1, 361)(2, 362)(3, 363)(4, 364)(5, 365)(6, 366)(7, 367)(8, 368)(9, 369)(10, 370)(11, 371)(12, 372)(13, 373)(14, 374)(15, 375)(16, 376)(17, 377)(18, 378)(19, 379)(20, 380)(21, 381)(22, 382)(23, 383)(24, 384)(25, 385)(26, 386)(27, 387)(28, 388)(29, 389)(30, 390)(31, 391)(32, 392)(33, 393)(34, 394)(35, 395)(36, 396)(37, 397)(38, 398)(39, 399)(40, 400)(41, 401)(42, 402)(43, 403)(44, 404)(45, 405)(46, 406)(47, 407)(48, 408)(49, 409)(50, 410)(51, 411)(52, 412)(53, 413)(54, 414)(55, 415)(56, 416)(57, 417)(58, 418)(59, 419)(60, 420)(61, 421)(62, 422)(63, 423)(64, 424)(65, 425)(66, 426)(67, 427)(68, 428)(69, 429)(70, 430)(71, 431)(72, 432)(73, 433)(74, 434)(75, 435)(76, 436)(77, 437)(78, 438)(79, 439)(80, 440)(81, 441)(82, 442)(83, 443)(84, 444)(85, 445)(86, 446)(87, 447)(88, 448)(89, 449)(90, 450)(91, 451)(92, 452)(93, 453)(94, 454)(95, 455)(96, 456)(97, 457)(98, 458)(99, 459)(100, 460)(101, 461)(102, 462)(103, 463)(104, 464)(105, 465)(106, 466)(107, 467)(108, 468)(109, 469)(110, 470)(111, 471)(112, 472)(113, 473)(114, 474)(115, 475)(116, 476)(117, 477)(118, 478)(119, 479)(120, 480)(121, 602)(122, 601)(123, 607)(124, 614)(125, 613)(126, 608)(127, 603)(128, 606)(129, 616)(130, 702)(131, 699)(132, 617)(133, 605)(134, 604)(135, 719)(136, 609)(137, 612)(138, 718)(139, 654)(140, 651)(141, 690)(142, 649)(143, 650)(144, 687)(145, 640)(146, 641)(147, 638)(148, 677)(149, 676)(150, 637)(151, 711)(152, 714)(153, 700)(154, 666)(155, 663)(156, 701)(157, 630)(158, 627)(159, 642)(160, 625)(161, 626)(162, 639)(163, 710)(164, 709)(165, 715)(166, 698)(167, 697)(168, 716)(169, 622)(170, 623)(171, 620)(172, 653)(173, 652)(174, 619)(175, 713)(176, 712)(177, 683)(178, 717)(179, 720)(180, 682)(181, 671)(182, 670)(183, 635)(184, 681)(185, 684)(186, 634)(187, 668)(188, 667)(189, 679)(190, 662)(191, 661)(192, 680)(193, 706)(194, 707)(195, 704)(196, 629)(197, 628)(198, 703)(199, 669)(200, 672)(201, 664)(202, 660)(203, 657)(204, 665)(205, 696)(206, 693)(207, 624)(208, 691)(209, 692)(210, 621)(211, 688)(212, 689)(213, 686)(214, 695)(215, 694)(216, 685)(217, 647)(218, 646)(219, 611)(220, 633)(221, 636)(222, 610)(223, 678)(224, 675)(225, 708)(226, 673)(227, 674)(228, 705)(229, 644)(230, 643)(231, 631)(232, 656)(233, 655)(234, 632)(235, 645)(236, 648)(237, 658)(238, 618)(239, 615)(240, 659)(241, 483)(242, 486)(243, 496)(244, 582)(245, 579)(246, 497)(247, 534)(248, 531)(249, 570)(250, 529)(251, 530)(252, 567)(253, 482)(254, 481)(255, 487)(256, 494)(257, 493)(258, 488)(259, 520)(260, 521)(261, 518)(262, 557)(263, 556)(264, 517)(265, 485)(266, 484)(267, 599)(268, 489)(269, 492)(270, 598)(271, 593)(272, 592)(273, 563)(274, 597)(275, 600)(276, 562)(277, 590)(278, 589)(279, 595)(280, 578)(281, 577)(282, 596)(283, 502)(284, 503)(285, 500)(286, 533)(287, 532)(288, 499)(289, 591)(290, 594)(291, 580)(292, 546)(293, 543)(294, 581)(295, 510)(296, 507)(297, 522)(298, 505)(299, 506)(300, 519)(301, 586)(302, 587)(303, 584)(304, 509)(305, 508)(306, 583)(307, 551)(308, 550)(309, 515)(310, 561)(311, 564)(312, 514)(313, 576)(314, 573)(315, 504)(316, 571)(317, 572)(318, 501)(319, 548)(320, 547)(321, 559)(322, 542)(323, 541)(324, 560)(325, 549)(326, 552)(327, 544)(328, 540)(329, 537)(330, 545)(331, 524)(332, 523)(333, 511)(334, 536)(335, 535)(336, 512)(337, 525)(338, 528)(339, 538)(340, 498)(341, 495)(342, 539)(343, 527)(344, 526)(345, 491)(346, 513)(347, 516)(348, 490)(349, 558)(350, 555)(351, 588)(352, 553)(353, 554)(354, 585)(355, 568)(356, 569)(357, 566)(358, 575)(359, 574)(360, 565)

MAP           : A4.29
NOTES         : type II, reflexible, isomorphic to DBar({4,5}), isomorphic to A4.7.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 2, 5 ]
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)^5 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^4, (x.2 * x.3^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^5, (x.2^-1 * x.3^-2 * x.2^-1 * x.3^-1)^2, x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^2 * x.2^-1 * x.3^-1 * x.2 * x.3 * x.2^-2 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 10, 8)
#DARTS        : 720
R = (1, 121, 241)(2, 122, 242)(3, 123, 243)(4, 124, 244)(5, 125, 245)(6, 126, 246)(7, 127, 247)(8, 128, 248)(9, 129, 249)(10, 130, 250)(11, 131, 251)(12, 132, 252)(13, 133, 253)(14, 134, 254)(15, 135, 255)(16, 136, 256)(17, 137, 257)(18, 138, 258)(19, 139, 259)(20, 140, 260)(21, 141, 261)(22, 142, 262)(23, 143, 263)(24, 144, 264)(25, 145, 265)(26, 146, 266)(27, 147, 267)(28, 148, 268)(29, 149, 269)(30, 150, 270)(31, 151, 271)(32, 152, 272)(33, 153, 273)(34, 154, 274)(35, 155, 275)(36, 156, 276)(37, 157, 277)(38, 158, 278)(39, 159, 279)(40, 160, 280)(41, 161, 281)(42, 162, 282)(43, 163, 283)(44, 164, 284)(45, 165, 285)(46, 166, 286)(47, 167, 287)(48, 168, 288)(49, 169, 289)(50, 170, 290)(51, 171, 291)(52, 172, 292)(53, 173, 293)(54, 174, 294)(55, 175, 295)(56, 176, 296)(57, 177, 297)(58, 178, 298)(59, 179, 299)(60, 180, 300)(61, 181, 301)(62, 182, 302)(63, 183, 303)(64, 184, 304)(65, 185, 305)(66, 186, 306)(67, 187, 307)(68, 188, 308)(69, 189, 309)(70, 190, 310)(71, 191, 311)(72, 192, 312)(73, 193, 313)(74, 194, 314)(75, 195, 315)(76, 196, 316)(77, 197, 317)(78, 198, 318)(79, 199, 319)(80, 200, 320)(81, 201, 321)(82, 202, 322)(83, 203, 323)(84, 204, 324)(85, 205, 325)(86, 206, 326)(87, 207, 327)(88, 208, 328)(89, 209, 329)(90, 210, 330)(91, 211, 331)(92, 212, 332)(93, 213, 333)(94, 214, 334)(95, 215, 335)(96, 216, 336)(97, 217, 337)(98, 218, 338)(99, 219, 339)(100, 220, 340)(101, 221, 341)(102, 222, 342)(103, 223, 343)(104, 224, 344)(105, 225, 345)(106, 226, 346)(107, 227, 347)(108, 228, 348)(109, 229, 349)(110, 230, 350)(111, 231, 351)(112, 232, 352)(113, 233, 353)(114, 234, 354)(115, 235, 355)(116, 236, 356)(117, 237, 357)(118, 238, 358)(119, 239, 359)(120, 240, 360)(361, 481, 601)(362, 482, 602)(363, 483, 603)(364, 484, 604)(365, 485, 605)(366, 486, 606)(367, 487, 607)(368, 488, 608)(369, 489, 609)(370, 490, 610)(371, 491, 611)(372, 492, 612)(373, 493, 613)(374, 494, 614)(375, 495, 615)(376, 496, 616)(377, 497, 617)(378, 498, 618)(379, 499, 619)(380, 500, 620)(381, 501, 621)(382, 502, 622)(383, 503, 623)(384, 504, 624)(385, 505, 625)(386, 506, 626)(387, 507, 627)(388, 508, 628)(389, 509, 629)(390, 510, 630)(391, 511, 631)(392, 512, 632)(393, 513, 633)(394, 514, 634)(395, 515, 635)(396, 516, 636)(397, 517, 637)(398, 518, 638)(399, 519, 639)(400, 520, 640)(401, 521, 641)(402, 522, 642)(403, 523, 643)(404, 524, 644)(405, 525, 645)(406, 526, 646)(407, 527, 647)(408, 528, 648)(409, 529, 649)(410, 530, 650)(411, 531, 651)(412, 532, 652)(413, 533, 653)(414, 534, 654)(415, 535, 655)(416, 536, 656)(417, 537, 657)(418, 538, 658)(419, 539, 659)(420, 540, 660)(421, 541, 661)(422, 542, 662)(423, 543, 663)(424, 544, 664)(425, 545, 665)(426, 546, 666)(427, 547, 667)(428, 548, 668)(429, 549, 669)(430, 550, 670)(431, 551, 671)(432, 552, 672)(433, 553, 673)(434, 554, 674)(435, 555, 675)(436, 556, 676)(437, 557, 677)(438, 558, 678)(439, 559, 679)(440, 560, 680)(441, 561, 681)(442, 562, 682)(443, 563, 683)(444, 564, 684)(445, 565, 685)(446, 566, 686)(447, 567, 687)(448, 568, 688)(449, 569, 689)(450, 570, 690)(451, 571, 691)(452, 572, 692)(453, 573, 693)(454, 574, 694)(455, 575, 695)(456, 576, 696)(457, 577, 697)(458, 578, 698)(459, 579, 699)(460, 580, 700)(461, 581, 701)(462, 582, 702)(463, 583, 703)(464, 584, 704)(465, 585, 705)(466, 586, 706)(467, 587, 707)(468, 588, 708)(469, 589, 709)(470, 590, 710)(471, 591, 711)(472, 592, 712)(473, 593, 713)(474, 594, 714)(475, 595, 715)(476, 596, 716)(477, 597, 717)(478, 598, 718)(479, 599, 719)(480, 600, 720)
L = (1, 361)(2, 362)(3, 363)(4, 364)(5, 365)(6, 366)(7, 367)(8, 368)(9, 369)(10, 370)(11, 371)(12, 372)(13, 373)(14, 374)(15, 375)(16, 376)(17, 377)(18, 378)(19, 379)(20, 380)(21, 381)(22, 382)(23, 383)(24, 384)(25, 385)(26, 386)(27, 387)(28, 388)(29, 389)(30, 390)(31, 391)(32, 392)(33, 393)(34, 394)(35, 395)(36, 396)(37, 397)(38, 398)(39, 399)(40, 400)(41, 401)(42, 402)(43, 403)(44, 404)(45, 405)(46, 406)(47, 407)(48, 408)(49, 409)(50, 410)(51, 411)(52, 412)(53, 413)(54, 414)(55, 415)(56, 416)(57, 417)(58, 418)(59, 419)(60, 420)(61, 421)(62, 422)(63, 423)(64, 424)(65, 425)(66, 426)(67, 427)(68, 428)(69, 429)(70, 430)(71, 431)(72, 432)(73, 433)(74, 434)(75, 435)(76, 436)(77, 437)(78, 438)(79, 439)(80, 440)(81, 441)(82, 442)(83, 443)(84, 444)(85, 445)(86, 446)(87, 447)(88, 448)(89, 449)(90, 450)(91, 451)(92, 452)(93, 453)(94, 454)(95, 455)(96, 456)(97, 457)(98, 458)(99, 459)(100, 460)(101, 461)(102, 462)(103, 463)(104, 464)(105, 465)(106, 466)(107, 467)(108, 468)(109, 469)(110, 470)(111, 471)(112, 472)(113, 473)(114, 474)(115, 475)(116, 476)(117, 477)(118, 478)(119, 479)(120, 480)(121, 603)(122, 606)(123, 616)(124, 702)(125, 699)(126, 617)(127, 654)(128, 651)(129, 690)(130, 649)(131, 650)(132, 687)(133, 602)(134, 601)(135, 607)(136, 614)(137, 613)(138, 608)(139, 640)(140, 641)(141, 638)(142, 677)(143, 676)(144, 637)(145, 605)(146, 604)(147, 719)(148, 609)(149, 612)(150, 718)(151, 713)(152, 712)(153, 683)(154, 717)(155, 720)(156, 682)(157, 710)(158, 709)(159, 715)(160, 698)(161, 697)(162, 716)(163, 622)(164, 623)(165, 620)(166, 653)(167, 652)(168, 619)(169, 711)(170, 714)(171, 700)(172, 666)(173, 663)(174, 701)(175, 630)(176, 627)(177, 642)(178, 625)(179, 626)(180, 639)(181, 706)(182, 707)(183, 704)(184, 629)(185, 628)(186, 703)(187, 671)(188, 670)(189, 635)(190, 681)(191, 684)(192, 634)(193, 696)(194, 693)(195, 624)(196, 691)(197, 692)(198, 621)(199, 668)(200, 667)(201, 679)(202, 662)(203, 661)(204, 680)(205, 669)(206, 672)(207, 664)(208, 660)(209, 657)(210, 665)(211, 644)(212, 643)(213, 631)(214, 656)(215, 655)(216, 632)(217, 645)(218, 648)(219, 658)(220, 618)(221, 615)(222, 659)(223, 647)(224, 646)(225, 611)(226, 633)(227, 636)(228, 610)(229, 678)(230, 675)(231, 708)(232, 673)(233, 674)(234, 705)(235, 688)(236, 689)(237, 686)(238, 695)(239, 694)(240, 685)(241, 486)(242, 483)(243, 534)(244, 481)(245, 482)(246, 531)(247, 496)(248, 497)(249, 494)(250, 539)(251, 538)(252, 493)(253, 579)(254, 582)(255, 574)(256, 570)(257, 567)(258, 575)(259, 581)(260, 580)(261, 545)(262, 591)(263, 594)(264, 544)(265, 578)(266, 577)(267, 589)(268, 572)(269, 571)(270, 590)(271, 588)(272, 585)(273, 498)(274, 583)(275, 584)(276, 495)(277, 598)(278, 599)(279, 596)(280, 485)(281, 484)(282, 595)(283, 555)(284, 558)(285, 568)(286, 528)(287, 525)(288, 569)(289, 557)(290, 556)(291, 521)(292, 543)(293, 546)(294, 520)(295, 554)(296, 553)(297, 541)(298, 566)(299, 565)(300, 542)(301, 564)(302, 561)(303, 600)(304, 559)(305, 560)(306, 597)(307, 550)(308, 551)(309, 548)(310, 587)(311, 586)(312, 547)(313, 513)(314, 516)(315, 526)(316, 492)(317, 489)(318, 527)(319, 515)(320, 514)(321, 509)(322, 519)(323, 522)(324, 508)(325, 512)(326, 511)(327, 517)(328, 524)(329, 523)(330, 518)(331, 540)(332, 537)(333, 552)(334, 535)(335, 536)(336, 549)(337, 532)(338, 533)(339, 530)(340, 563)(341, 562)(342, 529)(343, 501)(344, 504)(345, 490)(346, 576)(347, 573)(348, 491)(349, 503)(350, 502)(351, 593)(352, 507)(353, 510)(354, 592)(355, 500)(356, 499)(357, 505)(358, 488)(359, 487)(360, 506)

MAP           : A4.30
NOTES         : type II, reflexible, isomorphic to DBar({4,5}), isomorphic to A4.7.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^5, (x.2 * x.3^-1)^4, (x.1 * x.2^-1)^5, x.2^-2 * x.3 * x.2^2 * x.3 * x.2^-2 * x.3^-1 * x.2^2 * x.3^-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^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 10, 8)
#DARTS        : 720
R = (1, 121, 241)(2, 122, 242)(3, 123, 243)(4, 124, 244)(5, 125, 245)(6, 126, 246)(7, 127, 247)(8, 128, 248)(9, 129, 249)(10, 130, 250)(11, 131, 251)(12, 132, 252)(13, 133, 253)(14, 134, 254)(15, 135, 255)(16, 136, 256)(17, 137, 257)(18, 138, 258)(19, 139, 259)(20, 140, 260)(21, 141, 261)(22, 142, 262)(23, 143, 263)(24, 144, 264)(25, 145, 265)(26, 146, 266)(27, 147, 267)(28, 148, 268)(29, 149, 269)(30, 150, 270)(31, 151, 271)(32, 152, 272)(33, 153, 273)(34, 154, 274)(35, 155, 275)(36, 156, 276)(37, 157, 277)(38, 158, 278)(39, 159, 279)(40, 160, 280)(41, 161, 281)(42, 162, 282)(43, 163, 283)(44, 164, 284)(45, 165, 285)(46, 166, 286)(47, 167, 287)(48, 168, 288)(49, 169, 289)(50, 170, 290)(51, 171, 291)(52, 172, 292)(53, 173, 293)(54, 174, 294)(55, 175, 295)(56, 176, 296)(57, 177, 297)(58, 178, 298)(59, 179, 299)(60, 180, 300)(61, 181, 301)(62, 182, 302)(63, 183, 303)(64, 184, 304)(65, 185, 305)(66, 186, 306)(67, 187, 307)(68, 188, 308)(69, 189, 309)(70, 190, 310)(71, 191, 311)(72, 192, 312)(73, 193, 313)(74, 194, 314)(75, 195, 315)(76, 196, 316)(77, 197, 317)(78, 198, 318)(79, 199, 319)(80, 200, 320)(81, 201, 321)(82, 202, 322)(83, 203, 323)(84, 204, 324)(85, 205, 325)(86, 206, 326)(87, 207, 327)(88, 208, 328)(89, 209, 329)(90, 210, 330)(91, 211, 331)(92, 212, 332)(93, 213, 333)(94, 214, 334)(95, 215, 335)(96, 216, 336)(97, 217, 337)(98, 218, 338)(99, 219, 339)(100, 220, 340)(101, 221, 341)(102, 222, 342)(103, 223, 343)(104, 224, 344)(105, 225, 345)(106, 226, 346)(107, 227, 347)(108, 228, 348)(109, 229, 349)(110, 230, 350)(111, 231, 351)(112, 232, 352)(113, 233, 353)(114, 234, 354)(115, 235, 355)(116, 236, 356)(117, 237, 357)(118, 238, 358)(119, 239, 359)(120, 240, 360)(361, 481, 601)(362, 482, 602)(363, 483, 603)(364, 484, 604)(365, 485, 605)(366, 486, 606)(367, 487, 607)(368, 488, 608)(369, 489, 609)(370, 490, 610)(371, 491, 611)(372, 492, 612)(373, 493, 613)(374, 494, 614)(375, 495, 615)(376, 496, 616)(377, 497, 617)(378, 498, 618)(379, 499, 619)(380, 500, 620)(381, 501, 621)(382, 502, 622)(383, 503, 623)(384, 504, 624)(385, 505, 625)(386, 506, 626)(387, 507, 627)(388, 508, 628)(389, 509, 629)(390, 510, 630)(391, 511, 631)(392, 512, 632)(393, 513, 633)(394, 514, 634)(395, 515, 635)(396, 516, 636)(397, 517, 637)(398, 518, 638)(399, 519, 639)(400, 520, 640)(401, 521, 641)(402, 522, 642)(403, 523, 643)(404, 524, 644)(405, 525, 645)(406, 526, 646)(407, 527, 647)(408, 528, 648)(409, 529, 649)(410, 530, 650)(411, 531, 651)(412, 532, 652)(413, 533, 653)(414, 534, 654)(415, 535, 655)(416, 536, 656)(417, 537, 657)(418, 538, 658)(419, 539, 659)(420, 540, 660)(421, 541, 661)(422, 542, 662)(423, 543, 663)(424, 544, 664)(425, 545, 665)(426, 546, 666)(427, 547, 667)(428, 548, 668)(429, 549, 669)(430, 550, 670)(431, 551, 671)(432, 552, 672)(433, 553, 673)(434, 554, 674)(435, 555, 675)(436, 556, 676)(437, 557, 677)(438, 558, 678)(439, 559, 679)(440, 560, 680)(441, 561, 681)(442, 562, 682)(443, 563, 683)(444, 564, 684)(445, 565, 685)(446, 566, 686)(447, 567, 687)(448, 568, 688)(449, 569, 689)(450, 570, 690)(451, 571, 691)(452, 572, 692)(453, 573, 693)(454, 574, 694)(455, 575, 695)(456, 576, 696)(457, 577, 697)(458, 578, 698)(459, 579, 699)(460, 580, 700)(461, 581, 701)(462, 582, 702)(463, 583, 703)(464, 584, 704)(465, 585, 705)(466, 586, 706)(467, 587, 707)(468, 588, 708)(469, 589, 709)(470, 590, 710)(471, 591, 711)(472, 592, 712)(473, 593, 713)(474, 594, 714)(475, 595, 715)(476, 596, 716)(477, 597, 717)(478, 598, 718)(479, 599, 719)(480, 600, 720)
L = (1, 361)(2, 362)(3, 363)(4, 364)(5, 365)(6, 366)(7, 367)(8, 368)(9, 369)(10, 370)(11, 371)(12, 372)(13, 373)(14, 374)(15, 375)(16, 376)(17, 377)(18, 378)(19, 379)(20, 380)(21, 381)(22, 382)(23, 383)(24, 384)(25, 385)(26, 386)(27, 387)(28, 388)(29, 389)(30, 390)(31, 391)(32, 392)(33, 393)(34, 394)(35, 395)(36, 396)(37, 397)(38, 398)(39, 399)(40, 400)(41, 401)(42, 402)(43, 403)(44, 404)(45, 405)(46, 406)(47, 407)(48, 408)(49, 409)(50, 410)(51, 411)(52, 412)(53, 413)(54, 414)(55, 415)(56, 416)(57, 417)(58, 418)(59, 419)(60, 420)(61, 421)(62, 422)(63, 423)(64, 424)(65, 425)(66, 426)(67, 427)(68, 428)(69, 429)(70, 430)(71, 431)(72, 432)(73, 433)(74, 434)(75, 435)(76, 436)(77, 437)(78, 438)(79, 439)(80, 440)(81, 441)(82, 442)(83, 443)(84, 444)(85, 445)(86, 446)(87, 447)(88, 448)(89, 449)(90, 450)(91, 451)(92, 452)(93, 453)(94, 454)(95, 455)(96, 456)(97, 457)(98, 458)(99, 459)(100, 460)(101, 461)(102, 462)(103, 463)(104, 464)(105, 465)(106, 466)(107, 467)(108, 468)(109, 469)(110, 470)(111, 471)(112, 472)(113, 473)(114, 474)(115, 475)(116, 476)(117, 477)(118, 478)(119, 479)(120, 480)(121, 604)(122, 605)(123, 602)(124, 641)(125, 640)(126, 601)(127, 719)(128, 718)(129, 677)(130, 705)(131, 708)(132, 676)(133, 612)(134, 609)(135, 636)(136, 607)(137, 608)(138, 633)(139, 716)(140, 715)(141, 703)(142, 710)(143, 709)(144, 704)(145, 717)(146, 720)(147, 712)(148, 684)(149, 681)(150, 713)(151, 686)(152, 685)(153, 673)(154, 680)(155, 679)(156, 674)(157, 687)(158, 690)(159, 682)(160, 654)(161, 651)(162, 683)(163, 689)(164, 688)(165, 647)(166, 675)(167, 678)(168, 646)(169, 702)(170, 699)(171, 606)(172, 697)(173, 698)(174, 603)(175, 694)(176, 695)(177, 692)(178, 611)(179, 610)(180, 691)(181, 657)(182, 660)(183, 652)(184, 624)(185, 621)(186, 653)(187, 672)(188, 669)(189, 696)(190, 667)(191, 668)(192, 693)(193, 656)(194, 655)(195, 643)(196, 650)(197, 649)(198, 644)(199, 664)(200, 665)(201, 662)(202, 701)(203, 700)(204, 661)(205, 659)(206, 658)(207, 617)(208, 645)(209, 648)(210, 616)(211, 629)(212, 628)(213, 707)(214, 615)(215, 618)(216, 706)(217, 626)(218, 625)(219, 613)(220, 620)(221, 619)(222, 614)(223, 634)(224, 635)(225, 632)(226, 671)(227, 670)(228, 631)(229, 627)(230, 630)(231, 622)(232, 714)(233, 711)(234, 623)(235, 642)(236, 639)(237, 666)(238, 637)(239, 638)(240, 663)(241, 482)(242, 481)(243, 487)(244, 494)(245, 493)(246, 488)(247, 483)(248, 486)(249, 496)(250, 582)(251, 579)(252, 497)(253, 485)(254, 484)(255, 599)(256, 489)(257, 492)(258, 598)(259, 534)(260, 531)(261, 570)(262, 529)(263, 530)(264, 567)(265, 520)(266, 521)(267, 518)(268, 557)(269, 556)(270, 517)(271, 591)(272, 594)(273, 580)(274, 546)(275, 543)(276, 581)(277, 510)(278, 507)(279, 522)(280, 505)(281, 506)(282, 519)(283, 590)(284, 589)(285, 595)(286, 578)(287, 577)(288, 596)(289, 502)(290, 503)(291, 500)(292, 533)(293, 532)(294, 499)(295, 593)(296, 592)(297, 563)(298, 597)(299, 600)(300, 562)(301, 551)(302, 550)(303, 515)(304, 561)(305, 564)(306, 514)(307, 548)(308, 547)(309, 559)(310, 542)(311, 541)(312, 560)(313, 586)(314, 587)(315, 584)(316, 509)(317, 508)(318, 583)(319, 549)(320, 552)(321, 544)(322, 540)(323, 537)(324, 545)(325, 576)(326, 573)(327, 504)(328, 571)(329, 572)(330, 501)(331, 568)(332, 569)(333, 566)(334, 575)(335, 574)(336, 565)(337, 527)(338, 526)(339, 491)(340, 513)(341, 516)(342, 490)(343, 558)(344, 555)(345, 588)(346, 553)(347, 554)(348, 585)(349, 524)(350, 523)(351, 511)(352, 536)(353, 535)(354, 512)(355, 525)(356, 528)(357, 538)(358, 498)(359, 495)(360, 539)

MAP           : A4.31
NOTES         : type I, reflexible, isomorphic to Trun({4,5}), representative.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^5, (u.2 * u.3^-1)^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^2, (x.3 * x.1^-1)^2, x.2^5, (x.2^2 * x.3)^3, (x.2 * x.3)^5, (x.2^-2 * x.3 * x.2 * x.3)^2, (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 10, 10)
#DARTS        : 360
R = (1, 61, 121)(2, 62, 122)(3, 63, 123)(4, 64, 124)(5, 65, 125)(6, 66, 126)(7, 67, 127)(8, 68, 128)(9, 69, 129)(10, 70, 130)(11, 71, 131)(12, 72, 132)(13, 73, 133)(14, 74, 134)(15, 75, 135)(16, 76, 136)(17, 77, 137)(18, 78, 138)(19, 79, 139)(20, 80, 140)(21, 81, 141)(22, 82, 142)(23, 83, 143)(24, 84, 144)(25, 85, 145)(26, 86, 146)(27, 87, 147)(28, 88, 148)(29, 89, 149)(30, 90, 150)(31, 91, 151)(32, 92, 152)(33, 93, 153)(34, 94, 154)(35, 95, 155)(36, 96, 156)(37, 97, 157)(38, 98, 158)(39, 99, 159)(40, 100, 160)(41, 101, 161)(42, 102, 162)(43, 103, 163)(44, 104, 164)(45, 105, 165)(46, 106, 166)(47, 107, 167)(48, 108, 168)(49, 109, 169)(50, 110, 170)(51, 111, 171)(52, 112, 172)(53, 113, 173)(54, 114, 174)(55, 115, 175)(56, 116, 176)(57, 117, 177)(58, 118, 178)(59, 119, 179)(60, 120, 180)(181, 241, 301)(182, 242, 302)(183, 243, 303)(184, 244, 304)(185, 245, 305)(186, 246, 306)(187, 247, 307)(188, 248, 308)(189, 249, 309)(190, 250, 310)(191, 251, 311)(192, 252, 312)(193, 253, 313)(194, 254, 314)(195, 255, 315)(196, 256, 316)(197, 257, 317)(198, 258, 318)(199, 259, 319)(200, 260, 320)(201, 261, 321)(202, 262, 322)(203, 263, 323)(204, 264, 324)(205, 265, 325)(206, 266, 326)(207, 267, 327)(208, 268, 328)(209, 269, 329)(210, 270, 330)(211, 271, 331)(212, 272, 332)(213, 273, 333)(214, 274, 334)(215, 275, 335)(216, 276, 336)(217, 277, 337)(218, 278, 338)(219, 279, 339)(220, 280, 340)(221, 281, 341)(222, 282, 342)(223, 283, 343)(224, 284, 344)(225, 285, 345)(226, 286, 346)(227, 287, 347)(228, 288, 348)(229, 289, 349)(230, 290, 350)(231, 291, 351)(232, 292, 352)(233, 293, 353)(234, 294, 354)(235, 295, 355)(236, 296, 356)(237, 297, 357)(238, 298, 358)(239, 299, 359)(240, 300, 360)
L = (1, 181)(2, 182)(3, 183)(4, 184)(5, 185)(6, 186)(7, 187)(8, 188)(9, 189)(10, 190)(11, 191)(12, 192)(13, 193)(14, 194)(15, 195)(16, 196)(17, 197)(18, 198)(19, 199)(20, 200)(21, 201)(22, 202)(23, 203)(24, 204)(25, 205)(26, 206)(27, 207)(28, 208)(29, 209)(30, 210)(31, 211)(32, 212)(33, 213)(34, 214)(35, 215)(36, 216)(37, 217)(38, 218)(39, 219)(40, 220)(41, 221)(42, 222)(43, 223)(44, 224)(45, 225)(46, 226)(47, 227)(48, 228)(49, 229)(50, 230)(51, 231)(52, 232)(53, 233)(54, 234)(55, 235)(56, 236)(57, 237)(58, 238)(59, 239)(60, 240)(61, 305)(62, 318)(63, 341)(64, 302)(65, 304)(66, 334)(67, 314)(68, 317)(69, 319)(70, 313)(71, 330)(72, 329)(73, 327)(74, 303)(75, 340)(76, 339)(77, 351)(78, 301)(79, 328)(80, 325)(81, 312)(82, 354)(83, 326)(84, 356)(85, 342)(86, 352)(87, 338)(88, 353)(89, 349)(90, 315)(91, 311)(92, 336)(93, 323)(94, 308)(95, 310)(96, 316)(97, 332)(98, 335)(99, 337)(100, 331)(101, 348)(102, 347)(103, 345)(104, 309)(105, 322)(106, 321)(107, 357)(108, 307)(109, 346)(110, 343)(111, 306)(112, 360)(113, 344)(114, 350)(115, 324)(116, 358)(117, 320)(118, 359)(119, 355)(120, 333)(121, 283)(122, 284)(123, 285)(124, 286)(125, 287)(126, 288)(127, 289)(128, 290)(129, 291)(130, 292)(131, 293)(132, 294)(133, 295)(134, 296)(135, 297)(136, 298)(137, 299)(138, 300)(139, 265)(140, 266)(141, 267)(142, 268)(143, 269)(144, 270)(145, 259)(146, 260)(147, 261)(148, 262)(149, 263)(150, 264)(151, 277)(152, 278)(153, 279)(154, 280)(155, 281)(156, 282)(157, 271)(158, 272)(159, 273)(160, 274)(161, 275)(162, 276)(163, 241)(164, 242)(165, 243)(166, 244)(167, 245)(168, 246)(169, 247)(170, 248)(171, 249)(172, 250)(173, 251)(174, 252)(175, 253)(176, 254)(177, 255)(178, 256)(179, 257)(180, 258)

MAP           : A4.32
NOTES         : type I, reflexible, isomorphic to Trun({4,5}), isomorphic to A4.31.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 5 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^5, (u.2 * u.3^-1)^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^2, (x.1 * x.2)^2, (x.3 * x.2 * x.3)^3, (x.3 * x.1^-1)^5, (x.3 * x.2 * x.3^-2 * x.2)^2, (x.2 * x.3^-1)^5, (x.3^-1 * x.2 * x.3 * x.2 * x.3^-1 * x.2)^2 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 10, 10)
#DARTS        : 360
R = (1, 61, 121)(2, 62, 122)(3, 63, 123)(4, 64, 124)(5, 65, 125)(6, 66, 126)(7, 67, 127)(8, 68, 128)(9, 69, 129)(10, 70, 130)(11, 71, 131)(12, 72, 132)(13, 73, 133)(14, 74, 134)(15, 75, 135)(16, 76, 136)(17, 77, 137)(18, 78, 138)(19, 79, 139)(20, 80, 140)(21, 81, 141)(22, 82, 142)(23, 83, 143)(24, 84, 144)(25, 85, 145)(26, 86, 146)(27, 87, 147)(28, 88, 148)(29, 89, 149)(30, 90, 150)(31, 91, 151)(32, 92, 152)(33, 93, 153)(34, 94, 154)(35, 95, 155)(36, 96, 156)(37, 97, 157)(38, 98, 158)(39, 99, 159)(40, 100, 160)(41, 101, 161)(42, 102, 162)(43, 103, 163)(44, 104, 164)(45, 105, 165)(46, 106, 166)(47, 107, 167)(48, 108, 168)(49, 109, 169)(50, 110, 170)(51, 111, 171)(52, 112, 172)(53, 113, 173)(54, 114, 174)(55, 115, 175)(56, 116, 176)(57, 117, 177)(58, 118, 178)(59, 119, 179)(60, 120, 180)(181, 241, 301)(182, 242, 302)(183, 243, 303)(184, 244, 304)(185, 245, 305)(186, 246, 306)(187, 247, 307)(188, 248, 308)(189, 249, 309)(190, 250, 310)(191, 251, 311)(192, 252, 312)(193, 253, 313)(194, 254, 314)(195, 255, 315)(196, 256, 316)(197, 257, 317)(198, 258, 318)(199, 259, 319)(200, 260, 320)(201, 261, 321)(202, 262, 322)(203, 263, 323)(204, 264, 324)(205, 265, 325)(206, 266, 326)(207, 267, 327)(208, 268, 328)(209, 269, 329)(210, 270, 330)(211, 271, 331)(212, 272, 332)(213, 273, 333)(214, 274, 334)(215, 275, 335)(216, 276, 336)(217, 277, 337)(218, 278, 338)(219, 279, 339)(220, 280, 340)(221, 281, 341)(222, 282, 342)(223, 283, 343)(224, 284, 344)(225, 285, 345)(226, 286, 346)(227, 287, 347)(228, 288, 348)(229, 289, 349)(230, 290, 350)(231, 291, 351)(232, 292, 352)(233, 293, 353)(234, 294, 354)(235, 295, 355)(236, 296, 356)(237, 297, 357)(238, 298, 358)(239, 299, 359)(240, 300, 360)
L = (1, 181)(2, 182)(3, 183)(4, 184)(5, 185)(6, 186)(7, 187)(8, 188)(9, 189)(10, 190)(11, 191)(12, 192)(13, 193)(14, 194)(15, 195)(16, 196)(17, 197)(18, 198)(19, 199)(20, 200)(21, 201)(22, 202)(23, 203)(24, 204)(25, 205)(26, 206)(27, 207)(28, 208)(29, 209)(30, 210)(31, 211)(32, 212)(33, 213)(34, 214)(35, 215)(36, 216)(37, 217)(38, 218)(39, 219)(40, 220)(41, 221)(42, 222)(43, 223)(44, 224)(45, 225)(46, 226)(47, 227)(48, 228)(49, 229)(50, 230)(51, 231)(52, 232)(53, 233)(54, 234)(55, 235)(56, 236)(57, 237)(58, 238)(59, 239)(60, 240)(61, 307)(62, 308)(63, 309)(64, 310)(65, 311)(66, 312)(67, 301)(68, 302)(69, 303)(70, 304)(71, 305)(72, 306)(73, 331)(74, 332)(75, 333)(76, 334)(77, 335)(78, 336)(79, 337)(80, 338)(81, 339)(82, 340)(83, 341)(84, 342)(85, 343)(86, 344)(87, 345)(88, 346)(89, 347)(90, 348)(91, 313)(92, 314)(93, 315)(94, 316)(95, 317)(96, 318)(97, 319)(98, 320)(99, 321)(100, 322)(101, 323)(102, 324)(103, 325)(104, 326)(105, 327)(106, 328)(107, 329)(108, 330)(109, 355)(110, 356)(111, 357)(112, 358)(113, 359)(114, 360)(115, 349)(116, 350)(117, 351)(118, 352)(119, 353)(120, 354)(121, 281)(122, 246)(123, 293)(124, 278)(125, 280)(126, 286)(127, 242)(128, 245)(129, 247)(130, 241)(131, 258)(132, 257)(133, 255)(134, 279)(135, 292)(136, 291)(137, 267)(138, 277)(139, 256)(140, 253)(141, 276)(142, 270)(143, 254)(144, 260)(145, 294)(146, 268)(147, 290)(148, 269)(149, 265)(150, 243)(151, 275)(152, 288)(153, 251)(154, 272)(155, 274)(156, 244)(157, 284)(158, 287)(159, 289)(160, 283)(161, 300)(162, 299)(163, 297)(164, 273)(165, 250)(166, 249)(167, 261)(168, 271)(169, 298)(170, 295)(171, 282)(172, 264)(173, 296)(174, 266)(175, 252)(176, 262)(177, 248)(178, 263)(179, 259)(180, 285)

MAP           : A4.33
NOTES         : type I, reflexible, isomorphic to Trun({4,5}), isomorphic to A4.31.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^5, (u.2 * u.3^-1)^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^2, (x.3 * x.1^-1)^2, x.2^5, (x.2^2 * x.3)^3, (x.2 * x.3)^5, (x.2^-2 * x.3 * x.2 * x.3)^2, (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 10, 10)
#DARTS        : 360
R = (1, 61, 121)(2, 62, 122)(3, 63, 123)(4, 64, 124)(5, 65, 125)(6, 66, 126)(7, 67, 127)(8, 68, 128)(9, 69, 129)(10, 70, 130)(11, 71, 131)(12, 72, 132)(13, 73, 133)(14, 74, 134)(15, 75, 135)(16, 76, 136)(17, 77, 137)(18, 78, 138)(19, 79, 139)(20, 80, 140)(21, 81, 141)(22, 82, 142)(23, 83, 143)(24, 84, 144)(25, 85, 145)(26, 86, 146)(27, 87, 147)(28, 88, 148)(29, 89, 149)(30, 90, 150)(31, 91, 151)(32, 92, 152)(33, 93, 153)(34, 94, 154)(35, 95, 155)(36, 96, 156)(37, 97, 157)(38, 98, 158)(39, 99, 159)(40, 100, 160)(41, 101, 161)(42, 102, 162)(43, 103, 163)(44, 104, 164)(45, 105, 165)(46, 106, 166)(47, 107, 167)(48, 108, 168)(49, 109, 169)(50, 110, 170)(51, 111, 171)(52, 112, 172)(53, 113, 173)(54, 114, 174)(55, 115, 175)(56, 116, 176)(57, 117, 177)(58, 118, 178)(59, 119, 179)(60, 120, 180)(181, 241, 301)(182, 242, 302)(183, 243, 303)(184, 244, 304)(185, 245, 305)(186, 246, 306)(187, 247, 307)(188, 248, 308)(189, 249, 309)(190, 250, 310)(191, 251, 311)(192, 252, 312)(193, 253, 313)(194, 254, 314)(195, 255, 315)(196, 256, 316)(197, 257, 317)(198, 258, 318)(199, 259, 319)(200, 260, 320)(201, 261, 321)(202, 262, 322)(203, 263, 323)(204, 264, 324)(205, 265, 325)(206, 266, 326)(207, 267, 327)(208, 268, 328)(209, 269, 329)(210, 270, 330)(211, 271, 331)(212, 272, 332)(213, 273, 333)(214, 274, 334)(215, 275, 335)(216, 276, 336)(217, 277, 337)(218, 278, 338)(219, 279, 339)(220, 280, 340)(221, 281, 341)(222, 282, 342)(223, 283, 343)(224, 284, 344)(225, 285, 345)(226, 286, 346)(227, 287, 347)(228, 288, 348)(229, 289, 349)(230, 290, 350)(231, 291, 351)(232, 292, 352)(233, 293, 353)(234, 294, 354)(235, 295, 355)(236, 296, 356)(237, 297, 357)(238, 298, 358)(239, 299, 359)(240, 300, 360)
L = (1, 181)(2, 182)(3, 183)(4, 184)(5, 185)(6, 186)(7, 187)(8, 188)(9, 189)(10, 190)(11, 191)(12, 192)(13, 193)(14, 194)(15, 195)(16, 196)(17, 197)(18, 198)(19, 199)(20, 200)(21, 201)(22, 202)(23, 203)(24, 204)(25, 205)(26, 206)(27, 207)(28, 208)(29, 209)(30, 210)(31, 211)(32, 212)(33, 213)(34, 214)(35, 215)(36, 216)(37, 217)(38, 218)(39, 219)(40, 220)(41, 221)(42, 222)(43, 223)(44, 224)(45, 225)(46, 226)(47, 227)(48, 228)(49, 229)(50, 230)(51, 231)(52, 232)(53, 233)(54, 234)(55, 235)(56, 236)(57, 237)(58, 238)(59, 239)(60, 240)(61, 302)(62, 305)(63, 307)(64, 301)(65, 318)(66, 317)(67, 341)(68, 306)(69, 353)(70, 338)(71, 340)(72, 346)(73, 335)(74, 348)(75, 311)(76, 332)(77, 334)(78, 304)(79, 344)(80, 347)(81, 349)(82, 343)(83, 360)(84, 359)(85, 357)(86, 333)(87, 310)(88, 309)(89, 321)(90, 331)(91, 315)(92, 339)(93, 352)(94, 351)(95, 327)(96, 337)(97, 316)(98, 313)(99, 336)(100, 330)(101, 314)(102, 320)(103, 354)(104, 328)(105, 350)(106, 329)(107, 325)(108, 303)(109, 312)(110, 322)(111, 308)(112, 323)(113, 319)(114, 345)(115, 358)(116, 355)(117, 342)(118, 324)(119, 356)(120, 326)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)(127, 241)(128, 242)(129, 243)(130, 244)(131, 245)(132, 246)(133, 271)(134, 272)(135, 273)(136, 274)(137, 275)(138, 276)(139, 277)(140, 278)(141, 279)(142, 280)(143, 281)(144, 282)(145, 283)(146, 284)(147, 285)(148, 286)(149, 287)(150, 288)(151, 253)(152, 254)(153, 255)(154, 256)(155, 257)(156, 258)(157, 259)(158, 260)(159, 261)(160, 262)(161, 263)(162, 264)(163, 265)(164, 266)(165, 267)(166, 268)(167, 269)(168, 270)(169, 295)(170, 296)(171, 297)(172, 298)(173, 299)(174, 300)(175, 289)(176, 290)(177, 291)(178, 292)(179, 293)(180, 294)

MAP           : A4.34
NOTES         : type I, reflexible, isomorphic to Trun({4,5}), isomorphic to A4.31.
QUOTIENT      : R = (1, 2, 3) L = (2, 3)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 5 ]
UNIGROUP      : < u.1, u.2 | u.1^2, u.2^4, (u.1 * u.2^-1)^5 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2 | x.1^2, x.2^4, (x.1 * x.2^-1)^5, (x.1 * x.2^-1 * x.1 * x.2)^3, (x.2 * x.1 * x.2^2 * x.1 * x.2 * x.1 * x.2)^2, x.2^2 * x.1 * x.2 * x.1 * x.2^-2 * x.1 * x.2 * x.1 * x.2^-1 * x.1 * x.2^-1 * x.1 * x.2 * x.1 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (4, 10, 10)
#DARTS        : 360
R = (1, 121, 241)(2, 122, 242)(3, 123, 243)(4, 124, 244)(5, 125, 245)(6, 126, 246)(7, 127, 247)(8, 128, 248)(9, 129, 249)(10, 130, 250)(11, 131, 251)(12, 132, 252)(13, 133, 253)(14, 134, 254)(15, 135, 255)(16, 136, 256)(17, 137, 257)(18, 138, 258)(19, 139, 259)(20, 140, 260)(21, 141, 261)(22, 142, 262)(23, 143, 263)(24, 144, 264)(25, 145, 265)(26, 146, 266)(27, 147, 267)(28, 148, 268)(29, 149, 269)(30, 150, 270)(31, 151, 271)(32, 152, 272)(33, 153, 273)(34, 154, 274)(35, 155, 275)(36, 156, 276)(37, 157, 277)(38, 158, 278)(39, 159, 279)(40, 160, 280)(41, 161, 281)(42, 162, 282)(43, 163, 283)(44, 164, 284)(45, 165, 285)(46, 166, 286)(47, 167, 287)(48, 168, 288)(49, 169, 289)(50, 170, 290)(51, 171, 291)(52, 172, 292)(53, 173, 293)(54, 174, 294)(55, 175, 295)(56, 176, 296)(57, 177, 297)(58, 178, 298)(59, 179, 299)(60, 180, 300)(61, 181, 301)(62, 182, 302)(63, 183, 303)(64, 184, 304)(65, 185, 305)(66, 186, 306)(67, 187, 307)(68, 188, 308)(69, 189, 309)(70, 190, 310)(71, 191, 311)(72, 192, 312)(73, 193, 313)(74, 194, 314)(75, 195, 315)(76, 196, 316)(77, 197, 317)(78, 198, 318)(79, 199, 319)(80, 200, 320)(81, 201, 321)(82, 202, 322)(83, 203, 323)(84, 204, 324)(85, 205, 325)(86, 206, 326)(87, 207, 327)(88, 208, 328)(89, 209, 329)(90, 210, 330)(91, 211, 331)(92, 212, 332)(93, 213, 333)(94, 214, 334)(95, 215, 335)(96, 216, 336)(97, 217, 337)(98, 218, 338)(99, 219, 339)(100, 220, 340)(101, 221, 341)(102, 222, 342)(103, 223, 343)(104, 224, 344)(105, 225, 345)(106, 226, 346)(107, 227, 347)(108, 228, 348)(109, 229, 349)(110, 230, 350)(111, 231, 351)(112, 232, 352)(113, 233, 353)(114, 234, 354)(115, 235, 355)(116, 236, 356)(117, 237, 357)(118, 238, 358)(119, 239, 359)(120, 240, 360)
L = (1, 2)(3, 7)(4, 14)(5, 13)(6, 8)(9, 16)(10, 102)(11, 99)(12, 17)(15, 119)(18, 118)(19, 54)(20, 51)(21, 90)(22, 49)(23, 50)(24, 87)(25, 40)(26, 41)(27, 38)(28, 77)(29, 76)(30, 37)(31, 111)(32, 114)(33, 100)(34, 66)(35, 63)(36, 101)(39, 42)(43, 110)(44, 109)(45, 115)(46, 98)(47, 97)(48, 116)(52, 53)(55, 113)(56, 112)(57, 83)(58, 117)(59, 120)(60, 82)(61, 71)(62, 70)(64, 81)(65, 84)(67, 68)(69, 79)(72, 80)(73, 106)(74, 107)(75, 104)(78, 103)(85, 96)(86, 93)(88, 91)(89, 92)(94, 95)(105, 108)(121, 243)(122, 246)(123, 256)(124, 342)(125, 339)(126, 257)(127, 294)(128, 291)(129, 330)(130, 289)(131, 290)(132, 327)(133, 242)(134, 241)(135, 247)(136, 254)(137, 253)(138, 248)(139, 280)(140, 281)(141, 278)(142, 317)(143, 316)(144, 277)(145, 245)(146, 244)(147, 359)(148, 249)(149, 252)(150, 358)(151, 353)(152, 352)(153, 323)(154, 357)(155, 360)(156, 322)(157, 350)(158, 349)(159, 355)(160, 338)(161, 337)(162, 356)(163, 262)(164, 263)(165, 260)(166, 293)(167, 292)(168, 259)(169, 351)(170, 354)(171, 340)(172, 306)(173, 303)(174, 341)(175, 270)(176, 267)(177, 282)(178, 265)(179, 266)(180, 279)(181, 346)(182, 347)(183, 344)(184, 269)(185, 268)(186, 343)(187, 311)(188, 310)(189, 275)(190, 321)(191, 324)(192, 274)(193, 336)(194, 333)(195, 264)(196, 331)(197, 332)(198, 261)(199, 308)(200, 307)(201, 319)(202, 302)(203, 301)(204, 320)(205, 309)(206, 312)(207, 304)(208, 300)(209, 297)(210, 305)(211, 284)(212, 283)(213, 271)(214, 296)(215, 295)(216, 272)(217, 285)(218, 288)(219, 298)(220, 258)(221, 255)(222, 299)(223, 287)(224, 286)(225, 251)(226, 273)(227, 276)(228, 250)(229, 318)(230, 315)(231, 348)(232, 313)(233, 314)(234, 345)(235, 328)(236, 329)(237, 326)(238, 335)(239, 334)(240, 325)

MAP           : A4.35
NOTES         : type I, reflexible, isomorphic to Trun({4,5}), isomorphic to A4.31.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 2, 5 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^5, (u.1 * u.2^-1)^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3 * x.2)^3, (x.2^-1 * x.3^-2 * x.2^-1)^2, (x.3 * x.1^-1)^5, (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 10, 10)
#DARTS        : 360
R = (1, 61, 121)(2, 62, 122)(3, 63, 123)(4, 64, 124)(5, 65, 125)(6, 66, 126)(7, 67, 127)(8, 68, 128)(9, 69, 129)(10, 70, 130)(11, 71, 131)(12, 72, 132)(13, 73, 133)(14, 74, 134)(15, 75, 135)(16, 76, 136)(17, 77, 137)(18, 78, 138)(19, 79, 139)(20, 80, 140)(21, 81, 141)(22, 82, 142)(23, 83, 143)(24, 84, 144)(25, 85, 145)(26, 86, 146)(27, 87, 147)(28, 88, 148)(29, 89, 149)(30, 90, 150)(31, 91, 151)(32, 92, 152)(33, 93, 153)(34, 94, 154)(35, 95, 155)(36, 96, 156)(37, 97, 157)(38, 98, 158)(39, 99, 159)(40, 100, 160)(41, 101, 161)(42, 102, 162)(43, 103, 163)(44, 104, 164)(45, 105, 165)(46, 106, 166)(47, 107, 167)(48, 108, 168)(49, 109, 169)(50, 110, 170)(51, 111, 171)(52, 112, 172)(53, 113, 173)(54, 114, 174)(55, 115, 175)(56, 116, 176)(57, 117, 177)(58, 118, 178)(59, 119, 179)(60, 120, 180)(181, 241, 301)(182, 242, 302)(183, 243, 303)(184, 244, 304)(185, 245, 305)(186, 246, 306)(187, 247, 307)(188, 248, 308)(189, 249, 309)(190, 250, 310)(191, 251, 311)(192, 252, 312)(193, 253, 313)(194, 254, 314)(195, 255, 315)(196, 256, 316)(197, 257, 317)(198, 258, 318)(199, 259, 319)(200, 260, 320)(201, 261, 321)(202, 262, 322)(203, 263, 323)(204, 264, 324)(205, 265, 325)(206, 266, 326)(207, 267, 327)(208, 268, 328)(209, 269, 329)(210, 270, 330)(211, 271, 331)(212, 272, 332)(213, 273, 333)(214, 274, 334)(215, 275, 335)(216, 276, 336)(217, 277, 337)(218, 278, 338)(219, 279, 339)(220, 280, 340)(221, 281, 341)(222, 282, 342)(223, 283, 343)(224, 284, 344)(225, 285, 345)(226, 286, 346)(227, 287, 347)(228, 288, 348)(229, 289, 349)(230, 290, 350)(231, 291, 351)(232, 292, 352)(233, 293, 353)(234, 294, 354)(235, 295, 355)(236, 296, 356)(237, 297, 357)(238, 298, 358)(239, 299, 359)(240, 300, 360)
L = (1, 181)(2, 182)(3, 183)(4, 184)(5, 185)(6, 186)(7, 187)(8, 188)(9, 189)(10, 190)(11, 191)(12, 192)(13, 193)(14, 194)(15, 195)(16, 196)(17, 197)(18, 198)(19, 199)(20, 200)(21, 201)(22, 202)(23, 203)(24, 204)(25, 205)(26, 206)(27, 207)(28, 208)(29, 209)(30, 210)(31, 211)(32, 212)(33, 213)(34, 214)(35, 215)(36, 216)(37, 217)(38, 218)(39, 219)(40, 220)(41, 221)(42, 222)(43, 223)(44, 224)(45, 225)(46, 226)(47, 227)(48, 228)(49, 229)(50, 230)(51, 231)(52, 232)(53, 233)(54, 234)(55, 235)(56, 236)(57, 237)(58, 238)(59, 239)(60, 240)(61, 302)(62, 305)(63, 307)(64, 301)(65, 318)(66, 317)(67, 341)(68, 306)(69, 353)(70, 338)(71, 340)(72, 346)(73, 335)(74, 348)(75, 311)(76, 332)(77, 334)(78, 304)(79, 344)(80, 347)(81, 349)(82, 343)(83, 360)(84, 359)(85, 357)(86, 333)(87, 310)(88, 309)(89, 321)(90, 331)(91, 315)(92, 339)(93, 352)(94, 351)(95, 327)(96, 337)(97, 316)(98, 313)(99, 336)(100, 330)(101, 314)(102, 320)(103, 354)(104, 328)(105, 350)(106, 329)(107, 325)(108, 303)(109, 312)(110, 322)(111, 308)(112, 323)(113, 319)(114, 345)(115, 358)(116, 355)(117, 342)(118, 324)(119, 356)(120, 326)(121, 272)(122, 275)(123, 277)(124, 271)(125, 288)(126, 287)(127, 251)(128, 276)(129, 263)(130, 248)(131, 250)(132, 256)(133, 245)(134, 258)(135, 281)(136, 242)(137, 244)(138, 274)(139, 254)(140, 257)(141, 259)(142, 253)(143, 270)(144, 269)(145, 267)(146, 243)(147, 280)(148, 279)(149, 291)(150, 241)(151, 285)(152, 249)(153, 262)(154, 261)(155, 297)(156, 247)(157, 286)(158, 283)(159, 246)(160, 300)(161, 284)(162, 290)(163, 264)(164, 298)(165, 260)(166, 299)(167, 295)(168, 273)(169, 282)(170, 292)(171, 278)(172, 293)(173, 289)(174, 255)(175, 268)(176, 265)(177, 252)(178, 294)(179, 266)(180, 296)

MAP           : A4.36
NOTES         : type I, reflexible, isomorphic to Trun({4,5}), isomorphic to A4.31.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 5 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^5, (u.2 * u.3^-1)^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^2, (x.1 * x.2)^2, (x.3 * x.2 * x.3)^3, (x.3 * x.1^-1)^5, (x.3 * x.2 * x.3^-2 * x.2)^2, (x.2 * x.3^-1)^5, (x.3^-1 * x.2 * x.3 * x.2 * x.3^-1 * x.2)^2 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 10, 10)
#DARTS        : 360
R = (1, 61, 121)(2, 62, 122)(3, 63, 123)(4, 64, 124)(5, 65, 125)(6, 66, 126)(7, 67, 127)(8, 68, 128)(9, 69, 129)(10, 70, 130)(11, 71, 131)(12, 72, 132)(13, 73, 133)(14, 74, 134)(15, 75, 135)(16, 76, 136)(17, 77, 137)(18, 78, 138)(19, 79, 139)(20, 80, 140)(21, 81, 141)(22, 82, 142)(23, 83, 143)(24, 84, 144)(25, 85, 145)(26, 86, 146)(27, 87, 147)(28, 88, 148)(29, 89, 149)(30, 90, 150)(31, 91, 151)(32, 92, 152)(33, 93, 153)(34, 94, 154)(35, 95, 155)(36, 96, 156)(37, 97, 157)(38, 98, 158)(39, 99, 159)(40, 100, 160)(41, 101, 161)(42, 102, 162)(43, 103, 163)(44, 104, 164)(45, 105, 165)(46, 106, 166)(47, 107, 167)(48, 108, 168)(49, 109, 169)(50, 110, 170)(51, 111, 171)(52, 112, 172)(53, 113, 173)(54, 114, 174)(55, 115, 175)(56, 116, 176)(57, 117, 177)(58, 118, 178)(59, 119, 179)(60, 120, 180)(181, 241, 301)(182, 242, 302)(183, 243, 303)(184, 244, 304)(185, 245, 305)(186, 246, 306)(187, 247, 307)(188, 248, 308)(189, 249, 309)(190, 250, 310)(191, 251, 311)(192, 252, 312)(193, 253, 313)(194, 254, 314)(195, 255, 315)(196, 256, 316)(197, 257, 317)(198, 258, 318)(199, 259, 319)(200, 260, 320)(201, 261, 321)(202, 262, 322)(203, 263, 323)(204, 264, 324)(205, 265, 325)(206, 266, 326)(207, 267, 327)(208, 268, 328)(209, 269, 329)(210, 270, 330)(211, 271, 331)(212, 272, 332)(213, 273, 333)(214, 274, 334)(215, 275, 335)(216, 276, 336)(217, 277, 337)(218, 278, 338)(219, 279, 339)(220, 280, 340)(221, 281, 341)(222, 282, 342)(223, 283, 343)(224, 284, 344)(225, 285, 345)(226, 286, 346)(227, 287, 347)(228, 288, 348)(229, 289, 349)(230, 290, 350)(231, 291, 351)(232, 292, 352)(233, 293, 353)(234, 294, 354)(235, 295, 355)(236, 296, 356)(237, 297, 357)(238, 298, 358)(239, 299, 359)(240, 300, 360)
L = (1, 181)(2, 182)(3, 183)(4, 184)(5, 185)(6, 186)(7, 187)(8, 188)(9, 189)(10, 190)(11, 191)(12, 192)(13, 193)(14, 194)(15, 195)(16, 196)(17, 197)(18, 198)(19, 199)(20, 200)(21, 201)(22, 202)(23, 203)(24, 204)(25, 205)(26, 206)(27, 207)(28, 208)(29, 209)(30, 210)(31, 211)(32, 212)(33, 213)(34, 214)(35, 215)(36, 216)(37, 217)(38, 218)(39, 219)(40, 220)(41, 221)(42, 222)(43, 223)(44, 224)(45, 225)(46, 226)(47, 227)(48, 228)(49, 229)(50, 230)(51, 231)(52, 232)(53, 233)(54, 234)(55, 235)(56, 236)(57, 237)(58, 238)(59, 239)(60, 240)(61, 307)(62, 308)(63, 309)(64, 310)(65, 311)(66, 312)(67, 301)(68, 302)(69, 303)(70, 304)(71, 305)(72, 306)(73, 331)(74, 332)(75, 333)(76, 334)(77, 335)(78, 336)(79, 337)(80, 338)(81, 339)(82, 340)(83, 341)(84, 342)(85, 343)(86, 344)(87, 345)(88, 346)(89, 347)(90, 348)(91, 313)(92, 314)(93, 315)(94, 316)(95, 317)(96, 318)(97, 319)(98, 320)(99, 321)(100, 322)(101, 323)(102, 324)(103, 325)(104, 326)(105, 327)(106, 328)(107, 329)(108, 330)(109, 355)(110, 356)(111, 357)(112, 358)(113, 359)(114, 360)(115, 349)(116, 350)(117, 351)(118, 352)(119, 353)(120, 354)(121, 242)(122, 245)(123, 247)(124, 241)(125, 258)(126, 257)(127, 281)(128, 246)(129, 293)(130, 278)(131, 280)(132, 286)(133, 275)(134, 288)(135, 251)(136, 272)(137, 274)(138, 244)(139, 284)(140, 287)(141, 289)(142, 283)(143, 300)(144, 299)(145, 297)(146, 273)(147, 250)(148, 249)(149, 261)(150, 271)(151, 255)(152, 279)(153, 292)(154, 291)(155, 267)(156, 277)(157, 256)(158, 253)(159, 276)(160, 270)(161, 254)(162, 260)(163, 294)(164, 268)(165, 290)(166, 269)(167, 265)(168, 243)(169, 252)(170, 262)(171, 248)(172, 263)(173, 259)(174, 285)(175, 298)(176, 295)(177, 282)(178, 264)(179, 296)(180, 266)

MAP           : A4.37
NOTES         : type I, reflexible, isomorphic to Trun({4,5}), isomorphic to A4.31.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 2, 5 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^5, (u.1 * u.2^-1)^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.3 * x.2)^3, (x.2^-1 * x.3^-2 * x.2^-1)^2, (x.3 * x.1^-1)^5, (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 10, 10)
#DARTS        : 360
R = (1, 61, 121)(2, 62, 122)(3, 63, 123)(4, 64, 124)(5, 65, 125)(6, 66, 126)(7, 67, 127)(8, 68, 128)(9, 69, 129)(10, 70, 130)(11, 71, 131)(12, 72, 132)(13, 73, 133)(14, 74, 134)(15, 75, 135)(16, 76, 136)(17, 77, 137)(18, 78, 138)(19, 79, 139)(20, 80, 140)(21, 81, 141)(22, 82, 142)(23, 83, 143)(24, 84, 144)(25, 85, 145)(26, 86, 146)(27, 87, 147)(28, 88, 148)(29, 89, 149)(30, 90, 150)(31, 91, 151)(32, 92, 152)(33, 93, 153)(34, 94, 154)(35, 95, 155)(36, 96, 156)(37, 97, 157)(38, 98, 158)(39, 99, 159)(40, 100, 160)(41, 101, 161)(42, 102, 162)(43, 103, 163)(44, 104, 164)(45, 105, 165)(46, 106, 166)(47, 107, 167)(48, 108, 168)(49, 109, 169)(50, 110, 170)(51, 111, 171)(52, 112, 172)(53, 113, 173)(54, 114, 174)(55, 115, 175)(56, 116, 176)(57, 117, 177)(58, 118, 178)(59, 119, 179)(60, 120, 180)(181, 241, 301)(182, 242, 302)(183, 243, 303)(184, 244, 304)(185, 245, 305)(186, 246, 306)(187, 247, 307)(188, 248, 308)(189, 249, 309)(190, 250, 310)(191, 251, 311)(192, 252, 312)(193, 253, 313)(194, 254, 314)(195, 255, 315)(196, 256, 316)(197, 257, 317)(198, 258, 318)(199, 259, 319)(200, 260, 320)(201, 261, 321)(202, 262, 322)(203, 263, 323)(204, 264, 324)(205, 265, 325)(206, 266, 326)(207, 267, 327)(208, 268, 328)(209, 269, 329)(210, 270, 330)(211, 271, 331)(212, 272, 332)(213, 273, 333)(214, 274, 334)(215, 275, 335)(216, 276, 336)(217, 277, 337)(218, 278, 338)(219, 279, 339)(220, 280, 340)(221, 281, 341)(222, 282, 342)(223, 283, 343)(224, 284, 344)(225, 285, 345)(226, 286, 346)(227, 287, 347)(228, 288, 348)(229, 289, 349)(230, 290, 350)(231, 291, 351)(232, 292, 352)(233, 293, 353)(234, 294, 354)(235, 295, 355)(236, 296, 356)(237, 297, 357)(238, 298, 358)(239, 299, 359)(240, 300, 360)
L = (1, 181)(2, 182)(3, 183)(4, 184)(5, 185)(6, 186)(7, 187)(8, 188)(9, 189)(10, 190)(11, 191)(12, 192)(13, 193)(14, 194)(15, 195)(16, 196)(17, 197)(18, 198)(19, 199)(20, 200)(21, 201)(22, 202)(23, 203)(24, 204)(25, 205)(26, 206)(27, 207)(28, 208)(29, 209)(30, 210)(31, 211)(32, 212)(33, 213)(34, 214)(35, 215)(36, 216)(37, 217)(38, 218)(39, 219)(40, 220)(41, 221)(42, 222)(43, 223)(44, 224)(45, 225)(46, 226)(47, 227)(48, 228)(49, 229)(50, 230)(51, 231)(52, 232)(53, 233)(54, 234)(55, 235)(56, 236)(57, 237)(58, 238)(59, 239)(60, 240)(61, 305)(62, 318)(63, 341)(64, 302)(65, 304)(66, 334)(67, 314)(68, 317)(69, 319)(70, 313)(71, 330)(72, 329)(73, 327)(74, 303)(75, 340)(76, 339)(77, 351)(78, 301)(79, 328)(80, 325)(81, 312)(82, 354)(83, 326)(84, 356)(85, 342)(86, 352)(87, 338)(88, 353)(89, 349)(90, 315)(91, 311)(92, 336)(93, 323)(94, 308)(95, 310)(96, 316)(97, 332)(98, 335)(99, 337)(100, 331)(101, 348)(102, 347)(103, 345)(104, 309)(105, 322)(106, 321)(107, 357)(108, 307)(109, 346)(110, 343)(111, 306)(112, 360)(113, 344)(114, 350)(115, 324)(116, 358)(117, 320)(118, 359)(119, 355)(120, 333)(121, 263)(122, 252)(123, 299)(124, 260)(125, 262)(126, 268)(127, 248)(128, 251)(129, 241)(130, 247)(131, 276)(132, 275)(133, 273)(134, 261)(135, 298)(136, 297)(137, 285)(138, 259)(139, 274)(140, 271)(141, 258)(142, 288)(143, 272)(144, 278)(145, 300)(146, 286)(147, 296)(148, 287)(149, 283)(150, 249)(151, 257)(152, 270)(153, 245)(154, 254)(155, 256)(156, 250)(157, 266)(158, 269)(159, 295)(160, 265)(161, 294)(162, 293)(163, 291)(164, 255)(165, 244)(166, 243)(167, 279)(168, 253)(169, 292)(170, 289)(171, 264)(172, 282)(173, 290)(174, 284)(175, 246)(176, 280)(177, 242)(178, 281)(179, 277)(180, 267)

MAP           : A4.38
NOTES         : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A4.10.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^4, (x.3 * x.1^-1)^2, x.3 * x.2^-1 * x.3^2 * x.2 * x.3, (x.3^-1 * x.2 * x.3^-1 * x.2^-1)^2, (x.2 * x.3)^4, 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)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 8)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 362)(74, 365)(75, 368)(76, 363)(77, 426)(78, 369)(79, 416)(80, 419)(81, 422)(82, 417)(83, 372)(84, 423)(85, 420)(86, 411)(87, 414)(88, 425)(89, 406)(90, 377)(91, 366)(92, 393)(93, 396)(94, 371)(95, 388)(96, 431)(97, 364)(98, 391)(99, 394)(100, 379)(101, 392)(102, 385)(103, 382)(104, 373)(105, 376)(106, 361)(107, 374)(108, 367)(109, 402)(110, 429)(111, 432)(112, 407)(113, 424)(114, 395)(115, 400)(116, 427)(117, 430)(118, 415)(119, 428)(120, 421)(121, 418)(122, 409)(123, 412)(124, 397)(125, 410)(126, 403)(127, 398)(128, 401)(129, 404)(130, 399)(131, 390)(132, 405)(133, 380)(134, 383)(135, 386)(136, 381)(137, 408)(138, 387)(139, 384)(140, 375)(141, 378)(142, 389)(143, 370)(144, 413)(145, 291)(146, 310)(147, 289)(148, 294)(149, 301)(150, 292)(151, 297)(152, 304)(153, 295)(154, 300)(155, 307)(156, 298)(157, 293)(158, 354)(159, 347)(160, 296)(161, 315)(162, 350)(163, 299)(164, 348)(165, 353)(166, 290)(167, 339)(168, 344)(169, 359)(170, 342)(171, 305)(172, 320)(173, 345)(174, 338)(175, 321)(176, 316)(177, 319)(178, 324)(179, 349)(180, 322)(181, 327)(182, 346)(183, 325)(184, 330)(185, 337)(186, 328)(187, 333)(188, 340)(189, 331)(190, 336)(191, 343)(192, 334)(193, 329)(194, 318)(195, 311)(196, 332)(197, 351)(198, 314)(199, 335)(200, 312)(201, 317)(202, 326)(203, 303)(204, 308)(205, 323)(206, 306)(207, 341)(208, 356)(209, 309)(210, 302)(211, 357)(212, 352)(213, 355)(214, 360)(215, 313)(216, 358)

MAP           : A4.39
NOTES         : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A4.10.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^4, (x.3 * x.1^-1)^2, x.3 * x.2^-1 * x.3^2 * x.2 * x.3, (x.3^-1 * x.2 * x.3^-1 * x.2^-1)^2, (x.2 * x.3)^4, 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)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 8)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 371)(74, 420)(75, 425)(76, 362)(77, 411)(78, 416)(79, 431)(80, 414)(81, 377)(82, 392)(83, 417)(84, 410)(85, 393)(86, 388)(87, 391)(88, 396)(89, 421)(90, 394)(91, 363)(92, 382)(93, 361)(94, 366)(95, 373)(96, 364)(97, 369)(98, 376)(99, 367)(100, 372)(101, 379)(102, 370)(103, 365)(104, 426)(105, 419)(106, 368)(107, 387)(108, 422)(109, 407)(110, 384)(111, 389)(112, 398)(113, 375)(114, 380)(115, 395)(116, 378)(117, 413)(118, 428)(119, 381)(120, 374)(121, 429)(122, 424)(123, 427)(124, 432)(125, 385)(126, 430)(127, 399)(128, 418)(129, 397)(130, 402)(131, 409)(132, 400)(133, 405)(134, 412)(135, 403)(136, 408)(137, 415)(138, 406)(139, 401)(140, 390)(141, 383)(142, 404)(143, 423)(144, 386)(145, 354)(146, 315)(147, 318)(148, 347)(149, 322)(150, 311)(151, 352)(152, 313)(153, 316)(154, 355)(155, 314)(156, 319)(157, 358)(158, 325)(159, 328)(160, 349)(161, 326)(162, 343)(163, 350)(164, 353)(165, 344)(166, 351)(167, 294)(168, 345)(169, 296)(170, 299)(171, 290)(172, 297)(173, 348)(174, 291)(175, 300)(176, 333)(177, 336)(178, 293)(179, 340)(180, 329)(181, 302)(182, 305)(183, 338)(184, 303)(185, 324)(186, 339)(187, 356)(188, 359)(189, 320)(190, 357)(191, 342)(192, 321)(193, 360)(194, 327)(195, 330)(196, 323)(197, 346)(198, 335)(199, 306)(200, 309)(201, 312)(202, 341)(203, 292)(204, 317)(205, 304)(206, 307)(207, 310)(208, 295)(209, 308)(210, 289)(211, 298)(212, 331)(213, 334)(214, 301)(215, 332)(216, 337)

MAP           : A4.40
NOTES         : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A4.10.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^4, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^4, (x.2^-1, x.3^-1, x.2^-1), (x.2 * x.3^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 8)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 426)(74, 387)(75, 390)(76, 419)(77, 394)(78, 383)(79, 424)(80, 385)(81, 388)(82, 427)(83, 386)(84, 391)(85, 430)(86, 397)(87, 400)(88, 421)(89, 398)(90, 415)(91, 422)(92, 425)(93, 416)(94, 423)(95, 366)(96, 417)(97, 368)(98, 371)(99, 362)(100, 369)(101, 420)(102, 363)(103, 372)(104, 405)(105, 408)(106, 365)(107, 412)(108, 401)(109, 374)(110, 377)(111, 410)(112, 375)(113, 396)(114, 411)(115, 428)(116, 431)(117, 392)(118, 429)(119, 414)(120, 393)(121, 432)(122, 399)(123, 402)(124, 395)(125, 418)(126, 407)(127, 378)(128, 381)(129, 384)(130, 413)(131, 364)(132, 389)(133, 376)(134, 379)(135, 382)(136, 367)(137, 380)(138, 361)(139, 370)(140, 403)(141, 406)(142, 373)(143, 404)(144, 409)(145, 292)(146, 319)(147, 322)(148, 307)(149, 320)(150, 313)(151, 294)(152, 321)(153, 324)(154, 299)(155, 316)(156, 359)(157, 290)(158, 293)(159, 296)(160, 291)(161, 354)(162, 297)(163, 310)(164, 301)(165, 304)(166, 289)(167, 302)(168, 295)(169, 312)(170, 303)(171, 306)(172, 317)(173, 298)(174, 341)(175, 308)(176, 311)(177, 314)(178, 309)(179, 336)(180, 315)(181, 346)(182, 337)(183, 340)(184, 325)(185, 338)(186, 331)(187, 348)(188, 339)(189, 342)(190, 353)(191, 334)(192, 305)(193, 344)(194, 347)(195, 350)(196, 345)(197, 300)(198, 351)(199, 328)(200, 355)(201, 358)(202, 343)(203, 356)(204, 349)(205, 330)(206, 357)(207, 360)(208, 335)(209, 352)(210, 323)(211, 326)(212, 329)(213, 332)(214, 327)(215, 318)(216, 333)

MAP           : A4.41
NOTES         : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A4.10.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^4, (x.1 * x.2^-1)^2, (x.3 * x.1^-1)^4, (x.2^-1, x.3^-1, x.2^-1), (x.2 * x.3^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 8)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 363)(74, 382)(75, 361)(76, 366)(77, 373)(78, 364)(79, 369)(80, 376)(81, 367)(82, 372)(83, 379)(84, 370)(85, 365)(86, 426)(87, 419)(88, 368)(89, 387)(90, 422)(91, 371)(92, 420)(93, 425)(94, 362)(95, 411)(96, 416)(97, 431)(98, 414)(99, 377)(100, 392)(101, 417)(102, 410)(103, 393)(104, 388)(105, 391)(106, 396)(107, 421)(108, 394)(109, 399)(110, 418)(111, 397)(112, 402)(113, 409)(114, 400)(115, 405)(116, 412)(117, 403)(118, 408)(119, 415)(120, 406)(121, 401)(122, 390)(123, 383)(124, 404)(125, 423)(126, 386)(127, 407)(128, 384)(129, 389)(130, 398)(131, 375)(132, 380)(133, 395)(134, 378)(135, 413)(136, 428)(137, 381)(138, 374)(139, 429)(140, 424)(141, 427)(142, 432)(143, 385)(144, 430)(145, 292)(146, 319)(147, 322)(148, 307)(149, 320)(150, 313)(151, 294)(152, 321)(153, 324)(154, 299)(155, 316)(156, 359)(157, 290)(158, 293)(159, 296)(160, 291)(161, 354)(162, 297)(163, 310)(164, 301)(165, 304)(166, 289)(167, 302)(168, 295)(169, 312)(170, 303)(171, 306)(172, 317)(173, 298)(174, 341)(175, 308)(176, 311)(177, 314)(178, 309)(179, 336)(180, 315)(181, 346)(182, 337)(183, 340)(184, 325)(185, 338)(186, 331)(187, 348)(188, 339)(189, 342)(190, 353)(191, 334)(192, 305)(193, 344)(194, 347)(195, 350)(196, 345)(197, 300)(198, 351)(199, 328)(200, 355)(201, 358)(202, 343)(203, 356)(204, 349)(205, 330)(206, 357)(207, 360)(208, 335)(209, 352)(210, 323)(211, 326)(212, 329)(213, 332)(214, 327)(215, 318)(216, 333)

MAP           : A4.42
NOTES         : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A4.10.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^4, (x.2 * x.3^-1)^2, x.3^6, x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^2 * x.2^2, (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        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 364)(74, 391)(75, 394)(76, 379)(77, 392)(78, 385)(79, 366)(80, 393)(81, 396)(82, 371)(83, 388)(84, 431)(85, 362)(86, 365)(87, 368)(88, 363)(89, 426)(90, 369)(91, 382)(92, 373)(93, 376)(94, 361)(95, 374)(96, 367)(97, 384)(98, 375)(99, 378)(100, 389)(101, 370)(102, 413)(103, 380)(104, 383)(105, 386)(106, 381)(107, 408)(108, 387)(109, 418)(110, 409)(111, 412)(112, 397)(113, 410)(114, 403)(115, 420)(116, 411)(117, 414)(118, 425)(119, 406)(120, 377)(121, 416)(122, 419)(123, 422)(124, 417)(125, 372)(126, 423)(127, 400)(128, 427)(129, 430)(130, 415)(131, 428)(132, 421)(133, 402)(134, 429)(135, 432)(136, 407)(137, 424)(138, 395)(139, 398)(140, 401)(141, 404)(142, 399)(143, 390)(144, 405)(145, 294)(146, 321)(147, 324)(148, 299)(149, 316)(150, 359)(151, 292)(152, 319)(153, 322)(154, 307)(155, 320)(156, 313)(157, 310)(158, 301)(159, 304)(160, 289)(161, 302)(162, 295)(163, 290)(164, 293)(165, 296)(166, 291)(167, 354)(168, 297)(169, 344)(170, 347)(171, 350)(172, 345)(173, 300)(174, 351)(175, 348)(176, 339)(177, 342)(178, 353)(179, 334)(180, 305)(181, 326)(182, 329)(183, 332)(184, 327)(185, 318)(186, 333)(187, 308)(188, 311)(189, 314)(190, 309)(191, 336)(192, 315)(193, 312)(194, 303)(195, 306)(196, 317)(197, 298)(198, 341)(199, 330)(200, 357)(201, 360)(202, 335)(203, 352)(204, 323)(205, 328)(206, 355)(207, 358)(208, 343)(209, 356)(210, 349)(211, 346)(212, 337)(213, 340)(214, 325)(215, 338)(216, 331)

MAP           : A4.43
NOTES         : type II, reflexible, isomorphic to DBar({4,6}), isomorphic to A4.10.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^4, (x.2 * x.3^-1)^2, x.3^6, x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^2 * x.2^2, (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        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 364)(74, 391)(75, 394)(76, 379)(77, 392)(78, 385)(79, 366)(80, 393)(81, 396)(82, 371)(83, 388)(84, 431)(85, 362)(86, 365)(87, 368)(88, 363)(89, 426)(90, 369)(91, 382)(92, 373)(93, 376)(94, 361)(95, 374)(96, 367)(97, 384)(98, 375)(99, 378)(100, 389)(101, 370)(102, 413)(103, 380)(104, 383)(105, 386)(106, 381)(107, 408)(108, 387)(109, 418)(110, 409)(111, 412)(112, 397)(113, 410)(114, 403)(115, 420)(116, 411)(117, 414)(118, 425)(119, 406)(120, 377)(121, 416)(122, 419)(123, 422)(124, 417)(125, 372)(126, 423)(127, 400)(128, 427)(129, 430)(130, 415)(131, 428)(132, 421)(133, 402)(134, 429)(135, 432)(136, 407)(137, 424)(138, 395)(139, 398)(140, 401)(141, 404)(142, 399)(143, 390)(144, 405)(145, 347)(146, 300)(147, 293)(148, 350)(149, 333)(150, 296)(151, 311)(152, 336)(153, 329)(154, 314)(155, 297)(156, 332)(157, 315)(158, 322)(159, 313)(160, 318)(161, 289)(162, 316)(163, 351)(164, 358)(165, 349)(166, 354)(167, 325)(168, 352)(169, 345)(170, 328)(171, 343)(172, 348)(173, 355)(174, 346)(175, 353)(176, 294)(177, 299)(178, 344)(179, 321)(180, 290)(181, 341)(182, 360)(183, 323)(184, 302)(185, 327)(186, 356)(187, 317)(188, 330)(189, 335)(190, 308)(191, 357)(192, 326)(193, 309)(194, 292)(195, 307)(196, 312)(197, 319)(198, 310)(199, 303)(200, 298)(201, 301)(202, 306)(203, 331)(204, 304)(205, 339)(206, 334)(207, 337)(208, 342)(209, 295)(210, 340)(211, 305)(212, 324)(213, 359)(214, 338)(215, 291)(216, 320)

MAP           : A4.44
NOTES         : type I, reflexible, isomorphic to Trun({4,6}), representative.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6)
ORBIFOLD      : O(0, {4, 4, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 4, 3 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, u.2^4, u.3^4, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^3 >
CTG (small)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.2^4, x.3^4, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 75)(38, 94)(39, 79)(40, 89)(41, 108)(42, 98)(43, 81)(44, 88)(45, 73)(46, 95)(47, 102)(48, 104)(49, 96)(50, 87)(51, 92)(52, 74)(53, 82)(54, 85)(55, 90)(56, 93)(57, 86)(58, 80)(59, 76)(60, 91)(61, 106)(62, 84)(63, 107)(64, 97)(65, 99)(66, 77)(67, 100)(68, 78)(69, 101)(70, 103)(71, 105)(72, 83)(145, 198)(146, 201)(147, 194)(148, 188)(149, 184)(150, 199)(151, 214)(152, 192)(153, 215)(154, 205)(155, 207)(156, 185)(157, 208)(158, 186)(159, 209)(160, 211)(161, 213)(162, 191)(163, 183)(164, 202)(165, 187)(166, 197)(167, 216)(168, 206)(169, 189)(170, 196)(171, 181)(172, 203)(173, 210)(174, 212)(175, 204)(176, 195)(177, 200)(178, 182)(179, 190)(180, 193)

MAP           : A4.45
NOTES         : type I, reflexible, isomorphic to Trun({4,6}), isomorphic to A4.44.
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: [ 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^2, (u.3 * u.1 * u.4^-1 * u.2)^3 >
CTG (small)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, (x.4 * x.3^-1)^2, (x.2 * x.1)^2, x.4 * x.1 * x.4 * x.2 * x.4^-1 * x.1 * x.4^-1 * x.2, x.4 * x.2 * x.4 * x.1 * x.4^-1 * x.2 * x.4^-1 * x.1, (x.3 * x.1 * x.4^-1 * x.2)^3 >
SCHREIER VEC. : (x.3, x.1, x.4)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 46)(38, 48)(39, 42)(40, 41)(43, 50)(44, 49)(45, 55)(47, 56)(51, 67)(52, 61)(53, 68)(54, 62)(57, 71)(58, 72)(59, 69)(60, 70)(63, 66)(64, 65)(73, 150)(74, 148)(75, 164)(76, 146)(77, 163)(78, 145)(79, 180)(80, 178)(81, 170)(82, 176)(83, 169)(84, 175)(85, 179)(86, 177)(87, 172)(88, 171)(89, 174)(90, 173)(91, 149)(92, 147)(93, 166)(94, 165)(95, 168)(96, 167)(97, 155)(98, 153)(99, 160)(100, 159)(101, 162)(102, 161)(103, 156)(104, 154)(105, 158)(106, 152)(107, 157)(108, 151)(181, 182)(183, 187)(184, 193)(185, 188)(186, 194)(189, 191)(190, 192)(195, 216)(196, 215)(197, 214)(198, 213)(199, 200)(201, 205)(202, 211)(203, 206)(204, 212)(207, 209)(208, 210)

MAP           : A4.46
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), representative.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 2, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^6, (u.1 * u.2^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.2^-1 * x.3^-1 * x.2^2 * x.3 * x.2^-1, (x.3^-2 * x.2^-1)^2, (x.3 * x.1^-1)^6, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 184)(38, 207)(39, 212)(40, 189)(41, 181)(42, 206)(43, 205)(44, 191)(45, 211)(46, 210)(47, 182)(48, 185)(49, 199)(50, 198)(51, 194)(52, 216)(53, 213)(54, 202)(55, 201)(56, 195)(57, 209)(58, 215)(59, 214)(60, 208)(61, 197)(62, 203)(63, 190)(64, 193)(65, 204)(66, 188)(67, 192)(68, 186)(69, 196)(70, 183)(71, 200)(72, 187)(73, 171)(74, 148)(75, 145)(76, 170)(77, 176)(78, 153)(79, 154)(80, 149)(81, 174)(82, 175)(83, 180)(84, 155)(85, 147)(86, 160)(87, 157)(88, 146)(89, 152)(90, 165)(91, 166)(92, 161)(93, 150)(94, 151)(95, 156)(96, 167)(97, 159)(98, 172)(99, 169)(100, 158)(101, 164)(102, 177)(103, 178)(104, 173)(105, 162)(106, 163)(107, 168)(108, 179)

MAP           : A4.47
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 2, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^6, (u.1 * u.2^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.2^-1 * x.3^-1 * x.2^2 * x.3 * x.2^-1, (x.3^-2 * x.2^-1)^2, (x.3 * x.1^-1)^6, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 185)(38, 191)(39, 214)(40, 181)(41, 192)(42, 212)(43, 216)(44, 210)(45, 184)(46, 207)(47, 188)(48, 211)(49, 208)(50, 195)(51, 200)(52, 213)(53, 205)(54, 194)(55, 193)(56, 215)(57, 199)(58, 198)(59, 206)(60, 209)(61, 187)(62, 186)(63, 182)(64, 204)(65, 201)(66, 190)(67, 189)(68, 183)(69, 197)(70, 203)(71, 202)(72, 196)(73, 147)(74, 160)(75, 157)(76, 146)(77, 152)(78, 165)(79, 166)(80, 161)(81, 150)(82, 151)(83, 156)(84, 167)(85, 159)(86, 172)(87, 169)(88, 158)(89, 164)(90, 177)(91, 178)(92, 173)(93, 162)(94, 163)(95, 168)(96, 179)(97, 171)(98, 148)(99, 145)(100, 170)(101, 176)(102, 153)(103, 154)(104, 149)(105, 174)(106, 175)(107, 180)(108, 155)

MAP           : A4.48
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 2, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^6, (u.1 * u.2^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.2^-1 * x.3^-1 * x.2^2 * x.3 * x.2^-1, (x.3^-2 * x.2^-1)^2, (x.3 * x.1^-1)^6, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 188)(38, 192)(39, 211)(40, 183)(41, 203)(42, 185)(43, 191)(44, 189)(45, 182)(46, 181)(47, 197)(48, 190)(49, 206)(50, 205)(51, 209)(52, 210)(53, 207)(54, 208)(55, 195)(56, 216)(57, 214)(58, 213)(59, 184)(60, 212)(61, 202)(62, 201)(63, 196)(64, 215)(65, 198)(66, 187)(67, 186)(68, 193)(69, 200)(70, 204)(71, 199)(72, 194)(73, 171)(74, 148)(75, 145)(76, 170)(77, 176)(78, 153)(79, 154)(80, 149)(81, 174)(82, 175)(83, 180)(84, 155)(85, 147)(86, 160)(87, 157)(88, 146)(89, 152)(90, 165)(91, 166)(92, 161)(93, 150)(94, 151)(95, 156)(96, 167)(97, 159)(98, 172)(99, 169)(100, 158)(101, 164)(102, 177)(103, 178)(104, 173)(105, 162)(106, 163)(107, 168)(108, 179)

MAP           : A4.49
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 2, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^6, (u.1 * u.2^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.2^-1 * x.3^-1 * x.2^2 * x.3 * x.2^-1, (x.3^-2 * x.2^-1)^2, (x.3 * x.1^-1)^6, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 190)(38, 189)(39, 184)(40, 203)(41, 186)(42, 211)(43, 210)(44, 181)(45, 188)(46, 192)(47, 187)(48, 182)(49, 212)(50, 216)(51, 199)(52, 207)(53, 191)(54, 209)(55, 215)(56, 213)(57, 206)(58, 205)(59, 185)(60, 214)(61, 194)(62, 193)(63, 197)(64, 198)(65, 195)(66, 196)(67, 183)(68, 204)(69, 202)(70, 201)(71, 208)(72, 200)(73, 147)(74, 160)(75, 157)(76, 146)(77, 152)(78, 165)(79, 166)(80, 161)(81, 150)(82, 151)(83, 156)(84, 167)(85, 159)(86, 172)(87, 169)(88, 158)(89, 164)(90, 177)(91, 178)(92, 173)(93, 162)(94, 163)(95, 168)(96, 179)(97, 171)(98, 148)(99, 145)(100, 170)(101, 176)(102, 153)(103, 154)(104, 149)(105, 174)(106, 175)(107, 180)(108, 155)

MAP           : A4.50
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 6, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3 * x.2^-1, x.3^3 * x.2 * x.3^-3 * x.2^-1, x.3^-1 * x.2 * x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1, x.2 * x.3^-4 * x.2^2 * x.3^-1 * x.2^2 * x.3^-1 * x.2, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 182)(38, 181)(39, 185)(40, 186)(41, 183)(42, 184)(43, 207)(44, 192)(45, 190)(46, 189)(47, 196)(48, 188)(49, 214)(50, 213)(51, 208)(52, 191)(53, 210)(54, 199)(55, 198)(56, 205)(57, 212)(58, 216)(59, 211)(60, 206)(61, 200)(62, 204)(63, 187)(64, 195)(65, 215)(66, 197)(67, 203)(68, 201)(69, 194)(70, 193)(71, 209)(72, 202)(73, 147)(74, 160)(75, 157)(76, 146)(77, 152)(78, 165)(79, 166)(80, 161)(81, 150)(82, 151)(83, 156)(84, 167)(85, 159)(86, 172)(87, 169)(88, 158)(89, 164)(90, 177)(91, 178)(92, 173)(93, 162)(94, 163)(95, 168)(96, 179)(97, 171)(98, 148)(99, 145)(100, 170)(101, 176)(102, 153)(103, 154)(104, 149)(105, 174)(106, 175)(107, 180)(108, 155)

MAP           : A4.51
NOTES         : type I, reflexible, isomorphic to Trun({4,6}), isomorphic to A4.44.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6)
ORBIFOLD      : O(0, {4, 4, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 4, 3 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, u.2^4, u.3^4, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^3 >
CTG (small)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.2^4, x.3^4, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 75)(38, 94)(39, 79)(40, 89)(41, 108)(42, 98)(43, 81)(44, 88)(45, 73)(46, 95)(47, 102)(48, 104)(49, 96)(50, 87)(51, 92)(52, 74)(53, 82)(54, 85)(55, 90)(56, 93)(57, 86)(58, 80)(59, 76)(60, 91)(61, 106)(62, 84)(63, 107)(64, 97)(65, 99)(66, 77)(67, 100)(68, 78)(69, 101)(70, 103)(71, 105)(72, 83)(145, 186)(146, 213)(147, 182)(148, 200)(149, 208)(150, 211)(151, 190)(152, 204)(153, 191)(154, 193)(155, 195)(156, 209)(157, 196)(158, 210)(159, 197)(160, 187)(161, 189)(162, 203)(163, 207)(164, 214)(165, 199)(166, 185)(167, 192)(168, 194)(169, 201)(170, 184)(171, 205)(172, 215)(173, 198)(174, 188)(175, 216)(176, 183)(177, 212)(178, 206)(179, 202)(180, 181)

MAP           : A4.52
NOTES         : type I, reflexible, isomorphic to Trun({4,6}), isomorphic to A4.44.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6)
ORBIFOLD      : O(0, {4, 4, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 4, 3 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, u.2^4, u.3^4, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^3 >
CTG (small)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.2^4, x.3^4, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 81)(38, 88)(39, 73)(40, 95)(41, 102)(42, 104)(43, 75)(44, 94)(45, 79)(46, 89)(47, 108)(48, 98)(49, 90)(50, 93)(51, 86)(52, 80)(53, 76)(54, 91)(55, 96)(56, 87)(57, 92)(58, 74)(59, 82)(60, 85)(61, 100)(62, 78)(63, 101)(64, 103)(65, 105)(66, 83)(67, 106)(68, 84)(69, 107)(70, 97)(71, 99)(72, 77)(145, 207)(146, 214)(147, 199)(148, 185)(149, 192)(150, 194)(151, 201)(152, 184)(153, 205)(154, 215)(155, 198)(156, 188)(157, 216)(158, 183)(159, 212)(160, 206)(161, 202)(162, 181)(163, 186)(164, 213)(165, 182)(166, 200)(167, 208)(168, 211)(169, 190)(170, 204)(171, 191)(172, 193)(173, 195)(174, 209)(175, 196)(176, 210)(177, 197)(178, 187)(179, 189)(180, 203)

MAP           : A4.53
NOTES         : type I, reflexible, isomorphic to Trun({4,6}), isomorphic to A4.44.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6)
ORBIFOLD      : O(0, {4, 4, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 4, 3 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, u.2^4, u.3^4, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^3 >
CTG (small)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.2^4, x.3^4, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 81)(38, 88)(39, 73)(40, 95)(41, 102)(42, 104)(43, 75)(44, 94)(45, 79)(46, 89)(47, 108)(48, 98)(49, 90)(50, 93)(51, 86)(52, 80)(53, 76)(54, 91)(55, 96)(56, 87)(57, 92)(58, 74)(59, 82)(60, 85)(61, 100)(62, 78)(63, 101)(64, 103)(65, 105)(66, 83)(67, 106)(68, 84)(69, 107)(70, 97)(71, 99)(72, 77)(145, 216)(146, 183)(147, 212)(148, 206)(149, 202)(150, 181)(151, 196)(152, 210)(153, 197)(154, 187)(155, 189)(156, 203)(157, 190)(158, 204)(159, 191)(160, 193)(161, 195)(162, 209)(163, 201)(164, 184)(165, 205)(166, 215)(167, 198)(168, 188)(169, 207)(170, 214)(171, 199)(172, 185)(173, 192)(174, 194)(175, 186)(176, 213)(177, 182)(178, 200)(179, 208)(180, 211)

MAP           : A4.54
NOTES         : type I, reflexible, isomorphic to Trun({4,6}), isomorphic to A4.44.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^6, x.2^-2 * x.3 * x.2^-2 * x.3^-1, (x.2 * x.3^-1)^6, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 182)(38, 186)(39, 188)(40, 187)(41, 181)(42, 202)(43, 200)(44, 204)(45, 206)(46, 205)(47, 199)(48, 184)(49, 214)(50, 213)(51, 203)(52, 183)(53, 210)(54, 209)(55, 196)(56, 195)(57, 185)(58, 201)(59, 192)(60, 191)(61, 197)(62, 193)(63, 208)(64, 216)(65, 189)(66, 194)(67, 215)(68, 211)(69, 190)(70, 198)(71, 207)(72, 212)(73, 147)(74, 167)(75, 145)(76, 149)(77, 148)(78, 163)(79, 174)(80, 178)(81, 180)(82, 176)(83, 170)(84, 177)(85, 171)(86, 179)(87, 169)(88, 173)(89, 172)(90, 175)(91, 150)(92, 166)(93, 168)(94, 164)(95, 146)(96, 165)(97, 159)(98, 155)(99, 157)(100, 161)(101, 160)(102, 151)(103, 162)(104, 154)(105, 156)(106, 152)(107, 158)(108, 153)

MAP           : A4.55
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 2, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^6, (u.1 * u.2^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.3^2 * x.2 * x.3^-2 * x.2^-1, x.3^3 * x.2 * x.3 * x.2, (x.3 * x.1^-1)^6, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 196)(39, 193)(40, 182)(41, 188)(42, 201)(43, 202)(44, 197)(45, 186)(46, 187)(47, 192)(48, 203)(49, 195)(50, 208)(51, 205)(52, 194)(53, 200)(54, 213)(55, 214)(56, 209)(57, 198)(58, 199)(59, 204)(60, 215)(61, 207)(62, 184)(63, 181)(64, 206)(65, 212)(66, 189)(67, 190)(68, 185)(69, 210)(70, 211)(71, 216)(72, 191)(73, 149)(74, 155)(75, 178)(76, 145)(77, 156)(78, 176)(79, 180)(80, 174)(81, 148)(82, 171)(83, 152)(84, 175)(85, 172)(86, 159)(87, 164)(88, 177)(89, 169)(90, 158)(91, 157)(92, 179)(93, 163)(94, 162)(95, 170)(96, 173)(97, 151)(98, 150)(99, 146)(100, 168)(101, 165)(102, 154)(103, 153)(104, 147)(105, 161)(106, 167)(107, 166)(108, 160)

MAP           : A4.56
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 2, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^6, (u.1 * u.2^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.3^2 * x.2 * x.3^-2 * x.2^-1, x.3^3 * x.2 * x.3 * x.2, (x.3 * x.1^-1)^6, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 196)(39, 193)(40, 182)(41, 188)(42, 201)(43, 202)(44, 197)(45, 186)(46, 187)(47, 192)(48, 203)(49, 195)(50, 208)(51, 205)(52, 194)(53, 200)(54, 213)(55, 214)(56, 209)(57, 198)(58, 199)(59, 204)(60, 215)(61, 207)(62, 184)(63, 181)(64, 206)(65, 212)(66, 189)(67, 190)(68, 185)(69, 210)(70, 211)(71, 216)(72, 191)(73, 154)(74, 153)(75, 148)(76, 167)(77, 150)(78, 175)(79, 174)(80, 145)(81, 152)(82, 156)(83, 151)(84, 146)(85, 176)(86, 180)(87, 163)(88, 171)(89, 155)(90, 173)(91, 179)(92, 177)(93, 170)(94, 169)(95, 149)(96, 178)(97, 158)(98, 157)(99, 161)(100, 162)(101, 159)(102, 160)(103, 147)(104, 168)(105, 166)(106, 165)(107, 172)(108, 164)

MAP           : A4.57
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 2, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^6, (u.1 * u.2^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.3^2 * x.2 * x.3^-2 * x.2^-1, x.3^3 * x.2 * x.3 * x.2, (x.3 * x.1^-1)^6, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 207)(38, 184)(39, 181)(40, 206)(41, 212)(42, 189)(43, 190)(44, 185)(45, 210)(46, 211)(47, 216)(48, 191)(49, 183)(50, 196)(51, 193)(52, 182)(53, 188)(54, 201)(55, 202)(56, 197)(57, 186)(58, 187)(59, 192)(60, 203)(61, 195)(62, 208)(63, 205)(64, 194)(65, 200)(66, 213)(67, 214)(68, 209)(69, 198)(70, 199)(71, 204)(72, 215)(73, 148)(74, 171)(75, 176)(76, 153)(77, 145)(78, 170)(79, 169)(80, 155)(81, 175)(82, 174)(83, 146)(84, 149)(85, 163)(86, 162)(87, 158)(88, 180)(89, 177)(90, 166)(91, 165)(92, 159)(93, 173)(94, 179)(95, 178)(96, 172)(97, 161)(98, 167)(99, 154)(100, 157)(101, 168)(102, 152)(103, 156)(104, 150)(105, 160)(106, 147)(107, 164)(108, 151)

MAP           : A4.58
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 2, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^6, (u.1 * u.2^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.2^-1)^2, x.3^2 * x.2 * x.3^-2 * x.2^-1, x.3^3 * x.2 * x.3 * x.2, (x.3 * x.1^-1)^6, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 207)(38, 184)(39, 181)(40, 206)(41, 212)(42, 189)(43, 190)(44, 185)(45, 210)(46, 211)(47, 216)(48, 191)(49, 183)(50, 196)(51, 193)(52, 182)(53, 188)(54, 201)(55, 202)(56, 197)(57, 186)(58, 187)(59, 192)(60, 203)(61, 195)(62, 208)(63, 205)(64, 194)(65, 200)(66, 213)(67, 214)(68, 209)(69, 198)(70, 199)(71, 204)(72, 215)(73, 152)(74, 156)(75, 175)(76, 147)(77, 167)(78, 149)(79, 155)(80, 153)(81, 146)(82, 145)(83, 161)(84, 154)(85, 170)(86, 169)(87, 173)(88, 174)(89, 171)(90, 172)(91, 159)(92, 180)(93, 178)(94, 177)(95, 148)(96, 176)(97, 166)(98, 165)(99, 160)(100, 179)(101, 162)(102, 151)(103, 150)(104, 157)(105, 164)(106, 168)(107, 163)(108, 158)

MAP           : A4.59
NOTES         : type I, reflexible, isomorphic to Trun({4,6}), isomorphic to A4.44.
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: [ 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.3, u.1^2, u.2^2, (u.4 * u.3^-1)^2, (u.3 * u.1 * u.4^-1 * u.2)^3 >
CTG (small)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, (x.4 * x.3^-1)^2, (x.2 * x.1)^2, x.4 * x.1 * x.4 * x.2 * x.4^-1 * x.1 * x.4^-1 * x.2, x.4 * x.2 * x.4 * x.1 * x.4^-1 * x.2 * x.4^-1 * x.1, (x.3 * x.1 * x.4^-1 * x.2)^3 >
SCHREIER VEC. : (x.3, x.1, x.4)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 38)(39, 43)(40, 49)(41, 44)(42, 50)(45, 47)(46, 48)(51, 72)(52, 71)(53, 70)(54, 69)(55, 56)(57, 61)(58, 67)(59, 62)(60, 68)(63, 65)(64, 66)(73, 150)(74, 148)(75, 164)(76, 146)(77, 163)(78, 145)(79, 180)(80, 178)(81, 170)(82, 176)(83, 169)(84, 175)(85, 179)(86, 177)(87, 172)(88, 171)(89, 174)(90, 173)(91, 149)(92, 147)(93, 166)(94, 165)(95, 168)(96, 167)(97, 155)(98, 153)(99, 160)(100, 159)(101, 162)(102, 161)(103, 156)(104, 154)(105, 158)(106, 152)(107, 157)(108, 151)(181, 190)(182, 192)(183, 186)(184, 185)(187, 194)(188, 193)(189, 199)(191, 200)(195, 211)(196, 205)(197, 212)(198, 206)(201, 215)(202, 216)(203, 213)(204, 214)(207, 210)(208, 209)

MAP           : A4.60
NOTES         : type I, reflexible, isomorphic to Trun({4,6}), isomorphic to A4.44.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 6, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 10>
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.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 203)(39, 181)(40, 185)(41, 184)(42, 199)(43, 210)(44, 214)(45, 216)(46, 212)(47, 206)(48, 213)(49, 207)(50, 215)(51, 205)(52, 209)(53, 208)(54, 211)(55, 186)(56, 202)(57, 204)(58, 200)(59, 182)(60, 201)(61, 195)(62, 191)(63, 193)(64, 197)(65, 196)(66, 187)(67, 198)(68, 190)(69, 192)(70, 188)(71, 194)(72, 189)(73, 148)(74, 147)(75, 173)(76, 177)(77, 168)(78, 167)(79, 149)(80, 145)(81, 160)(82, 156)(83, 165)(84, 146)(85, 155)(86, 151)(87, 166)(88, 150)(89, 159)(90, 152)(91, 170)(92, 174)(93, 164)(94, 163)(95, 169)(96, 178)(97, 176)(98, 180)(99, 158)(100, 157)(101, 175)(102, 172)(103, 154)(104, 153)(105, 179)(106, 171)(107, 162)(108, 161)

MAP           : A4.61
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-2 * x.3 * x.2^3 * 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 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3^-2 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 196)(39, 193)(40, 182)(41, 188)(42, 201)(43, 202)(44, 197)(45, 186)(46, 187)(47, 192)(48, 203)(49, 195)(50, 208)(51, 205)(52, 194)(53, 200)(54, 213)(55, 214)(56, 209)(57, 198)(58, 199)(59, 204)(60, 215)(61, 207)(62, 184)(63, 181)(64, 206)(65, 212)(66, 189)(67, 190)(68, 185)(69, 210)(70, 211)(71, 216)(72, 191)(73, 146)(74, 145)(75, 149)(76, 150)(77, 147)(78, 148)(79, 171)(80, 156)(81, 154)(82, 153)(83, 160)(84, 152)(85, 178)(86, 177)(87, 172)(88, 155)(89, 174)(90, 163)(91, 162)(92, 169)(93, 176)(94, 180)(95, 175)(96, 170)(97, 164)(98, 168)(99, 151)(100, 159)(101, 179)(102, 161)(103, 167)(104, 165)(105, 158)(106, 157)(107, 173)(108, 166)

MAP           : A4.62
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-2 * x.3 * x.2^3 * 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 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3^-2 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 196)(39, 193)(40, 182)(41, 188)(42, 201)(43, 202)(44, 197)(45, 186)(46, 187)(47, 192)(48, 203)(49, 195)(50, 208)(51, 205)(52, 194)(53, 200)(54, 213)(55, 214)(56, 209)(57, 198)(58, 199)(59, 204)(60, 215)(61, 207)(62, 184)(63, 181)(64, 206)(65, 212)(66, 189)(67, 190)(68, 185)(69, 210)(70, 211)(71, 216)(72, 191)(73, 175)(74, 174)(75, 170)(76, 156)(77, 153)(78, 178)(79, 177)(80, 171)(81, 149)(82, 155)(83, 154)(84, 148)(85, 173)(86, 179)(87, 166)(88, 169)(89, 180)(90, 164)(91, 168)(92, 162)(93, 172)(94, 159)(95, 176)(96, 163)(97, 160)(98, 147)(99, 152)(100, 165)(101, 157)(102, 146)(103, 145)(104, 167)(105, 151)(106, 150)(107, 158)(108, 161)

MAP           : A4.63
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-2 * x.3 * x.2^3 * 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 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3^-2 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 207)(38, 184)(39, 181)(40, 206)(41, 212)(42, 189)(43, 190)(44, 185)(45, 210)(46, 211)(47, 216)(48, 191)(49, 183)(50, 196)(51, 193)(52, 182)(53, 188)(54, 201)(55, 202)(56, 197)(57, 186)(58, 187)(59, 192)(60, 203)(61, 195)(62, 208)(63, 205)(64, 194)(65, 200)(66, 213)(67, 214)(68, 209)(69, 198)(70, 199)(71, 204)(72, 215)(73, 146)(74, 145)(75, 149)(76, 150)(77, 147)(78, 148)(79, 171)(80, 156)(81, 154)(82, 153)(83, 160)(84, 152)(85, 178)(86, 177)(87, 172)(88, 155)(89, 174)(90, 163)(91, 162)(92, 169)(93, 176)(94, 180)(95, 175)(96, 170)(97, 164)(98, 168)(99, 151)(100, 159)(101, 179)(102, 161)(103, 167)(104, 165)(105, 158)(106, 157)(107, 173)(108, 166)

MAP           : A4.64
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 6, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3 * x.2^-1, x.3^3 * x.2 * x.3^-3 * x.2^-1, x.3^-1 * x.2 * x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1, x.2 * x.3^-4 * x.2^2 * x.3^-1 * x.2^2 * x.3^-1 * x.2, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 182)(38, 181)(39, 185)(40, 186)(41, 183)(42, 184)(43, 207)(44, 192)(45, 190)(46, 189)(47, 196)(48, 188)(49, 214)(50, 213)(51, 208)(52, 191)(53, 210)(54, 199)(55, 198)(56, 205)(57, 212)(58, 216)(59, 211)(60, 206)(61, 200)(62, 204)(63, 187)(64, 195)(65, 215)(66, 197)(67, 203)(68, 201)(69, 194)(70, 193)(71, 209)(72, 202)(73, 171)(74, 148)(75, 145)(76, 170)(77, 176)(78, 153)(79, 154)(80, 149)(81, 174)(82, 175)(83, 180)(84, 155)(85, 147)(86, 160)(87, 157)(88, 146)(89, 152)(90, 165)(91, 166)(92, 161)(93, 150)(94, 151)(95, 156)(96, 167)(97, 159)(98, 172)(99, 169)(100, 158)(101, 164)(102, 177)(103, 178)(104, 173)(105, 162)(106, 163)(107, 168)(108, 179)

MAP           : A4.65
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 6, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
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)^6, (x.2 * x.3^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 182)(38, 181)(39, 185)(40, 186)(41, 183)(42, 184)(43, 207)(44, 192)(45, 190)(46, 189)(47, 196)(48, 188)(49, 214)(50, 213)(51, 208)(52, 191)(53, 210)(54, 199)(55, 198)(56, 205)(57, 212)(58, 216)(59, 211)(60, 206)(61, 200)(62, 204)(63, 187)(64, 195)(65, 215)(66, 197)(67, 203)(68, 201)(69, 194)(70, 193)(71, 209)(72, 202)(73, 148)(74, 171)(75, 176)(76, 153)(77, 145)(78, 170)(79, 169)(80, 155)(81, 175)(82, 174)(83, 146)(84, 149)(85, 163)(86, 162)(87, 158)(88, 180)(89, 177)(90, 166)(91, 165)(92, 159)(93, 173)(94, 179)(95, 178)(96, 172)(97, 161)(98, 167)(99, 154)(100, 157)(101, 168)(102, 152)(103, 156)(104, 150)(105, 160)(106, 147)(107, 164)(108, 151)

MAP           : A4.66
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 6, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
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)^6, (x.2 * x.3^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 182)(38, 181)(39, 185)(40, 186)(41, 183)(42, 184)(43, 207)(44, 192)(45, 190)(46, 189)(47, 196)(48, 188)(49, 214)(50, 213)(51, 208)(52, 191)(53, 210)(54, 199)(55, 198)(56, 205)(57, 212)(58, 216)(59, 211)(60, 206)(61, 200)(62, 204)(63, 187)(64, 195)(65, 215)(66, 197)(67, 203)(68, 201)(69, 194)(70, 193)(71, 209)(72, 202)(73, 149)(74, 155)(75, 178)(76, 145)(77, 156)(78, 176)(79, 180)(80, 174)(81, 148)(82, 171)(83, 152)(84, 175)(85, 172)(86, 159)(87, 164)(88, 177)(89, 169)(90, 158)(91, 157)(92, 179)(93, 163)(94, 162)(95, 170)(96, 173)(97, 151)(98, 150)(99, 146)(100, 168)(101, 165)(102, 154)(103, 153)(104, 147)(105, 161)(106, 167)(107, 166)(108, 160)

MAP           : A4.67
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
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)^6, (x.2 * x.3^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 190)(38, 189)(39, 184)(40, 203)(41, 186)(42, 211)(43, 210)(44, 181)(45, 188)(46, 192)(47, 187)(48, 182)(49, 212)(50, 216)(51, 199)(52, 207)(53, 191)(54, 209)(55, 215)(56, 213)(57, 206)(58, 205)(59, 185)(60, 214)(61, 194)(62, 193)(63, 197)(64, 198)(65, 195)(66, 196)(67, 183)(68, 204)(69, 202)(70, 201)(71, 208)(72, 200)(73, 175)(74, 174)(75, 170)(76, 156)(77, 153)(78, 178)(79, 177)(80, 171)(81, 149)(82, 155)(83, 154)(84, 148)(85, 173)(86, 179)(87, 166)(88, 169)(89, 180)(90, 164)(91, 168)(92, 162)(93, 172)(94, 159)(95, 176)(96, 163)(97, 160)(98, 147)(99, 152)(100, 165)(101, 157)(102, 146)(103, 145)(104, 167)(105, 151)(106, 150)(107, 158)(108, 161)

MAP           : A4.68
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 6, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3 * x.2^-1, x.3^3 * x.2 * x.3^-3 * x.2^-1, x.3^-1 * x.2 * x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1, x.2 * x.3^-4 * x.2^2 * x.3^-1 * x.2^2 * x.3^-1 * x.2, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 211)(38, 210)(39, 206)(40, 192)(41, 189)(42, 214)(43, 213)(44, 207)(45, 185)(46, 191)(47, 190)(48, 184)(49, 209)(50, 215)(51, 202)(52, 205)(53, 216)(54, 200)(55, 204)(56, 198)(57, 208)(58, 195)(59, 212)(60, 199)(61, 196)(62, 183)(63, 188)(64, 201)(65, 193)(66, 182)(67, 181)(68, 203)(69, 187)(70, 186)(71, 194)(72, 197)(73, 171)(74, 148)(75, 145)(76, 170)(77, 176)(78, 153)(79, 154)(80, 149)(81, 174)(82, 175)(83, 180)(84, 155)(85, 147)(86, 160)(87, 157)(88, 146)(89, 152)(90, 165)(91, 166)(92, 161)(93, 150)(94, 151)(95, 156)(96, 167)(97, 159)(98, 172)(99, 169)(100, 158)(101, 164)(102, 177)(103, 178)(104, 173)(105, 162)(106, 163)(107, 168)(108, 179)

MAP           : A4.69
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 6, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
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)^6, (x.2 * x.3^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 211)(38, 210)(39, 206)(40, 192)(41, 189)(42, 214)(43, 213)(44, 207)(45, 185)(46, 191)(47, 190)(48, 184)(49, 209)(50, 215)(51, 202)(52, 205)(53, 216)(54, 200)(55, 204)(56, 198)(57, 208)(58, 195)(59, 212)(60, 199)(61, 196)(62, 183)(63, 188)(64, 201)(65, 193)(66, 182)(67, 181)(68, 203)(69, 187)(70, 186)(71, 194)(72, 197)(73, 152)(74, 156)(75, 175)(76, 147)(77, 167)(78, 149)(79, 155)(80, 153)(81, 146)(82, 145)(83, 161)(84, 154)(85, 170)(86, 169)(87, 173)(88, 174)(89, 171)(90, 172)(91, 159)(92, 180)(93, 178)(94, 177)(95, 148)(96, 176)(97, 166)(98, 165)(99, 160)(100, 179)(101, 162)(102, 151)(103, 150)(104, 157)(105, 164)(106, 168)(107, 163)(108, 158)

MAP           : A4.70
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 6, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
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)^6, (x.2 * x.3^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 211)(38, 210)(39, 206)(40, 192)(41, 189)(42, 214)(43, 213)(44, 207)(45, 185)(46, 191)(47, 190)(48, 184)(49, 209)(50, 215)(51, 202)(52, 205)(53, 216)(54, 200)(55, 204)(56, 198)(57, 208)(58, 195)(59, 212)(60, 199)(61, 196)(62, 183)(63, 188)(64, 201)(65, 193)(66, 182)(67, 181)(68, 203)(69, 187)(70, 186)(71, 194)(72, 197)(73, 154)(74, 153)(75, 148)(76, 167)(77, 150)(78, 175)(79, 174)(80, 145)(81, 152)(82, 156)(83, 151)(84, 146)(85, 176)(86, 180)(87, 163)(88, 171)(89, 155)(90, 173)(91, 179)(92, 177)(93, 170)(94, 169)(95, 149)(96, 178)(97, 158)(98, 157)(99, 161)(100, 162)(101, 159)(102, 160)(103, 147)(104, 168)(105, 166)(106, 165)(107, 172)(108, 164)

MAP           : A4.71
NOTES         : type I, reflexible, isomorphic to Trun({4,6}), isomorphic to A4.44.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 2, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^6, (u.1 * u.2^-1)^6 >
CTG (small)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2^-1)^2, (x.2 * x.3^-1)^2, (x.3 * x.1^-1)^6, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 184)(38, 183)(39, 209)(40, 213)(41, 204)(42, 203)(43, 185)(44, 181)(45, 196)(46, 192)(47, 201)(48, 182)(49, 191)(50, 187)(51, 202)(52, 186)(53, 195)(54, 188)(55, 206)(56, 210)(57, 200)(58, 199)(59, 205)(60, 214)(61, 212)(62, 216)(63, 194)(64, 193)(65, 211)(66, 208)(67, 190)(68, 189)(69, 215)(70, 207)(71, 198)(72, 197)(73, 146)(74, 150)(75, 152)(76, 151)(77, 145)(78, 166)(79, 164)(80, 168)(81, 170)(82, 169)(83, 163)(84, 148)(85, 178)(86, 177)(87, 167)(88, 147)(89, 174)(90, 173)(91, 160)(92, 159)(93, 149)(94, 165)(95, 156)(96, 155)(97, 161)(98, 157)(99, 172)(100, 180)(101, 153)(102, 158)(103, 179)(104, 175)(105, 154)(106, 162)(107, 171)(108, 176)

MAP           : A4.72
NOTES         : type I, reflexible, isomorphic to Trun({4,6}), isomorphic to A4.44.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 6, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 10>
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.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 203)(39, 181)(40, 185)(41, 184)(42, 199)(43, 210)(44, 214)(45, 216)(46, 212)(47, 206)(48, 213)(49, 207)(50, 215)(51, 205)(52, 209)(53, 208)(54, 211)(55, 186)(56, 202)(57, 204)(58, 200)(59, 182)(60, 201)(61, 195)(62, 191)(63, 193)(64, 197)(65, 196)(66, 187)(67, 198)(68, 190)(69, 192)(70, 188)(71, 194)(72, 189)(73, 146)(74, 150)(75, 152)(76, 151)(77, 145)(78, 166)(79, 164)(80, 168)(81, 170)(82, 169)(83, 163)(84, 148)(85, 178)(86, 177)(87, 167)(88, 147)(89, 174)(90, 173)(91, 160)(92, 159)(93, 149)(94, 165)(95, 156)(96, 155)(97, 161)(98, 157)(99, 172)(100, 180)(101, 153)(102, 158)(103, 179)(104, 175)(105, 154)(106, 162)(107, 171)(108, 176)

MAP           : A4.73
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^-2 * x.3 * x.2^3 * 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 * x.2 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3^-2 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^2 * x.3^-1 * x.2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 207)(38, 184)(39, 181)(40, 206)(41, 212)(42, 189)(43, 190)(44, 185)(45, 210)(46, 211)(47, 216)(48, 191)(49, 183)(50, 196)(51, 193)(52, 182)(53, 188)(54, 201)(55, 202)(56, 197)(57, 186)(58, 187)(59, 192)(60, 203)(61, 195)(62, 208)(63, 205)(64, 194)(65, 200)(66, 213)(67, 214)(68, 209)(69, 198)(70, 199)(71, 204)(72, 215)(73, 175)(74, 174)(75, 170)(76, 156)(77, 153)(78, 178)(79, 177)(80, 171)(81, 149)(82, 155)(83, 154)(84, 148)(85, 173)(86, 179)(87, 166)(88, 169)(89, 180)(90, 164)(91, 168)(92, 162)(93, 172)(94, 159)(95, 176)(96, 163)(97, 160)(98, 147)(99, 152)(100, 165)(101, 157)(102, 146)(103, 145)(104, 167)(105, 151)(106, 150)(107, 158)(108, 161)

MAP           : A4.74
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
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)^6, (x.2 * x.3^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 184)(38, 207)(39, 212)(40, 189)(41, 181)(42, 206)(43, 205)(44, 191)(45, 211)(46, 210)(47, 182)(48, 185)(49, 199)(50, 198)(51, 194)(52, 216)(53, 213)(54, 202)(55, 201)(56, 195)(57, 209)(58, 215)(59, 214)(60, 208)(61, 197)(62, 203)(63, 190)(64, 193)(65, 204)(66, 188)(67, 192)(68, 186)(69, 196)(70, 183)(71, 200)(72, 187)(73, 146)(74, 145)(75, 149)(76, 150)(77, 147)(78, 148)(79, 171)(80, 156)(81, 154)(82, 153)(83, 160)(84, 152)(85, 178)(86, 177)(87, 172)(88, 155)(89, 174)(90, 163)(91, 162)(92, 169)(93, 176)(94, 180)(95, 175)(96, 170)(97, 164)(98, 168)(99, 151)(100, 159)(101, 179)(102, 161)(103, 167)(104, 165)(105, 158)(106, 157)(107, 173)(108, 166)

MAP           : A4.75
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
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)^6, (x.2 * x.3^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 185)(38, 191)(39, 214)(40, 181)(41, 192)(42, 212)(43, 216)(44, 210)(45, 184)(46, 207)(47, 188)(48, 211)(49, 208)(50, 195)(51, 200)(52, 213)(53, 205)(54, 194)(55, 193)(56, 215)(57, 199)(58, 198)(59, 206)(60, 209)(61, 187)(62, 186)(63, 182)(64, 204)(65, 201)(66, 190)(67, 189)(68, 183)(69, 197)(70, 203)(71, 202)(72, 196)(73, 146)(74, 145)(75, 149)(76, 150)(77, 147)(78, 148)(79, 171)(80, 156)(81, 154)(82, 153)(83, 160)(84, 152)(85, 178)(86, 177)(87, 172)(88, 155)(89, 174)(90, 163)(91, 162)(92, 169)(93, 176)(94, 180)(95, 175)(96, 170)(97, 164)(98, 168)(99, 151)(100, 159)(101, 179)(102, 161)(103, 167)(104, 165)(105, 158)(106, 157)(107, 173)(108, 166)

MAP           : A4.76
NOTES         : type I, reflexible, isomorphic to Trun({4,6}), isomorphic to A4.44.
QUOTIENT      : R = (1, 2, 3) L = (2, 3)
ORBIFOLD      : O(0, {6, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 6 ]
UNIGROUP      : < u.1, u.2 | u.1^2, u.2^4, (u.1 * u.2^-1)^6 >
CTG (small)   : <72, 40>
CTG (fp)      : < x.1, x.2 | x.1^2, x.2^4, (x.1 * x.2^-1 * x.1 * x.2)^2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)
L = (1, 66)(2, 27)(3, 30)(4, 59)(5, 34)(6, 23)(7, 64)(8, 25)(9, 28)(10, 67)(11, 26)(12, 31)(13, 70)(14, 37)(15, 40)(16, 61)(17, 38)(18, 55)(19, 62)(20, 65)(21, 56)(22, 63)(24, 57)(29, 60)(32, 45)(33, 48)(35, 52)(36, 41)(39, 50)(42, 51)(43, 68)(44, 71)(46, 69)(47, 54)(49, 72)(53, 58)(73, 148)(74, 175)(75, 178)(76, 163)(77, 176)(78, 169)(79, 150)(80, 177)(81, 180)(82, 155)(83, 172)(84, 215)(85, 146)(86, 149)(87, 152)(88, 147)(89, 210)(90, 153)(91, 166)(92, 157)(93, 160)(94, 145)(95, 158)(96, 151)(97, 168)(98, 159)(99, 162)(100, 173)(101, 154)(102, 197)(103, 164)(104, 167)(105, 170)(106, 165)(107, 192)(108, 171)(109, 202)(110, 193)(111, 196)(112, 181)(113, 194)(114, 187)(115, 204)(116, 195)(117, 198)(118, 209)(119, 190)(120, 161)(121, 200)(122, 203)(123, 206)(124, 201)(125, 156)(126, 207)(127, 184)(128, 211)(129, 214)(130, 199)(131, 212)(132, 205)(133, 186)(134, 213)(135, 216)(136, 191)(137, 208)(138, 179)(139, 182)(140, 185)(141, 188)(142, 183)(143, 174)(144, 189)

MAP           : A4.77
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 6, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.1^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.1 * x.2^-1)^2, x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3 * x.2^-1, x.3^3 * x.2 * x.3^-3 * x.2^-1, x.3^-1 * x.2 * x.3 * x.2 * x.3 * x.2^-1 * x.3^-1 * x.2^-1, x.2 * x.3^-4 * x.2^2 * x.3^-1 * x.2^2 * x.3^-1 * x.2, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 211)(38, 210)(39, 206)(40, 192)(41, 189)(42, 214)(43, 213)(44, 207)(45, 185)(46, 191)(47, 190)(48, 184)(49, 209)(50, 215)(51, 202)(52, 205)(53, 216)(54, 200)(55, 204)(56, 198)(57, 208)(58, 195)(59, 212)(60, 199)(61, 196)(62, 183)(63, 188)(64, 201)(65, 193)(66, 182)(67, 181)(68, 203)(69, 187)(70, 186)(71, 194)(72, 197)(73, 147)(74, 160)(75, 157)(76, 146)(77, 152)(78, 165)(79, 166)(80, 161)(81, 150)(82, 151)(83, 156)(84, 167)(85, 159)(86, 172)(87, 169)(88, 158)(89, 164)(90, 177)(91, 178)(92, 173)(93, 162)(94, 163)(95, 168)(96, 179)(97, 171)(98, 148)(99, 145)(100, 170)(101, 176)(102, 153)(103, 154)(104, 149)(105, 174)(106, 175)(107, 180)(108, 155)

MAP           : A4.78
NOTES         : type I, reflexible, isomorphic to Trun({4,6}), isomorphic to A4.44.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, x.2^6, x.2^-2 * x.3 * x.2^-2 * x.3^-1, (x.2 * x.3^-1)^6, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 184)(38, 183)(39, 209)(40, 213)(41, 204)(42, 203)(43, 185)(44, 181)(45, 196)(46, 192)(47, 201)(48, 182)(49, 191)(50, 187)(51, 202)(52, 186)(53, 195)(54, 188)(55, 206)(56, 210)(57, 200)(58, 199)(59, 205)(60, 214)(61, 212)(62, 216)(63, 194)(64, 193)(65, 211)(66, 208)(67, 190)(68, 189)(69, 215)(70, 207)(71, 198)(72, 197)(73, 147)(74, 167)(75, 145)(76, 149)(77, 148)(78, 163)(79, 174)(80, 178)(81, 180)(82, 176)(83, 170)(84, 177)(85, 171)(86, 179)(87, 169)(88, 173)(89, 172)(90, 175)(91, 150)(92, 166)(93, 168)(94, 164)(95, 146)(96, 165)(97, 159)(98, 155)(99, 157)(100, 161)(101, 160)(102, 151)(103, 162)(104, 154)(105, 156)(106, 152)(107, 158)(108, 153)

MAP           : A4.79
NOTES         : type I, reflexible, isomorphic to Trun({4,6}), isomorphic to A4.44.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 2, 6 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.1^-1)^6, (u.1 * u.2^-1)^6 >
CTG (small)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2^-1)^2, (x.2 * x.3^-1)^2, (x.3 * x.1^-1)^6, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 182)(38, 186)(39, 188)(40, 187)(41, 181)(42, 202)(43, 200)(44, 204)(45, 206)(46, 205)(47, 199)(48, 184)(49, 214)(50, 213)(51, 203)(52, 183)(53, 210)(54, 209)(55, 196)(56, 195)(57, 185)(58, 201)(59, 192)(60, 191)(61, 197)(62, 193)(63, 208)(64, 216)(65, 189)(66, 194)(67, 215)(68, 211)(69, 190)(70, 198)(71, 207)(72, 212)(73, 148)(74, 147)(75, 173)(76, 177)(77, 168)(78, 167)(79, 149)(80, 145)(81, 160)(82, 156)(83, 165)(84, 146)(85, 155)(86, 151)(87, 166)(88, 150)(89, 159)(90, 152)(91, 170)(92, 174)(93, 164)(94, 163)(95, 169)(96, 178)(97, 176)(98, 180)(99, 158)(100, 157)(101, 175)(102, 172)(103, 154)(104, 153)(105, 179)(106, 171)(107, 162)(108, 161)

MAP           : A4.80
NOTES         : type II, reflexible, isomorphic to DBar({6,6}), isomorphic to A4.46.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, (u.3 * u.1^-1)^2, (u.1 * u.2^-1)^6, (u.2 * u.3^-1)^6 >
CTG (small)   : <36, 12>
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)^6, (x.2 * x.3^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 188)(38, 192)(39, 211)(40, 183)(41, 203)(42, 185)(43, 191)(44, 189)(45, 182)(46, 181)(47, 197)(48, 190)(49, 206)(50, 205)(51, 209)(52, 210)(53, 207)(54, 208)(55, 195)(56, 216)(57, 214)(58, 213)(59, 184)(60, 212)(61, 202)(62, 201)(63, 196)(64, 215)(65, 198)(66, 187)(67, 186)(68, 193)(69, 200)(70, 204)(71, 199)(72, 194)(73, 175)(74, 174)(75, 170)(76, 156)(77, 153)(78, 178)(79, 177)(80, 171)(81, 149)(82, 155)(83, 154)(84, 148)(85, 173)(86, 179)(87, 166)(88, 169)(89, 180)(90, 164)(91, 168)(92, 162)(93, 172)(94, 159)(95, 176)(96, 163)(97, 160)(98, 147)(99, 152)(100, 165)(101, 157)(102, 146)(103, 145)(104, 167)(105, 151)(106, 150)(107, 158)(108, 161)

MAP           : A4.81
NOTES         : type I, reflexible, isomorphic to Trun({4,6}), isomorphic to A4.44.
QUOTIENT      : R = (1, 2, 3) L = (2, 3)
ORBIFOLD      : O(0, {6, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 6 ]
UNIGROUP      : < u.1, u.2 | u.1^2, u.2^4, (u.1 * u.2^-1)^6 >
CTG (small)   : <72, 40>
CTG (fp)      : < x.1, x.2 | x.1^2, x.2^4, (x.1 * x.2^-1 * x.1 * x.2)^2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (4, 12, 12)
#DARTS        : 216
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)
L = (1, 3)(2, 22)(4, 6)(5, 13)(7, 9)(8, 16)(10, 12)(11, 19)(14, 66)(15, 59)(17, 27)(18, 62)(20, 60)(21, 65)(23, 51)(24, 56)(25, 71)(26, 54)(28, 32)(29, 57)(30, 50)(31, 33)(34, 36)(35, 61)(37, 39)(38, 58)(40, 42)(41, 49)(43, 45)(44, 52)(46, 48)(47, 55)(53, 63)(64, 68)(67, 69)(70, 72)(73, 148)(74, 175)(75, 178)(76, 163)(77, 176)(78, 169)(79, 150)(80, 177)(81, 180)(82, 155)(83, 172)(84, 215)(85, 146)(86, 149)(87, 152)(88, 147)(89, 210)(90, 153)(91, 166)(92, 157)(93, 160)(94, 145)(95, 158)(96, 151)(97, 168)(98, 159)(99, 162)(100, 173)(101, 154)(102, 197)(103, 164)(104, 167)(105, 170)(106, 165)(107, 192)(108, 171)(109, 202)(110, 193)(111, 196)(112, 181)(113, 194)(114, 187)(115, 204)(116, 195)(117, 198)(118, 209)(119, 190)(120, 161)(121, 200)(122, 203)(123, 206)(124, 201)(125, 156)(126, 207)(127, 184)(128, 211)(129, 214)(130, 199)(131, 212)(132, 205)(133, 186)(134, 213)(135, 216)(136, 191)(137, 208)(138, 179)(139, 182)(140, 185)(141, 188)(142, 183)(143, 174)(144, 189)

MAP           : A4.82
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 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)^10 >
CTG (small)   : <40, 8>
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.2 * x.3^-1)^4, (x.1 * x.2^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 20, 8)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 204)(42, 201)(43, 225)(44, 209)(45, 202)(46, 221)(47, 222)(48, 230)(49, 213)(50, 205)(51, 224)(52, 234)(53, 217)(54, 210)(55, 229)(56, 238)(57, 218)(58, 214)(59, 233)(60, 237)(61, 203)(62, 208)(63, 227)(64, 207)(65, 212)(66, 231)(67, 226)(68, 223)(69, 206)(70, 216)(71, 235)(72, 228)(73, 211)(74, 220)(75, 239)(76, 232)(77, 215)(78, 219)(79, 240)(80, 236)(81, 167)(82, 163)(83, 162)(84, 166)(85, 168)(86, 164)(87, 161)(88, 165)(89, 171)(90, 172)(91, 169)(92, 170)(93, 175)(94, 176)(95, 173)(96, 174)(97, 179)(98, 180)(99, 177)(100, 178)(101, 187)(102, 183)(103, 182)(104, 186)(105, 188)(106, 184)(107, 181)(108, 185)(109, 191)(110, 192)(111, 189)(112, 190)(113, 195)(114, 196)(115, 193)(116, 194)(117, 199)(118, 200)(119, 197)(120, 198)

MAP           : A4.83
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 2, 10 ]
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)^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.2^-1 * x.3^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 20, 8)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 203)(42, 208)(43, 227)(44, 207)(45, 212)(46, 231)(47, 226)(48, 223)(49, 206)(50, 216)(51, 235)(52, 228)(53, 211)(54, 220)(55, 239)(56, 232)(57, 215)(58, 219)(59, 240)(60, 236)(61, 204)(62, 201)(63, 225)(64, 209)(65, 202)(66, 221)(67, 222)(68, 230)(69, 213)(70, 205)(71, 224)(72, 234)(73, 217)(74, 210)(75, 229)(76, 238)(77, 218)(78, 214)(79, 233)(80, 237)(81, 170)(82, 174)(83, 189)(84, 165)(85, 178)(86, 197)(87, 193)(88, 184)(89, 162)(90, 177)(91, 198)(92, 181)(93, 161)(94, 173)(95, 194)(96, 182)(97, 164)(98, 169)(99, 190)(100, 185)(101, 175)(102, 171)(103, 196)(104, 179)(105, 166)(106, 188)(107, 192)(108, 200)(109, 180)(110, 167)(111, 183)(112, 199)(113, 176)(114, 163)(115, 187)(116, 195)(117, 172)(118, 168)(119, 186)(120, 191)

MAP           : A4.84
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 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)^10 >
CTG (small)   : <40, 8>
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.2 * x.3^-1)^4, (x.1 * x.2^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 20, 8)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 202)(42, 205)(43, 221)(44, 201)(45, 210)(46, 229)(47, 224)(48, 222)(49, 204)(50, 214)(51, 233)(52, 225)(53, 209)(54, 218)(55, 237)(56, 230)(57, 213)(58, 217)(59, 238)(60, 234)(61, 206)(62, 207)(63, 228)(64, 211)(65, 203)(66, 227)(67, 223)(68, 232)(69, 215)(70, 208)(71, 226)(72, 236)(73, 219)(74, 212)(75, 231)(76, 240)(77, 220)(78, 216)(79, 235)(80, 239)(81, 167)(82, 163)(83, 162)(84, 166)(85, 168)(86, 164)(87, 161)(88, 165)(89, 171)(90, 172)(91, 169)(92, 170)(93, 175)(94, 176)(95, 173)(96, 174)(97, 179)(98, 180)(99, 177)(100, 178)(101, 187)(102, 183)(103, 182)(104, 186)(105, 188)(106, 184)(107, 181)(108, 185)(109, 191)(110, 192)(111, 189)(112, 190)(113, 195)(114, 196)(115, 193)(116, 194)(117, 199)(118, 200)(119, 197)(120, 198)

MAP           : A4.85
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 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)^10 >
CTG (small)   : <40, 8>
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.2 * x.3^-1)^4, (x.1 * x.2^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 20, 8)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 213)(42, 209)(43, 234)(44, 217)(45, 204)(46, 225)(47, 230)(48, 238)(49, 218)(50, 201)(51, 222)(52, 237)(53, 214)(54, 202)(55, 221)(56, 233)(57, 210)(58, 205)(59, 224)(60, 229)(61, 212)(62, 216)(63, 231)(64, 208)(65, 220)(66, 239)(67, 235)(68, 226)(69, 203)(70, 219)(71, 240)(72, 227)(73, 207)(74, 215)(75, 236)(76, 223)(77, 206)(78, 211)(79, 232)(80, 228)(81, 167)(82, 163)(83, 162)(84, 166)(85, 168)(86, 164)(87, 161)(88, 165)(89, 171)(90, 172)(91, 169)(92, 170)(93, 175)(94, 176)(95, 173)(96, 174)(97, 179)(98, 180)(99, 177)(100, 178)(101, 187)(102, 183)(103, 182)(104, 186)(105, 188)(106, 184)(107, 181)(108, 185)(109, 191)(110, 192)(111, 189)(112, 190)(113, 195)(114, 196)(115, 193)(116, 194)(117, 199)(118, 200)(119, 197)(120, 198)

MAP           : A4.86
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 2, 10 ]
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)^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.2^-1 * x.3^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 20, 8)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 203)(42, 208)(43, 227)(44, 207)(45, 212)(46, 231)(47, 226)(48, 223)(49, 206)(50, 216)(51, 235)(52, 228)(53, 211)(54, 220)(55, 239)(56, 232)(57, 215)(58, 219)(59, 240)(60, 236)(61, 204)(62, 201)(63, 225)(64, 209)(65, 202)(66, 221)(67, 222)(68, 230)(69, 213)(70, 205)(71, 224)(72, 234)(73, 217)(74, 210)(75, 229)(76, 238)(77, 218)(78, 214)(79, 233)(80, 237)(81, 162)(82, 165)(83, 181)(84, 161)(85, 170)(86, 189)(87, 184)(88, 182)(89, 164)(90, 174)(91, 193)(92, 185)(93, 169)(94, 178)(95, 197)(96, 190)(97, 173)(98, 177)(99, 198)(100, 194)(101, 166)(102, 167)(103, 188)(104, 171)(105, 163)(106, 187)(107, 183)(108, 192)(109, 175)(110, 168)(111, 186)(112, 196)(113, 179)(114, 172)(115, 191)(116, 200)(117, 180)(118, 176)(119, 195)(120, 199)

MAP           : A4.87
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 2, 10 ]
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)^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.2^-1 * x.3^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 20, 8)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 203)(42, 208)(43, 227)(44, 207)(45, 212)(46, 231)(47, 226)(48, 223)(49, 206)(50, 216)(51, 235)(52, 228)(53, 211)(54, 220)(55, 239)(56, 232)(57, 215)(58, 219)(59, 240)(60, 236)(61, 204)(62, 201)(63, 225)(64, 209)(65, 202)(66, 221)(67, 222)(68, 230)(69, 213)(70, 205)(71, 224)(72, 234)(73, 217)(74, 210)(75, 229)(76, 238)(77, 218)(78, 214)(79, 233)(80, 237)(81, 164)(82, 161)(83, 185)(84, 169)(85, 162)(86, 181)(87, 182)(88, 190)(89, 173)(90, 165)(91, 184)(92, 194)(93, 177)(94, 170)(95, 189)(96, 198)(97, 178)(98, 174)(99, 193)(100, 197)(101, 163)(102, 168)(103, 187)(104, 167)(105, 172)(106, 191)(107, 186)(108, 183)(109, 166)(110, 176)(111, 195)(112, 188)(113, 171)(114, 180)(115, 199)(116, 192)(117, 175)(118, 179)(119, 200)(120, 196)

MAP           : A4.88
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 10, 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)^10 >
CTG (small)   : <40, 8>
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)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 20, 8)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 207)(42, 203)(43, 202)(44, 206)(45, 208)(46, 204)(47, 201)(48, 205)(49, 211)(50, 212)(51, 209)(52, 210)(53, 215)(54, 216)(55, 213)(56, 214)(57, 219)(58, 220)(59, 217)(60, 218)(61, 227)(62, 223)(63, 222)(64, 226)(65, 228)(66, 224)(67, 221)(68, 225)(69, 231)(70, 232)(71, 229)(72, 230)(73, 235)(74, 236)(75, 233)(76, 234)(77, 239)(78, 240)(79, 237)(80, 238)(81, 163)(82, 168)(83, 187)(84, 167)(85, 172)(86, 191)(87, 186)(88, 183)(89, 166)(90, 176)(91, 195)(92, 188)(93, 171)(94, 180)(95, 199)(96, 192)(97, 175)(98, 179)(99, 200)(100, 196)(101, 164)(102, 161)(103, 185)(104, 169)(105, 162)(106, 181)(107, 182)(108, 190)(109, 173)(110, 165)(111, 184)(112, 194)(113, 177)(114, 170)(115, 189)(116, 198)(117, 178)(118, 174)(119, 193)(120, 197)

MAP           : A4.89
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 2, 10 ]
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)^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.2 * x.3^-1)^2, (x.2^-1 * x.3^-1)^2, (x.1 * x.2^-1)^4, (x.3 * x.1^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 20, 8)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 203)(42, 208)(43, 227)(44, 207)(45, 212)(46, 231)(47, 226)(48, 223)(49, 206)(50, 216)(51, 235)(52, 228)(53, 211)(54, 220)(55, 239)(56, 232)(57, 215)(58, 219)(59, 240)(60, 236)(61, 204)(62, 201)(63, 225)(64, 209)(65, 202)(66, 221)(67, 222)(68, 230)(69, 213)(70, 205)(71, 224)(72, 234)(73, 217)(74, 210)(75, 229)(76, 238)(77, 218)(78, 214)(79, 233)(80, 237)(81, 173)(82, 169)(83, 194)(84, 177)(85, 164)(86, 185)(87, 190)(88, 198)(89, 178)(90, 161)(91, 182)(92, 197)(93, 174)(94, 162)(95, 181)(96, 193)(97, 170)(98, 165)(99, 184)(100, 189)(101, 172)(102, 176)(103, 191)(104, 168)(105, 180)(106, 199)(107, 195)(108, 186)(109, 163)(110, 179)(111, 200)(112, 187)(113, 167)(114, 175)(115, 196)(116, 183)(117, 166)(118, 171)(119, 192)(120, 188)

MAP           : A4.90
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 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)^10 >
CTG (small)   : <40, 8>
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.2 * x.3^-1)^4, (x.1 * x.2^-1)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 20, 8)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 210)(42, 214)(43, 229)(44, 205)(45, 218)(46, 237)(47, 233)(48, 224)(49, 202)(50, 217)(51, 238)(52, 221)(53, 201)(54, 213)(55, 234)(56, 222)(57, 204)(58, 209)(59, 230)(60, 225)(61, 215)(62, 211)(63, 236)(64, 219)(65, 206)(66, 228)(67, 232)(68, 240)(69, 220)(70, 207)(71, 223)(72, 239)(73, 216)(74, 203)(75, 227)(76, 235)(77, 212)(78, 208)(79, 226)(80, 231)(81, 167)(82, 163)(83, 162)(84, 166)(85, 168)(86, 164)(87, 161)(88, 165)(89, 171)(90, 172)(91, 169)(92, 170)(93, 175)(94, 176)(95, 173)(96, 174)(97, 179)(98, 180)(99, 177)(100, 178)(101, 187)(102, 183)(103, 182)(104, 186)(105, 188)(106, 184)(107, 181)(108, 185)(109, 191)(110, 192)(111, 189)(112, 190)(113, 195)(114, 196)(115, 193)(116, 194)(117, 199)(118, 200)(119, 197)(120, 198)

MAP           : A4.91
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 10, 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)^10 >
CTG (small)   : <40, 8>
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)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 20, 8)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 207)(42, 203)(43, 202)(44, 206)(45, 208)(46, 204)(47, 201)(48, 205)(49, 211)(50, 212)(51, 209)(52, 210)(53, 215)(54, 216)(55, 213)(56, 214)(57, 219)(58, 220)(59, 217)(60, 218)(61, 227)(62, 223)(63, 222)(64, 226)(65, 228)(66, 224)(67, 221)(68, 225)(69, 231)(70, 232)(71, 229)(72, 230)(73, 235)(74, 236)(75, 233)(76, 234)(77, 239)(78, 240)(79, 237)(80, 238)(81, 182)(82, 185)(83, 161)(84, 181)(85, 190)(86, 169)(87, 164)(88, 162)(89, 184)(90, 194)(91, 173)(92, 165)(93, 189)(94, 198)(95, 177)(96, 170)(97, 193)(98, 197)(99, 178)(100, 174)(101, 186)(102, 187)(103, 168)(104, 191)(105, 183)(106, 167)(107, 163)(108, 172)(109, 195)(110, 188)(111, 166)(112, 176)(113, 199)(114, 192)(115, 171)(116, 180)(117, 200)(118, 196)(119, 175)(120, 179)

MAP           : A4.92
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 10, 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)^10 >
CTG (small)   : <40, 8>
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)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 20, 8)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 207)(42, 203)(43, 202)(44, 206)(45, 208)(46, 204)(47, 201)(48, 205)(49, 211)(50, 212)(51, 209)(52, 210)(53, 215)(54, 216)(55, 213)(56, 214)(57, 219)(58, 220)(59, 217)(60, 218)(61, 227)(62, 223)(63, 222)(64, 226)(65, 228)(66, 224)(67, 221)(68, 225)(69, 231)(70, 232)(71, 229)(72, 230)(73, 235)(74, 236)(75, 233)(76, 234)(77, 239)(78, 240)(79, 237)(80, 238)(81, 190)(82, 194)(83, 169)(84, 185)(85, 198)(86, 177)(87, 173)(88, 164)(89, 182)(90, 197)(91, 178)(92, 161)(93, 181)(94, 193)(95, 174)(96, 162)(97, 184)(98, 189)(99, 170)(100, 165)(101, 195)(102, 191)(103, 176)(104, 199)(105, 186)(106, 168)(107, 172)(108, 180)(109, 200)(110, 187)(111, 163)(112, 179)(113, 196)(114, 183)(115, 167)(116, 175)(117, 192)(118, 188)(119, 166)(120, 171)

MAP           : A4.93
NOTES         : type II, reflexible, isomorphic to DBar({4,10}), isomorphic to A4.16.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 6)(3, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 10, 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)^10 >
CTG (small)   : <40, 8>
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)^10 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 20, 8)
#DARTS        : 240
R = (1, 41, 81)(2, 42, 82)(3, 43, 83)(4, 44, 84)(5, 45, 85)(6, 46, 86)(7, 47, 87)(8, 48, 88)(9, 49, 89)(10, 50, 90)(11, 51, 91)(12, 52, 92)(13, 53, 93)(14, 54, 94)(15, 55, 95)(16, 56, 96)(17, 57, 97)(18, 58, 98)(19, 59, 99)(20, 60, 100)(21, 61, 101)(22, 62, 102)(23, 63, 103)(24, 64, 104)(25, 65, 105)(26, 66, 106)(27, 67, 107)(28, 68, 108)(29, 69, 109)(30, 70, 110)(31, 71, 111)(32, 72, 112)(33, 73, 113)(34, 74, 114)(35, 75, 115)(36, 76, 116)(37, 77, 117)(38, 78, 118)(39, 79, 119)(40, 80, 120)(121, 161, 201)(122, 162, 202)(123, 163, 203)(124, 164, 204)(125, 165, 205)(126, 166, 206)(127, 167, 207)(128, 168, 208)(129, 169, 209)(130, 170, 210)(131, 171, 211)(132, 172, 212)(133, 173, 213)(134, 174, 214)(135, 175, 215)(136, 176, 216)(137, 177, 217)(138, 178, 218)(139, 179, 219)(140, 180, 220)(141, 181, 221)(142, 182, 222)(143, 183, 223)(144, 184, 224)(145, 185, 225)(146, 186, 226)(147, 187, 227)(148, 188, 228)(149, 189, 229)(150, 190, 230)(151, 191, 231)(152, 192, 232)(153, 193, 233)(154, 194, 234)(155, 195, 235)(156, 196, 236)(157, 197, 237)(158, 198, 238)(159, 199, 239)(160, 200, 240)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 207)(42, 203)(43, 202)(44, 206)(45, 208)(46, 204)(47, 201)(48, 205)(49, 211)(50, 212)(51, 209)(52, 210)(53, 215)(54, 216)(55, 213)(56, 214)(57, 219)(58, 220)(59, 217)(60, 218)(61, 227)(62, 223)(63, 222)(64, 226)(65, 228)(66, 224)(67, 221)(68, 225)(69, 231)(70, 232)(71, 229)(72, 230)(73, 235)(74, 236)(75, 233)(76, 234)(77, 239)(78, 240)(79, 237)(80, 238)(81, 172)(82, 176)(83, 191)(84, 168)(85, 180)(86, 199)(87, 195)(88, 186)(89, 163)(90, 179)(91, 200)(92, 187)(93, 167)(94, 175)(95, 196)(96, 183)(97, 166)(98, 171)(99, 192)(100, 188)(101, 173)(102, 169)(103, 194)(104, 177)(105, 164)(106, 185)(107, 190)(108, 198)(109, 178)(110, 161)(111, 182)(112, 197)(113, 174)(114, 162)(115, 181)(116, 193)(117, 170)(118, 165)(119, 184)(120, 189)

MAP           : A4.94
NOTES         : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A4.1.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^3, (x.3 * x.2^-1)^2, (x.1 * x.2^-1)^3, (x.3 * x.2 * x.3)^3, x.3^4 * x.2 * x.3^-4 * x.2^-1, (x.3 * x.1^-1)^12 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 24, 6)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 366)(74, 371)(75, 361)(76, 369)(77, 364)(78, 363)(79, 396)(80, 362)(81, 365)(82, 403)(83, 368)(84, 370)(85, 378)(86, 383)(87, 373)(88, 381)(89, 376)(90, 375)(91, 420)(92, 374)(93, 377)(94, 391)(95, 380)(96, 382)(97, 414)(98, 419)(99, 409)(100, 417)(101, 412)(102, 411)(103, 384)(104, 410)(105, 413)(106, 427)(107, 416)(108, 418)(109, 390)(110, 395)(111, 385)(112, 393)(113, 388)(114, 387)(115, 372)(116, 386)(117, 389)(118, 379)(119, 392)(120, 394)(121, 402)(122, 407)(123, 397)(124, 405)(125, 400)(126, 399)(127, 432)(128, 398)(129, 401)(130, 367)(131, 404)(132, 406)(133, 426)(134, 431)(135, 421)(136, 429)(137, 424)(138, 423)(139, 408)(140, 422)(141, 425)(142, 415)(143, 428)(144, 430)(145, 290)(146, 295)(147, 292)(148, 326)(149, 289)(150, 331)(151, 304)(152, 294)(153, 355)(154, 291)(155, 340)(156, 338)(157, 309)(158, 303)(159, 312)(160, 306)(161, 324)(162, 311)(163, 308)(164, 321)(165, 347)(166, 323)(167, 348)(168, 345)(169, 346)(170, 305)(171, 344)(172, 310)(173, 296)(174, 341)(175, 301)(176, 298)(177, 339)(178, 293)(179, 337)(180, 342)(181, 314)(182, 319)(183, 316)(184, 302)(185, 313)(186, 307)(187, 328)(188, 318)(189, 343)(190, 315)(191, 352)(192, 350)(193, 333)(194, 327)(195, 336)(196, 330)(197, 300)(198, 335)(199, 332)(200, 297)(201, 359)(202, 299)(203, 360)(204, 357)(205, 358)(206, 329)(207, 356)(208, 334)(209, 320)(210, 353)(211, 325)(212, 322)(213, 351)(214, 317)(215, 349)(216, 354)

MAP           : A4.95
NOTES         : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A4.1.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^3, (x.3 * x.2^-1)^2, (x.1 * x.2^-1)^3, (x.3 * x.2 * x.3)^3, x.3^4 * x.2 * x.3^-4 * x.2^-1, (x.3 * x.1^-1)^12 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 24, 6)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 363)(74, 368)(75, 366)(76, 365)(77, 369)(78, 361)(79, 418)(80, 371)(81, 364)(82, 372)(83, 362)(84, 403)(85, 375)(86, 380)(87, 378)(88, 377)(89, 381)(90, 373)(91, 406)(92, 383)(93, 376)(94, 384)(95, 374)(96, 391)(97, 399)(98, 404)(99, 402)(100, 401)(101, 405)(102, 397)(103, 382)(104, 407)(105, 400)(106, 408)(107, 398)(108, 367)(109, 411)(110, 416)(111, 414)(112, 413)(113, 417)(114, 409)(115, 370)(116, 419)(117, 412)(118, 420)(119, 410)(120, 427)(121, 387)(122, 392)(123, 390)(124, 389)(125, 393)(126, 385)(127, 430)(128, 395)(129, 388)(130, 396)(131, 386)(132, 379)(133, 423)(134, 428)(135, 426)(136, 425)(137, 429)(138, 421)(139, 394)(140, 431)(141, 424)(142, 432)(143, 422)(144, 415)(145, 331)(146, 340)(147, 290)(148, 355)(149, 326)(150, 292)(151, 342)(152, 295)(153, 289)(154, 328)(155, 294)(156, 291)(157, 311)(158, 348)(159, 309)(160, 347)(161, 306)(162, 312)(163, 357)(164, 303)(165, 324)(166, 301)(167, 321)(168, 323)(169, 335)(170, 360)(171, 333)(172, 359)(173, 330)(174, 336)(175, 345)(176, 327)(177, 300)(178, 325)(179, 297)(180, 299)(181, 341)(182, 337)(183, 346)(184, 339)(185, 310)(186, 344)(187, 338)(188, 305)(189, 296)(190, 308)(191, 298)(192, 293)(193, 307)(194, 352)(195, 314)(196, 343)(197, 302)(198, 316)(199, 354)(200, 319)(201, 313)(202, 304)(203, 318)(204, 315)(205, 353)(206, 349)(207, 358)(208, 351)(209, 334)(210, 356)(211, 350)(212, 329)(213, 320)(214, 332)(215, 322)(216, 317)

MAP           : A4.96
NOTES         : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A4.1.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.2 * x.3^-1)^3, x.2^-2 * x.3 * x.2^4 * 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.1 * x.2^-1)^12 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 24, 6)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 362)(74, 367)(75, 364)(76, 398)(77, 361)(78, 403)(79, 376)(80, 366)(81, 427)(82, 363)(83, 412)(84, 410)(85, 381)(86, 375)(87, 384)(88, 378)(89, 396)(90, 383)(91, 380)(92, 393)(93, 419)(94, 395)(95, 420)(96, 417)(97, 418)(98, 377)(99, 416)(100, 382)(101, 368)(102, 413)(103, 373)(104, 370)(105, 411)(106, 365)(107, 409)(108, 414)(109, 386)(110, 391)(111, 388)(112, 374)(113, 385)(114, 379)(115, 400)(116, 390)(117, 415)(118, 387)(119, 424)(120, 422)(121, 405)(122, 399)(123, 408)(124, 402)(125, 372)(126, 407)(127, 404)(128, 369)(129, 431)(130, 371)(131, 432)(132, 429)(133, 430)(134, 401)(135, 428)(136, 406)(137, 392)(138, 425)(139, 397)(140, 394)(141, 423)(142, 389)(143, 421)(144, 426)(145, 292)(146, 294)(147, 331)(148, 289)(149, 355)(150, 290)(151, 299)(152, 340)(153, 326)(154, 338)(155, 295)(156, 328)(157, 312)(158, 321)(159, 311)(160, 324)(161, 347)(162, 309)(163, 315)(164, 348)(165, 306)(166, 345)(167, 303)(168, 301)(169, 316)(170, 318)(171, 307)(172, 313)(173, 343)(174, 314)(175, 323)(176, 352)(177, 302)(178, 350)(179, 319)(180, 304)(181, 336)(182, 297)(183, 335)(184, 300)(185, 359)(186, 333)(187, 291)(188, 360)(189, 330)(190, 357)(191, 327)(192, 325)(193, 344)(194, 298)(195, 341)(196, 296)(197, 339)(198, 346)(199, 317)(200, 337)(201, 310)(202, 342)(203, 305)(204, 308)(205, 356)(206, 322)(207, 353)(208, 320)(209, 351)(210, 358)(211, 293)(212, 349)(213, 334)(214, 354)(215, 329)(216, 332)

MAP           : A4.97
NOTES         : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A4.1.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^3, (x.1 * x.2^-1)^2, x.2^2 * x.3 * x.2^-2 * x.3^-1, (x.3 * x.1^-1)^3, (x.3^-1, x.2^-1)^3, x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, (x.2 * x.3^-1)^12 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 24, 6)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 364)(74, 366)(75, 403)(76, 361)(77, 427)(78, 362)(79, 371)(80, 412)(81, 398)(82, 410)(83, 367)(84, 400)(85, 384)(86, 393)(87, 383)(88, 396)(89, 419)(90, 381)(91, 387)(92, 420)(93, 378)(94, 417)(95, 375)(96, 373)(97, 388)(98, 390)(99, 379)(100, 385)(101, 415)(102, 386)(103, 395)(104, 424)(105, 374)(106, 422)(107, 391)(108, 376)(109, 408)(110, 369)(111, 407)(112, 372)(113, 431)(114, 405)(115, 363)(116, 432)(117, 402)(118, 429)(119, 399)(120, 397)(121, 416)(122, 370)(123, 413)(124, 368)(125, 411)(126, 418)(127, 389)(128, 409)(129, 382)(130, 414)(131, 377)(132, 380)(133, 428)(134, 394)(135, 425)(136, 392)(137, 423)(138, 430)(139, 365)(140, 421)(141, 406)(142, 426)(143, 401)(144, 404)(145, 291)(146, 296)(147, 294)(148, 293)(149, 297)(150, 289)(151, 346)(152, 299)(153, 292)(154, 300)(155, 290)(156, 331)(157, 303)(158, 308)(159, 306)(160, 305)(161, 309)(162, 301)(163, 334)(164, 311)(165, 304)(166, 312)(167, 302)(168, 319)(169, 327)(170, 332)(171, 330)(172, 329)(173, 333)(174, 325)(175, 310)(176, 335)(177, 328)(178, 336)(179, 326)(180, 295)(181, 339)(182, 344)(183, 342)(184, 341)(185, 345)(186, 337)(187, 298)(188, 347)(189, 340)(190, 348)(191, 338)(192, 355)(193, 315)(194, 320)(195, 318)(196, 317)(197, 321)(198, 313)(199, 358)(200, 323)(201, 316)(202, 324)(203, 314)(204, 307)(205, 351)(206, 356)(207, 354)(208, 353)(209, 357)(210, 349)(211, 322)(212, 359)(213, 352)(214, 360)(215, 350)(216, 343)

MAP           : A4.98
NOTES         : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A4.1.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^2, (x.2 * x.3^-1)^3, x.2^-2 * x.3 * x.2^4 * 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.1 * x.2^-1)^12 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 24, 6)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 383)(74, 420)(75, 381)(76, 419)(77, 378)(78, 384)(79, 429)(80, 375)(81, 396)(82, 373)(83, 393)(84, 395)(85, 425)(86, 421)(87, 430)(88, 423)(89, 406)(90, 428)(91, 422)(92, 401)(93, 392)(94, 404)(95, 394)(96, 389)(97, 379)(98, 424)(99, 386)(100, 415)(101, 374)(102, 388)(103, 426)(104, 391)(105, 385)(106, 376)(107, 390)(108, 387)(109, 407)(110, 432)(111, 405)(112, 431)(113, 402)(114, 408)(115, 417)(116, 399)(117, 372)(118, 397)(119, 369)(120, 371)(121, 413)(122, 409)(123, 418)(124, 411)(125, 382)(126, 416)(127, 410)(128, 377)(129, 368)(130, 380)(131, 370)(132, 365)(133, 403)(134, 412)(135, 362)(136, 427)(137, 398)(138, 364)(139, 414)(140, 367)(141, 361)(142, 400)(143, 366)(144, 363)(145, 292)(146, 294)(147, 331)(148, 289)(149, 355)(150, 290)(151, 299)(152, 340)(153, 326)(154, 338)(155, 295)(156, 328)(157, 312)(158, 321)(159, 311)(160, 324)(161, 347)(162, 309)(163, 315)(164, 348)(165, 306)(166, 345)(167, 303)(168, 301)(169, 316)(170, 318)(171, 307)(172, 313)(173, 343)(174, 314)(175, 323)(176, 352)(177, 302)(178, 350)(179, 319)(180, 304)(181, 336)(182, 297)(183, 335)(184, 300)(185, 359)(186, 333)(187, 291)(188, 360)(189, 330)(190, 357)(191, 327)(192, 325)(193, 344)(194, 298)(195, 341)(196, 296)(197, 339)(198, 346)(199, 317)(200, 337)(201, 310)(202, 342)(203, 305)(204, 308)(205, 356)(206, 322)(207, 353)(208, 320)(209, 351)(210, 358)(211, 293)(212, 349)(213, 334)(214, 354)(215, 329)(216, 332)

MAP           : A4.99
NOTES         : type II, reflexible, isomorphic to DBar({3,12}), isomorphic to A4.1.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^3, (x.1 * x.2^-1)^2, x.2^2 * x.3 * x.2^-2 * x.3^-1, (x.3 * x.1^-1)^3, (x.3^-1, x.2^-1)^3, x.3 * x.2 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 * x.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1, (x.2 * x.3^-1)^12 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (4, 24, 6)
#DARTS        : 432
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)(217, 289, 361)(218, 290, 362)(219, 291, 363)(220, 292, 364)(221, 293, 365)(222, 294, 366)(223, 295, 367)(224, 296, 368)(225, 297, 369)(226, 298, 370)(227, 299, 371)(228, 300, 372)(229, 301, 373)(230, 302, 374)(231, 303, 375)(232, 304, 376)(233, 305, 377)(234, 306, 378)(235, 307, 379)(236, 308, 380)(237, 309, 381)(238, 310, 382)(239, 311, 383)(240, 312, 384)(241, 313, 385)(242, 314, 386)(243, 315, 387)(244, 316, 388)(245, 317, 389)(246, 318, 390)(247, 319, 391)(248, 320, 392)(249, 321, 393)(250, 322, 394)(251, 323, 395)(252, 324, 396)(253, 325, 397)(254, 326, 398)(255, 327, 399)(256, 328, 400)(257, 329, 401)(258, 330, 402)(259, 331, 403)(260, 332, 404)(261, 333, 405)(262, 334, 406)(263, 335, 407)(264, 336, 408)(265, 337, 409)(266, 338, 410)(267, 339, 411)(268, 340, 412)(269, 341, 413)(270, 342, 414)(271, 343, 415)(272, 344, 416)(273, 345, 417)(274, 346, 418)(275, 347, 419)(276, 348, 420)(277, 349, 421)(278, 350, 422)(279, 351, 423)(280, 352, 424)(281, 353, 425)(282, 354, 426)(283, 355, 427)(284, 356, 428)(285, 357, 429)(286, 358, 430)(287, 359, 431)(288, 360, 432)
L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 364)(74, 366)(75, 403)(76, 361)(77, 427)(78, 362)(79, 371)(80, 412)(81, 398)(82, 410)(83, 367)(84, 400)(85, 384)(86, 393)(87, 383)(88, 396)(89, 419)(90, 381)(91, 387)(92, 420)(93, 378)(94, 417)(95, 375)(96, 373)(97, 388)(98, 390)(99, 379)(100, 385)(101, 415)(102, 386)(103, 395)(104, 424)(105, 374)(106, 422)(107, 391)(108, 376)(109, 408)(110, 369)(111, 407)(112, 372)(113, 431)(114, 405)(115, 363)(116, 432)(117, 402)(118, 429)(119, 399)(120, 397)(121, 416)(122, 370)(123, 413)(124, 368)(125, 411)(126, 418)(127, 389)(128, 409)(129, 382)(130, 414)(131, 377)(132, 380)(133, 428)(134, 394)(135, 425)(136, 392)(137, 423)(138, 430)(139, 365)(140, 421)(141, 406)(142, 426)(143, 401)(144, 404)(145, 294)(146, 299)(147, 289)(148, 297)(149, 292)(150, 291)(151, 324)(152, 290)(153, 293)(154, 331)(155, 296)(156, 298)(157, 306)(158, 311)(159, 301)(160, 309)(161, 304)(162, 303)(163, 348)(164, 302)(165, 305)(166, 319)(167, 308)(168, 310)(169, 342)(170, 347)(171, 337)(172, 345)(173, 340)(174, 339)(175, 312)(176, 338)(177, 341)(178, 355)(179, 344)(180, 346)(181, 318)(182, 323)(183, 313)(184, 321)(185, 316)(186, 315)(187, 300)(188, 314)(189, 317)(190, 307)(191, 320)(192, 322)(193, 330)(194, 335)(195, 325)(196, 333)(197, 328)(198, 327)(199, 360)(200, 326)(201, 329)(202, 295)(203, 332)(204, 334)(205, 354)(206, 359)(207, 349)(208, 357)(209, 352)(210, 351)(211, 336)(212, 350)(213, 353)(214, 343)(215, 356)(216, 358)

MAP           : A4.100
NOTES         : type I, reflexible, isomorphic to TDual({4,5}), representative.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, u.2^5, u.3^5, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^2 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.2^-1 * x.3^-1)^2, x.2^5, x.3^5, (x.3 * x.2^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^2, (x.3^-2 * x.2^2)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (5, 8, 8)
#DARTS        : 360
R = (1, 61, 121)(2, 62, 122)(3, 63, 123)(4, 64, 124)(5, 65, 125)(6, 66, 126)(7, 67, 127)(8, 68, 128)(9, 69, 129)(10, 70, 130)(11, 71, 131)(12, 72, 132)(13, 73, 133)(14, 74, 134)(15, 75, 135)(16, 76, 136)(17, 77, 137)(18, 78, 138)(19, 79, 139)(20, 80, 140)(21, 81, 141)(22, 82, 142)(23, 83, 143)(24, 84, 144)(25, 85, 145)(26, 86, 146)(27, 87, 147)(28, 88, 148)(29, 89, 149)(30, 90, 150)(31, 91, 151)(32, 92, 152)(33, 93, 153)(34, 94, 154)(35, 95, 155)(36, 96, 156)(37, 97, 157)(38, 98, 158)(39, 99, 159)(40, 100, 160)(41, 101, 161)(42, 102, 162)(43, 103, 163)(44, 104, 164)(45, 105, 165)(46, 106, 166)(47, 107, 167)(48, 108, 168)(49, 109, 169)(50, 110, 170)(51, 111, 171)(52, 112, 172)(53, 113, 173)(54, 114, 174)(55, 115, 175)(56, 116, 176)(57, 117, 177)(58, 118, 178)(59, 119, 179)(60, 120, 180)(181, 241, 301)(182, 242, 302)(183, 243, 303)(184, 244, 304)(185, 245, 305)(186, 246, 306)(187, 247, 307)(188, 248, 308)(189, 249, 309)(190, 250, 310)(191, 251, 311)(192, 252, 312)(193, 253, 313)(194, 254, 314)(195, 255, 315)(196, 256, 316)(197, 257, 317)(198, 258, 318)(199, 259, 319)(200, 260, 320)(201, 261, 321)(202, 262, 322)(203, 263, 323)(204, 264, 324)(205, 265, 325)(206, 266, 326)(207, 267, 327)(208, 268, 328)(209, 269, 329)(210, 270, 330)(211, 271, 331)(212, 272, 332)(213, 273, 333)(214, 274, 334)(215, 275, 335)(216, 276, 336)(217, 277, 337)(218, 278, 338)(219, 279, 339)(220, 280, 340)(221, 281, 341)(222, 282, 342)(223, 283, 343)(224, 284, 344)(225, 285, 345)(226, 286, 346)(227, 287, 347)(228, 288, 348)(229, 289, 349)(230, 290, 350)(231, 291, 351)(232, 292, 352)(233, 293, 353)(234, 294, 354)(235, 295, 355)(236, 296, 356)(237, 297, 357)(238, 298, 358)(239, 299, 359)(240, 300, 360)
L = (1, 181)(2, 182)(3, 183)(4, 184)(5, 185)(6, 186)(7, 187)(8, 188)(9, 189)(10, 190)(11, 191)(12, 192)(13, 193)(14, 194)(15, 195)(16, 196)(17, 197)(18, 198)(19, 199)(20, 200)(21, 201)(22, 202)(23, 203)(24, 204)(25, 205)(26, 206)(27, 207)(28, 208)(29, 209)(30, 210)(31, 211)(32, 212)(33, 213)(34, 214)(35, 215)(36, 216)(37, 217)(38, 218)(39, 219)(40, 220)(41, 221)(42, 222)(43, 223)(44, 224)(45, 225)(46, 226)(47, 227)(48, 228)(49, 229)(50, 230)(51, 231)(52, 232)(53, 233)(54, 234)(55, 235)(56, 236)(57, 237)(58, 238)(59, 239)(60, 240)(61, 125)(62, 138)(63, 161)(64, 122)(65, 124)(66, 154)(67, 134)(68, 137)(69, 139)(70, 133)(71, 150)(72, 149)(73, 147)(74, 123)(75, 160)(76, 159)(77, 171)(78, 121)(79, 148)(80, 145)(81, 132)(82, 174)(83, 146)(84, 176)(85, 162)(86, 172)(87, 158)(88, 173)(89, 169)(90, 135)(91, 131)(92, 156)(93, 143)(94, 128)(95, 130)(96, 136)(97, 152)(98, 155)(99, 157)(100, 151)(101, 168)(102, 167)(103, 165)(104, 129)(105, 142)(106, 141)(107, 177)(108, 127)(109, 166)(110, 163)(111, 126)(112, 180)(113, 164)(114, 170)(115, 144)(116, 178)(117, 140)(118, 179)(119, 175)(120, 153)(241, 309)(242, 357)(243, 346)(244, 345)(245, 333)(246, 355)(247, 310)(248, 307)(249, 330)(250, 336)(251, 308)(252, 302)(253, 348)(254, 334)(255, 344)(256, 335)(257, 331)(258, 321)(259, 318)(260, 304)(261, 314)(262, 305)(263, 301)(264, 351)(265, 340)(266, 337)(267, 360)(268, 306)(269, 338)(270, 332)(271, 320)(272, 323)(273, 313)(274, 319)(275, 312)(276, 311)(277, 359)(278, 324)(279, 347)(280, 356)(281, 358)(282, 352)(283, 329)(284, 354)(285, 317)(286, 326)(287, 328)(288, 322)(289, 350)(290, 353)(291, 343)(292, 349)(293, 342)(294, 341)(295, 339)(296, 327)(297, 316)(298, 315)(299, 303)(300, 325)

MAP           : A4.101
NOTES         : type I, reflexible, isomorphic to TDual({4,5}), isomorphic to A4.100.
QUOTIENT      : R = (1, 2, 3)(4, 5, 6) L = (1, 4)(2, 3)(5, 6)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, u.2^5, u.3^5, (u.1 * u.2^-1 * u.1^-1 * u.3^-1)^2 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.2^-1 * x.3^-1)^2, x.2^5, x.3^5, (x.3 * x.2^-1)^3, (x.1 * x.2^-1 * x.1^-1 * x.3^-1)^2, (x.3^-2 * x.2^2)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (5, 8, 8)
#DARTS        : 360
R = (1, 61, 121)(2, 62, 122)(3, 63, 123)(4, 64, 124)(5, 65, 125)(6, 66, 126)(7, 67, 127)(8, 68, 128)(9, 69, 129)(10, 70, 130)(11, 71, 131)(12, 72, 132)(13, 73, 133)(14, 74, 134)(15, 75, 135)(16, 76, 136)(17, 77, 137)(18, 78, 138)(19, 79, 139)(20, 80, 140)(21, 81, 141)(22, 82, 142)(23, 83, 143)(24, 84, 144)(25, 85, 145)(26, 86, 146)(27, 87, 147)(28, 88, 148)(29, 89, 149)(30, 90, 150)(31, 91, 151)(32, 92, 152)(33, 93, 153)(34, 94, 154)(35, 95, 155)(36, 96, 156)(37, 97, 157)(38, 98, 158)(39, 99, 159)(40, 100, 160)(41, 101, 161)(42, 102, 162)(43, 103, 163)(44, 104, 164)(45, 105, 165)(46, 106, 166)(47, 107, 167)(48, 108, 168)(49, 109, 169)(50, 110, 170)(51, 111, 171)(52, 112, 172)(53, 113, 173)(54, 114, 174)(55, 115, 175)(56, 116, 176)(57, 117, 177)(58, 118, 178)(59, 119, 179)(60, 120, 180)(181, 241, 301)(182, 242, 302)(183, 243, 303)(184, 244, 304)(185, 245, 305)(186, 246, 306)(187, 247, 307)(188, 248, 308)(189, 249, 309)(190, 250, 310)(191, 251, 311)(192, 252, 312)(193, 253, 313)(194, 254, 314)(195, 255, 315)(196, 256, 316)(197, 257, 317)(198, 258, 318)(199, 259, 319)(200, 260, 320)(201, 261, 321)(202, 262, 322)(203, 263, 323)(204, 264, 324)(205, 265, 325)(206, 266, 326)(207, 267, 327)(208, 268, 328)(209, 269, 329)(210, 270, 330)(211, 271, 331)(212, 272, 332)(213, 273, 333)(214, 274, 334)(215, 275, 335)(216, 276, 336)(217, 277, 337)(218, 278, 338)(219, 279, 339)(220, 280, 340)(221, 281, 341)(222, 282, 342)(223, 283, 343)(224, 284, 344)(225, 285, 345)(226, 286, 346)(227, 287, 347)(228, 288, 348)(229, 289, 349)(230, 290, 350)(231, 291, 351)(232, 292, 352)(233, 293, 353)(234, 294, 354)(235, 295, 355)(236, 296, 356)(237, 297, 357)(238, 298, 358)(239, 299, 359)(240, 300, 360)
L = (1, 181)(2, 182)(3, 183)(4, 184)(5, 185)(6, 186)(7, 187)(8, 188)(9, 189)(10, 190)(11, 191)(12, 192)(13, 193)(14, 194)(15, 195)(16, 196)(17, 197)(18, 198)(19, 199)(20, 200)(21, 201)(22, 202)(23, 203)(24, 204)(25, 205)(26, 206)(27, 207)(28, 208)(29, 209)(30, 210)(31, 211)(32, 212)(33, 213)(34, 214)(35, 215)(36, 216)(37, 217)(38, 218)(39, 219)(40, 220)(41, 221)(42, 222)(43, 223)(44, 224)(45, 225)(46, 226)(47, 227)(48, 228)(49, 229)(50, 230)(51, 231)(52, 232)(53, 233)(54, 234)(55, 235)(56, 236)(57, 237)(58, 238)(59, 239)(60, 240)(61, 122)(62, 125)(63, 127)(64, 121)(65, 138)(66, 137)(67, 161)(68, 126)(69, 173)(70, 158)(71, 160)(72, 166)(73, 155)(74, 168)(75, 131)(76, 152)(77, 154)(78, 124)(79, 164)(80, 167)(81, 169)(82, 163)(83, 180)(84, 179)(85, 177)(86, 153)(87, 130)(88, 129)(89, 141)(90, 151)(91, 135)(92, 159)(93, 172)(94, 171)(95, 147)(96, 157)(97, 136)(98, 133)(99, 156)(100, 150)(101, 134)(102, 140)(103, 174)(104, 148)(105, 170)(106, 149)(107, 145)(108, 123)(109, 132)(110, 142)(111, 128)(112, 143)(113, 139)(114, 165)(115, 178)(116, 175)(117, 162)(118, 144)(119, 176)(120, 146)(241, 330)(242, 316)(243, 326)(244, 317)(245, 313)(246, 339)(247, 336)(248, 310)(249, 332)(250, 311)(251, 307)(252, 357)(253, 322)(254, 319)(255, 354)(256, 312)(257, 320)(258, 314)(259, 321)(260, 345)(261, 334)(262, 333)(263, 309)(264, 343)(265, 356)(266, 359)(267, 325)(268, 355)(269, 324)(270, 323)(271, 304)(272, 301)(273, 348)(274, 318)(275, 302)(276, 308)(277, 303)(278, 351)(279, 328)(280, 327)(281, 315)(282, 349)(283, 338)(284, 341)(285, 331)(286, 337)(287, 306)(288, 305)(289, 353)(290, 342)(291, 329)(292, 350)(293, 352)(294, 358)(295, 347)(296, 360)(297, 335)(298, 344)(299, 346)(300, 340)

MAP           : A4.102
NOTES         : type I, reflexible, isomorphic to TDual({4,5}), isomorphic to A4.100.
QUOTIENT      : R = (1, 2, 3) L = (2, 3)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 4 ]
UNIGROUP      : < u.1, u.2 | u.1^2, u.2^5, (u.1 * u.2^-1)^4 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2 | x.1^2, x.2^5, (x.1 * x.2^-1)^4, (x.2^-1 * x.1 * x.2^2 * x.1 * x.2^-1)^2, (x.2^-1 * x.1 * x.2 * x.1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (5, 8, 8)
#DARTS        : 360
R = (1, 121, 241)(2, 122, 242)(3, 123, 243)(4, 124, 244)(5, 125, 245)(6, 126, 246)(7, 127, 247)(8, 128, 248)(9, 129, 249)(10, 130, 250)(11, 131, 251)(12, 132, 252)(13, 133, 253)(14, 134, 254)(15, 135, 255)(16, 136, 256)(17, 137, 257)(18, 138, 258)(19, 139, 259)(20, 140, 260)(21, 141, 261)(22, 142, 262)(23, 143, 263)(24, 144, 264)(25, 145, 265)(26, 146, 266)(27, 147, 267)(28, 148, 268)(29, 149, 269)(30, 150, 270)(31, 151, 271)(32, 152, 272)(33, 153, 273)(34, 154, 274)(35, 155, 275)(36, 156, 276)(37, 157, 277)(38, 158, 278)(39, 159, 279)(40, 160, 280)(41, 161, 281)(42, 162, 282)(43, 163, 283)(44, 164, 284)(45, 165, 285)(46, 166, 286)(47, 167, 287)(48, 168, 288)(49, 169, 289)(50, 170, 290)(51, 171, 291)(52, 172, 292)(53, 173, 293)(54, 174, 294)(55, 175, 295)(56, 176, 296)(57, 177, 297)(58, 178, 298)(59, 179, 299)(60, 180, 300)(61, 181, 301)(62, 182, 302)(63, 183, 303)(64, 184, 304)(65, 185, 305)(66, 186, 306)(67, 187, 307)(68, 188, 308)(69, 189, 309)(70, 190, 310)(71, 191, 311)(72, 192, 312)(73, 193, 313)(74, 194, 314)(75, 195, 315)(76, 196, 316)(77, 197, 317)(78, 198, 318)(79, 199, 319)(80, 200, 320)(81, 201, 321)(82, 202, 322)(83, 203, 323)(84, 204, 324)(85, 205, 325)(86, 206, 326)(87, 207, 327)(88, 208, 328)(89, 209, 329)(90, 210, 330)(91, 211, 331)(92, 212, 332)(93, 213, 333)(94, 214, 334)(95, 215, 335)(96, 216, 336)(97, 217, 337)(98, 218, 338)(99, 219, 339)(100, 220, 340)(101, 221, 341)(102, 222, 342)(103, 223, 343)(104, 224, 344)(105, 225, 345)(106, 226, 346)(107, 227, 347)(108, 228, 348)(109, 229, 349)(110, 230, 350)(111, 231, 351)(112, 232, 352)(113, 233, 353)(114, 234, 354)(115, 235, 355)(116, 236, 356)(117, 237, 357)(118, 238, 358)(119, 239, 359)(120, 240, 360)
L = (1, 2)(3, 7)(4, 14)(5, 13)(6, 8)(9, 16)(10, 102)(11, 99)(12, 17)(15, 119)(18, 118)(19, 54)(20, 51)(21, 90)(22, 49)(23, 50)(24, 87)(25, 40)(26, 41)(27, 38)(28, 77)(29, 76)(30, 37)(31, 111)(32, 114)(33, 100)(34, 66)(35, 63)(36, 101)(39, 42)(43, 110)(44, 109)(45, 115)(46, 98)(47, 97)(48, 116)(52, 53)(55, 113)(56, 112)(57, 83)(58, 117)(59, 120)(60, 82)(61, 71)(62, 70)(64, 81)(65, 84)(67, 68)(69, 79)(72, 80)(73, 106)(74, 107)(75, 104)(78, 103)(85, 96)(86, 93)(88, 91)(89, 92)(94, 95)(105, 108)(121, 244)(122, 245)(123, 242)(124, 281)(125, 280)(126, 241)(127, 359)(128, 358)(129, 317)(130, 345)(131, 348)(132, 316)(133, 252)(134, 249)(135, 276)(136, 247)(137, 248)(138, 273)(139, 356)(140, 355)(141, 343)(142, 350)(143, 349)(144, 344)(145, 357)(146, 360)(147, 352)(148, 324)(149, 321)(150, 353)(151, 326)(152, 325)(153, 313)(154, 320)(155, 319)(156, 314)(157, 327)(158, 330)(159, 322)(160, 294)(161, 291)(162, 323)(163, 329)(164, 328)(165, 287)(166, 315)(167, 318)(168, 286)(169, 342)(170, 339)(171, 246)(172, 337)(173, 338)(174, 243)(175, 334)(176, 335)(177, 332)(178, 251)(179, 250)(180, 331)(181, 297)(182, 300)(183, 292)(184, 264)(185, 261)(186, 293)(187, 312)(188, 309)(189, 336)(190, 307)(191, 308)(192, 333)(193, 296)(194, 295)(195, 283)(196, 290)(197, 289)(198, 284)(199, 304)(200, 305)(201, 302)(202, 341)(203, 340)(204, 301)(205, 299)(206, 298)(207, 257)(208, 285)(209, 288)(210, 256)(211, 269)(212, 268)(213, 347)(214, 255)(215, 258)(216, 346)(217, 266)(218, 265)(219, 253)(220, 260)(221, 259)(222, 254)(223, 274)(224, 275)(225, 272)(226, 311)(227, 310)(228, 271)(229, 267)(230, 270)(231, 262)(232, 354)(233, 351)(234, 263)(235, 282)(236, 279)(237, 306)(238, 277)(239, 278)(240, 303)

MAP           : A4.103
NOTES         : type I, reflexible, isomorphic to Trun({5,5}), representative.
QUOTIENT      : R = (1, 2, 3) L = (2, 3)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 5 ]
UNIGROUP      : < u.1, u.2 | u.1^2, u.2^5, (u.1 * u.2^-1)^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2 | x.1^2, x.2^5, (x.1 * x.2^-2)^3, (x.2 * x.1 * x.2)^3, (x.1 * x.2^-1)^5, (x.2^2 * x.1 * x.2^-1 * x.1)^2, (x.2 * x.1 * x.2^-1 * x.1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (5, 10, 10)
#DARTS        : 180
R = (1, 61, 121)(2, 62, 122)(3, 63, 123)(4, 64, 124)(5, 65, 125)(6, 66, 126)(7, 67, 127)(8, 68, 128)(9, 69, 129)(10, 70, 130)(11, 71, 131)(12, 72, 132)(13, 73, 133)(14, 74, 134)(15, 75, 135)(16, 76, 136)(17, 77, 137)(18, 78, 138)(19, 79, 139)(20, 80, 140)(21, 81, 141)(22, 82, 142)(23, 83, 143)(24, 84, 144)(25, 85, 145)(26, 86, 146)(27, 87, 147)(28, 88, 148)(29, 89, 149)(30, 90, 150)(31, 91, 151)(32, 92, 152)(33, 93, 153)(34, 94, 154)(35, 95, 155)(36, 96, 156)(37, 97, 157)(38, 98, 158)(39, 99, 159)(40, 100, 160)(41, 101, 161)(42, 102, 162)(43, 103, 163)(44, 104, 164)(45, 105, 165)(46, 106, 166)(47, 107, 167)(48, 108, 168)(49, 109, 169)(50, 110, 170)(51, 111, 171)(52, 112, 172)(53, 113, 173)(54, 114, 174)(55, 115, 175)(56, 116, 176)(57, 117, 177)(58, 118, 178)(59, 119, 179)(60, 120, 180)
L = (1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)(19, 37)(20, 38)(21, 39)(22, 40)(23, 41)(24, 42)(25, 43)(26, 44)(27, 45)(28, 46)(29, 47)(30, 48)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(61, 161)(62, 126)(63, 173)(64, 158)(65, 160)(66, 166)(67, 122)(68, 125)(69, 127)(70, 121)(71, 138)(72, 137)(73, 135)(74, 159)(75, 172)(76, 171)(77, 147)(78, 157)(79, 136)(80, 133)(81, 156)(82, 150)(83, 134)(84, 140)(85, 174)(86, 148)(87, 170)(88, 149)(89, 145)(90, 123)(91, 155)(92, 168)(93, 131)(94, 152)(95, 154)(96, 124)(97, 164)(98, 167)(99, 169)(100, 163)(101, 180)(102, 179)(103, 177)(104, 153)(105, 130)(106, 129)(107, 141)(108, 151)(109, 178)(110, 175)(111, 162)(112, 144)(113, 176)(114, 146)(115, 132)(116, 142)(117, 128)(118, 143)(119, 139)(120, 165)

MAP           : A4.104
NOTES         : type I, reflexible, isomorphic to Trun({5,5}), isomorphic to A4.103.
QUOTIENT      : R = (1, 2, 3) L = (2, 3)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 5 ]
UNIGROUP      : < u.1, u.2 | u.1^2, u.2^5, (u.1 * u.2^-1)^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2 | x.1^2, x.2^5, (x.1 * x.2^-2)^3, (x.2 * x.1 * x.2)^3, (x.1 * x.2^-1)^5, (x.2^2 * x.1 * x.2^-1 * x.1)^2, (x.2 * x.1 * x.2^-1 * x.1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (5, 10, 10)
#DARTS        : 180
R = (1, 61, 121)(2, 62, 122)(3, 63, 123)(4, 64, 124)(5, 65, 125)(6, 66, 126)(7, 67, 127)(8, 68, 128)(9, 69, 129)(10, 70, 130)(11, 71, 131)(12, 72, 132)(13, 73, 133)(14, 74, 134)(15, 75, 135)(16, 76, 136)(17, 77, 137)(18, 78, 138)(19, 79, 139)(20, 80, 140)(21, 81, 141)(22, 82, 142)(23, 83, 143)(24, 84, 144)(25, 85, 145)(26, 86, 146)(27, 87, 147)(28, 88, 148)(29, 89, 149)(30, 90, 150)(31, 91, 151)(32, 92, 152)(33, 93, 153)(34, 94, 154)(35, 95, 155)(36, 96, 156)(37, 97, 157)(38, 98, 158)(39, 99, 159)(40, 100, 160)(41, 101, 161)(42, 102, 162)(43, 103, 163)(44, 104, 164)(45, 105, 165)(46, 106, 166)(47, 107, 167)(48, 108, 168)(49, 109, 169)(50, 110, 170)(51, 111, 171)(52, 112, 172)(53, 113, 173)(54, 114, 174)(55, 115, 175)(56, 116, 176)(57, 117, 177)(58, 118, 178)(59, 119, 179)(60, 120, 180)
L = (1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)(19, 37)(20, 38)(21, 39)(22, 40)(23, 41)(24, 42)(25, 43)(26, 44)(27, 45)(28, 46)(29, 47)(30, 48)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(61, 122)(62, 125)(63, 127)(64, 121)(65, 138)(66, 137)(67, 161)(68, 126)(69, 173)(70, 158)(71, 160)(72, 166)(73, 155)(74, 168)(75, 131)(76, 152)(77, 154)(78, 124)(79, 164)(80, 167)(81, 169)(82, 163)(83, 180)(84, 179)(85, 177)(86, 153)(87, 130)(88, 129)(89, 141)(90, 151)(91, 135)(92, 159)(93, 172)(94, 171)(95, 147)(96, 157)(97, 136)(98, 133)(99, 156)(100, 150)(101, 134)(102, 140)(103, 174)(104, 148)(105, 170)(106, 149)(107, 145)(108, 123)(109, 132)(110, 142)(111, 128)(112, 143)(113, 139)(114, 165)(115, 178)(116, 175)(117, 162)(118, 144)(119, 176)(120, 146)

MAP           : A4.105
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: [ 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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^-1 * x.2^-1 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 186)(38, 202)(39, 212)(40, 203)(41, 195)(42, 196)(43, 200)(44, 189)(45, 214)(46, 216)(47, 209)(48, 213)(49, 182)(50, 184)(51, 205)(52, 181)(53, 190)(54, 183)(55, 191)(56, 206)(57, 207)(58, 193)(59, 194)(60, 210)(61, 185)(62, 187)(63, 215)(64, 192)(65, 199)(66, 211)(67, 204)(68, 198)(69, 208)(70, 188)(71, 201)(72, 197)(73, 147)(74, 152)(75, 153)(76, 165)(77, 179)(78, 156)(79, 162)(80, 171)(81, 180)(82, 177)(83, 159)(84, 178)(85, 148)(86, 145)(87, 150)(88, 146)(89, 157)(90, 169)(91, 158)(92, 166)(93, 176)(94, 149)(95, 151)(96, 160)(97, 154)(98, 155)(99, 173)(100, 174)(101, 168)(102, 164)(103, 161)(104, 175)(105, 167)(106, 170)(107, 172)(108, 163)

MAP           : A4.106
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^-1 * x.2^-1 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 188)(38, 201)(39, 190)(40, 183)(41, 213)(42, 189)(43, 195)(44, 191)(45, 209)(46, 184)(47, 181)(48, 200)(49, 215)(50, 198)(51, 208)(52, 214)(53, 194)(54, 197)(55, 196)(56, 205)(57, 210)(58, 207)(59, 212)(60, 193)(61, 192)(62, 185)(63, 211)(64, 187)(65, 186)(66, 182)(67, 202)(68, 216)(69, 206)(70, 199)(71, 204)(72, 203)(73, 147)(74, 152)(75, 153)(76, 165)(77, 179)(78, 156)(79, 162)(80, 171)(81, 180)(82, 177)(83, 159)(84, 178)(85, 148)(86, 145)(87, 150)(88, 146)(89, 157)(90, 169)(91, 158)(92, 166)(93, 176)(94, 149)(95, 151)(96, 160)(97, 154)(98, 155)(99, 173)(100, 174)(101, 168)(102, 164)(103, 161)(104, 175)(105, 167)(106, 170)(107, 172)(108, 163)

MAP           : A4.107
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^3, x.3^-1 * x.2^-2 * x.3 * x.2^2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 194)(38, 196)(39, 181)(40, 193)(41, 202)(42, 195)(43, 203)(44, 182)(45, 183)(46, 205)(47, 206)(48, 186)(49, 197)(50, 199)(51, 191)(52, 204)(53, 211)(54, 187)(55, 216)(56, 210)(57, 184)(58, 200)(59, 213)(60, 209)(61, 198)(62, 214)(63, 188)(64, 215)(65, 207)(66, 208)(67, 212)(68, 201)(69, 190)(70, 192)(71, 185)(72, 189)(73, 160)(74, 157)(75, 162)(76, 158)(77, 169)(78, 145)(79, 170)(80, 178)(81, 152)(82, 161)(83, 163)(84, 172)(85, 166)(86, 167)(87, 149)(88, 150)(89, 180)(90, 176)(91, 173)(92, 151)(93, 179)(94, 146)(95, 148)(96, 175)(97, 159)(98, 164)(99, 165)(100, 177)(101, 155)(102, 168)(103, 174)(104, 147)(105, 156)(106, 153)(107, 171)(108, 154)

MAP           : A4.108
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^-1 * x.2^-1 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 196)(38, 193)(39, 198)(40, 194)(41, 205)(42, 181)(43, 206)(44, 214)(45, 188)(46, 197)(47, 199)(48, 208)(49, 202)(50, 203)(51, 185)(52, 186)(53, 216)(54, 212)(55, 209)(56, 187)(57, 215)(58, 182)(59, 184)(60, 211)(61, 195)(62, 200)(63, 201)(64, 213)(65, 191)(66, 204)(67, 210)(68, 183)(69, 192)(70, 189)(71, 207)(72, 190)(73, 158)(74, 160)(75, 145)(76, 157)(77, 166)(78, 159)(79, 167)(80, 146)(81, 147)(82, 169)(83, 170)(84, 150)(85, 161)(86, 163)(87, 155)(88, 168)(89, 175)(90, 151)(91, 180)(92, 174)(93, 148)(94, 164)(95, 177)(96, 173)(97, 162)(98, 178)(99, 152)(100, 179)(101, 171)(102, 172)(103, 176)(104, 165)(105, 154)(106, 156)(107, 149)(108, 153)

MAP           : A4.109
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
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.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 182)(38, 184)(39, 205)(40, 181)(41, 190)(42, 183)(43, 191)(44, 206)(45, 207)(46, 193)(47, 194)(48, 210)(49, 185)(50, 187)(51, 215)(52, 192)(53, 199)(54, 211)(55, 204)(56, 198)(57, 208)(58, 188)(59, 201)(60, 197)(61, 186)(62, 202)(63, 212)(64, 203)(65, 195)(66, 196)(67, 200)(68, 189)(69, 214)(70, 216)(71, 209)(72, 213)(73, 160)(74, 157)(75, 162)(76, 158)(77, 169)(78, 145)(79, 170)(80, 178)(81, 152)(82, 161)(83, 163)(84, 172)(85, 166)(86, 167)(87, 149)(88, 150)(89, 180)(90, 176)(91, 173)(92, 151)(93, 179)(94, 146)(95, 148)(96, 175)(97, 159)(98, 164)(99, 165)(100, 177)(101, 155)(102, 168)(103, 174)(104, 147)(105, 156)(106, 153)(107, 171)(108, 154)

MAP           : A4.110
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
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.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 182)(38, 184)(39, 205)(40, 181)(41, 190)(42, 183)(43, 191)(44, 206)(45, 207)(46, 193)(47, 194)(48, 210)(49, 185)(50, 187)(51, 215)(52, 192)(53, 199)(54, 211)(55, 204)(56, 198)(57, 208)(58, 188)(59, 201)(60, 197)(61, 186)(62, 202)(63, 212)(64, 203)(65, 195)(66, 196)(67, 200)(68, 189)(69, 214)(70, 216)(71, 209)(72, 213)(73, 152)(74, 165)(75, 154)(76, 147)(77, 177)(78, 153)(79, 159)(80, 155)(81, 173)(82, 148)(83, 145)(84, 164)(85, 179)(86, 162)(87, 172)(88, 178)(89, 158)(90, 161)(91, 160)(92, 169)(93, 174)(94, 171)(95, 176)(96, 157)(97, 156)(98, 149)(99, 175)(100, 151)(101, 150)(102, 146)(103, 166)(104, 180)(105, 170)(106, 163)(107, 168)(108, 167)

MAP           : A4.111
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
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.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 184)(38, 181)(39, 186)(40, 182)(41, 193)(42, 205)(43, 194)(44, 202)(45, 212)(46, 185)(47, 187)(48, 196)(49, 190)(50, 191)(51, 209)(52, 210)(53, 204)(54, 200)(55, 197)(56, 211)(57, 203)(58, 206)(59, 208)(60, 199)(61, 183)(62, 188)(63, 189)(64, 201)(65, 215)(66, 192)(67, 198)(68, 207)(69, 216)(70, 213)(71, 195)(72, 214)(73, 150)(74, 166)(75, 176)(76, 167)(77, 159)(78, 160)(79, 164)(80, 153)(81, 178)(82, 180)(83, 173)(84, 177)(85, 146)(86, 148)(87, 169)(88, 145)(89, 154)(90, 147)(91, 155)(92, 170)(93, 171)(94, 157)(95, 158)(96, 174)(97, 149)(98, 151)(99, 179)(100, 156)(101, 163)(102, 175)(103, 168)(104, 162)(105, 172)(106, 152)(107, 165)(108, 161)

MAP           : A4.112
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^3, x.3^-1 * x.2^-2 * x.3 * x.2^2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 194)(38, 196)(39, 181)(40, 193)(41, 202)(42, 195)(43, 203)(44, 182)(45, 183)(46, 205)(47, 206)(48, 186)(49, 197)(50, 199)(51, 191)(52, 204)(53, 211)(54, 187)(55, 216)(56, 210)(57, 184)(58, 200)(59, 213)(60, 209)(61, 198)(62, 214)(63, 188)(64, 215)(65, 207)(66, 208)(67, 212)(68, 201)(69, 190)(70, 192)(71, 185)(72, 189)(73, 152)(74, 165)(75, 154)(76, 147)(77, 177)(78, 153)(79, 159)(80, 155)(81, 173)(82, 148)(83, 145)(84, 164)(85, 179)(86, 162)(87, 172)(88, 178)(89, 158)(90, 161)(91, 160)(92, 169)(93, 174)(94, 171)(95, 176)(96, 157)(97, 156)(98, 149)(99, 175)(100, 151)(101, 150)(102, 146)(103, 166)(104, 180)(105, 170)(106, 163)(107, 168)(108, 167)

MAP           : A4.113
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^-1 * x.2^-1 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 184)(38, 181)(39, 186)(40, 182)(41, 193)(42, 205)(43, 194)(44, 202)(45, 212)(46, 185)(47, 187)(48, 196)(49, 190)(50, 191)(51, 209)(52, 210)(53, 204)(54, 200)(55, 197)(56, 211)(57, 203)(58, 206)(59, 208)(60, 199)(61, 183)(62, 188)(63, 189)(64, 201)(65, 215)(66, 192)(67, 198)(68, 207)(69, 216)(70, 213)(71, 195)(72, 214)(73, 158)(74, 160)(75, 145)(76, 157)(77, 166)(78, 159)(79, 167)(80, 146)(81, 147)(82, 169)(83, 170)(84, 150)(85, 161)(86, 163)(87, 155)(88, 168)(89, 175)(90, 151)(91, 180)(92, 174)(93, 148)(94, 164)(95, 177)(96, 173)(97, 162)(98, 178)(99, 152)(100, 179)(101, 171)(102, 172)(103, 176)(104, 165)(105, 154)(106, 156)(107, 149)(108, 153)

MAP           : A4.114
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
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.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 186)(38, 202)(39, 212)(40, 203)(41, 195)(42, 196)(43, 200)(44, 189)(45, 214)(46, 216)(47, 209)(48, 213)(49, 182)(50, 184)(51, 205)(52, 181)(53, 190)(54, 183)(55, 191)(56, 206)(57, 207)(58, 193)(59, 194)(60, 210)(61, 185)(62, 187)(63, 215)(64, 192)(65, 199)(66, 211)(67, 204)(68, 198)(69, 208)(70, 188)(71, 201)(72, 197)(73, 156)(74, 149)(75, 175)(76, 151)(77, 150)(78, 146)(79, 166)(80, 180)(81, 170)(82, 163)(83, 168)(84, 167)(85, 152)(86, 165)(87, 154)(88, 147)(89, 177)(90, 153)(91, 159)(92, 155)(93, 173)(94, 148)(95, 145)(96, 164)(97, 179)(98, 162)(99, 172)(100, 178)(101, 158)(102, 161)(103, 160)(104, 169)(105, 174)(106, 171)(107, 176)(108, 157)

MAP           : A4.115
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
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.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 196)(38, 193)(39, 198)(40, 194)(41, 205)(42, 181)(43, 206)(44, 214)(45, 188)(46, 197)(47, 199)(48, 208)(49, 202)(50, 203)(51, 185)(52, 186)(53, 216)(54, 212)(55, 209)(56, 187)(57, 215)(58, 182)(59, 184)(60, 211)(61, 195)(62, 200)(63, 201)(64, 213)(65, 191)(66, 204)(67, 210)(68, 183)(69, 192)(70, 189)(71, 207)(72, 190)(73, 146)(74, 148)(75, 169)(76, 145)(77, 154)(78, 147)(79, 155)(80, 170)(81, 171)(82, 157)(83, 158)(84, 174)(85, 149)(86, 151)(87, 179)(88, 156)(89, 163)(90, 175)(91, 168)(92, 162)(93, 172)(94, 152)(95, 165)(96, 161)(97, 150)(98, 166)(99, 176)(100, 167)(101, 159)(102, 160)(103, 164)(104, 153)(105, 178)(106, 180)(107, 173)(108, 177)

MAP           : A4.116
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
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.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 196)(38, 193)(39, 198)(40, 194)(41, 205)(42, 181)(43, 206)(44, 214)(45, 188)(46, 197)(47, 199)(48, 208)(49, 202)(50, 203)(51, 185)(52, 186)(53, 216)(54, 212)(55, 209)(56, 187)(57, 215)(58, 182)(59, 184)(60, 211)(61, 195)(62, 200)(63, 201)(64, 213)(65, 191)(66, 204)(67, 210)(68, 183)(69, 192)(70, 189)(71, 207)(72, 190)(73, 167)(74, 150)(75, 160)(76, 166)(77, 146)(78, 149)(79, 148)(80, 157)(81, 162)(82, 159)(83, 164)(84, 145)(85, 180)(86, 173)(87, 163)(88, 175)(89, 174)(90, 170)(91, 154)(92, 168)(93, 158)(94, 151)(95, 156)(96, 155)(97, 176)(98, 153)(99, 178)(100, 171)(101, 165)(102, 177)(103, 147)(104, 179)(105, 161)(106, 172)(107, 169)(108, 152)

MAP           : A4.117
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
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.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 188)(38, 201)(39, 190)(40, 183)(41, 213)(42, 189)(43, 195)(44, 191)(45, 209)(46, 184)(47, 181)(48, 200)(49, 215)(50, 198)(51, 208)(52, 214)(53, 194)(54, 197)(55, 196)(56, 205)(57, 210)(58, 207)(59, 212)(60, 193)(61, 192)(62, 185)(63, 211)(64, 187)(65, 186)(66, 182)(67, 202)(68, 216)(69, 206)(70, 199)(71, 204)(72, 203)(73, 146)(74, 148)(75, 169)(76, 145)(77, 154)(78, 147)(79, 155)(80, 170)(81, 171)(82, 157)(83, 158)(84, 174)(85, 149)(86, 151)(87, 179)(88, 156)(89, 163)(90, 175)(91, 168)(92, 162)(93, 172)(94, 152)(95, 165)(96, 161)(97, 150)(98, 166)(99, 176)(100, 167)(101, 159)(102, 160)(103, 164)(104, 153)(105, 178)(106, 180)(107, 173)(108, 177)

MAP           : A4.118
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
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.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 188)(38, 201)(39, 190)(40, 183)(41, 213)(42, 189)(43, 195)(44, 191)(45, 209)(46, 184)(47, 181)(48, 200)(49, 215)(50, 198)(51, 208)(52, 214)(53, 194)(54, 197)(55, 196)(56, 205)(57, 210)(58, 207)(59, 212)(60, 193)(61, 192)(62, 185)(63, 211)(64, 187)(65, 186)(66, 182)(67, 202)(68, 216)(69, 206)(70, 199)(71, 204)(72, 203)(73, 154)(74, 155)(75, 173)(76, 174)(77, 168)(78, 164)(79, 161)(80, 175)(81, 167)(82, 170)(83, 172)(84, 163)(85, 147)(86, 152)(87, 153)(88, 165)(89, 179)(90, 156)(91, 162)(92, 171)(93, 180)(94, 177)(95, 159)(96, 178)(97, 148)(98, 145)(99, 150)(100, 146)(101, 157)(102, 169)(103, 158)(104, 166)(105, 176)(106, 149)(107, 151)(108, 160)

MAP           : A4.119
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
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.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 191)(38, 210)(39, 184)(40, 190)(41, 206)(42, 209)(43, 208)(44, 181)(45, 186)(46, 183)(47, 188)(48, 205)(49, 204)(50, 197)(51, 187)(52, 199)(53, 198)(54, 194)(55, 214)(56, 192)(57, 182)(58, 211)(59, 216)(60, 215)(61, 200)(62, 213)(63, 202)(64, 195)(65, 189)(66, 201)(67, 207)(68, 203)(69, 185)(70, 196)(71, 193)(72, 212)(73, 148)(74, 145)(75, 150)(76, 146)(77, 157)(78, 169)(79, 158)(80, 166)(81, 176)(82, 149)(83, 151)(84, 160)(85, 154)(86, 155)(87, 173)(88, 174)(89, 168)(90, 164)(91, 161)(92, 175)(93, 167)(94, 170)(95, 172)(96, 163)(97, 147)(98, 152)(99, 153)(100, 165)(101, 179)(102, 156)(103, 162)(104, 171)(105, 180)(106, 177)(107, 159)(108, 178)

MAP           : A4.120
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
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.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 191)(38, 210)(39, 184)(40, 190)(41, 206)(42, 209)(43, 208)(44, 181)(45, 186)(46, 183)(47, 188)(48, 205)(49, 204)(50, 197)(51, 187)(52, 199)(53, 198)(54, 194)(55, 214)(56, 192)(57, 182)(58, 211)(59, 216)(60, 215)(61, 200)(62, 213)(63, 202)(64, 195)(65, 189)(66, 201)(67, 207)(68, 203)(69, 185)(70, 196)(71, 193)(72, 212)(73, 170)(74, 172)(75, 157)(76, 169)(77, 178)(78, 171)(79, 179)(80, 158)(81, 159)(82, 145)(83, 146)(84, 162)(85, 173)(86, 175)(87, 167)(88, 180)(89, 151)(90, 163)(91, 156)(92, 150)(93, 160)(94, 176)(95, 153)(96, 149)(97, 174)(98, 154)(99, 164)(100, 155)(101, 147)(102, 148)(103, 152)(104, 177)(105, 166)(106, 168)(107, 161)(108, 165)

MAP           : A4.121
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^-1 * x.2^-1 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 191)(38, 210)(39, 184)(40, 190)(41, 206)(42, 209)(43, 208)(44, 181)(45, 186)(46, 183)(47, 188)(48, 205)(49, 204)(50, 197)(51, 187)(52, 199)(53, 198)(54, 194)(55, 214)(56, 192)(57, 182)(58, 211)(59, 216)(60, 215)(61, 200)(62, 213)(63, 202)(64, 195)(65, 189)(66, 201)(67, 207)(68, 203)(69, 185)(70, 196)(71, 193)(72, 212)(73, 158)(74, 160)(75, 145)(76, 157)(77, 166)(78, 159)(79, 167)(80, 146)(81, 147)(82, 169)(83, 170)(84, 150)(85, 161)(86, 163)(87, 155)(88, 168)(89, 175)(90, 151)(91, 180)(92, 174)(93, 148)(94, 164)(95, 177)(96, 173)(97, 162)(98, 178)(99, 152)(100, 179)(101, 171)(102, 172)(103, 176)(104, 165)(105, 154)(106, 156)(107, 149)(108, 153)

MAP           : A4.122
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^3, x.3^-1 * x.2^-2 * x.3 * x.2^2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 188)(39, 189)(40, 201)(41, 215)(42, 192)(43, 198)(44, 207)(45, 216)(46, 213)(47, 195)(48, 214)(49, 184)(50, 181)(51, 186)(52, 182)(53, 193)(54, 205)(55, 194)(56, 202)(57, 212)(58, 185)(59, 187)(60, 196)(61, 190)(62, 191)(63, 209)(64, 210)(65, 204)(66, 200)(67, 197)(68, 211)(69, 203)(70, 206)(71, 208)(72, 199)(73, 146)(74, 148)(75, 169)(76, 145)(77, 154)(78, 147)(79, 155)(80, 170)(81, 171)(82, 157)(83, 158)(84, 174)(85, 149)(86, 151)(87, 179)(88, 156)(89, 163)(90, 175)(91, 168)(92, 162)(93, 172)(94, 152)(95, 165)(96, 161)(97, 150)(98, 166)(99, 176)(100, 167)(101, 159)(102, 160)(103, 164)(104, 153)(105, 178)(106, 180)(107, 173)(108, 177)

MAP           : A4.123
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^3, x.3^-1 * x.2^-2 * x.3 * x.2^2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 188)(39, 189)(40, 201)(41, 215)(42, 192)(43, 198)(44, 207)(45, 216)(46, 213)(47, 195)(48, 214)(49, 184)(50, 181)(51, 186)(52, 182)(53, 193)(54, 205)(55, 194)(56, 202)(57, 212)(58, 185)(59, 187)(60, 196)(61, 190)(62, 191)(63, 209)(64, 210)(65, 204)(66, 200)(67, 197)(68, 211)(69, 203)(70, 206)(71, 208)(72, 199)(73, 148)(74, 145)(75, 150)(76, 146)(77, 157)(78, 169)(79, 158)(80, 166)(81, 176)(82, 149)(83, 151)(84, 160)(85, 154)(86, 155)(87, 173)(88, 174)(89, 168)(90, 164)(91, 161)(92, 175)(93, 167)(94, 170)(95, 172)(96, 163)(97, 147)(98, 152)(99, 153)(100, 165)(101, 179)(102, 156)(103, 162)(104, 171)(105, 180)(106, 177)(107, 159)(108, 178)

MAP           : A4.124
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^3, x.3^-1 * x.2^-2 * x.3 * x.2^2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 194)(38, 196)(39, 181)(40, 193)(41, 202)(42, 195)(43, 203)(44, 182)(45, 183)(46, 205)(47, 206)(48, 186)(49, 197)(50, 199)(51, 191)(52, 204)(53, 211)(54, 187)(55, 216)(56, 210)(57, 184)(58, 200)(59, 213)(60, 209)(61, 198)(62, 214)(63, 188)(64, 215)(65, 207)(66, 208)(67, 212)(68, 201)(69, 190)(70, 192)(71, 185)(72, 189)(73, 155)(74, 174)(75, 148)(76, 154)(77, 170)(78, 173)(79, 172)(80, 145)(81, 150)(82, 147)(83, 152)(84, 169)(85, 168)(86, 161)(87, 151)(88, 163)(89, 162)(90, 158)(91, 178)(92, 156)(93, 146)(94, 175)(95, 180)(96, 179)(97, 164)(98, 177)(99, 166)(100, 159)(101, 153)(102, 165)(103, 171)(104, 167)(105, 149)(106, 160)(107, 157)(108, 176)

MAP           : A4.125
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^-1 * x.2^-1 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 182)(38, 184)(39, 205)(40, 181)(41, 190)(42, 183)(43, 191)(44, 206)(45, 207)(46, 193)(47, 194)(48, 210)(49, 185)(50, 187)(51, 215)(52, 192)(53, 199)(54, 211)(55, 204)(56, 198)(57, 208)(58, 188)(59, 201)(60, 197)(61, 186)(62, 202)(63, 212)(64, 203)(65, 195)(66, 196)(67, 200)(68, 189)(69, 214)(70, 216)(71, 209)(72, 213)(73, 158)(74, 160)(75, 145)(76, 157)(77, 166)(78, 159)(79, 167)(80, 146)(81, 147)(82, 169)(83, 170)(84, 150)(85, 161)(86, 163)(87, 155)(88, 168)(89, 175)(90, 151)(91, 180)(92, 174)(93, 148)(94, 164)(95, 177)(96, 173)(97, 162)(98, 178)(99, 152)(100, 179)(101, 171)(102, 172)(103, 176)(104, 165)(105, 154)(106, 156)(107, 149)(108, 153)

MAP           : A4.126
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^3, x.3^-1 * x.2^-2 * x.3 * x.2^2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 188)(39, 189)(40, 201)(41, 215)(42, 192)(43, 198)(44, 207)(45, 216)(46, 213)(47, 195)(48, 214)(49, 184)(50, 181)(51, 186)(52, 182)(53, 193)(54, 205)(55, 194)(56, 202)(57, 212)(58, 185)(59, 187)(60, 196)(61, 190)(62, 191)(63, 209)(64, 210)(65, 204)(66, 200)(67, 197)(68, 211)(69, 203)(70, 206)(71, 208)(72, 199)(73, 152)(74, 165)(75, 154)(76, 147)(77, 177)(78, 153)(79, 159)(80, 155)(81, 173)(82, 148)(83, 145)(84, 164)(85, 179)(86, 162)(87, 172)(88, 178)(89, 158)(90, 161)(91, 160)(92, 169)(93, 174)(94, 171)(95, 176)(96, 157)(97, 156)(98, 149)(99, 175)(100, 151)(101, 150)(102, 146)(103, 166)(104, 180)(105, 170)(106, 163)(107, 168)(108, 167)

MAP           : A4.127
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^3, x.3^-1 * x.2^-2 * x.3 * x.2^2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 188)(39, 189)(40, 201)(41, 215)(42, 192)(43, 198)(44, 207)(45, 216)(46, 213)(47, 195)(48, 214)(49, 184)(50, 181)(51, 186)(52, 182)(53, 193)(54, 205)(55, 194)(56, 202)(57, 212)(58, 185)(59, 187)(60, 196)(61, 190)(62, 191)(63, 209)(64, 210)(65, 204)(66, 200)(67, 197)(68, 211)(69, 203)(70, 206)(71, 208)(72, 199)(73, 155)(74, 174)(75, 148)(76, 154)(77, 170)(78, 173)(79, 172)(80, 145)(81, 150)(82, 147)(83, 152)(84, 169)(85, 168)(86, 161)(87, 151)(88, 163)(89, 162)(90, 158)(91, 178)(92, 156)(93, 146)(94, 175)(95, 180)(96, 179)(97, 164)(98, 177)(99, 166)(100, 159)(101, 153)(102, 165)(103, 171)(104, 167)(105, 149)(106, 160)(107, 157)(108, 176)

MAP           : A4.128
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^3, x.3^-1 * x.2^-2 * x.3 * x.2^2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 188)(39, 189)(40, 201)(41, 215)(42, 192)(43, 198)(44, 207)(45, 216)(46, 213)(47, 195)(48, 214)(49, 184)(50, 181)(51, 186)(52, 182)(53, 193)(54, 205)(55, 194)(56, 202)(57, 212)(58, 185)(59, 187)(60, 196)(61, 190)(62, 191)(63, 209)(64, 210)(65, 204)(66, 200)(67, 197)(68, 211)(69, 203)(70, 206)(71, 208)(72, 199)(73, 150)(74, 166)(75, 176)(76, 167)(77, 159)(78, 160)(79, 164)(80, 153)(81, 178)(82, 180)(83, 173)(84, 177)(85, 146)(86, 148)(87, 169)(88, 145)(89, 154)(90, 147)(91, 155)(92, 170)(93, 171)(94, 157)(95, 158)(96, 174)(97, 149)(98, 151)(99, 179)(100, 156)(101, 163)(102, 175)(103, 168)(104, 162)(105, 172)(106, 152)(107, 165)(108, 161)

MAP           : A4.129
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^3, x.3^-1 * x.2^-2 * x.3 * x.2^2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 188)(39, 189)(40, 201)(41, 215)(42, 192)(43, 198)(44, 207)(45, 216)(46, 213)(47, 195)(48, 214)(49, 184)(50, 181)(51, 186)(52, 182)(53, 193)(54, 205)(55, 194)(56, 202)(57, 212)(58, 185)(59, 187)(60, 196)(61, 190)(62, 191)(63, 209)(64, 210)(65, 204)(66, 200)(67, 197)(68, 211)(69, 203)(70, 206)(71, 208)(72, 199)(73, 160)(74, 157)(75, 162)(76, 158)(77, 169)(78, 145)(79, 170)(80, 178)(81, 152)(82, 161)(83, 163)(84, 172)(85, 166)(86, 167)(87, 149)(88, 150)(89, 180)(90, 176)(91, 173)(92, 151)(93, 179)(94, 146)(95, 148)(96, 175)(97, 159)(98, 164)(99, 165)(100, 177)(101, 155)(102, 168)(103, 174)(104, 147)(105, 156)(106, 153)(107, 171)(108, 154)

MAP           : A4.130
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^3, x.3^-1 * x.2^-2 * x.3 * x.2^2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 194)(38, 196)(39, 181)(40, 193)(41, 202)(42, 195)(43, 203)(44, 182)(45, 183)(46, 205)(47, 206)(48, 186)(49, 197)(50, 199)(51, 191)(52, 204)(53, 211)(54, 187)(55, 216)(56, 210)(57, 184)(58, 200)(59, 213)(60, 209)(61, 198)(62, 214)(63, 188)(64, 215)(65, 207)(66, 208)(67, 212)(68, 201)(69, 190)(70, 192)(71, 185)(72, 189)(73, 150)(74, 166)(75, 176)(76, 167)(77, 159)(78, 160)(79, 164)(80, 153)(81, 178)(82, 180)(83, 173)(84, 177)(85, 146)(86, 148)(87, 169)(88, 145)(89, 154)(90, 147)(91, 155)(92, 170)(93, 171)(94, 157)(95, 158)(96, 174)(97, 149)(98, 151)(99, 179)(100, 156)(101, 163)(102, 175)(103, 168)(104, 162)(105, 172)(106, 152)(107, 165)(108, 161)

MAP           : A4.131
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^-1 * x.2^-1 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 184)(38, 181)(39, 186)(40, 182)(41, 193)(42, 205)(43, 194)(44, 202)(45, 212)(46, 185)(47, 187)(48, 196)(49, 190)(50, 191)(51, 209)(52, 210)(53, 204)(54, 200)(55, 197)(56, 211)(57, 203)(58, 206)(59, 208)(60, 199)(61, 183)(62, 188)(63, 189)(64, 201)(65, 215)(66, 192)(67, 198)(68, 207)(69, 216)(70, 213)(71, 195)(72, 214)(73, 147)(74, 152)(75, 153)(76, 165)(77, 179)(78, 156)(79, 162)(80, 171)(81, 180)(82, 177)(83, 159)(84, 178)(85, 148)(86, 145)(87, 150)(88, 146)(89, 157)(90, 169)(91, 158)(92, 166)(93, 176)(94, 149)(95, 151)(96, 160)(97, 154)(98, 155)(99, 173)(100, 174)(101, 168)(102, 164)(103, 161)(104, 175)(105, 167)(106, 170)(107, 172)(108, 163)

MAP           : A4.132
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^3, x.3^-1 * x.2^-2 * x.3 * x.2^2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 194)(38, 196)(39, 181)(40, 193)(41, 202)(42, 195)(43, 203)(44, 182)(45, 183)(46, 205)(47, 206)(48, 186)(49, 197)(50, 199)(51, 191)(52, 204)(53, 211)(54, 187)(55, 216)(56, 210)(57, 184)(58, 200)(59, 213)(60, 209)(61, 198)(62, 214)(63, 188)(64, 215)(65, 207)(66, 208)(67, 212)(68, 201)(69, 190)(70, 192)(71, 185)(72, 189)(73, 146)(74, 148)(75, 169)(76, 145)(77, 154)(78, 147)(79, 155)(80, 170)(81, 171)(82, 157)(83, 158)(84, 174)(85, 149)(86, 151)(87, 179)(88, 156)(89, 163)(90, 175)(91, 168)(92, 162)(93, 172)(94, 152)(95, 165)(96, 161)(97, 150)(98, 166)(99, 176)(100, 167)(101, 159)(102, 160)(103, 164)(104, 153)(105, 178)(106, 180)(107, 173)(108, 177)

MAP           : A4.133
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3 * x.1^-1)^3, (x.2^-1 * x.3^-1)^3, (x.2 * x.3^-1)^3, x.3^-1 * x.2^-2 * x.3 * x.2^2, (x.1 * x.2^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 194)(38, 196)(39, 181)(40, 193)(41, 202)(42, 195)(43, 203)(44, 182)(45, 183)(46, 205)(47, 206)(48, 186)(49, 197)(50, 199)(51, 191)(52, 204)(53, 211)(54, 187)(55, 216)(56, 210)(57, 184)(58, 200)(59, 213)(60, 209)(61, 198)(62, 214)(63, 188)(64, 215)(65, 207)(66, 208)(67, 212)(68, 201)(69, 190)(70, 192)(71, 185)(72, 189)(73, 148)(74, 145)(75, 150)(76, 146)(77, 157)(78, 169)(79, 158)(80, 166)(81, 176)(82, 149)(83, 151)(84, 160)(85, 154)(86, 155)(87, 173)(88, 174)(89, 168)(90, 164)(91, 161)(92, 175)(93, 167)(94, 170)(95, 172)(96, 163)(97, 147)(98, 152)(99, 153)(100, 165)(101, 179)(102, 156)(103, 162)(104, 171)(105, 180)(106, 177)(107, 159)(108, 178)

MAP           : A4.134
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^-1 * x.2^-1 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 186)(38, 202)(39, 212)(40, 203)(41, 195)(42, 196)(43, 200)(44, 189)(45, 214)(46, 216)(47, 209)(48, 213)(49, 182)(50, 184)(51, 205)(52, 181)(53, 190)(54, 183)(55, 191)(56, 206)(57, 207)(58, 193)(59, 194)(60, 210)(61, 185)(62, 187)(63, 215)(64, 192)(65, 199)(66, 211)(67, 204)(68, 198)(69, 208)(70, 188)(71, 201)(72, 197)(73, 158)(74, 160)(75, 145)(76, 157)(77, 166)(78, 159)(79, 167)(80, 146)(81, 147)(82, 169)(83, 170)(84, 150)(85, 161)(86, 163)(87, 155)(88, 168)(89, 175)(90, 151)(91, 180)(92, 174)(93, 148)(94, 164)(95, 177)(96, 173)(97, 162)(98, 178)(99, 152)(100, 179)(101, 171)(102, 172)(103, 176)(104, 165)(105, 154)(106, 156)(107, 149)(108, 153)

MAP           : A4.135
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^-1 * x.2^-1 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 196)(38, 193)(39, 198)(40, 194)(41, 205)(42, 181)(43, 206)(44, 214)(45, 188)(46, 197)(47, 199)(48, 208)(49, 202)(50, 203)(51, 185)(52, 186)(53, 216)(54, 212)(55, 209)(56, 187)(57, 215)(58, 182)(59, 184)(60, 211)(61, 195)(62, 200)(63, 201)(64, 213)(65, 191)(66, 204)(67, 210)(68, 183)(69, 192)(70, 189)(71, 207)(72, 190)(73, 147)(74, 152)(75, 153)(76, 165)(77, 179)(78, 156)(79, 162)(80, 171)(81, 180)(82, 177)(83, 159)(84, 178)(85, 148)(86, 145)(87, 150)(88, 146)(89, 157)(90, 169)(91, 158)(92, 166)(93, 176)(94, 149)(95, 151)(96, 160)(97, 154)(98, 155)(99, 173)(100, 174)(101, 168)(102, 164)(103, 161)(104, 175)(105, 167)(106, 170)(107, 172)(108, 163)

MAP           : A4.136
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
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.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 186)(38, 202)(39, 212)(40, 203)(41, 195)(42, 196)(43, 200)(44, 189)(45, 214)(46, 216)(47, 209)(48, 213)(49, 182)(50, 184)(51, 205)(52, 181)(53, 190)(54, 183)(55, 191)(56, 206)(57, 207)(58, 193)(59, 194)(60, 210)(61, 185)(62, 187)(63, 215)(64, 192)(65, 199)(66, 211)(67, 204)(68, 198)(69, 208)(70, 188)(71, 201)(72, 197)(73, 148)(74, 145)(75, 150)(76, 146)(77, 157)(78, 169)(79, 158)(80, 166)(81, 176)(82, 149)(83, 151)(84, 160)(85, 154)(86, 155)(87, 173)(88, 174)(89, 168)(90, 164)(91, 161)(92, 175)(93, 167)(94, 170)(95, 172)(96, 163)(97, 147)(98, 152)(99, 153)(100, 165)(101, 179)(102, 156)(103, 162)(104, 171)(105, 180)(106, 177)(107, 159)(108, 178)

MAP           : A4.137
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2 | x.1^2, (x.1 * x.2^-1)^3, x.2^-2 * x.1 * x.2^4 * x.1 * x.2^-2, x.2 * x.1 * x.2^-1 * x.1 * x.2^2 * x.1 * x.2^3 * x.1 * x.2, x.2^12 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)
L = (1, 4)(2, 6)(3, 43)(5, 67)(7, 11)(8, 52)(9, 38)(10, 50)(12, 40)(13, 24)(14, 33)(15, 23)(16, 36)(17, 59)(18, 21)(19, 27)(20, 60)(22, 57)(25, 28)(26, 30)(29, 55)(31, 35)(32, 64)(34, 62)(37, 48)(39, 47)(41, 71)(42, 45)(44, 72)(46, 69)(49, 56)(51, 53)(54, 58)(61, 68)(63, 65)(66, 70)(73, 167)(74, 204)(75, 165)(76, 203)(77, 162)(78, 168)(79, 213)(80, 159)(81, 180)(82, 157)(83, 177)(84, 179)(85, 209)(86, 205)(87, 214)(88, 207)(89, 190)(90, 212)(91, 206)(92, 185)(93, 176)(94, 188)(95, 178)(96, 173)(97, 163)(98, 208)(99, 170)(100, 199)(101, 158)(102, 172)(103, 210)(104, 175)(105, 169)(106, 160)(107, 174)(108, 171)(109, 191)(110, 216)(111, 189)(112, 215)(113, 186)(114, 192)(115, 201)(116, 183)(117, 156)(118, 181)(119, 153)(120, 155)(121, 197)(122, 193)(123, 202)(124, 195)(125, 166)(126, 200)(127, 194)(128, 161)(129, 152)(130, 164)(131, 154)(132, 149)(133, 187)(134, 196)(135, 146)(136, 211)(137, 182)(138, 148)(139, 198)(140, 151)(141, 145)(142, 184)(143, 150)(144, 147)

MAP           : A4.138
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^-1 * x.2^-1 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 188)(38, 201)(39, 190)(40, 183)(41, 213)(42, 189)(43, 195)(44, 191)(45, 209)(46, 184)(47, 181)(48, 200)(49, 215)(50, 198)(51, 208)(52, 214)(53, 194)(54, 197)(55, 196)(56, 205)(57, 210)(58, 207)(59, 212)(60, 193)(61, 192)(62, 185)(63, 211)(64, 187)(65, 186)(66, 182)(67, 202)(68, 216)(69, 206)(70, 199)(71, 204)(72, 203)(73, 158)(74, 160)(75, 145)(76, 157)(77, 166)(78, 159)(79, 167)(80, 146)(81, 147)(82, 169)(83, 170)(84, 150)(85, 161)(86, 163)(87, 155)(88, 168)(89, 175)(90, 151)(91, 180)(92, 174)(93, 148)(94, 164)(95, 177)(96, 173)(97, 162)(98, 178)(99, 152)(100, 179)(101, 171)(102, 172)(103, 176)(104, 165)(105, 154)(106, 156)(107, 149)(108, 153)

MAP           : A4.139
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^-1 * x.2^-1 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 191)(38, 210)(39, 184)(40, 190)(41, 206)(42, 209)(43, 208)(44, 181)(45, 186)(46, 183)(47, 188)(48, 205)(49, 204)(50, 197)(51, 187)(52, 199)(53, 198)(54, 194)(55, 214)(56, 192)(57, 182)(58, 211)(59, 216)(60, 215)(61, 200)(62, 213)(63, 202)(64, 195)(65, 189)(66, 201)(67, 207)(68, 203)(69, 185)(70, 196)(71, 193)(72, 212)(73, 147)(74, 152)(75, 153)(76, 165)(77, 179)(78, 156)(79, 162)(80, 171)(81, 180)(82, 177)(83, 159)(84, 178)(85, 148)(86, 145)(87, 150)(88, 146)(89, 157)(90, 169)(91, 158)(92, 166)(93, 176)(94, 149)(95, 151)(96, 160)(97, 154)(98, 155)(99, 173)(100, 174)(101, 168)(102, 164)(103, 161)(104, 175)(105, 167)(106, 170)(107, 172)(108, 163)

MAP           : A4.140
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2 | x.1^2, (x.1 * x.2^-1)^3, x.2^-2 * x.1 * x.2^4 * x.1 * x.2^-2, x.2 * x.1 * x.2^-1 * x.1 * x.2^2 * x.1 * x.2^3 * x.1 * x.2, x.2^12 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)
L = (1, 4)(2, 6)(3, 43)(5, 67)(7, 11)(8, 52)(9, 38)(10, 50)(12, 40)(13, 24)(14, 33)(15, 23)(16, 36)(17, 59)(18, 21)(19, 27)(20, 60)(22, 57)(25, 28)(26, 30)(29, 55)(31, 35)(32, 64)(34, 62)(37, 48)(39, 47)(41, 71)(42, 45)(44, 72)(46, 69)(49, 56)(51, 53)(54, 58)(61, 68)(63, 65)(66, 70)(73, 146)(74, 151)(75, 148)(76, 182)(77, 145)(78, 187)(79, 160)(80, 150)(81, 211)(82, 147)(83, 196)(84, 194)(85, 165)(86, 159)(87, 168)(88, 162)(89, 180)(90, 167)(91, 164)(92, 177)(93, 203)(94, 179)(95, 204)(96, 201)(97, 202)(98, 161)(99, 200)(100, 166)(101, 152)(102, 197)(103, 157)(104, 154)(105, 195)(106, 149)(107, 193)(108, 198)(109, 170)(110, 175)(111, 172)(112, 158)(113, 169)(114, 163)(115, 184)(116, 174)(117, 199)(118, 171)(119, 208)(120, 206)(121, 189)(122, 183)(123, 192)(124, 186)(125, 156)(126, 191)(127, 188)(128, 153)(129, 215)(130, 155)(131, 216)(132, 213)(133, 214)(134, 185)(135, 212)(136, 190)(137, 176)(138, 209)(139, 181)(140, 178)(141, 207)(142, 173)(143, 205)(144, 210)

MAP           : A4.141
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^-1 * x.2^-1 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, (x.2 * x.3^-1)^3, (x.2^-1 * x.3^-1)^3, (x.3 * x.1^-1)^6 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 182)(38, 184)(39, 205)(40, 181)(41, 190)(42, 183)(43, 191)(44, 206)(45, 207)(46, 193)(47, 194)(48, 210)(49, 185)(50, 187)(51, 215)(52, 192)(53, 199)(54, 211)(55, 204)(56, 198)(57, 208)(58, 188)(59, 201)(60, 197)(61, 186)(62, 202)(63, 212)(64, 203)(65, 195)(66, 196)(67, 200)(68, 189)(69, 214)(70, 216)(71, 209)(72, 213)(73, 147)(74, 152)(75, 153)(76, 165)(77, 179)(78, 156)(79, 162)(80, 171)(81, 180)(82, 177)(83, 159)(84, 178)(85, 148)(86, 145)(87, 150)(88, 146)(89, 157)(90, 169)(91, 158)(92, 166)(93, 176)(94, 149)(95, 151)(96, 160)(97, 154)(98, 155)(99, 173)(100, 174)(101, 168)(102, 164)(103, 161)(104, 175)(105, 167)(106, 170)(107, 172)(108, 163)

MAP           : A4.142
NOTES         : type I, reflexible, isomorphic to TDual({3,12}), isomorphic to A4.105.
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)   : <36, 11>
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.3 * x.2^-1 * x.3 * x.2 * x.3^-1 * x.2 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 6, 12)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 184)(38, 181)(39, 186)(40, 182)(41, 193)(42, 205)(43, 194)(44, 202)(45, 212)(46, 185)(47, 187)(48, 196)(49, 190)(50, 191)(51, 209)(52, 210)(53, 204)(54, 200)(55, 197)(56, 211)(57, 203)(58, 206)(59, 208)(60, 199)(61, 183)(62, 188)(63, 189)(64, 201)(65, 215)(66, 192)(67, 198)(68, 207)(69, 216)(70, 213)(71, 195)(72, 214)(73, 155)(74, 174)(75, 148)(76, 154)(77, 170)(78, 173)(79, 172)(80, 145)(81, 150)(82, 147)(83, 152)(84, 169)(85, 168)(86, 161)(87, 151)(88, 163)(89, 162)(90, 158)(91, 178)(92, 156)(93, 146)(94, 175)(95, 180)(96, 179)(97, 164)(98, 177)(99, 166)(100, 159)(101, 153)(102, 165)(103, 171)(104, 167)(105, 149)(106, 160)(107, 157)(108, 176)

MAP           : A4.143
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), representative.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^4, x.3^-1 * x.2 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3 * x.2 * x.3 * x.2^-1, (x.3 * x.1^-1)^4 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 8, 8)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 182)(38, 185)(39, 190)(40, 189)(41, 181)(42, 184)(43, 191)(44, 187)(45, 186)(46, 192)(47, 188)(48, 183)(49, 194)(50, 197)(51, 214)(52, 213)(53, 193)(54, 196)(55, 203)(56, 199)(57, 210)(58, 204)(59, 200)(60, 207)(61, 206)(62, 209)(63, 202)(64, 201)(65, 205)(66, 208)(67, 215)(68, 211)(69, 198)(70, 216)(71, 212)(72, 195)(73, 147)(74, 166)(75, 151)(76, 161)(77, 180)(78, 170)(79, 153)(80, 160)(81, 145)(82, 167)(83, 174)(84, 176)(85, 168)(86, 159)(87, 164)(88, 146)(89, 154)(90, 157)(91, 162)(92, 165)(93, 158)(94, 152)(95, 148)(96, 163)(97, 178)(98, 156)(99, 179)(100, 169)(101, 171)(102, 149)(103, 172)(104, 150)(105, 173)(106, 175)(107, 177)(108, 155)

MAP           : A4.144
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^4, x.3^-1 * x.2 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3 * x.2 * x.3 * x.2^-1, (x.3 * x.1^-1)^4 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 8, 8)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 182)(38, 185)(39, 190)(40, 189)(41, 181)(42, 184)(43, 191)(44, 187)(45, 186)(46, 192)(47, 188)(48, 183)(49, 194)(50, 197)(51, 214)(52, 213)(53, 193)(54, 196)(55, 203)(56, 199)(57, 210)(58, 204)(59, 200)(60, 207)(61, 206)(62, 209)(63, 202)(64, 201)(65, 205)(66, 208)(67, 215)(68, 211)(69, 198)(70, 216)(71, 212)(72, 195)(73, 153)(74, 160)(75, 145)(76, 167)(77, 174)(78, 176)(79, 147)(80, 166)(81, 151)(82, 161)(83, 180)(84, 170)(85, 162)(86, 165)(87, 158)(88, 152)(89, 148)(90, 163)(91, 168)(92, 159)(93, 164)(94, 146)(95, 154)(96, 157)(97, 172)(98, 150)(99, 173)(100, 175)(101, 177)(102, 155)(103, 178)(104, 156)(105, 179)(106, 169)(107, 171)(108, 149)

MAP           : A4.145
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^4, x.3^-1 * x.2 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3 * x.2 * x.3 * x.2^-1, (x.3 * x.1^-1)^4 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 8, 8)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 187)(56, 188)(57, 189)(58, 190)(59, 191)(60, 192)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 147)(74, 166)(75, 151)(76, 161)(77, 180)(78, 170)(79, 153)(80, 160)(81, 145)(82, 167)(83, 174)(84, 176)(85, 168)(86, 159)(87, 164)(88, 146)(89, 154)(90, 157)(91, 162)(92, 165)(93, 158)(94, 152)(95, 148)(96, 163)(97, 178)(98, 156)(99, 179)(100, 169)(101, 171)(102, 149)(103, 172)(104, 150)(105, 173)(106, 175)(107, 177)(108, 155)

MAP           : A4.146
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^4, x.3^-1 * x.2 * x.3^2 * x.2 * x.3^-1, (x.1 * x.2^-1)^3, x.3^-1 * x.2^-1 * x.3^-1 * x.2^-1 * x.3 * x.2 * x.3 * x.2^-1, (x.3 * x.1^-1)^4 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 8, 8)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 187)(56, 188)(57, 189)(58, 190)(59, 191)(60, 192)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 153)(74, 160)(75, 145)(76, 167)(77, 174)(78, 176)(79, 147)(80, 166)(81, 151)(82, 161)(83, 180)(84, 170)(85, 162)(86, 165)(87, 158)(88, 152)(89, 148)(90, 163)(91, 168)(92, 159)(93, 164)(94, 146)(95, 154)(96, 157)(97, 172)(98, 150)(99, 173)(100, 175)(101, 177)(102, 155)(103, 178)(104, 156)(105, 179)(106, 169)(107, 171)(108, 149)

MAP           : A4.147
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2^-1)^2, (x.3 * x.2^-1)^2, x.3^6, x.2^6, (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        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 74)(38, 78)(39, 80)(40, 79)(41, 73)(42, 94)(43, 92)(44, 96)(45, 98)(46, 97)(47, 91)(48, 76)(49, 106)(50, 105)(51, 95)(52, 75)(53, 102)(54, 101)(55, 88)(56, 87)(57, 77)(58, 93)(59, 84)(60, 83)(61, 89)(62, 85)(63, 100)(64, 108)(65, 81)(66, 86)(67, 107)(68, 103)(69, 82)(70, 90)(71, 99)(72, 104)(145, 184)(146, 183)(147, 209)(148, 213)(149, 204)(150, 203)(151, 185)(152, 181)(153, 196)(154, 192)(155, 201)(156, 182)(157, 191)(158, 187)(159, 202)(160, 186)(161, 195)(162, 188)(163, 206)(164, 210)(165, 200)(166, 199)(167, 205)(168, 214)(169, 212)(170, 216)(171, 194)(172, 193)(173, 211)(174, 208)(175, 190)(176, 189)(177, 215)(178, 207)(179, 198)(180, 197)

MAP           : A4.148
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.3^-1 * x.2^-1)^2, (x.3 * x.2^-1)^2, x.3^6, x.2^6, (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        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 76)(38, 75)(39, 101)(40, 105)(41, 96)(42, 95)(43, 77)(44, 73)(45, 88)(46, 84)(47, 93)(48, 74)(49, 83)(50, 79)(51, 94)(52, 78)(53, 87)(54, 80)(55, 98)(56, 102)(57, 92)(58, 91)(59, 97)(60, 106)(61, 104)(62, 108)(63, 86)(64, 85)(65, 103)(66, 100)(67, 82)(68, 81)(69, 107)(70, 99)(71, 90)(72, 89)(145, 182)(146, 186)(147, 188)(148, 187)(149, 181)(150, 202)(151, 200)(152, 204)(153, 206)(154, 205)(155, 199)(156, 184)(157, 214)(158, 213)(159, 203)(160, 183)(161, 210)(162, 209)(163, 196)(164, 195)(165, 185)(166, 201)(167, 192)(168, 191)(169, 197)(170, 193)(171, 208)(172, 216)(173, 189)(174, 194)(175, 215)(176, 211)(177, 190)(178, 198)(179, 207)(180, 212)

MAP           : A4.149
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2 | x.1^2, x.2^6, (x.2 * x.1)^4, (x.2 * x.1 * x.2^-1 * x.1)^2, x.2^2 * x.1 * x.2^2 * x.1 * x.2^-2 * x.1 * x.2^-2 * x.1 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (6, 8, 8)
#DARTS        : 216
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)
L = (1, 3)(2, 22)(4, 6)(5, 13)(7, 9)(8, 16)(10, 12)(11, 19)(14, 66)(15, 59)(17, 27)(18, 62)(20, 60)(21, 65)(23, 51)(24, 56)(25, 71)(26, 54)(28, 32)(29, 57)(30, 50)(31, 33)(34, 36)(35, 61)(37, 39)(38, 58)(40, 42)(41, 49)(43, 45)(44, 52)(46, 48)(47, 55)(53, 63)(64, 68)(67, 69)(70, 72)(73, 146)(74, 149)(75, 152)(76, 147)(77, 210)(78, 153)(79, 200)(80, 203)(81, 206)(82, 201)(83, 156)(84, 207)(85, 204)(86, 195)(87, 198)(88, 209)(89, 190)(90, 161)(91, 150)(92, 177)(93, 180)(94, 155)(95, 172)(96, 215)(97, 148)(98, 175)(99, 178)(100, 163)(101, 176)(102, 169)(103, 166)(104, 157)(105, 160)(106, 145)(107, 158)(108, 151)(109, 186)(110, 213)(111, 216)(112, 191)(113, 208)(114, 179)(115, 184)(116, 211)(117, 214)(118, 199)(119, 212)(120, 205)(121, 202)(122, 193)(123, 196)(124, 181)(125, 194)(126, 187)(127, 182)(128, 185)(129, 188)(130, 183)(131, 174)(132, 189)(133, 164)(134, 167)(135, 170)(136, 165)(137, 192)(138, 171)(139, 168)(140, 159)(141, 162)(142, 173)(143, 154)(144, 197)

MAP           : A4.150
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, (x.2 * x.1)^2, x.2 * x.4 * x.2 * x.1 * x.4 * x.1, (x.4 * x.3^-1)^3, x.3 * x.2 * x.4 * x.1 * x.3 * x.1 * x.4^-1 * x.2, x.4^-1 * x.2 * x.4^-1 * x.2 * x.4 * x.1 * x.4^-1 * x.1 >
SCHREIER VEC. : (x.3, x.1, x.4)
LOCAL TYPE    : (6, 8, 8)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 38)(39, 43)(40, 49)(41, 44)(42, 50)(45, 47)(46, 48)(51, 72)(52, 71)(53, 70)(54, 69)(55, 56)(57, 61)(58, 67)(59, 62)(60, 68)(63, 65)(64, 66)(73, 149)(74, 147)(75, 166)(76, 165)(77, 168)(78, 167)(79, 155)(80, 153)(81, 160)(82, 159)(83, 162)(84, 161)(85, 156)(86, 154)(87, 158)(88, 152)(89, 157)(90, 151)(91, 150)(92, 148)(93, 164)(94, 146)(95, 163)(96, 145)(97, 180)(98, 178)(99, 170)(100, 176)(101, 169)(102, 175)(103, 179)(104, 177)(105, 172)(106, 171)(107, 174)(108, 173)(181, 207)(182, 209)(183, 197)(184, 198)(185, 195)(186, 196)(187, 214)(188, 216)(189, 192)(190, 191)(193, 213)(194, 215)(199, 208)(200, 210)(201, 204)(202, 203)(205, 212)(206, 211)

MAP           : A4.151
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, (x.2 * x.1)^2, x.2 * x.4 * x.2 * x.1 * x.4 * x.1, (x.4 * x.3^-1)^3, x.3 * x.2 * x.4 * x.1 * x.3 * x.1 * x.4^-1 * x.2, x.4^-1 * x.2 * x.4^-1 * x.2 * x.4 * x.1 * x.4^-1 * x.1 >
SCHREIER VEC. : (x.3, x.1, x.4)
LOCAL TYPE    : (6, 8, 8)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 63)(38, 65)(39, 53)(40, 54)(41, 51)(42, 52)(43, 70)(44, 72)(45, 48)(46, 47)(49, 69)(50, 71)(55, 64)(56, 66)(57, 60)(58, 59)(61, 68)(62, 67)(73, 149)(74, 147)(75, 166)(76, 165)(77, 168)(78, 167)(79, 155)(80, 153)(81, 160)(82, 159)(83, 162)(84, 161)(85, 156)(86, 154)(87, 158)(88, 152)(89, 157)(90, 151)(91, 150)(92, 148)(93, 164)(94, 146)(95, 163)(96, 145)(97, 180)(98, 178)(99, 170)(100, 176)(101, 169)(102, 175)(103, 179)(104, 177)(105, 172)(106, 171)(107, 174)(108, 173)(181, 182)(183, 187)(184, 193)(185, 188)(186, 194)(189, 191)(190, 192)(195, 216)(196, 215)(197, 214)(198, 213)(199, 200)(201, 205)(202, 211)(203, 206)(204, 212)(207, 209)(208, 210)

MAP           : A4.152
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^4, x.2^4, (x.3^-1 * x.2^-1)^2, (x.2 * x.3^-1)^3, (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        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 189)(38, 196)(39, 181)(40, 203)(41, 210)(42, 212)(43, 183)(44, 202)(45, 187)(46, 197)(47, 216)(48, 206)(49, 198)(50, 201)(51, 194)(52, 188)(53, 184)(54, 199)(55, 204)(56, 195)(57, 200)(58, 182)(59, 190)(60, 193)(61, 208)(62, 186)(63, 209)(64, 211)(65, 213)(66, 191)(67, 214)(68, 192)(69, 215)(70, 205)(71, 207)(72, 185)(73, 150)(74, 177)(75, 146)(76, 164)(77, 172)(78, 175)(79, 154)(80, 168)(81, 155)(82, 157)(83, 159)(84, 173)(85, 160)(86, 174)(87, 161)(88, 151)(89, 153)(90, 167)(91, 171)(92, 178)(93, 163)(94, 149)(95, 156)(96, 158)(97, 165)(98, 148)(99, 169)(100, 179)(101, 162)(102, 152)(103, 180)(104, 147)(105, 176)(106, 170)(107, 166)(108, 145)

MAP           : A4.153
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2 | x.1^2, x.2^6, (x.2 * x.1)^4, (x.2 * x.1 * x.2^-1 * x.1)^2, x.2^2 * x.1 * x.2^2 * x.1 * x.2^-2 * x.1 * x.2^-2 * x.1 >
SCHREIER VEC. : (x.1, x.2, x.2^-1)
LOCAL TYPE    : (6, 8, 8)
#DARTS        : 216
R = (1, 73, 145)(2, 74, 146)(3, 75, 147)(4, 76, 148)(5, 77, 149)(6, 78, 150)(7, 79, 151)(8, 80, 152)(9, 81, 153)(10, 82, 154)(11, 83, 155)(12, 84, 156)(13, 85, 157)(14, 86, 158)(15, 87, 159)(16, 88, 160)(17, 89, 161)(18, 90, 162)(19, 91, 163)(20, 92, 164)(21, 93, 165)(22, 94, 166)(23, 95, 167)(24, 96, 168)(25, 97, 169)(26, 98, 170)(27, 99, 171)(28, 100, 172)(29, 101, 173)(30, 102, 174)(31, 103, 175)(32, 104, 176)(33, 105, 177)(34, 106, 178)(35, 107, 179)(36, 108, 180)(37, 109, 181)(38, 110, 182)(39, 111, 183)(40, 112, 184)(41, 113, 185)(42, 114, 186)(43, 115, 187)(44, 116, 188)(45, 117, 189)(46, 118, 190)(47, 119, 191)(48, 120, 192)(49, 121, 193)(50, 122, 194)(51, 123, 195)(52, 124, 196)(53, 125, 197)(54, 126, 198)(55, 127, 199)(56, 128, 200)(57, 129, 201)(58, 130, 202)(59, 131, 203)(60, 132, 204)(61, 133, 205)(62, 134, 206)(63, 135, 207)(64, 136, 208)(65, 137, 209)(66, 138, 210)(67, 139, 211)(68, 140, 212)(69, 141, 213)(70, 142, 214)(71, 143, 215)(72, 144, 216)
L = (1, 66)(2, 27)(3, 30)(4, 59)(5, 34)(6, 23)(7, 64)(8, 25)(9, 28)(10, 67)(11, 26)(12, 31)(13, 70)(14, 37)(15, 40)(16, 61)(17, 38)(18, 55)(19, 62)(20, 65)(21, 56)(22, 63)(24, 57)(29, 60)(32, 45)(33, 48)(35, 52)(36, 41)(39, 50)(42, 51)(43, 68)(44, 71)(46, 69)(47, 54)(49, 72)(53, 58)(73, 155)(74, 204)(75, 209)(76, 146)(77, 195)(78, 200)(79, 215)(80, 198)(81, 161)(82, 176)(83, 201)(84, 194)(85, 177)(86, 172)(87, 175)(88, 180)(89, 205)(90, 178)(91, 147)(92, 166)(93, 145)(94, 150)(95, 157)(96, 148)(97, 153)(98, 160)(99, 151)(100, 156)(101, 163)(102, 154)(103, 149)(104, 210)(105, 203)(106, 152)(107, 171)(108, 206)(109, 191)(110, 168)(111, 173)(112, 182)(113, 159)(114, 164)(115, 179)(116, 162)(117, 197)(118, 212)(119, 165)(120, 158)(121, 213)(122, 208)(123, 211)(124, 216)(125, 169)(126, 214)(127, 183)(128, 202)(129, 181)(130, 186)(131, 193)(132, 184)(133, 189)(134, 196)(135, 187)(136, 192)(137, 199)(138, 190)(139, 185)(140, 174)(141, 167)(142, 188)(143, 207)(144, 170)

MAP           : A4.154
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^4, x.3 * x.2^2 * x.3 * x.2^-2, (x.3 * x.1^-1)^3, (x.3 * x.2 * x.3^-1 * x.2)^2, (x.1 * x.2^-1)^4 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 8, 8)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 202)(39, 187)(40, 197)(41, 216)(42, 206)(43, 189)(44, 196)(45, 181)(46, 203)(47, 210)(48, 212)(49, 204)(50, 195)(51, 200)(52, 182)(53, 190)(54, 193)(55, 198)(56, 201)(57, 194)(58, 188)(59, 184)(60, 199)(61, 214)(62, 192)(63, 215)(64, 205)(65, 207)(66, 185)(67, 208)(68, 186)(69, 209)(70, 211)(71, 213)(72, 191)(73, 146)(74, 149)(75, 154)(76, 153)(77, 145)(78, 148)(79, 155)(80, 151)(81, 150)(82, 156)(83, 152)(84, 147)(85, 158)(86, 161)(87, 178)(88, 177)(89, 157)(90, 160)(91, 167)(92, 163)(93, 174)(94, 168)(95, 164)(96, 171)(97, 170)(98, 173)(99, 166)(100, 165)(101, 169)(102, 172)(103, 179)(104, 175)(105, 162)(106, 180)(107, 176)(108, 159)

MAP           : A4.155
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^4, x.3 * x.2^2 * x.3 * x.2^-2, (x.3 * x.1^-1)^3, (x.3 * x.2 * x.3^-1 * x.2)^2, (x.1 * x.2^-1)^4 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 8, 8)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 202)(39, 187)(40, 197)(41, 216)(42, 206)(43, 189)(44, 196)(45, 181)(46, 203)(47, 210)(48, 212)(49, 204)(50, 195)(51, 200)(52, 182)(53, 190)(54, 193)(55, 198)(56, 201)(57, 194)(58, 188)(59, 184)(60, 199)(61, 214)(62, 192)(63, 215)(64, 205)(65, 207)(66, 185)(67, 208)(68, 186)(69, 209)(70, 211)(71, 213)(72, 191)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 169)(86, 170)(87, 171)(88, 172)(89, 173)(90, 174)(91, 151)(92, 152)(93, 153)(94, 154)(95, 155)(96, 156)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 163)(104, 164)(105, 165)(106, 166)(107, 167)(108, 168)

MAP           : A4.156
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^4, x.3 * x.2^2 * x.3 * x.2^-2, (x.3 * x.1^-1)^3, (x.3 * x.2 * x.3^-1 * x.2)^2, (x.1 * x.2^-1)^4 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 8, 8)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 189)(38, 196)(39, 181)(40, 203)(41, 210)(42, 212)(43, 183)(44, 202)(45, 187)(46, 197)(47, 216)(48, 206)(49, 198)(50, 201)(51, 194)(52, 188)(53, 184)(54, 199)(55, 204)(56, 195)(57, 200)(58, 182)(59, 190)(60, 193)(61, 208)(62, 186)(63, 209)(64, 211)(65, 213)(66, 191)(67, 214)(68, 192)(69, 215)(70, 205)(71, 207)(72, 185)(73, 146)(74, 149)(75, 154)(76, 153)(77, 145)(78, 148)(79, 155)(80, 151)(81, 150)(82, 156)(83, 152)(84, 147)(85, 158)(86, 161)(87, 178)(88, 177)(89, 157)(90, 160)(91, 167)(92, 163)(93, 174)(94, 168)(95, 164)(96, 171)(97, 170)(98, 173)(99, 166)(100, 165)(101, 169)(102, 172)(103, 179)(104, 175)(105, 162)(106, 180)(107, 176)(108, 159)

MAP           : A4.157
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.2^4, x.3 * x.2^2 * x.3 * x.2^-2, (x.3 * x.1^-1)^3, (x.3 * x.2 * x.3^-1 * x.2)^2, (x.1 * x.2^-1)^4 >
SCHREIER VEC. : (x.1, x.2, x.3)
LOCAL TYPE    : (6, 8, 8)
#DARTS        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 189)(38, 196)(39, 181)(40, 203)(41, 210)(42, 212)(43, 183)(44, 202)(45, 187)(46, 197)(47, 216)(48, 206)(49, 198)(50, 201)(51, 194)(52, 188)(53, 184)(54, 199)(55, 204)(56, 195)(57, 200)(58, 182)(59, 190)(60, 193)(61, 208)(62, 186)(63, 209)(64, 211)(65, 213)(66, 191)(67, 214)(68, 192)(69, 215)(70, 205)(71, 207)(72, 185)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 169)(86, 170)(87, 171)(88, 172)(89, 173)(90, 174)(91, 151)(92, 152)(93, 153)(94, 154)(95, 155)(96, 156)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 163)(104, 164)(105, 165)(106, 166)(107, 167)(108, 168)

MAP           : A4.158
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^4, x.2^4, (x.3^-1 * x.2^-1)^2, (x.2 * x.3^-1)^3, (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        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 202)(39, 187)(40, 197)(41, 216)(42, 206)(43, 189)(44, 196)(45, 181)(46, 203)(47, 210)(48, 212)(49, 204)(50, 195)(51, 200)(52, 182)(53, 190)(54, 193)(55, 198)(56, 201)(57, 194)(58, 188)(59, 184)(60, 199)(61, 214)(62, 192)(63, 215)(64, 205)(65, 207)(66, 185)(67, 208)(68, 186)(69, 209)(70, 211)(71, 213)(72, 191)(73, 171)(74, 178)(75, 163)(76, 149)(77, 156)(78, 158)(79, 165)(80, 148)(81, 169)(82, 179)(83, 162)(84, 152)(85, 180)(86, 147)(87, 176)(88, 170)(89, 166)(90, 145)(91, 150)(92, 177)(93, 146)(94, 164)(95, 172)(96, 175)(97, 154)(98, 168)(99, 155)(100, 157)(101, 159)(102, 173)(103, 160)(104, 174)(105, 161)(106, 151)(107, 153)(108, 167)

MAP           : A4.159
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^4, x.2^4, (x.3^-1 * x.2^-1)^2, (x.2 * x.3^-1)^3, (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        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 183)(38, 202)(39, 187)(40, 197)(41, 216)(42, 206)(43, 189)(44, 196)(45, 181)(46, 203)(47, 210)(48, 212)(49, 204)(50, 195)(51, 200)(52, 182)(53, 190)(54, 193)(55, 198)(56, 201)(57, 194)(58, 188)(59, 184)(60, 199)(61, 214)(62, 192)(63, 215)(64, 205)(65, 207)(66, 185)(67, 208)(68, 186)(69, 209)(70, 211)(71, 213)(72, 191)(73, 180)(74, 147)(75, 176)(76, 170)(77, 166)(78, 145)(79, 160)(80, 174)(81, 161)(82, 151)(83, 153)(84, 167)(85, 154)(86, 168)(87, 155)(88, 157)(89, 159)(90, 173)(91, 165)(92, 148)(93, 169)(94, 179)(95, 162)(96, 152)(97, 171)(98, 178)(99, 163)(100, 149)(101, 156)(102, 158)(103, 150)(104, 177)(105, 146)(106, 164)(107, 172)(108, 175)

MAP           : A4.160
NOTES         : type I, reflexible, isomorphic to TDual({4,6}), isomorphic to A4.143.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1, x.3^4, x.2^4, (x.3^-1 * x.2^-1)^2, (x.2 * x.3^-1)^3, (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        : 216
R = (1, 37, 73)(2, 38, 74)(3, 39, 75)(4, 40, 76)(5, 41, 77)(6, 42, 78)(7, 43, 79)(8, 44, 80)(9, 45, 81)(10, 46, 82)(11, 47, 83)(12, 48, 84)(13, 49, 85)(14, 50, 86)(15, 51, 87)(16, 52, 88)(17, 53, 89)(18, 54, 90)(19, 55, 91)(20, 56, 92)(21, 57, 93)(22, 58, 94)(23, 59, 95)(24, 60, 96)(25, 61, 97)(26, 62, 98)(27, 63, 99)(28, 64, 100)(29, 65, 101)(30, 66, 102)(31, 67, 103)(32, 68, 104)(33, 69, 105)(34, 70, 106)(35, 71, 107)(36, 72, 108)(109, 145, 181)(110, 146, 182)(111, 147, 183)(112, 148, 184)(113, 149, 185)(114, 150, 186)(115, 151, 187)(116, 152, 188)(117, 153, 189)(118, 154, 190)(119, 155, 191)(120, 156, 192)(121, 157, 193)(122, 158, 194)(123, 159, 195)(124, 160, 196)(125, 161, 197)(126, 162, 198)(127, 163, 199)(128, 164, 200)(129, 165, 201)(130, 166, 202)(131, 167, 203)(132, 168, 204)(133, 169, 205)(134, 170, 206)(135, 171, 207)(136, 172, 208)(137, 173, 209)(138, 174, 210)(139, 175, 211)(140, 176, 212)(141, 177, 213)(142, 178, 214)(143, 179, 215)(144, 180, 216)
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, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 189)(38, 196)(39, 181)(40, 203)(41, 210)(42, 212)(43, 183)(44, 202)(45, 187)(46, 197)(47, 216)(48, 206)(49, 198)(50, 201)(51, 194)(52, 188)(53, 184)(54, 199)(55, 204)(56, 195)(57, 200)(58, 182)(59, 190)(60, 193)(61, 208)(62, 186)(63, 209)(64, 211)(65, 213)(66, 191)(67, 214)(68, 192)(69, 215)(70, 205)(71, 207)(72, 185)(73, 162)(74, 165)(75, 158)(76, 152)(77, 148)(78, 163)(79, 178)(80, 156)(81, 179)(82, 169)(83, 171)(84, 149)(85, 172)(86, 150)(87, 173)(88, 175)(89, 177)(90, 155)(91, 147)(92, 166)(93, 151)(94, 161)(95, 180)(96, 170)(97, 153)(98, 160)(99, 145)(100, 167)(101, 174)(102, 176)(103, 168)(104, 159)(105, 164)(106, 146)(107, 154)(108, 157)

MAP           : A4.161
NOTES         : type II, reflexible, representative.
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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, (x.2 * x.1)^2, (x.2 * x.4^-1 * x.1)^2, (x.4^-1 * x.1)^3, (x.4 * x.2)^3, x.3 * x.4^-1 * x.1 * x.4 * x.3 * x.1 * x.4^-1 * x.2, (x.4 * x.3^-1)^4 >
SCHREIER VEC. : (x.3, x.1, x.4)
LOCAL TYPE    : (8, 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, 42)(26, 44)(27, 41)(28, 43)(29, 39)(30, 37)(31, 40)(32, 38)(33, 48)(34, 47)(35, 46)(36, 45)(49, 98)(50, 100)(51, 97)(52, 99)(53, 103)(54, 101)(55, 104)(56, 102)(57, 112)(58, 111)(59, 110)(60, 109)(61, 118)(62, 120)(63, 117)(64, 119)(65, 107)(66, 105)(67, 108)(68, 106)(69, 116)(70, 115)(71, 114)(72, 113)(121, 133)(122, 134)(123, 135)(124, 136)(125, 137)(126, 138)(127, 139)(128, 140)(129, 141)(130, 142)(131, 143)(132, 144)

MAP           : A4.162
NOTES         : type II, reflexible, isomorphic to A4.161.
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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.3, x.1^2, x.2^2, x.4^4, x.4^-1 * x.1 * x.4 * x.2, x.4^-2 * x.2 * x.4 * x.2 * x.1, (x.2 * x.1)^3, (x.4 * x.3^-1)^4, (x.3 * x.1 * x.4^-1 * x.2)^2 >
SCHREIER VEC. : (x.3, x.1, x.4)
LOCAL TYPE    : (8, 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, 42)(26, 44)(27, 41)(28, 43)(29, 39)(30, 37)(31, 40)(32, 38)(33, 48)(34, 47)(35, 46)(36, 45)(49, 98)(50, 100)(51, 97)(52, 99)(53, 103)(54, 101)(55, 104)(56, 102)(57, 112)(58, 111)(59, 110)(60, 109)(61, 118)(62, 120)(63, 117)(64, 119)(65, 107)(66, 105)(67, 108)(68, 106)(69, 116)(70, 115)(71, 114)(72, 113)(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           : A4.163
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), representative.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3 * x.2 * x.4, x.2^3, x.4^3, x.1^-1 * x.4 * x.1^-1 * x.4^-1, x.3^-2 * x.2^-1 * x.3 * x.4^-1, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 83)(38, 102)(39, 76)(40, 82)(41, 98)(42, 101)(43, 100)(44, 73)(45, 78)(46, 75)(47, 80)(48, 97)(49, 96)(50, 89)(51, 79)(52, 91)(53, 90)(54, 86)(55, 106)(56, 84)(57, 74)(58, 103)(59, 108)(60, 107)(61, 92)(62, 105)(63, 94)(64, 87)(65, 81)(66, 93)(67, 99)(68, 95)(69, 77)(70, 88)(71, 85)(72, 104)(109, 183)(110, 188)(111, 189)(112, 201)(113, 215)(114, 192)(115, 198)(116, 207)(117, 216)(118, 213)(119, 195)(120, 214)(121, 184)(122, 181)(123, 186)(124, 182)(125, 193)(126, 205)(127, 194)(128, 202)(129, 212)(130, 185)(131, 187)(132, 196)(133, 190)(134, 191)(135, 209)(136, 210)(137, 204)(138, 200)(139, 197)(140, 211)(141, 203)(142, 206)(143, 208)(144, 199)(217, 270)(218, 286)(219, 260)(220, 287)(221, 279)(222, 280)(223, 284)(224, 273)(225, 262)(226, 264)(227, 257)(228, 261)(229, 266)(230, 268)(231, 253)(232, 265)(233, 274)(234, 267)(235, 275)(236, 254)(237, 255)(238, 277)(239, 278)(240, 258)(241, 269)(242, 271)(243, 263)(244, 276)(245, 283)(246, 259)(247, 288)(248, 282)(249, 256)(250, 272)(251, 285)(252, 281)

MAP           : A4.164
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3 * x.2 * x.4, x.2^3, x.4^3, x.1^-1 * x.4 * x.1^-1 * x.4^-1, x.3^-2 * x.2^-1 * x.3 * x.4^-1, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 74)(38, 76)(39, 97)(40, 73)(41, 82)(42, 75)(43, 83)(44, 98)(45, 99)(46, 85)(47, 86)(48, 102)(49, 77)(50, 79)(51, 107)(52, 84)(53, 91)(54, 103)(55, 96)(56, 90)(57, 100)(58, 80)(59, 93)(60, 89)(61, 78)(62, 94)(63, 104)(64, 95)(65, 87)(66, 88)(67, 92)(68, 81)(69, 106)(70, 108)(71, 101)(72, 105)(109, 194)(110, 196)(111, 181)(112, 193)(113, 202)(114, 195)(115, 203)(116, 182)(117, 183)(118, 205)(119, 206)(120, 186)(121, 197)(122, 199)(123, 191)(124, 204)(125, 211)(126, 187)(127, 216)(128, 210)(129, 184)(130, 200)(131, 213)(132, 209)(133, 198)(134, 214)(135, 188)(136, 215)(137, 207)(138, 208)(139, 212)(140, 201)(141, 190)(142, 192)(143, 185)(144, 189)(217, 258)(218, 274)(219, 284)(220, 275)(221, 267)(222, 268)(223, 272)(224, 261)(225, 286)(226, 288)(227, 281)(228, 285)(229, 254)(230, 256)(231, 277)(232, 253)(233, 262)(234, 255)(235, 263)(236, 278)(237, 279)(238, 265)(239, 266)(240, 282)(241, 257)(242, 259)(243, 287)(244, 264)(245, 271)(246, 283)(247, 276)(248, 270)(249, 280)(250, 260)(251, 273)(252, 269)

MAP           : A4.165
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3 * x.2 * x.4, x.2^3, x.4^3, x.1^-1 * x.4 * x.1^-1 * x.4^-1, x.3^-2 * x.2^-1 * x.3 * x.4^-1, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 76)(38, 73)(39, 78)(40, 74)(41, 85)(42, 97)(43, 86)(44, 94)(45, 104)(46, 77)(47, 79)(48, 88)(49, 82)(50, 83)(51, 101)(52, 102)(53, 96)(54, 92)(55, 89)(56, 103)(57, 95)(58, 98)(59, 100)(60, 91)(61, 75)(62, 80)(63, 81)(64, 93)(65, 107)(66, 84)(67, 90)(68, 99)(69, 108)(70, 105)(71, 87)(72, 106)(109, 194)(110, 196)(111, 181)(112, 193)(113, 202)(114, 195)(115, 203)(116, 182)(117, 183)(118, 205)(119, 206)(120, 186)(121, 197)(122, 199)(123, 191)(124, 204)(125, 211)(126, 187)(127, 216)(128, 210)(129, 184)(130, 200)(131, 213)(132, 209)(133, 198)(134, 214)(135, 188)(136, 215)(137, 207)(138, 208)(139, 212)(140, 201)(141, 190)(142, 192)(143, 185)(144, 189)(217, 277)(218, 278)(219, 279)(220, 280)(221, 281)(222, 282)(223, 283)(224, 284)(225, 285)(226, 286)(227, 287)(228, 288)(229, 253)(230, 254)(231, 255)(232, 256)(233, 257)(234, 258)(235, 259)(236, 260)(237, 261)(238, 262)(239, 263)(240, 264)(241, 265)(242, 266)(243, 267)(244, 268)(245, 269)(246, 270)(247, 271)(248, 272)(249, 273)(250, 274)(251, 275)(252, 276)

MAP           : A4.166
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3 * x.2 * x.4, x.2^3, x.4^3, x.1^-1 * x.4 * x.1^-1 * x.4^-1, x.3^-2 * x.2^-1 * x.3 * x.4^-1, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 88)(38, 85)(39, 90)(40, 86)(41, 97)(42, 73)(43, 98)(44, 106)(45, 80)(46, 89)(47, 91)(48, 100)(49, 94)(50, 95)(51, 77)(52, 78)(53, 108)(54, 104)(55, 101)(56, 79)(57, 107)(58, 74)(59, 76)(60, 103)(61, 87)(62, 92)(63, 93)(64, 105)(65, 83)(66, 96)(67, 102)(68, 75)(69, 84)(70, 81)(71, 99)(72, 82)(109, 194)(110, 196)(111, 181)(112, 193)(113, 202)(114, 195)(115, 203)(116, 182)(117, 183)(118, 205)(119, 206)(120, 186)(121, 197)(122, 199)(123, 191)(124, 204)(125, 211)(126, 187)(127, 216)(128, 210)(129, 184)(130, 200)(131, 213)(132, 209)(133, 198)(134, 214)(135, 188)(136, 215)(137, 207)(138, 208)(139, 212)(140, 201)(141, 190)(142, 192)(143, 185)(144, 189)(217, 284)(218, 261)(219, 286)(220, 279)(221, 273)(222, 285)(223, 255)(224, 287)(225, 269)(226, 280)(227, 277)(228, 260)(229, 275)(230, 258)(231, 268)(232, 274)(233, 254)(234, 257)(235, 256)(236, 265)(237, 270)(238, 267)(239, 272)(240, 253)(241, 288)(242, 281)(243, 271)(244, 283)(245, 282)(246, 278)(247, 262)(248, 276)(249, 266)(250, 259)(251, 264)(252, 263)

MAP           : A4.167
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3 * x.2 * x.4, x.2^3, x.4^3, x.1^-1 * x.4 * x.1^-1 * x.4^-1, x.3^-2 * x.2^-1 * x.3 * x.4^-1, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 80)(38, 93)(39, 82)(40, 75)(41, 105)(42, 81)(43, 87)(44, 83)(45, 101)(46, 76)(47, 73)(48, 92)(49, 107)(50, 90)(51, 100)(52, 106)(53, 86)(54, 89)(55, 88)(56, 97)(57, 102)(58, 99)(59, 104)(60, 85)(61, 84)(62, 77)(63, 103)(64, 79)(65, 78)(66, 74)(67, 94)(68, 108)(69, 98)(70, 91)(71, 96)(72, 95)(109, 194)(110, 196)(111, 181)(112, 193)(113, 202)(114, 195)(115, 203)(116, 182)(117, 183)(118, 205)(119, 206)(120, 186)(121, 197)(122, 199)(123, 191)(124, 204)(125, 211)(126, 187)(127, 216)(128, 210)(129, 184)(130, 200)(131, 213)(132, 209)(133, 198)(134, 214)(135, 188)(136, 215)(137, 207)(138, 208)(139, 212)(140, 201)(141, 190)(142, 192)(143, 185)(144, 189)(217, 256)(218, 253)(219, 258)(220, 254)(221, 265)(222, 277)(223, 266)(224, 274)(225, 284)(226, 257)(227, 259)(228, 268)(229, 262)(230, 263)(231, 281)(232, 282)(233, 276)(234, 272)(235, 269)(236, 283)(237, 275)(238, 278)(239, 280)(240, 271)(241, 255)(242, 260)(243, 261)(244, 273)(245, 287)(246, 264)(247, 270)(248, 279)(249, 288)(250, 285)(251, 267)(252, 286)

MAP           : A4.168
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3 * x.2 * x.4, x.2^3, x.4^3, x.1^-1 * x.4 * x.1^-1 * x.4^-1, x.3^-2 * x.2^-1 * x.3 * x.4^-1, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 83)(38, 102)(39, 76)(40, 82)(41, 98)(42, 101)(43, 100)(44, 73)(45, 78)(46, 75)(47, 80)(48, 97)(49, 96)(50, 89)(51, 79)(52, 91)(53, 90)(54, 86)(55, 106)(56, 84)(57, 74)(58, 103)(59, 108)(60, 107)(61, 92)(62, 105)(63, 94)(64, 87)(65, 81)(66, 93)(67, 99)(68, 95)(69, 77)(70, 88)(71, 85)(72, 104)(109, 194)(110, 196)(111, 181)(112, 193)(113, 202)(114, 195)(115, 203)(116, 182)(117, 183)(118, 205)(119, 206)(120, 186)(121, 197)(122, 199)(123, 191)(124, 204)(125, 211)(126, 187)(127, 216)(128, 210)(129, 184)(130, 200)(131, 213)(132, 209)(133, 198)(134, 214)(135, 188)(136, 215)(137, 207)(138, 208)(139, 212)(140, 201)(141, 190)(142, 192)(143, 185)(144, 189)(217, 262)(218, 263)(219, 281)(220, 282)(221, 276)(222, 272)(223, 269)(224, 283)(225, 275)(226, 278)(227, 280)(228, 271)(229, 255)(230, 260)(231, 261)(232, 273)(233, 287)(234, 264)(235, 270)(236, 279)(237, 288)(238, 285)(239, 267)(240, 286)(241, 256)(242, 253)(243, 258)(244, 254)(245, 265)(246, 277)(247, 266)(248, 274)(249, 284)(250, 257)(251, 259)(252, 268)

MAP           : A4.169
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2 | x.1^3, (x.2 * x.1)^2, (x.1 * x.2^-2)^3, x.2^3 * x.1^-1 * x.2^-5 * x.1^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 4, 12, 4)
#DARTS        : 288
R = (1, 73, 145, 217)(2, 74, 146, 218)(3, 75, 147, 219)(4, 76, 148, 220)(5, 77, 149, 221)(6, 78, 150, 222)(7, 79, 151, 223)(8, 80, 152, 224)(9, 81, 153, 225)(10, 82, 154, 226)(11, 83, 155, 227)(12, 84, 156, 228)(13, 85, 157, 229)(14, 86, 158, 230)(15, 87, 159, 231)(16, 88, 160, 232)(17, 89, 161, 233)(18, 90, 162, 234)(19, 91, 163, 235)(20, 92, 164, 236)(21, 93, 165, 237)(22, 94, 166, 238)(23, 95, 167, 239)(24, 96, 168, 240)(25, 97, 169, 241)(26, 98, 170, 242)(27, 99, 171, 243)(28, 100, 172, 244)(29, 101, 173, 245)(30, 102, 174, 246)(31, 103, 175, 247)(32, 104, 176, 248)(33, 105, 177, 249)(34, 106, 178, 250)(35, 107, 179, 251)(36, 108, 180, 252)(37, 109, 181, 253)(38, 110, 182, 254)(39, 111, 183, 255)(40, 112, 184, 256)(41, 113, 185, 257)(42, 114, 186, 258)(43, 115, 187, 259)(44, 116, 188, 260)(45, 117, 189, 261)(46, 118, 190, 262)(47, 119, 191, 263)(48, 120, 192, 264)(49, 121, 193, 265)(50, 122, 194, 266)(51, 123, 195, 267)(52, 124, 196, 268)(53, 125, 197, 269)(54, 126, 198, 270)(55, 127, 199, 271)(56, 128, 200, 272)(57, 129, 201, 273)(58, 130, 202, 274)(59, 131, 203, 275)(60, 132, 204, 276)(61, 133, 205, 277)(62, 134, 206, 278)(63, 135, 207, 279)(64, 136, 208, 280)(65, 137, 209, 281)(66, 138, 210, 282)(67, 139, 211, 283)(68, 140, 212, 284)(69, 141, 213, 285)(70, 142, 214, 286)(71, 143, 215, 287)(72, 144, 216, 288)
L = (1, 75)(2, 80)(3, 78)(4, 77)(5, 81)(6, 73)(7, 130)(8, 83)(9, 76)(10, 84)(11, 74)(12, 115)(13, 87)(14, 92)(15, 90)(16, 89)(17, 93)(18, 85)(19, 118)(20, 95)(21, 88)(22, 96)(23, 86)(24, 103)(25, 111)(26, 116)(27, 114)(28, 113)(29, 117)(30, 109)(31, 94)(32, 119)(33, 112)(34, 120)(35, 110)(36, 79)(37, 123)(38, 128)(39, 126)(40, 125)(41, 129)(42, 121)(43, 82)(44, 131)(45, 124)(46, 132)(47, 122)(48, 139)(49, 99)(50, 104)(51, 102)(52, 101)(53, 105)(54, 97)(55, 142)(56, 107)(57, 100)(58, 108)(59, 98)(60, 91)(61, 135)(62, 140)(63, 138)(64, 137)(65, 141)(66, 133)(67, 106)(68, 143)(69, 136)(70, 144)(71, 134)(72, 127)(145, 218)(146, 223)(147, 220)(148, 254)(149, 217)(150, 259)(151, 232)(152, 222)(153, 283)(154, 219)(155, 268)(156, 266)(157, 237)(158, 231)(159, 240)(160, 234)(161, 252)(162, 239)(163, 236)(164, 249)(165, 275)(166, 251)(167, 276)(168, 273)(169, 274)(170, 233)(171, 272)(172, 238)(173, 224)(174, 269)(175, 229)(176, 226)(177, 267)(178, 221)(179, 265)(180, 270)(181, 242)(182, 247)(183, 244)(184, 230)(185, 241)(186, 235)(187, 256)(188, 246)(189, 271)(190, 243)(191, 280)(192, 278)(193, 261)(194, 255)(195, 264)(196, 258)(197, 228)(198, 263)(199, 260)(200, 225)(201, 287)(202, 227)(203, 288)(204, 285)(205, 286)(206, 257)(207, 284)(208, 262)(209, 248)(210, 281)(211, 253)(212, 250)(213, 279)(214, 245)(215, 277)(216, 282)

MAP           : A4.170
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2 | x.1^3, (x.2 * x.1)^2, (x.1 * x.2^-2)^3, x.2^3 * x.1^-1 * x.2^-5 * x.1^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 4, 12, 4)
#DARTS        : 288
R = (1, 73, 145, 217)(2, 74, 146, 218)(3, 75, 147, 219)(4, 76, 148, 220)(5, 77, 149, 221)(6, 78, 150, 222)(7, 79, 151, 223)(8, 80, 152, 224)(9, 81, 153, 225)(10, 82, 154, 226)(11, 83, 155, 227)(12, 84, 156, 228)(13, 85, 157, 229)(14, 86, 158, 230)(15, 87, 159, 231)(16, 88, 160, 232)(17, 89, 161, 233)(18, 90, 162, 234)(19, 91, 163, 235)(20, 92, 164, 236)(21, 93, 165, 237)(22, 94, 166, 238)(23, 95, 167, 239)(24, 96, 168, 240)(25, 97, 169, 241)(26, 98, 170, 242)(27, 99, 171, 243)(28, 100, 172, 244)(29, 101, 173, 245)(30, 102, 174, 246)(31, 103, 175, 247)(32, 104, 176, 248)(33, 105, 177, 249)(34, 106, 178, 250)(35, 107, 179, 251)(36, 108, 180, 252)(37, 109, 181, 253)(38, 110, 182, 254)(39, 111, 183, 255)(40, 112, 184, 256)(41, 113, 185, 257)(42, 114, 186, 258)(43, 115, 187, 259)(44, 116, 188, 260)(45, 117, 189, 261)(46, 118, 190, 262)(47, 119, 191, 263)(48, 120, 192, 264)(49, 121, 193, 265)(50, 122, 194, 266)(51, 123, 195, 267)(52, 124, 196, 268)(53, 125, 197, 269)(54, 126, 198, 270)(55, 127, 199, 271)(56, 128, 200, 272)(57, 129, 201, 273)(58, 130, 202, 274)(59, 131, 203, 275)(60, 132, 204, 276)(61, 133, 205, 277)(62, 134, 206, 278)(63, 135, 207, 279)(64, 136, 208, 280)(65, 137, 209, 281)(66, 138, 210, 282)(67, 139, 211, 283)(68, 140, 212, 284)(69, 141, 213, 285)(70, 142, 214, 286)(71, 143, 215, 287)(72, 144, 216, 288)
L = (1, 78)(2, 83)(3, 73)(4, 81)(5, 76)(6, 75)(7, 108)(8, 74)(9, 77)(10, 115)(11, 80)(12, 82)(13, 90)(14, 95)(15, 85)(16, 93)(17, 88)(18, 87)(19, 132)(20, 86)(21, 89)(22, 103)(23, 92)(24, 94)(25, 126)(26, 131)(27, 121)(28, 129)(29, 124)(30, 123)(31, 96)(32, 122)(33, 125)(34, 139)(35, 128)(36, 130)(37, 102)(38, 107)(39, 97)(40, 105)(41, 100)(42, 99)(43, 84)(44, 98)(45, 101)(46, 91)(47, 104)(48, 106)(49, 114)(50, 119)(51, 109)(52, 117)(53, 112)(54, 111)(55, 144)(56, 110)(57, 113)(58, 79)(59, 116)(60, 118)(61, 138)(62, 143)(63, 133)(64, 141)(65, 136)(66, 135)(67, 120)(68, 134)(69, 137)(70, 127)(71, 140)(72, 142)(145, 259)(146, 268)(147, 218)(148, 283)(149, 254)(150, 220)(151, 270)(152, 223)(153, 217)(154, 256)(155, 222)(156, 219)(157, 239)(158, 276)(159, 237)(160, 275)(161, 234)(162, 240)(163, 285)(164, 231)(165, 252)(166, 229)(167, 249)(168, 251)(169, 263)(170, 288)(171, 261)(172, 287)(173, 258)(174, 264)(175, 273)(176, 255)(177, 228)(178, 253)(179, 225)(180, 227)(181, 269)(182, 265)(183, 274)(184, 267)(185, 238)(186, 272)(187, 266)(188, 233)(189, 224)(190, 236)(191, 226)(192, 221)(193, 235)(194, 280)(195, 242)(196, 271)(197, 230)(198, 244)(199, 282)(200, 247)(201, 241)(202, 232)(203, 246)(204, 243)(205, 281)(206, 277)(207, 286)(208, 279)(209, 262)(210, 284)(211, 278)(212, 257)(213, 248)(214, 260)(215, 250)(216, 245)

MAP           : A4.171
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3 * x.2 * x.4, x.2^3, x.4^3, x.1^-1 * x.4 * x.1^-1 * x.4^-1, x.3^-2 * x.2^-1 * x.3 * x.4^-1, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 74)(38, 76)(39, 97)(40, 73)(41, 82)(42, 75)(43, 83)(44, 98)(45, 99)(46, 85)(47, 86)(48, 102)(49, 77)(50, 79)(51, 107)(52, 84)(53, 91)(54, 103)(55, 96)(56, 90)(57, 100)(58, 80)(59, 93)(60, 89)(61, 78)(62, 94)(63, 104)(64, 95)(65, 87)(66, 88)(67, 92)(68, 81)(69, 106)(70, 108)(71, 101)(72, 105)(109, 183)(110, 188)(111, 189)(112, 201)(113, 215)(114, 192)(115, 198)(116, 207)(117, 216)(118, 213)(119, 195)(120, 214)(121, 184)(122, 181)(123, 186)(124, 182)(125, 193)(126, 205)(127, 194)(128, 202)(129, 212)(130, 185)(131, 187)(132, 196)(133, 190)(134, 191)(135, 209)(136, 210)(137, 204)(138, 200)(139, 197)(140, 211)(141, 203)(142, 206)(143, 208)(144, 199)(217, 263)(218, 282)(219, 256)(220, 262)(221, 278)(222, 281)(223, 280)(224, 253)(225, 258)(226, 255)(227, 260)(228, 277)(229, 276)(230, 269)(231, 259)(232, 271)(233, 270)(234, 266)(235, 286)(236, 264)(237, 254)(238, 283)(239, 288)(240, 287)(241, 272)(242, 285)(243, 274)(244, 267)(245, 261)(246, 273)(247, 279)(248, 275)(249, 257)(250, 268)(251, 265)(252, 284)

MAP           : A4.172
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3 * x.2 * x.4, x.2^3, x.4^3, x.1^-1 * x.4 * x.1^-1 * x.4^-1, x.3^-2 * x.2^-1 * x.3 * x.4^-1, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 76)(38, 73)(39, 78)(40, 74)(41, 85)(42, 97)(43, 86)(44, 94)(45, 104)(46, 77)(47, 79)(48, 88)(49, 82)(50, 83)(51, 101)(52, 102)(53, 96)(54, 92)(55, 89)(56, 103)(57, 95)(58, 98)(59, 100)(60, 91)(61, 75)(62, 80)(63, 81)(64, 93)(65, 107)(66, 84)(67, 90)(68, 99)(69, 108)(70, 105)(71, 87)(72, 106)(109, 183)(110, 188)(111, 189)(112, 201)(113, 215)(114, 192)(115, 198)(116, 207)(117, 216)(118, 213)(119, 195)(120, 214)(121, 184)(122, 181)(123, 186)(124, 182)(125, 193)(126, 205)(127, 194)(128, 202)(129, 212)(130, 185)(131, 187)(132, 196)(133, 190)(134, 191)(135, 209)(136, 210)(137, 204)(138, 200)(139, 197)(140, 211)(141, 203)(142, 206)(143, 208)(144, 199)(217, 259)(218, 264)(219, 254)(220, 257)(221, 260)(222, 287)(223, 273)(224, 256)(225, 277)(226, 258)(227, 274)(228, 255)(229, 271)(230, 276)(231, 266)(232, 269)(233, 272)(234, 263)(235, 285)(236, 268)(237, 253)(238, 270)(239, 286)(240, 267)(241, 283)(242, 288)(243, 278)(244, 281)(245, 284)(246, 275)(247, 261)(248, 280)(249, 265)(250, 282)(251, 262)(252, 279)

MAP           : A4.173
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3 * x.2 * x.4, x.2^3, x.4^3, x.1^-1 * x.4 * x.1^-1 * x.4^-1, x.3^-2 * x.2^-1 * x.3 * x.4^-1, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 78)(38, 94)(39, 104)(40, 95)(41, 87)(42, 88)(43, 92)(44, 81)(45, 106)(46, 108)(47, 101)(48, 105)(49, 74)(50, 76)(51, 97)(52, 73)(53, 82)(54, 75)(55, 83)(56, 98)(57, 99)(58, 85)(59, 86)(60, 102)(61, 77)(62, 79)(63, 107)(64, 84)(65, 91)(66, 103)(67, 96)(68, 90)(69, 100)(70, 80)(71, 93)(72, 89)(109, 183)(110, 188)(111, 189)(112, 201)(113, 215)(114, 192)(115, 198)(116, 207)(117, 216)(118, 213)(119, 195)(120, 214)(121, 184)(122, 181)(123, 186)(124, 182)(125, 193)(126, 205)(127, 194)(128, 202)(129, 212)(130, 185)(131, 187)(132, 196)(133, 190)(134, 191)(135, 209)(136, 210)(137, 204)(138, 200)(139, 197)(140, 211)(141, 203)(142, 206)(143, 208)(144, 199)(217, 275)(218, 258)(219, 268)(220, 274)(221, 254)(222, 257)(223, 256)(224, 265)(225, 270)(226, 267)(227, 272)(228, 253)(229, 288)(230, 281)(231, 271)(232, 283)(233, 282)(234, 278)(235, 262)(236, 276)(237, 266)(238, 259)(239, 264)(240, 263)(241, 284)(242, 261)(243, 286)(244, 279)(245, 273)(246, 285)(247, 255)(248, 287)(249, 269)(250, 280)(251, 277)(252, 260)

MAP           : A4.174
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3 * x.2 * x.4, x.2^3, x.4^3, x.1^-1 * x.4 * x.1^-1 * x.4^-1, x.3^-2 * x.2^-1 * x.3 * x.4^-1, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 88)(38, 85)(39, 90)(40, 86)(41, 97)(42, 73)(43, 98)(44, 106)(45, 80)(46, 89)(47, 91)(48, 100)(49, 94)(50, 95)(51, 77)(52, 78)(53, 108)(54, 104)(55, 101)(56, 79)(57, 107)(58, 74)(59, 76)(60, 103)(61, 87)(62, 92)(63, 93)(64, 105)(65, 83)(66, 96)(67, 102)(68, 75)(69, 84)(70, 81)(71, 99)(72, 82)(109, 183)(110, 188)(111, 189)(112, 201)(113, 215)(114, 192)(115, 198)(116, 207)(117, 216)(118, 213)(119, 195)(120, 214)(121, 184)(122, 181)(123, 186)(124, 182)(125, 193)(126, 205)(127, 194)(128, 202)(129, 212)(130, 185)(131, 187)(132, 196)(133, 190)(134, 191)(135, 209)(136, 210)(137, 204)(138, 200)(139, 197)(140, 211)(141, 203)(142, 206)(143, 208)(144, 199)(217, 256)(218, 253)(219, 258)(220, 254)(221, 265)(222, 277)(223, 266)(224, 274)(225, 284)(226, 257)(227, 259)(228, 268)(229, 262)(230, 263)(231, 281)(232, 282)(233, 276)(234, 272)(235, 269)(236, 283)(237, 275)(238, 278)(239, 280)(240, 271)(241, 255)(242, 260)(243, 261)(244, 273)(245, 287)(246, 264)(247, 270)(248, 279)(249, 288)(250, 285)(251, 267)(252, 286)

MAP           : A4.175
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3 * x.2 * x.4, x.2^3, x.4^3, x.1^-1 * x.4 * x.1^-1 * x.4^-1, x.3^-2 * x.2^-1 * x.3 * x.4^-1, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 80)(38, 93)(39, 82)(40, 75)(41, 105)(42, 81)(43, 87)(44, 83)(45, 101)(46, 76)(47, 73)(48, 92)(49, 107)(50, 90)(51, 100)(52, 106)(53, 86)(54, 89)(55, 88)(56, 97)(57, 102)(58, 99)(59, 104)(60, 85)(61, 84)(62, 77)(63, 103)(64, 79)(65, 78)(66, 74)(67, 94)(68, 108)(69, 98)(70, 91)(71, 96)(72, 95)(109, 183)(110, 188)(111, 189)(112, 201)(113, 215)(114, 192)(115, 198)(116, 207)(117, 216)(118, 213)(119, 195)(120, 214)(121, 184)(122, 181)(123, 186)(124, 182)(125, 193)(126, 205)(127, 194)(128, 202)(129, 212)(130, 185)(131, 187)(132, 196)(133, 190)(134, 191)(135, 209)(136, 210)(137, 204)(138, 200)(139, 197)(140, 211)(141, 203)(142, 206)(143, 208)(144, 199)(217, 269)(218, 271)(219, 263)(220, 276)(221, 283)(222, 259)(223, 288)(224, 282)(225, 256)(226, 272)(227, 285)(228, 281)(229, 270)(230, 286)(231, 260)(232, 287)(233, 279)(234, 280)(235, 284)(236, 273)(237, 262)(238, 264)(239, 257)(240, 261)(241, 266)(242, 268)(243, 253)(244, 265)(245, 274)(246, 267)(247, 275)(248, 254)(249, 255)(250, 277)(251, 278)(252, 258)

MAP           : A4.176
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2 | x.2^3, (x.1 * x.2)^2, (x.1^2 * x.2^-1)^3, x.1^-2 * x.2^-1 * x.1^3 * x.2^-1 * x.1^-3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 4, 12, 4)
#DARTS        : 288
R = (1, 73, 145, 217)(2, 74, 146, 218)(3, 75, 147, 219)(4, 76, 148, 220)(5, 77, 149, 221)(6, 78, 150, 222)(7, 79, 151, 223)(8, 80, 152, 224)(9, 81, 153, 225)(10, 82, 154, 226)(11, 83, 155, 227)(12, 84, 156, 228)(13, 85, 157, 229)(14, 86, 158, 230)(15, 87, 159, 231)(16, 88, 160, 232)(17, 89, 161, 233)(18, 90, 162, 234)(19, 91, 163, 235)(20, 92, 164, 236)(21, 93, 165, 237)(22, 94, 166, 238)(23, 95, 167, 239)(24, 96, 168, 240)(25, 97, 169, 241)(26, 98, 170, 242)(27, 99, 171, 243)(28, 100, 172, 244)(29, 101, 173, 245)(30, 102, 174, 246)(31, 103, 175, 247)(32, 104, 176, 248)(33, 105, 177, 249)(34, 106, 178, 250)(35, 107, 179, 251)(36, 108, 180, 252)(37, 109, 181, 253)(38, 110, 182, 254)(39, 111, 183, 255)(40, 112, 184, 256)(41, 113, 185, 257)(42, 114, 186, 258)(43, 115, 187, 259)(44, 116, 188, 260)(45, 117, 189, 261)(46, 118, 190, 262)(47, 119, 191, 263)(48, 120, 192, 264)(49, 121, 193, 265)(50, 122, 194, 266)(51, 123, 195, 267)(52, 124, 196, 268)(53, 125, 197, 269)(54, 126, 198, 270)(55, 127, 199, 271)(56, 128, 200, 272)(57, 129, 201, 273)(58, 130, 202, 274)(59, 131, 203, 275)(60, 132, 204, 276)(61, 133, 205, 277)(62, 134, 206, 278)(63, 135, 207, 279)(64, 136, 208, 280)(65, 137, 209, 281)(66, 138, 210, 282)(67, 139, 211, 283)(68, 140, 212, 284)(69, 141, 213, 285)(70, 142, 214, 286)(71, 143, 215, 287)(72, 144, 216, 288)
L = (1, 74)(2, 79)(3, 76)(4, 110)(5, 73)(6, 115)(7, 88)(8, 78)(9, 139)(10, 75)(11, 124)(12, 122)(13, 93)(14, 87)(15, 96)(16, 90)(17, 108)(18, 95)(19, 92)(20, 105)(21, 131)(22, 107)(23, 132)(24, 129)(25, 130)(26, 89)(27, 128)(28, 94)(29, 80)(30, 125)(31, 85)(32, 82)(33, 123)(34, 77)(35, 121)(36, 126)(37, 98)(38, 103)(39, 100)(40, 86)(41, 97)(42, 91)(43, 112)(44, 102)(45, 127)(46, 99)(47, 136)(48, 134)(49, 117)(50, 111)(51, 120)(52, 114)(53, 84)(54, 119)(55, 116)(56, 81)(57, 143)(58, 83)(59, 144)(60, 141)(61, 142)(62, 113)(63, 140)(64, 118)(65, 104)(66, 137)(67, 109)(68, 106)(69, 135)(70, 101)(71, 133)(72, 138)(145, 219)(146, 224)(147, 222)(148, 221)(149, 225)(150, 217)(151, 274)(152, 227)(153, 220)(154, 228)(155, 218)(156, 259)(157, 231)(158, 236)(159, 234)(160, 233)(161, 237)(162, 229)(163, 262)(164, 239)(165, 232)(166, 240)(167, 230)(168, 247)(169, 255)(170, 260)(171, 258)(172, 257)(173, 261)(174, 253)(175, 238)(176, 263)(177, 256)(178, 264)(179, 254)(180, 223)(181, 267)(182, 272)(183, 270)(184, 269)(185, 273)(186, 265)(187, 226)(188, 275)(189, 268)(190, 276)(191, 266)(192, 283)(193, 243)(194, 248)(195, 246)(196, 245)(197, 249)(198, 241)(199, 286)(200, 251)(201, 244)(202, 252)(203, 242)(204, 235)(205, 279)(206, 284)(207, 282)(208, 281)(209, 285)(210, 277)(211, 250)(212, 287)(213, 280)(214, 288)(215, 278)(216, 271)

MAP           : A4.177
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2 | x.2^3, (x.1 * x.2)^2, (x.1^2 * x.2^-1)^3, x.1^-2 * x.2^-1 * x.1^3 * x.2^-1 * x.1^-3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 4, 12, 4)
#DARTS        : 288
R = (1, 73, 145, 217)(2, 74, 146, 218)(3, 75, 147, 219)(4, 76, 148, 220)(5, 77, 149, 221)(6, 78, 150, 222)(7, 79, 151, 223)(8, 80, 152, 224)(9, 81, 153, 225)(10, 82, 154, 226)(11, 83, 155, 227)(12, 84, 156, 228)(13, 85, 157, 229)(14, 86, 158, 230)(15, 87, 159, 231)(16, 88, 160, 232)(17, 89, 161, 233)(18, 90, 162, 234)(19, 91, 163, 235)(20, 92, 164, 236)(21, 93, 165, 237)(22, 94, 166, 238)(23, 95, 167, 239)(24, 96, 168, 240)(25, 97, 169, 241)(26, 98, 170, 242)(27, 99, 171, 243)(28, 100, 172, 244)(29, 101, 173, 245)(30, 102, 174, 246)(31, 103, 175, 247)(32, 104, 176, 248)(33, 105, 177, 249)(34, 106, 178, 250)(35, 107, 179, 251)(36, 108, 180, 252)(37, 109, 181, 253)(38, 110, 182, 254)(39, 111, 183, 255)(40, 112, 184, 256)(41, 113, 185, 257)(42, 114, 186, 258)(43, 115, 187, 259)(44, 116, 188, 260)(45, 117, 189, 261)(46, 118, 190, 262)(47, 119, 191, 263)(48, 120, 192, 264)(49, 121, 193, 265)(50, 122, 194, 266)(51, 123, 195, 267)(52, 124, 196, 268)(53, 125, 197, 269)(54, 126, 198, 270)(55, 127, 199, 271)(56, 128, 200, 272)(57, 129, 201, 273)(58, 130, 202, 274)(59, 131, 203, 275)(60, 132, 204, 276)(61, 133, 205, 277)(62, 134, 206, 278)(63, 135, 207, 279)(64, 136, 208, 280)(65, 137, 209, 281)(66, 138, 210, 282)(67, 139, 211, 283)(68, 140, 212, 284)(69, 141, 213, 285)(70, 142, 214, 286)(71, 143, 215, 287)(72, 144, 216, 288)
L = (1, 95)(2, 132)(3, 93)(4, 131)(5, 90)(6, 96)(7, 141)(8, 87)(9, 108)(10, 85)(11, 105)(12, 107)(13, 137)(14, 133)(15, 142)(16, 135)(17, 118)(18, 140)(19, 134)(20, 113)(21, 104)(22, 116)(23, 106)(24, 101)(25, 91)(26, 136)(27, 98)(28, 127)(29, 86)(30, 100)(31, 138)(32, 103)(33, 97)(34, 88)(35, 102)(36, 99)(37, 119)(38, 144)(39, 117)(40, 143)(41, 114)(42, 120)(43, 129)(44, 111)(45, 84)(46, 109)(47, 81)(48, 83)(49, 125)(50, 121)(51, 130)(52, 123)(53, 94)(54, 128)(55, 122)(56, 89)(57, 80)(58, 92)(59, 82)(60, 77)(61, 115)(62, 124)(63, 74)(64, 139)(65, 110)(66, 76)(67, 126)(68, 79)(69, 73)(70, 112)(71, 78)(72, 75)(145, 273)(146, 267)(147, 276)(148, 270)(149, 288)(150, 275)(151, 272)(152, 285)(153, 239)(154, 287)(155, 240)(156, 237)(157, 250)(158, 221)(159, 248)(160, 226)(161, 284)(162, 245)(163, 217)(164, 286)(165, 243)(166, 281)(167, 241)(168, 246)(169, 225)(170, 219)(171, 228)(172, 222)(173, 264)(174, 227)(175, 224)(176, 261)(177, 251)(178, 263)(179, 252)(180, 249)(181, 238)(182, 269)(183, 236)(184, 274)(185, 260)(186, 233)(187, 265)(188, 262)(189, 231)(190, 257)(191, 229)(192, 234)(193, 278)(194, 283)(195, 280)(196, 266)(197, 277)(198, 271)(199, 220)(200, 282)(201, 235)(202, 279)(203, 244)(204, 242)(205, 254)(206, 259)(207, 256)(208, 218)(209, 253)(210, 223)(211, 268)(212, 258)(213, 247)(214, 255)(215, 232)(216, 230)

MAP           : A4.178
NOTES         : type I, reflexible, isomorphic to Med2({3,12}), isomorphic to A4.163.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3 * x.2 * x.4, x.2^3, x.4^3, x.1^-1 * x.4 * x.1^-1 * x.4^-1, x.3^-2 * x.2^-1 * x.3 * x.4^-1, x.4 * x.2 * x.3 * x.2^-1 * x.4^-1 * x.3^-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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 78)(38, 94)(39, 104)(40, 95)(41, 87)(42, 88)(43, 92)(44, 81)(45, 106)(46, 108)(47, 101)(48, 105)(49, 74)(50, 76)(51, 97)(52, 73)(53, 82)(54, 75)(55, 83)(56, 98)(57, 99)(58, 85)(59, 86)(60, 102)(61, 77)(62, 79)(63, 107)(64, 84)(65, 91)(66, 103)(67, 96)(68, 90)(69, 100)(70, 80)(71, 93)(72, 89)(109, 194)(110, 196)(111, 181)(112, 193)(113, 202)(114, 195)(115, 203)(116, 182)(117, 183)(118, 205)(119, 206)(120, 186)(121, 197)(122, 199)(123, 191)(124, 204)(125, 211)(126, 187)(127, 216)(128, 210)(129, 184)(130, 200)(131, 213)(132, 209)(133, 198)(134, 214)(135, 188)(136, 215)(137, 207)(138, 208)(139, 212)(140, 201)(141, 190)(142, 192)(143, 185)(144, 189)(217, 270)(218, 286)(219, 260)(220, 287)(221, 279)(222, 280)(223, 284)(224, 273)(225, 262)(226, 264)(227, 257)(228, 261)(229, 266)(230, 268)(231, 253)(232, 265)(233, 274)(234, 267)(235, 275)(236, 254)(237, 255)(238, 277)(239, 278)(240, 258)(241, 269)(242, 271)(243, 263)(244, 276)(245, 283)(246, 259)(247, 288)(248, 282)(249, 256)(250, 272)(251, 285)(252, 281)

MAP           : A4.179
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.2^3, x.1^6, (x.1^-1 * x.2^-1)^3, x.2 * x.1^2 * x.2^-1 * x.1^-2, (x.2 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 50)(2, 52)(3, 37)(4, 49)(5, 58)(6, 51)(7, 59)(8, 38)(9, 39)(10, 61)(11, 62)(12, 42)(13, 53)(14, 55)(15, 47)(16, 60)(17, 67)(18, 43)(19, 72)(20, 66)(21, 40)(22, 56)(23, 69)(24, 65)(25, 54)(26, 70)(27, 44)(28, 71)(29, 63)(30, 64)(31, 68)(32, 57)(33, 46)(34, 48)(35, 41)(36, 45)(73, 112)(74, 109)(75, 114)(76, 110)(77, 121)(78, 133)(79, 122)(80, 130)(81, 140)(82, 113)(83, 115)(84, 124)(85, 118)(86, 119)(87, 137)(88, 138)(89, 132)(90, 128)(91, 125)(92, 139)(93, 131)(94, 134)(95, 136)(96, 127)(97, 111)(98, 116)(99, 117)(100, 129)(101, 143)(102, 120)(103, 126)(104, 135)(105, 144)(106, 141)(107, 123)(108, 142)

MAP           : A4.180
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.2^3, x.1^6, (x.1^-1 * x.2^-1)^3, x.2 * x.1^2 * x.2^-1 * x.1^-2, (x.2 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 39)(2, 44)(3, 45)(4, 57)(5, 71)(6, 48)(7, 54)(8, 63)(9, 72)(10, 69)(11, 51)(12, 70)(13, 40)(14, 37)(15, 42)(16, 38)(17, 49)(18, 61)(19, 50)(20, 58)(21, 68)(22, 41)(23, 43)(24, 52)(25, 46)(26, 47)(27, 65)(28, 66)(29, 60)(30, 56)(31, 53)(32, 67)(33, 59)(34, 62)(35, 64)(36, 55)(73, 116)(74, 129)(75, 118)(76, 111)(77, 141)(78, 117)(79, 123)(80, 119)(81, 137)(82, 112)(83, 109)(84, 128)(85, 143)(86, 126)(87, 136)(88, 142)(89, 122)(90, 125)(91, 124)(92, 133)(93, 138)(94, 135)(95, 140)(96, 121)(97, 120)(98, 113)(99, 139)(100, 115)(101, 114)(102, 110)(103, 130)(104, 144)(105, 134)(106, 127)(107, 132)(108, 131)

MAP           : A4.181
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.2^3, x.1^6, (x.1^-1 * x.2^-1)^3, x.2 * x.1^2 * x.2^-1 * x.1^-2, (x.2 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 39)(2, 44)(3, 45)(4, 57)(5, 71)(6, 48)(7, 54)(8, 63)(9, 72)(10, 69)(11, 51)(12, 70)(13, 40)(14, 37)(15, 42)(16, 38)(17, 49)(18, 61)(19, 50)(20, 58)(21, 68)(22, 41)(23, 43)(24, 52)(25, 46)(26, 47)(27, 65)(28, 66)(29, 60)(30, 56)(31, 53)(32, 67)(33, 59)(34, 62)(35, 64)(36, 55)(73, 119)(74, 138)(75, 112)(76, 118)(77, 134)(78, 137)(79, 136)(80, 109)(81, 114)(82, 111)(83, 116)(84, 133)(85, 132)(86, 125)(87, 115)(88, 127)(89, 126)(90, 122)(91, 142)(92, 120)(93, 110)(94, 139)(95, 144)(96, 143)(97, 128)(98, 141)(99, 130)(100, 123)(101, 117)(102, 129)(103, 135)(104, 131)(105, 113)(106, 124)(107, 121)(108, 140)

MAP           : A4.182
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.1^3, x.2^6, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.2^-2 * x.1^-1 * x.2^2 * x.1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 47)(2, 66)(3, 40)(4, 46)(5, 62)(6, 65)(7, 64)(8, 37)(9, 42)(10, 39)(11, 44)(12, 61)(13, 60)(14, 53)(15, 43)(16, 55)(17, 54)(18, 50)(19, 70)(20, 48)(21, 38)(22, 67)(23, 72)(24, 71)(25, 56)(26, 69)(27, 58)(28, 51)(29, 45)(30, 57)(31, 63)(32, 59)(33, 41)(34, 52)(35, 49)(36, 68)(73, 122)(74, 124)(75, 109)(76, 121)(77, 130)(78, 123)(79, 131)(80, 110)(81, 111)(82, 133)(83, 134)(84, 114)(85, 125)(86, 127)(87, 119)(88, 132)(89, 139)(90, 115)(91, 144)(92, 138)(93, 112)(94, 128)(95, 141)(96, 137)(97, 126)(98, 142)(99, 116)(100, 143)(101, 135)(102, 136)(103, 140)(104, 129)(105, 118)(106, 120)(107, 113)(108, 117)

MAP           : A4.183
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.2^3, x.1^6, (x.1^-1 * x.2^-1)^3, x.2 * x.1^2 * x.2^-1 * x.1^-2, (x.2 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 50)(2, 52)(3, 37)(4, 49)(5, 58)(6, 51)(7, 59)(8, 38)(9, 39)(10, 61)(11, 62)(12, 42)(13, 53)(14, 55)(15, 47)(16, 60)(17, 67)(18, 43)(19, 72)(20, 66)(21, 40)(22, 56)(23, 69)(24, 65)(25, 54)(26, 70)(27, 44)(28, 71)(29, 63)(30, 64)(31, 68)(32, 57)(33, 46)(34, 48)(35, 41)(36, 45)(73, 116)(74, 129)(75, 118)(76, 111)(77, 141)(78, 117)(79, 123)(80, 119)(81, 137)(82, 112)(83, 109)(84, 128)(85, 143)(86, 126)(87, 136)(88, 142)(89, 122)(90, 125)(91, 124)(92, 133)(93, 138)(94, 135)(95, 140)(96, 121)(97, 120)(98, 113)(99, 139)(100, 115)(101, 114)(102, 110)(103, 130)(104, 144)(105, 134)(106, 127)(107, 132)(108, 131)

MAP           : A4.184
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.2^3, x.1^6, (x.1^-1 * x.2^-1)^3, x.2 * x.1^2 * x.2^-1 * x.1^-2, (x.2 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 50)(2, 52)(3, 37)(4, 49)(5, 58)(6, 51)(7, 59)(8, 38)(9, 39)(10, 61)(11, 62)(12, 42)(13, 53)(14, 55)(15, 47)(16, 60)(17, 67)(18, 43)(19, 72)(20, 66)(21, 40)(22, 56)(23, 69)(24, 65)(25, 54)(26, 70)(27, 44)(28, 71)(29, 63)(30, 64)(31, 68)(32, 57)(33, 46)(34, 48)(35, 41)(36, 45)(73, 119)(74, 138)(75, 112)(76, 118)(77, 134)(78, 137)(79, 136)(80, 109)(81, 114)(82, 111)(83, 116)(84, 133)(85, 132)(86, 125)(87, 115)(88, 127)(89, 126)(90, 122)(91, 142)(92, 120)(93, 110)(94, 139)(95, 144)(96, 143)(97, 128)(98, 141)(99, 130)(100, 123)(101, 117)(102, 129)(103, 135)(104, 131)(105, 113)(106, 124)(107, 121)(108, 140)

MAP           : A4.185
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.2^3, x.1^6, (x.1^-1 * x.2^-1)^3, x.2 * x.1^2 * x.2^-1 * x.1^-2, (x.2 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 39)(2, 44)(3, 45)(4, 57)(5, 71)(6, 48)(7, 54)(8, 63)(9, 72)(10, 69)(11, 51)(12, 70)(13, 40)(14, 37)(15, 42)(16, 38)(17, 49)(18, 61)(19, 50)(20, 58)(21, 68)(22, 41)(23, 43)(24, 52)(25, 46)(26, 47)(27, 65)(28, 66)(29, 60)(30, 56)(31, 53)(32, 67)(33, 59)(34, 62)(35, 64)(36, 55)(73, 110)(74, 112)(75, 133)(76, 109)(77, 118)(78, 111)(79, 119)(80, 134)(81, 135)(82, 121)(83, 122)(84, 138)(85, 113)(86, 115)(87, 143)(88, 120)(89, 127)(90, 139)(91, 132)(92, 126)(93, 136)(94, 116)(95, 129)(96, 125)(97, 114)(98, 130)(99, 140)(100, 131)(101, 123)(102, 124)(103, 128)(104, 117)(105, 142)(106, 144)(107, 137)(108, 141)

MAP           : A4.186
NOTES         : type II, reflexible, 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, 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.4^3, u.5^3, u.3 * u.4^-1 * u.1 * u.3^-1 * u.2 * u.5^-1 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^3, x.5^3, x.5^-1 * x.1 * x.2 * x.4^-1, (x.4, x.5^-1), x.5^-1 * x.1 * x.4^-1 * x.1, x.3 * x.1 * x.5 * x.3^-1 * x.2 * x.5^-1 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 52)(20, 45)(21, 54)(22, 53)(23, 49)(24, 38)(25, 40)(26, 51)(27, 42)(28, 41)(29, 37)(30, 44)(31, 46)(32, 39)(33, 48)(34, 47)(35, 43)(36, 50)(55, 56)(57, 71)(58, 69)(59, 72)(60, 67)(61, 63)(62, 70)(64, 66)(65, 68)(91, 102)(92, 107)(93, 100)(94, 104)(95, 99)(96, 101)(97, 98)(103, 105)(106, 108)(109, 139)(110, 140)(111, 141)(112, 142)(113, 143)(114, 144)(115, 127)(116, 128)(117, 129)(118, 130)(119, 131)(120, 132)(121, 133)(122, 134)(123, 135)(124, 136)(125, 137)(126, 138)

MAP           : A4.187
NOTES         : type II, reflexible, isomorphic to A4.186.
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, 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.4^3, u.5^3, u.3 * u.4^-1 * u.1 * u.3^-1 * u.2 * u.5^-1 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^3, x.5^3, x.5^-1 * x.1 * x.2 * x.4^-1, (x.4, x.5^-1), x.5^-1 * x.1 * x.4^-1 * x.1, x.3 * x.1 * x.5 * x.3^-1 * x.2 * x.5^-1 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)(55, 56)(57, 71)(58, 69)(59, 72)(60, 67)(61, 63)(62, 70)(64, 66)(65, 68)(91, 102)(92, 107)(93, 100)(94, 104)(95, 99)(96, 101)(97, 98)(103, 105)(106, 108)(109, 142)(110, 135)(111, 144)(112, 143)(113, 139)(114, 128)(115, 130)(116, 141)(117, 132)(118, 131)(119, 127)(120, 134)(121, 136)(122, 129)(123, 138)(124, 137)(125, 133)(126, 140)

MAP           : A4.188
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.2^3, x.1^6, (x.1^-1 * x.2^-1)^3, x.2 * x.1^2 * x.2^-1 * x.1^-2, (x.2 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 39)(2, 44)(3, 45)(4, 57)(5, 71)(6, 48)(7, 54)(8, 63)(9, 72)(10, 69)(11, 51)(12, 70)(13, 40)(14, 37)(15, 42)(16, 38)(17, 49)(18, 61)(19, 50)(20, 58)(21, 68)(22, 41)(23, 43)(24, 52)(25, 46)(26, 47)(27, 65)(28, 66)(29, 60)(30, 56)(31, 53)(32, 67)(33, 59)(34, 62)(35, 64)(36, 55)(73, 124)(74, 121)(75, 126)(76, 122)(77, 133)(78, 109)(79, 134)(80, 142)(81, 116)(82, 125)(83, 127)(84, 136)(85, 130)(86, 131)(87, 113)(88, 114)(89, 144)(90, 140)(91, 137)(92, 115)(93, 143)(94, 110)(95, 112)(96, 139)(97, 123)(98, 128)(99, 129)(100, 141)(101, 119)(102, 132)(103, 138)(104, 111)(105, 120)(106, 117)(107, 135)(108, 118)

MAP           : A4.189
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.1^3, x.2^6, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.2^-2 * x.1^-1 * x.2^2 * x.1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 42)(2, 58)(3, 68)(4, 59)(5, 51)(6, 52)(7, 56)(8, 45)(9, 70)(10, 72)(11, 65)(12, 69)(13, 38)(14, 40)(15, 61)(16, 37)(17, 46)(18, 39)(19, 47)(20, 62)(21, 63)(22, 49)(23, 50)(24, 66)(25, 41)(26, 43)(27, 71)(28, 48)(29, 55)(30, 67)(31, 60)(32, 54)(33, 64)(34, 44)(35, 57)(36, 53)(73, 122)(74, 124)(75, 109)(76, 121)(77, 130)(78, 123)(79, 131)(80, 110)(81, 111)(82, 133)(83, 134)(84, 114)(85, 125)(86, 127)(87, 119)(88, 132)(89, 139)(90, 115)(91, 144)(92, 138)(93, 112)(94, 128)(95, 141)(96, 137)(97, 126)(98, 142)(99, 116)(100, 143)(101, 135)(102, 136)(103, 140)(104, 129)(105, 118)(106, 120)(107, 113)(108, 117)

MAP           : A4.190
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.1^3, x.2^6, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.2^-2 * x.1^-1 * x.2^2 * x.1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 52)(2, 49)(3, 54)(4, 50)(5, 61)(6, 37)(7, 62)(8, 70)(9, 44)(10, 53)(11, 55)(12, 64)(13, 58)(14, 59)(15, 41)(16, 42)(17, 72)(18, 68)(19, 65)(20, 43)(21, 71)(22, 38)(23, 40)(24, 67)(25, 51)(26, 56)(27, 57)(28, 69)(29, 47)(30, 60)(31, 66)(32, 39)(33, 48)(34, 45)(35, 63)(36, 46)(73, 111)(74, 116)(75, 117)(76, 129)(77, 143)(78, 120)(79, 126)(80, 135)(81, 144)(82, 141)(83, 123)(84, 142)(85, 112)(86, 109)(87, 114)(88, 110)(89, 121)(90, 133)(91, 122)(92, 130)(93, 140)(94, 113)(95, 115)(96, 124)(97, 118)(98, 119)(99, 137)(100, 138)(101, 132)(102, 128)(103, 125)(104, 139)(105, 131)(106, 134)(107, 136)(108, 127)

MAP           : A4.191
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.2^3, x.1^6, (x.1^-1 * x.2^-1)^3, x.2 * x.1^2 * x.2^-1 * x.1^-2, (x.2 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 50)(2, 52)(3, 37)(4, 49)(5, 58)(6, 51)(7, 59)(8, 38)(9, 39)(10, 61)(11, 62)(12, 42)(13, 53)(14, 55)(15, 47)(16, 60)(17, 67)(18, 43)(19, 72)(20, 66)(21, 40)(22, 56)(23, 69)(24, 65)(25, 54)(26, 70)(27, 44)(28, 71)(29, 63)(30, 64)(31, 68)(32, 57)(33, 46)(34, 48)(35, 41)(36, 45)(73, 110)(74, 112)(75, 133)(76, 109)(77, 118)(78, 111)(79, 119)(80, 134)(81, 135)(82, 121)(83, 122)(84, 138)(85, 113)(86, 115)(87, 143)(88, 120)(89, 127)(90, 139)(91, 132)(92, 126)(93, 136)(94, 116)(95, 129)(96, 125)(97, 114)(98, 130)(99, 140)(100, 131)(101, 123)(102, 124)(103, 128)(104, 117)(105, 142)(106, 144)(107, 137)(108, 141)

MAP           : A4.192
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.1^3, x.2^6, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.2^-2 * x.1^-1 * x.2^2 * x.1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 44)(2, 57)(3, 46)(4, 39)(5, 69)(6, 45)(7, 51)(8, 47)(9, 65)(10, 40)(11, 37)(12, 56)(13, 71)(14, 54)(15, 64)(16, 70)(17, 50)(18, 53)(19, 52)(20, 61)(21, 66)(22, 63)(23, 68)(24, 49)(25, 48)(26, 41)(27, 67)(28, 43)(29, 42)(30, 38)(31, 58)(32, 72)(33, 62)(34, 55)(35, 60)(36, 59)(73, 111)(74, 116)(75, 117)(76, 129)(77, 143)(78, 120)(79, 126)(80, 135)(81, 144)(82, 141)(83, 123)(84, 142)(85, 112)(86, 109)(87, 114)(88, 110)(89, 121)(90, 133)(91, 122)(92, 130)(93, 140)(94, 113)(95, 115)(96, 124)(97, 118)(98, 119)(99, 137)(100, 138)(101, 132)(102, 128)(103, 125)(104, 139)(105, 131)(106, 134)(107, 136)(108, 127)

MAP           : A4.193
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.1^3, x.2^6, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.2^-2 * x.1^-1 * x.2^2 * x.1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 44)(2, 57)(3, 46)(4, 39)(5, 69)(6, 45)(7, 51)(8, 47)(9, 65)(10, 40)(11, 37)(12, 56)(13, 71)(14, 54)(15, 64)(16, 70)(17, 50)(18, 53)(19, 52)(20, 61)(21, 66)(22, 63)(23, 68)(24, 49)(25, 48)(26, 41)(27, 67)(28, 43)(29, 42)(30, 38)(31, 58)(32, 72)(33, 62)(34, 55)(35, 60)(36, 59)(73, 122)(74, 124)(75, 109)(76, 121)(77, 130)(78, 123)(79, 131)(80, 110)(81, 111)(82, 133)(83, 134)(84, 114)(85, 125)(86, 127)(87, 119)(88, 132)(89, 139)(90, 115)(91, 144)(92, 138)(93, 112)(94, 128)(95, 141)(96, 137)(97, 126)(98, 142)(99, 116)(100, 143)(101, 135)(102, 136)(103, 140)(104, 129)(105, 118)(106, 120)(107, 113)(108, 117)

MAP           : A4.194
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.1^3, x.2^6, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.2^-2 * x.1^-1 * x.2^2 * x.1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 47)(2, 66)(3, 40)(4, 46)(5, 62)(6, 65)(7, 64)(8, 37)(9, 42)(10, 39)(11, 44)(12, 61)(13, 60)(14, 53)(15, 43)(16, 55)(17, 54)(18, 50)(19, 70)(20, 48)(21, 38)(22, 67)(23, 72)(24, 71)(25, 56)(26, 69)(27, 58)(28, 51)(29, 45)(30, 57)(31, 63)(32, 59)(33, 41)(34, 52)(35, 49)(36, 68)(73, 111)(74, 116)(75, 117)(76, 129)(77, 143)(78, 120)(79, 126)(80, 135)(81, 144)(82, 141)(83, 123)(84, 142)(85, 112)(86, 109)(87, 114)(88, 110)(89, 121)(90, 133)(91, 122)(92, 130)(93, 140)(94, 113)(95, 115)(96, 124)(97, 118)(98, 119)(99, 137)(100, 138)(101, 132)(102, 128)(103, 125)(104, 139)(105, 131)(106, 134)(107, 136)(108, 127)

MAP           : A4.195
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.2^3, x.1^6, (x.1^-1 * x.2^-1)^3, x.2 * x.1^2 * x.2^-1 * x.1^-2, (x.2 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 50)(2, 52)(3, 37)(4, 49)(5, 58)(6, 51)(7, 59)(8, 38)(9, 39)(10, 61)(11, 62)(12, 42)(13, 53)(14, 55)(15, 47)(16, 60)(17, 67)(18, 43)(19, 72)(20, 66)(21, 40)(22, 56)(23, 69)(24, 65)(25, 54)(26, 70)(27, 44)(28, 71)(29, 63)(30, 64)(31, 68)(32, 57)(33, 46)(34, 48)(35, 41)(36, 45)(73, 124)(74, 121)(75, 126)(76, 122)(77, 133)(78, 109)(79, 134)(80, 142)(81, 116)(82, 125)(83, 127)(84, 136)(85, 130)(86, 131)(87, 113)(88, 114)(89, 144)(90, 140)(91, 137)(92, 115)(93, 143)(94, 110)(95, 112)(96, 139)(97, 123)(98, 128)(99, 129)(100, 141)(101, 119)(102, 132)(103, 138)(104, 111)(105, 120)(106, 117)(107, 135)(108, 118)

MAP           : A4.196
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.2^3, x.1^6, (x.1^-1 * x.2^-1)^3, x.2 * x.1^2 * x.2^-1 * x.1^-2, (x.2 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 39)(2, 44)(3, 45)(4, 57)(5, 71)(6, 48)(7, 54)(8, 63)(9, 72)(10, 69)(11, 51)(12, 70)(13, 40)(14, 37)(15, 42)(16, 38)(17, 49)(18, 61)(19, 50)(20, 58)(21, 68)(22, 41)(23, 43)(24, 52)(25, 46)(26, 47)(27, 65)(28, 66)(29, 60)(30, 56)(31, 53)(32, 67)(33, 59)(34, 62)(35, 64)(36, 55)(73, 114)(74, 130)(75, 140)(76, 131)(77, 123)(78, 124)(79, 128)(80, 117)(81, 142)(82, 144)(83, 137)(84, 141)(85, 110)(86, 112)(87, 133)(88, 109)(89, 118)(90, 111)(91, 119)(92, 134)(93, 135)(94, 121)(95, 122)(96, 138)(97, 113)(98, 115)(99, 143)(100, 120)(101, 127)(102, 139)(103, 132)(104, 126)(105, 136)(106, 116)(107, 129)(108, 125)

MAP           : A4.197
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.1^3, x.2^6, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.2^-2 * x.1^-1 * x.2^2 * x.1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 40)(2, 37)(3, 42)(4, 38)(5, 49)(6, 61)(7, 50)(8, 58)(9, 68)(10, 41)(11, 43)(12, 52)(13, 46)(14, 47)(15, 65)(16, 66)(17, 60)(18, 56)(19, 53)(20, 67)(21, 59)(22, 62)(23, 64)(24, 55)(25, 39)(26, 44)(27, 45)(28, 57)(29, 71)(30, 48)(31, 54)(32, 63)(33, 72)(34, 69)(35, 51)(36, 70)(73, 122)(74, 124)(75, 109)(76, 121)(77, 130)(78, 123)(79, 131)(80, 110)(81, 111)(82, 133)(83, 134)(84, 114)(85, 125)(86, 127)(87, 119)(88, 132)(89, 139)(90, 115)(91, 144)(92, 138)(93, 112)(94, 128)(95, 141)(96, 137)(97, 126)(98, 142)(99, 116)(100, 143)(101, 135)(102, 136)(103, 140)(104, 129)(105, 118)(106, 120)(107, 113)(108, 117)

MAP           : A4.198
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.1^3, x.2^6, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.2^-2 * x.1^-1 * x.2^2 * x.1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 38)(2, 40)(3, 61)(4, 37)(5, 46)(6, 39)(7, 47)(8, 62)(9, 63)(10, 49)(11, 50)(12, 66)(13, 41)(14, 43)(15, 71)(16, 48)(17, 55)(18, 67)(19, 60)(20, 54)(21, 64)(22, 44)(23, 57)(24, 53)(25, 42)(26, 58)(27, 68)(28, 59)(29, 51)(30, 52)(31, 56)(32, 45)(33, 70)(34, 72)(35, 65)(36, 69)(73, 111)(74, 116)(75, 117)(76, 129)(77, 143)(78, 120)(79, 126)(80, 135)(81, 144)(82, 141)(83, 123)(84, 142)(85, 112)(86, 109)(87, 114)(88, 110)(89, 121)(90, 133)(91, 122)(92, 130)(93, 140)(94, 113)(95, 115)(96, 124)(97, 118)(98, 119)(99, 137)(100, 138)(101, 132)(102, 128)(103, 125)(104, 139)(105, 131)(106, 134)(107, 136)(108, 127)

MAP           : A4.199
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.2^3, x.1^6, (x.1^-1 * x.2^-1)^3, x.2 * x.1^2 * x.2^-1 * x.1^-2, (x.2 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 39)(2, 44)(3, 45)(4, 57)(5, 71)(6, 48)(7, 54)(8, 63)(9, 72)(10, 69)(11, 51)(12, 70)(13, 40)(14, 37)(15, 42)(16, 38)(17, 49)(18, 61)(19, 50)(20, 58)(21, 68)(22, 41)(23, 43)(24, 52)(25, 46)(26, 47)(27, 65)(28, 66)(29, 60)(30, 56)(31, 53)(32, 67)(33, 59)(34, 62)(35, 64)(36, 55)(73, 112)(74, 109)(75, 114)(76, 110)(77, 121)(78, 133)(79, 122)(80, 130)(81, 140)(82, 113)(83, 115)(84, 124)(85, 118)(86, 119)(87, 137)(88, 138)(89, 132)(90, 128)(91, 125)(92, 139)(93, 131)(94, 134)(95, 136)(96, 127)(97, 111)(98, 116)(99, 117)(100, 129)(101, 143)(102, 120)(103, 126)(104, 135)(105, 144)(106, 141)(107, 123)(108, 142)

MAP           : A4.200
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.1^3, x.2^6, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.2^-2 * x.1^-1 * x.2^2 * x.1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 52)(2, 49)(3, 54)(4, 50)(5, 61)(6, 37)(7, 62)(8, 70)(9, 44)(10, 53)(11, 55)(12, 64)(13, 58)(14, 59)(15, 41)(16, 42)(17, 72)(18, 68)(19, 65)(20, 43)(21, 71)(22, 38)(23, 40)(24, 67)(25, 51)(26, 56)(27, 57)(28, 69)(29, 47)(30, 60)(31, 66)(32, 39)(33, 48)(34, 45)(35, 63)(36, 46)(73, 122)(74, 124)(75, 109)(76, 121)(77, 130)(78, 123)(79, 131)(80, 110)(81, 111)(82, 133)(83, 134)(84, 114)(85, 125)(86, 127)(87, 119)(88, 132)(89, 139)(90, 115)(91, 144)(92, 138)(93, 112)(94, 128)(95, 141)(96, 137)(97, 126)(98, 142)(99, 116)(100, 143)(101, 135)(102, 136)(103, 140)(104, 129)(105, 118)(106, 120)(107, 113)(108, 117)

MAP           : A4.201
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.1^3, x.2^6, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.2^-2 * x.1^-1 * x.2^2 * x.1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 40)(2, 37)(3, 42)(4, 38)(5, 49)(6, 61)(7, 50)(8, 58)(9, 68)(10, 41)(11, 43)(12, 52)(13, 46)(14, 47)(15, 65)(16, 66)(17, 60)(18, 56)(19, 53)(20, 67)(21, 59)(22, 62)(23, 64)(24, 55)(25, 39)(26, 44)(27, 45)(28, 57)(29, 71)(30, 48)(31, 54)(32, 63)(33, 72)(34, 69)(35, 51)(36, 70)(73, 111)(74, 116)(75, 117)(76, 129)(77, 143)(78, 120)(79, 126)(80, 135)(81, 144)(82, 141)(83, 123)(84, 142)(85, 112)(86, 109)(87, 114)(88, 110)(89, 121)(90, 133)(91, 122)(92, 130)(93, 140)(94, 113)(95, 115)(96, 124)(97, 118)(98, 119)(99, 137)(100, 138)(101, 132)(102, 128)(103, 125)(104, 139)(105, 131)(106, 134)(107, 136)(108, 127)

MAP           : A4.202
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.1^3, x.2^6, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.2^-2 * x.1^-1 * x.2^2 * x.1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 42)(2, 58)(3, 68)(4, 59)(5, 51)(6, 52)(7, 56)(8, 45)(9, 70)(10, 72)(11, 65)(12, 69)(13, 38)(14, 40)(15, 61)(16, 37)(17, 46)(18, 39)(19, 47)(20, 62)(21, 63)(22, 49)(23, 50)(24, 66)(25, 41)(26, 43)(27, 71)(28, 48)(29, 55)(30, 67)(31, 60)(32, 54)(33, 64)(34, 44)(35, 57)(36, 53)(73, 111)(74, 116)(75, 117)(76, 129)(77, 143)(78, 120)(79, 126)(80, 135)(81, 144)(82, 141)(83, 123)(84, 142)(85, 112)(86, 109)(87, 114)(88, 110)(89, 121)(90, 133)(91, 122)(92, 130)(93, 140)(94, 113)(95, 115)(96, 124)(97, 118)(98, 119)(99, 137)(100, 138)(101, 132)(102, 128)(103, 125)(104, 139)(105, 131)(106, 134)(107, 136)(108, 127)

MAP           : A4.203
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.2^3, x.1^6, (x.1^-1 * x.2^-1)^3, x.2 * x.1^2 * x.2^-1 * x.1^-2, (x.2 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 50)(2, 52)(3, 37)(4, 49)(5, 58)(6, 51)(7, 59)(8, 38)(9, 39)(10, 61)(11, 62)(12, 42)(13, 53)(14, 55)(15, 47)(16, 60)(17, 67)(18, 43)(19, 72)(20, 66)(21, 40)(22, 56)(23, 69)(24, 65)(25, 54)(26, 70)(27, 44)(28, 71)(29, 63)(30, 64)(31, 68)(32, 57)(33, 46)(34, 48)(35, 41)(36, 45)(73, 114)(74, 130)(75, 140)(76, 131)(77, 123)(78, 124)(79, 128)(80, 117)(81, 142)(82, 144)(83, 137)(84, 141)(85, 110)(86, 112)(87, 133)(88, 109)(89, 118)(90, 111)(91, 119)(92, 134)(93, 135)(94, 121)(95, 122)(96, 138)(97, 113)(98, 115)(99, 143)(100, 120)(101, 127)(102, 139)(103, 132)(104, 126)(105, 136)(106, 116)(107, 129)(108, 125)

MAP           : A4.204
NOTES         : type I, reflexible, isomorphic to A4.179.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2 | x.1^3, x.2^6, (x.1^-1 * x.2^-1)^3, (x.2 * x.1^-1)^3, x.2^-2 * x.1^-1 * x.2^2 * x.1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (3, 6, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 38)(2, 40)(3, 61)(4, 37)(5, 46)(6, 39)(7, 47)(8, 62)(9, 63)(10, 49)(11, 50)(12, 66)(13, 41)(14, 43)(15, 71)(16, 48)(17, 55)(18, 67)(19, 60)(20, 54)(21, 64)(22, 44)(23, 57)(24, 53)(25, 42)(26, 58)(27, 68)(28, 59)(29, 51)(30, 52)(31, 56)(32, 45)(33, 70)(34, 72)(35, 65)(36, 69)(73, 122)(74, 124)(75, 109)(76, 121)(77, 130)(78, 123)(79, 131)(80, 110)(81, 111)(82, 133)(83, 134)(84, 114)(85, 125)(86, 127)(87, 119)(88, 132)(89, 139)(90, 115)(91, 144)(92, 138)(93, 112)(94, 128)(95, 141)(96, 137)(97, 126)(98, 142)(99, 116)(100, 143)(101, 135)(102, 136)(103, 140)(104, 129)(105, 118)(106, 120)(107, 113)(108, 117)

MAP           : A4.205
NOTES         : type I, reflexible, isomorphic to Med2({4,5}), representative.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.2^5, u.4^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^2, x.3 * x.2 * x.4, (x.3 * x.1^-1)^2, x.2^5, x.4^5, (x.4 * x.2^-1)^3, x.4 * x.2^2 * x.3 * x.2^-1 * x.4^-1 * x.2 * x.3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 5)
#DARTS        : 480
R = (1, 61, 121, 181)(2, 62, 122, 182)(3, 63, 123, 183)(4, 64, 124, 184)(5, 65, 125, 185)(6, 66, 126, 186)(7, 67, 127, 187)(8, 68, 128, 188)(9, 69, 129, 189)(10, 70, 130, 190)(11, 71, 131, 191)(12, 72, 132, 192)(13, 73, 133, 193)(14, 74, 134, 194)(15, 75, 135, 195)(16, 76, 136, 196)(17, 77, 137, 197)(18, 78, 138, 198)(19, 79, 139, 199)(20, 80, 140, 200)(21, 81, 141, 201)(22, 82, 142, 202)(23, 83, 143, 203)(24, 84, 144, 204)(25, 85, 145, 205)(26, 86, 146, 206)(27, 87, 147, 207)(28, 88, 148, 208)(29, 89, 149, 209)(30, 90, 150, 210)(31, 91, 151, 211)(32, 92, 152, 212)(33, 93, 153, 213)(34, 94, 154, 214)(35, 95, 155, 215)(36, 96, 156, 216)(37, 97, 157, 217)(38, 98, 158, 218)(39, 99, 159, 219)(40, 100, 160, 220)(41, 101, 161, 221)(42, 102, 162, 222)(43, 103, 163, 223)(44, 104, 164, 224)(45, 105, 165, 225)(46, 106, 166, 226)(47, 107, 167, 227)(48, 108, 168, 228)(49, 109, 169, 229)(50, 110, 170, 230)(51, 111, 171, 231)(52, 112, 172, 232)(53, 113, 173, 233)(54, 114, 174, 234)(55, 115, 175, 235)(56, 116, 176, 236)(57, 117, 177, 237)(58, 118, 178, 238)(59, 119, 179, 239)(60, 120, 180, 240)(241, 301, 361, 421)(242, 302, 362, 422)(243, 303, 363, 423)(244, 304, 364, 424)(245, 305, 365, 425)(246, 306, 366, 426)(247, 307, 367, 427)(248, 308, 368, 428)(249, 309, 369, 429)(250, 310, 370, 430)(251, 311, 371, 431)(252, 312, 372, 432)(253, 313, 373, 433)(254, 314, 374, 434)(255, 315, 375, 435)(256, 316, 376, 436)(257, 317, 377, 437)(258, 318, 378, 438)(259, 319, 379, 439)(260, 320, 380, 440)(261, 321, 381, 441)(262, 322, 382, 442)(263, 323, 383, 443)(264, 324, 384, 444)(265, 325, 385, 445)(266, 326, 386, 446)(267, 327, 387, 447)(268, 328, 388, 448)(269, 329, 389, 449)(270, 330, 390, 450)(271, 331, 391, 451)(272, 332, 392, 452)(273, 333, 393, 453)(274, 334, 394, 454)(275, 335, 395, 455)(276, 336, 396, 456)(277, 337, 397, 457)(278, 338, 398, 458)(279, 339, 399, 459)(280, 340, 400, 460)(281, 341, 401, 461)(282, 342, 402, 462)(283, 343, 403, 463)(284, 344, 404, 464)(285, 345, 405, 465)(286, 346, 406, 466)(287, 347, 407, 467)(288, 348, 408, 468)(289, 349, 409, 469)(290, 350, 410, 470)(291, 351, 411, 471)(292, 352, 412, 472)(293, 353, 413, 473)(294, 354, 414, 474)(295, 355, 415, 475)(296, 356, 416, 476)(297, 357, 417, 477)(298, 358, 418, 478)(299, 359, 419, 479)(300, 360, 420, 480)
L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 122)(62, 125)(63, 127)(64, 121)(65, 138)(66, 137)(67, 161)(68, 126)(69, 173)(70, 158)(71, 160)(72, 166)(73, 155)(74, 168)(75, 131)(76, 152)(77, 154)(78, 124)(79, 164)(80, 167)(81, 169)(82, 163)(83, 180)(84, 179)(85, 177)(86, 153)(87, 130)(88, 129)(89, 141)(90, 151)(91, 135)(92, 159)(93, 172)(94, 171)(95, 147)(96, 157)(97, 136)(98, 133)(99, 156)(100, 150)(101, 134)(102, 140)(103, 174)(104, 148)(105, 170)(106, 149)(107, 145)(108, 123)(109, 132)(110, 142)(111, 128)(112, 143)(113, 139)(114, 165)(115, 178)(116, 175)(117, 162)(118, 144)(119, 176)(120, 146)(181, 307)(182, 308)(183, 309)(184, 310)(185, 311)(186, 312)(187, 301)(188, 302)(189, 303)(190, 304)(191, 305)(192, 306)(193, 331)(194, 332)(195, 333)(196, 334)(197, 335)(198, 336)(199, 337)(200, 338)(201, 339)(202, 340)(203, 341)(204, 342)(205, 343)(206, 344)(207, 345)(208, 346)(209, 347)(210, 348)(211, 313)(212, 314)(213, 315)(214, 316)(215, 317)(216, 318)(217, 319)(218, 320)(219, 321)(220, 322)(221, 323)(222, 324)(223, 325)(224, 326)(225, 327)(226, 328)(227, 329)(228, 330)(229, 355)(230, 356)(231, 357)(232, 358)(233, 359)(234, 360)(235, 349)(236, 350)(237, 351)(238, 352)(239, 353)(240, 354)(361, 423)(362, 471)(363, 448)(364, 447)(365, 435)(366, 469)(367, 424)(368, 421)(369, 468)(370, 438)(371, 422)(372, 428)(373, 450)(374, 436)(375, 446)(376, 437)(377, 433)(378, 459)(379, 456)(380, 430)(381, 452)(382, 431)(383, 427)(384, 477)(385, 442)(386, 439)(387, 474)(388, 432)(389, 440)(390, 434)(391, 458)(392, 461)(393, 451)(394, 457)(395, 426)(396, 425)(397, 473)(398, 462)(399, 449)(400, 470)(401, 472)(402, 478)(403, 467)(404, 480)(405, 455)(406, 464)(407, 466)(408, 460)(409, 476)(410, 479)(411, 445)(412, 475)(413, 444)(414, 443)(415, 441)(416, 465)(417, 454)(418, 453)(419, 429)(420, 463)

MAP           : A4.206
NOTES         : type I, reflexible, isomorphic to Med2({4,5}), isomorphic to A4.205.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 5, 2 ]
UNIGROUP      : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^5 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, x.2^5, (x.2^-1 * x.1 * x.2^-1 * x.1 * x.2^-1)^2, x.2 * x.1^2 * x.2^2 * x.1 * x.2^-1 * x.1^-1 * x.2 * x.1 * x.2^-1 * x.1^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 4, 4, 5)
#DARTS        : 480
R = (1, 121, 241, 361)(2, 122, 242, 362)(3, 123, 243, 363)(4, 124, 244, 364)(5, 125, 245, 365)(6, 126, 246, 366)(7, 127, 247, 367)(8, 128, 248, 368)(9, 129, 249, 369)(10, 130, 250, 370)(11, 131, 251, 371)(12, 132, 252, 372)(13, 133, 253, 373)(14, 134, 254, 374)(15, 135, 255, 375)(16, 136, 256, 376)(17, 137, 257, 377)(18, 138, 258, 378)(19, 139, 259, 379)(20, 140, 260, 380)(21, 141, 261, 381)(22, 142, 262, 382)(23, 143, 263, 383)(24, 144, 264, 384)(25, 145, 265, 385)(26, 146, 266, 386)(27, 147, 267, 387)(28, 148, 268, 388)(29, 149, 269, 389)(30, 150, 270, 390)(31, 151, 271, 391)(32, 152, 272, 392)(33, 153, 273, 393)(34, 154, 274, 394)(35, 155, 275, 395)(36, 156, 276, 396)(37, 157, 277, 397)(38, 158, 278, 398)(39, 159, 279, 399)(40, 160, 280, 400)(41, 161, 281, 401)(42, 162, 282, 402)(43, 163, 283, 403)(44, 164, 284, 404)(45, 165, 285, 405)(46, 166, 286, 406)(47, 167, 287, 407)(48, 168, 288, 408)(49, 169, 289, 409)(50, 170, 290, 410)(51, 171, 291, 411)(52, 172, 292, 412)(53, 173, 293, 413)(54, 174, 294, 414)(55, 175, 295, 415)(56, 176, 296, 416)(57, 177, 297, 417)(58, 178, 298, 418)(59, 179, 299, 419)(60, 180, 300, 420)(61, 181, 301, 421)(62, 182, 302, 422)(63, 183, 303, 423)(64, 184, 304, 424)(65, 185, 305, 425)(66, 186, 306, 426)(67, 187, 307, 427)(68, 188, 308, 428)(69, 189, 309, 429)(70, 190, 310, 430)(71, 191, 311, 431)(72, 192, 312, 432)(73, 193, 313, 433)(74, 194, 314, 434)(75, 195, 315, 435)(76, 196, 316, 436)(77, 197, 317, 437)(78, 198, 318, 438)(79, 199, 319, 439)(80, 200, 320, 440)(81, 201, 321, 441)(82, 202, 322, 442)(83, 203, 323, 443)(84, 204, 324, 444)(85, 205, 325, 445)(86, 206, 326, 446)(87, 207, 327, 447)(88, 208, 328, 448)(89, 209, 329, 449)(90, 210, 330, 450)(91, 211, 331, 451)(92, 212, 332, 452)(93, 213, 333, 453)(94, 214, 334, 454)(95, 215, 335, 455)(96, 216, 336, 456)(97, 217, 337, 457)(98, 218, 338, 458)(99, 219, 339, 459)(100, 220, 340, 460)(101, 221, 341, 461)(102, 222, 342, 462)(103, 223, 343, 463)(104, 224, 344, 464)(105, 225, 345, 465)(106, 226, 346, 466)(107, 227, 347, 467)(108, 228, 348, 468)(109, 229, 349, 469)(110, 230, 350, 470)(111, 231, 351, 471)(112, 232, 352, 472)(113, 233, 353, 473)(114, 234, 354, 474)(115, 235, 355, 475)(116, 236, 356, 476)(117, 237, 357, 477)(118, 238, 358, 478)(119, 239, 359, 479)(120, 240, 360, 480)
L = (1, 123)(2, 126)(3, 136)(4, 222)(5, 219)(6, 137)(7, 174)(8, 171)(9, 210)(10, 169)(11, 170)(12, 207)(13, 122)(14, 121)(15, 127)(16, 134)(17, 133)(18, 128)(19, 160)(20, 161)(21, 158)(22, 197)(23, 196)(24, 157)(25, 125)(26, 124)(27, 239)(28, 129)(29, 132)(30, 238)(31, 233)(32, 232)(33, 203)(34, 237)(35, 240)(36, 202)(37, 230)(38, 229)(39, 235)(40, 218)(41, 217)(42, 236)(43, 142)(44, 143)(45, 140)(46, 173)(47, 172)(48, 139)(49, 231)(50, 234)(51, 220)(52, 186)(53, 183)(54, 221)(55, 150)(56, 147)(57, 162)(58, 145)(59, 146)(60, 159)(61, 226)(62, 227)(63, 224)(64, 149)(65, 148)(66, 223)(67, 191)(68, 190)(69, 155)(70, 201)(71, 204)(72, 154)(73, 216)(74, 213)(75, 144)(76, 211)(77, 212)(78, 141)(79, 188)(80, 187)(81, 199)(82, 182)(83, 181)(84, 200)(85, 189)(86, 192)(87, 184)(88, 180)(89, 177)(90, 185)(91, 164)(92, 163)(93, 151)(94, 176)(95, 175)(96, 152)(97, 165)(98, 168)(99, 178)(100, 138)(101, 135)(102, 179)(103, 167)(104, 166)(105, 131)(106, 153)(107, 156)(108, 130)(109, 198)(110, 195)(111, 228)(112, 193)(113, 194)(114, 225)(115, 208)(116, 209)(117, 206)(118, 215)(119, 214)(120, 205)(241, 364)(242, 365)(243, 362)(244, 401)(245, 400)(246, 361)(247, 479)(248, 478)(249, 437)(250, 465)(251, 468)(252, 436)(253, 372)(254, 369)(255, 396)(256, 367)(257, 368)(258, 393)(259, 476)(260, 475)(261, 463)(262, 470)(263, 469)(264, 464)(265, 477)(266, 480)(267, 472)(268, 444)(269, 441)(270, 473)(271, 446)(272, 445)(273, 433)(274, 440)(275, 439)(276, 434)(277, 447)(278, 450)(279, 442)(280, 414)(281, 411)(282, 443)(283, 449)(284, 448)(285, 407)(286, 435)(287, 438)(288, 406)(289, 462)(290, 459)(291, 366)(292, 457)(293, 458)(294, 363)(295, 454)(296, 455)(297, 452)(298, 371)(299, 370)(300, 451)(301, 417)(302, 420)(303, 412)(304, 384)(305, 381)(306, 413)(307, 432)(308, 429)(309, 456)(310, 427)(311, 428)(312, 453)(313, 416)(314, 415)(315, 403)(316, 410)(317, 409)(318, 404)(319, 424)(320, 425)(321, 422)(322, 461)(323, 460)(324, 421)(325, 419)(326, 418)(327, 377)(328, 405)(329, 408)(330, 376)(331, 389)(332, 388)(333, 467)(334, 375)(335, 378)(336, 466)(337, 386)(338, 385)(339, 373)(340, 380)(341, 379)(342, 374)(343, 394)(344, 395)(345, 392)(346, 431)(347, 430)(348, 391)(349, 387)(350, 390)(351, 382)(352, 474)(353, 471)(354, 383)(355, 402)(356, 399)(357, 426)(358, 397)(359, 398)(360, 423)

MAP           : A4.207
NOTES         : type I, reflexible, isomorphic to Med2({4,5}), isomorphic to A4.205.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.2^5, u.4^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^2, x.3 * x.2 * x.4, (x.3 * x.1^-1)^2, x.2^5, x.4^5, (x.4 * x.2^-1)^3, x.4 * x.2^2 * x.3 * x.2^-1 * x.4^-1 * x.2 * x.3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 5)
#DARTS        : 480
R = (1, 61, 121, 181)(2, 62, 122, 182)(3, 63, 123, 183)(4, 64, 124, 184)(5, 65, 125, 185)(6, 66, 126, 186)(7, 67, 127, 187)(8, 68, 128, 188)(9, 69, 129, 189)(10, 70, 130, 190)(11, 71, 131, 191)(12, 72, 132, 192)(13, 73, 133, 193)(14, 74, 134, 194)(15, 75, 135, 195)(16, 76, 136, 196)(17, 77, 137, 197)(18, 78, 138, 198)(19, 79, 139, 199)(20, 80, 140, 200)(21, 81, 141, 201)(22, 82, 142, 202)(23, 83, 143, 203)(24, 84, 144, 204)(25, 85, 145, 205)(26, 86, 146, 206)(27, 87, 147, 207)(28, 88, 148, 208)(29, 89, 149, 209)(30, 90, 150, 210)(31, 91, 151, 211)(32, 92, 152, 212)(33, 93, 153, 213)(34, 94, 154, 214)(35, 95, 155, 215)(36, 96, 156, 216)(37, 97, 157, 217)(38, 98, 158, 218)(39, 99, 159, 219)(40, 100, 160, 220)(41, 101, 161, 221)(42, 102, 162, 222)(43, 103, 163, 223)(44, 104, 164, 224)(45, 105, 165, 225)(46, 106, 166, 226)(47, 107, 167, 227)(48, 108, 168, 228)(49, 109, 169, 229)(50, 110, 170, 230)(51, 111, 171, 231)(52, 112, 172, 232)(53, 113, 173, 233)(54, 114, 174, 234)(55, 115, 175, 235)(56, 116, 176, 236)(57, 117, 177, 237)(58, 118, 178, 238)(59, 119, 179, 239)(60, 120, 180, 240)(241, 301, 361, 421)(242, 302, 362, 422)(243, 303, 363, 423)(244, 304, 364, 424)(245, 305, 365, 425)(246, 306, 366, 426)(247, 307, 367, 427)(248, 308, 368, 428)(249, 309, 369, 429)(250, 310, 370, 430)(251, 311, 371, 431)(252, 312, 372, 432)(253, 313, 373, 433)(254, 314, 374, 434)(255, 315, 375, 435)(256, 316, 376, 436)(257, 317, 377, 437)(258, 318, 378, 438)(259, 319, 379, 439)(260, 320, 380, 440)(261, 321, 381, 441)(262, 322, 382, 442)(263, 323, 383, 443)(264, 324, 384, 444)(265, 325, 385, 445)(266, 326, 386, 446)(267, 327, 387, 447)(268, 328, 388, 448)(269, 329, 389, 449)(270, 330, 390, 450)(271, 331, 391, 451)(272, 332, 392, 452)(273, 333, 393, 453)(274, 334, 394, 454)(275, 335, 395, 455)(276, 336, 396, 456)(277, 337, 397, 457)(278, 338, 398, 458)(279, 339, 399, 459)(280, 340, 400, 460)(281, 341, 401, 461)(282, 342, 402, 462)(283, 343, 403, 463)(284, 344, 404, 464)(285, 345, 405, 465)(286, 346, 406, 466)(287, 347, 407, 467)(288, 348, 408, 468)(289, 349, 409, 469)(290, 350, 410, 470)(291, 351, 411, 471)(292, 352, 412, 472)(293, 353, 413, 473)(294, 354, 414, 474)(295, 355, 415, 475)(296, 356, 416, 476)(297, 357, 417, 477)(298, 358, 418, 478)(299, 359, 419, 479)(300, 360, 420, 480)
L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 161)(62, 126)(63, 173)(64, 158)(65, 160)(66, 166)(67, 122)(68, 125)(69, 127)(70, 121)(71, 138)(72, 137)(73, 135)(74, 159)(75, 172)(76, 171)(77, 147)(78, 157)(79, 136)(80, 133)(81, 156)(82, 150)(83, 134)(84, 140)(85, 174)(86, 148)(87, 170)(88, 149)(89, 145)(90, 123)(91, 155)(92, 168)(93, 131)(94, 152)(95, 154)(96, 124)(97, 164)(98, 167)(99, 169)(100, 163)(101, 180)(102, 179)(103, 177)(104, 153)(105, 130)(106, 129)(107, 141)(108, 151)(109, 178)(110, 175)(111, 162)(112, 144)(113, 176)(114, 146)(115, 132)(116, 142)(117, 128)(118, 143)(119, 139)(120, 165)(181, 307)(182, 308)(183, 309)(184, 310)(185, 311)(186, 312)(187, 301)(188, 302)(189, 303)(190, 304)(191, 305)(192, 306)(193, 331)(194, 332)(195, 333)(196, 334)(197, 335)(198, 336)(199, 337)(200, 338)(201, 339)(202, 340)(203, 341)(204, 342)(205, 343)(206, 344)(207, 345)(208, 346)(209, 347)(210, 348)(211, 313)(212, 314)(213, 315)(214, 316)(215, 317)(216, 318)(217, 319)(218, 320)(219, 321)(220, 322)(221, 323)(222, 324)(223, 325)(224, 326)(225, 327)(226, 328)(227, 329)(228, 330)(229, 355)(230, 356)(231, 357)(232, 358)(233, 359)(234, 360)(235, 349)(236, 350)(237, 351)(238, 352)(239, 353)(240, 354)(361, 429)(362, 477)(363, 466)(364, 465)(365, 453)(366, 475)(367, 430)(368, 427)(369, 450)(370, 456)(371, 428)(372, 422)(373, 468)(374, 454)(375, 464)(376, 455)(377, 451)(378, 441)(379, 438)(380, 424)(381, 434)(382, 425)(383, 421)(384, 471)(385, 460)(386, 457)(387, 480)(388, 426)(389, 458)(390, 452)(391, 440)(392, 443)(393, 433)(394, 439)(395, 432)(396, 431)(397, 479)(398, 444)(399, 467)(400, 476)(401, 478)(402, 472)(403, 449)(404, 474)(405, 437)(406, 446)(407, 448)(408, 442)(409, 470)(410, 473)(411, 463)(412, 469)(413, 462)(414, 461)(415, 459)(416, 447)(417, 436)(418, 435)(419, 423)(420, 445)

MAP           : A4.208
NOTES         : type I, reflexible, isomorphic to Med2({4,5}), isomorphic to A4.205.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 4, 2 ]
UNIGROUP      : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^5 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, x.1^5, (x.2^-1 * x.1^2 * x.2^-1 * x.1)^2, x.2^2 * x.1^-1 * x.2 * x.1^2 * x.2 * x.1^-1 * x.2^-2 * x.1^-2 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 4, 4, 5)
#DARTS        : 480
R = (1, 121, 241, 361)(2, 122, 242, 362)(3, 123, 243, 363)(4, 124, 244, 364)(5, 125, 245, 365)(6, 126, 246, 366)(7, 127, 247, 367)(8, 128, 248, 368)(9, 129, 249, 369)(10, 130, 250, 370)(11, 131, 251, 371)(12, 132, 252, 372)(13, 133, 253, 373)(14, 134, 254, 374)(15, 135, 255, 375)(16, 136, 256, 376)(17, 137, 257, 377)(18, 138, 258, 378)(19, 139, 259, 379)(20, 140, 260, 380)(21, 141, 261, 381)(22, 142, 262, 382)(23, 143, 263, 383)(24, 144, 264, 384)(25, 145, 265, 385)(26, 146, 266, 386)(27, 147, 267, 387)(28, 148, 268, 388)(29, 149, 269, 389)(30, 150, 270, 390)(31, 151, 271, 391)(32, 152, 272, 392)(33, 153, 273, 393)(34, 154, 274, 394)(35, 155, 275, 395)(36, 156, 276, 396)(37, 157, 277, 397)(38, 158, 278, 398)(39, 159, 279, 399)(40, 160, 280, 400)(41, 161, 281, 401)(42, 162, 282, 402)(43, 163, 283, 403)(44, 164, 284, 404)(45, 165, 285, 405)(46, 166, 286, 406)(47, 167, 287, 407)(48, 168, 288, 408)(49, 169, 289, 409)(50, 170, 290, 410)(51, 171, 291, 411)(52, 172, 292, 412)(53, 173, 293, 413)(54, 174, 294, 414)(55, 175, 295, 415)(56, 176, 296, 416)(57, 177, 297, 417)(58, 178, 298, 418)(59, 179, 299, 419)(60, 180, 300, 420)(61, 181, 301, 421)(62, 182, 302, 422)(63, 183, 303, 423)(64, 184, 304, 424)(65, 185, 305, 425)(66, 186, 306, 426)(67, 187, 307, 427)(68, 188, 308, 428)(69, 189, 309, 429)(70, 190, 310, 430)(71, 191, 311, 431)(72, 192, 312, 432)(73, 193, 313, 433)(74, 194, 314, 434)(75, 195, 315, 435)(76, 196, 316, 436)(77, 197, 317, 437)(78, 198, 318, 438)(79, 199, 319, 439)(80, 200, 320, 440)(81, 201, 321, 441)(82, 202, 322, 442)(83, 203, 323, 443)(84, 204, 324, 444)(85, 205, 325, 445)(86, 206, 326, 446)(87, 207, 327, 447)(88, 208, 328, 448)(89, 209, 329, 449)(90, 210, 330, 450)(91, 211, 331, 451)(92, 212, 332, 452)(93, 213, 333, 453)(94, 214, 334, 454)(95, 215, 335, 455)(96, 216, 336, 456)(97, 217, 337, 457)(98, 218, 338, 458)(99, 219, 339, 459)(100, 220, 340, 460)(101, 221, 341, 461)(102, 222, 342, 462)(103, 223, 343, 463)(104, 224, 344, 464)(105, 225, 345, 465)(106, 226, 346, 466)(107, 227, 347, 467)(108, 228, 348, 468)(109, 229, 349, 469)(110, 230, 350, 470)(111, 231, 351, 471)(112, 232, 352, 472)(113, 233, 353, 473)(114, 234, 354, 474)(115, 235, 355, 475)(116, 236, 356, 476)(117, 237, 357, 477)(118, 238, 358, 478)(119, 239, 359, 479)(120, 240, 360, 480)
L = (1, 124)(2, 125)(3, 122)(4, 161)(5, 160)(6, 121)(7, 239)(8, 238)(9, 197)(10, 225)(11, 228)(12, 196)(13, 132)(14, 129)(15, 156)(16, 127)(17, 128)(18, 153)(19, 236)(20, 235)(21, 223)(22, 230)(23, 229)(24, 224)(25, 237)(26, 240)(27, 232)(28, 204)(29, 201)(30, 233)(31, 206)(32, 205)(33, 193)(34, 200)(35, 199)(36, 194)(37, 207)(38, 210)(39, 202)(40, 174)(41, 171)(42, 203)(43, 209)(44, 208)(45, 167)(46, 195)(47, 198)(48, 166)(49, 222)(50, 219)(51, 126)(52, 217)(53, 218)(54, 123)(55, 214)(56, 215)(57, 212)(58, 131)(59, 130)(60, 211)(61, 177)(62, 180)(63, 172)(64, 144)(65, 141)(66, 173)(67, 192)(68, 189)(69, 216)(70, 187)(71, 188)(72, 213)(73, 176)(74, 175)(75, 163)(76, 170)(77, 169)(78, 164)(79, 184)(80, 185)(81, 182)(82, 221)(83, 220)(84, 181)(85, 179)(86, 178)(87, 137)(88, 165)(89, 168)(90, 136)(91, 149)(92, 148)(93, 227)(94, 135)(95, 138)(96, 226)(97, 146)(98, 145)(99, 133)(100, 140)(101, 139)(102, 134)(103, 154)(104, 155)(105, 152)(106, 191)(107, 190)(108, 151)(109, 147)(110, 150)(111, 142)(112, 234)(113, 231)(114, 143)(115, 162)(116, 159)(117, 186)(118, 157)(119, 158)(120, 183)(241, 363)(242, 366)(243, 376)(244, 462)(245, 459)(246, 377)(247, 414)(248, 411)(249, 450)(250, 409)(251, 410)(252, 447)(253, 362)(254, 361)(255, 367)(256, 374)(257, 373)(258, 368)(259, 400)(260, 401)(261, 398)(262, 437)(263, 436)(264, 397)(265, 365)(266, 364)(267, 479)(268, 369)(269, 372)(270, 478)(271, 473)(272, 472)(273, 443)(274, 477)(275, 480)(276, 442)(277, 470)(278, 469)(279, 475)(280, 458)(281, 457)(282, 476)(283, 382)(284, 383)(285, 380)(286, 413)(287, 412)(288, 379)(289, 471)(290, 474)(291, 460)(292, 426)(293, 423)(294, 461)(295, 390)(296, 387)(297, 402)(298, 385)(299, 386)(300, 399)(301, 466)(302, 467)(303, 464)(304, 389)(305, 388)(306, 463)(307, 431)(308, 430)(309, 395)(310, 441)(311, 444)(312, 394)(313, 456)(314, 453)(315, 384)(316, 451)(317, 452)(318, 381)(319, 428)(320, 427)(321, 439)(322, 422)(323, 421)(324, 440)(325, 429)(326, 432)(327, 424)(328, 420)(329, 417)(330, 425)(331, 404)(332, 403)(333, 391)(334, 416)(335, 415)(336, 392)(337, 405)(338, 408)(339, 418)(340, 378)(341, 375)(342, 419)(343, 407)(344, 406)(345, 371)(346, 393)(347, 396)(348, 370)(349, 438)(350, 435)(351, 468)(352, 433)(353, 434)(354, 465)(355, 448)(356, 449)(357, 446)(358, 455)(359, 454)(360, 445)

MAP           : A4.209
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), representative.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^2, x.2 * x.4 * x.3, (x.2^-1 * x.4)^2, (x.3 * x.1^-1)^2, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 76)(38, 75)(39, 101)(40, 105)(41, 96)(42, 95)(43, 77)(44, 73)(45, 88)(46, 84)(47, 93)(48, 74)(49, 83)(50, 79)(51, 94)(52, 78)(53, 87)(54, 80)(55, 98)(56, 102)(57, 92)(58, 91)(59, 97)(60, 106)(61, 104)(62, 108)(63, 86)(64, 85)(65, 103)(66, 100)(67, 82)(68, 81)(69, 107)(70, 99)(71, 90)(72, 89)(109, 183)(110, 203)(111, 181)(112, 185)(113, 184)(114, 199)(115, 210)(116, 214)(117, 216)(118, 212)(119, 206)(120, 213)(121, 207)(122, 215)(123, 205)(124, 209)(125, 208)(126, 211)(127, 186)(128, 202)(129, 204)(130, 200)(131, 182)(132, 201)(133, 195)(134, 191)(135, 193)(136, 197)(137, 196)(138, 187)(139, 198)(140, 190)(141, 192)(142, 188)(143, 194)(144, 189)(217, 254)(218, 258)(219, 260)(220, 259)(221, 253)(222, 274)(223, 272)(224, 276)(225, 278)(226, 277)(227, 271)(228, 256)(229, 286)(230, 285)(231, 275)(232, 255)(233, 282)(234, 281)(235, 268)(236, 267)(237, 257)(238, 273)(239, 264)(240, 263)(241, 269)(242, 265)(243, 280)(244, 288)(245, 261)(246, 266)(247, 287)(248, 283)(249, 262)(250, 270)(251, 279)(252, 284)

MAP           : A4.210
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, (x.4 * x.1^-1)^2, (x.3 * x.4)^2, (x.1 * x.2^-1)^2, x.3 * x.4 * x.2 * x.4 * x.3^-1 * x.2^-1, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.2 * x.3^-1)^3, x.3^6, x.4 * x.2 * x.4 * 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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 254)(38, 253)(39, 259)(40, 265)(41, 260)(42, 266)(43, 255)(44, 257)(45, 263)(46, 264)(47, 261)(48, 262)(49, 256)(50, 258)(51, 288)(52, 287)(53, 286)(54, 285)(55, 272)(56, 271)(57, 277)(58, 283)(59, 278)(60, 284)(61, 273)(62, 275)(63, 281)(64, 282)(65, 279)(66, 280)(67, 274)(68, 276)(69, 270)(70, 269)(71, 268)(72, 267)(73, 219)(74, 221)(75, 227)(76, 228)(77, 225)(78, 226)(79, 238)(80, 240)(81, 234)(82, 233)(83, 232)(84, 231)(85, 237)(86, 239)(87, 245)(88, 246)(89, 243)(90, 244)(91, 220)(92, 222)(93, 252)(94, 251)(95, 250)(96, 249)(97, 236)(98, 235)(99, 241)(100, 247)(101, 242)(102, 248)(103, 218)(104, 217)(105, 223)(106, 229)(107, 224)(108, 230)(109, 186)(110, 184)(111, 200)(112, 182)(113, 199)(114, 181)(115, 216)(116, 214)(117, 206)(118, 212)(119, 205)(120, 211)(121, 215)(122, 213)(123, 208)(124, 207)(125, 210)(126, 209)(127, 185)(128, 183)(129, 202)(130, 201)(131, 204)(132, 203)(133, 191)(134, 189)(135, 196)(136, 195)(137, 198)(138, 197)(139, 192)(140, 190)(141, 194)(142, 188)(143, 193)(144, 187)

MAP           : A4.211
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.5 * x.4)^2, (x.3 * x.4)^2, (x.2 * x.1)^2, x.4 * x.1 * x.5^-1 * x.2, (x.5 * x.3^-1)^3 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 258)(38, 256)(39, 272)(40, 254)(41, 271)(42, 253)(43, 288)(44, 286)(45, 278)(46, 284)(47, 277)(48, 283)(49, 287)(50, 285)(51, 280)(52, 279)(53, 282)(54, 281)(55, 257)(56, 255)(57, 274)(58, 273)(59, 276)(60, 275)(61, 263)(62, 261)(63, 268)(64, 267)(65, 270)(66, 269)(67, 264)(68, 262)(69, 266)(70, 260)(71, 265)(72, 259)(73, 74)(75, 79)(76, 85)(77, 80)(78, 86)(81, 83)(82, 84)(87, 108)(88, 107)(89, 106)(90, 105)(91, 92)(93, 97)(94, 103)(95, 98)(96, 104)(99, 101)(100, 102)(109, 185)(110, 183)(111, 202)(112, 201)(113, 204)(114, 203)(115, 191)(116, 189)(117, 196)(118, 195)(119, 198)(120, 197)(121, 192)(122, 190)(123, 194)(124, 188)(125, 193)(126, 187)(127, 186)(128, 184)(129, 200)(130, 182)(131, 199)(132, 181)(133, 216)(134, 214)(135, 206)(136, 212)(137, 205)(138, 211)(139, 215)(140, 213)(141, 208)(142, 207)(143, 210)(144, 209)(217, 226)(218, 228)(219, 222)(220, 221)(223, 230)(224, 229)(225, 235)(227, 236)(231, 247)(232, 241)(233, 248)(234, 242)(237, 251)(238, 252)(239, 249)(240, 250)(243, 246)(244, 245)

MAP           : A4.212
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.3^2, x.2 * x.4 * x.3, (x.2^-1 * x.4)^2, (x.3 * x.1^-1)^2, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 74)(38, 78)(39, 80)(40, 79)(41, 73)(42, 94)(43, 92)(44, 96)(45, 98)(46, 97)(47, 91)(48, 76)(49, 106)(50, 105)(51, 95)(52, 75)(53, 102)(54, 101)(55, 88)(56, 87)(57, 77)(58, 93)(59, 84)(60, 83)(61, 89)(62, 85)(63, 100)(64, 108)(65, 81)(66, 86)(67, 107)(68, 103)(69, 82)(70, 90)(71, 99)(72, 104)(109, 183)(110, 203)(111, 181)(112, 185)(113, 184)(114, 199)(115, 210)(116, 214)(117, 216)(118, 212)(119, 206)(120, 213)(121, 207)(122, 215)(123, 205)(124, 209)(125, 208)(126, 211)(127, 186)(128, 202)(129, 204)(130, 200)(131, 182)(132, 201)(133, 195)(134, 191)(135, 193)(136, 197)(137, 196)(138, 187)(139, 198)(140, 190)(141, 192)(142, 188)(143, 194)(144, 189)(217, 268)(218, 267)(219, 257)(220, 273)(221, 264)(222, 263)(223, 269)(224, 265)(225, 280)(226, 288)(227, 261)(228, 266)(229, 287)(230, 283)(231, 262)(232, 270)(233, 279)(234, 284)(235, 254)(236, 258)(237, 260)(238, 259)(239, 253)(240, 274)(241, 272)(242, 276)(243, 278)(244, 277)(245, 271)(246, 256)(247, 286)(248, 285)(249, 275)(250, 255)(251, 282)(252, 281)

MAP           : A4.213
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, (x.3 * x.4)^2, (x.4 * x.1^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, x.3^2 * x.2 * x.3^-2 * x.2^-1, x.3^6, (x.2 * x.3^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 254)(38, 253)(39, 259)(40, 265)(41, 260)(42, 266)(43, 255)(44, 257)(45, 263)(46, 264)(47, 261)(48, 262)(49, 256)(50, 258)(51, 288)(52, 287)(53, 286)(54, 285)(55, 272)(56, 271)(57, 277)(58, 283)(59, 278)(60, 284)(61, 273)(62, 275)(63, 281)(64, 282)(65, 279)(66, 280)(67, 274)(68, 276)(69, 270)(70, 269)(71, 268)(72, 267)(73, 219)(74, 221)(75, 227)(76, 228)(77, 225)(78, 226)(79, 238)(80, 240)(81, 234)(82, 233)(83, 232)(84, 231)(85, 237)(86, 239)(87, 245)(88, 246)(89, 243)(90, 244)(91, 220)(92, 222)(93, 252)(94, 251)(95, 250)(96, 249)(97, 236)(98, 235)(99, 241)(100, 247)(101, 242)(102, 248)(103, 218)(104, 217)(105, 223)(106, 229)(107, 224)(108, 230)(109, 207)(110, 209)(111, 197)(112, 198)(113, 195)(114, 196)(115, 214)(116, 216)(117, 192)(118, 191)(119, 190)(120, 189)(121, 213)(122, 215)(123, 185)(124, 186)(125, 183)(126, 184)(127, 208)(128, 210)(129, 204)(130, 203)(131, 202)(132, 201)(133, 212)(134, 211)(135, 181)(136, 199)(137, 182)(138, 200)(139, 206)(140, 205)(141, 193)(142, 187)(143, 194)(144, 188)

MAP           : A4.214
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
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.2 * x.3)^3, x.4 * x.2 * x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.4 * x.2^-1 * x.3, x.4 * x.2 * x.3 * x.4 * x.2 * x.4 * x.2^-1 * x.3 * x.4 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 258)(38, 256)(39, 272)(40, 254)(41, 271)(42, 253)(43, 288)(44, 286)(45, 278)(46, 284)(47, 277)(48, 283)(49, 287)(50, 285)(51, 280)(52, 279)(53, 282)(54, 281)(55, 257)(56, 255)(57, 274)(58, 273)(59, 276)(60, 275)(61, 263)(62, 261)(63, 268)(64, 267)(65, 270)(66, 269)(67, 264)(68, 262)(69, 266)(70, 260)(71, 265)(72, 259)(73, 228)(74, 226)(75, 230)(76, 224)(77, 229)(78, 223)(79, 222)(80, 220)(81, 236)(82, 218)(83, 235)(84, 217)(85, 221)(86, 219)(87, 238)(88, 237)(89, 240)(90, 239)(91, 227)(92, 225)(93, 232)(94, 231)(95, 234)(96, 233)(97, 251)(98, 249)(99, 244)(100, 243)(101, 246)(102, 245)(103, 252)(104, 250)(105, 242)(106, 248)(107, 241)(108, 247)(109, 190)(110, 192)(111, 186)(112, 185)(113, 184)(114, 183)(115, 194)(116, 193)(117, 199)(118, 181)(119, 200)(120, 182)(121, 188)(122, 187)(123, 211)(124, 205)(125, 212)(126, 206)(127, 189)(128, 191)(129, 215)(130, 216)(131, 213)(132, 214)(133, 196)(134, 198)(135, 210)(136, 209)(137, 208)(138, 207)(139, 195)(140, 197)(141, 203)(142, 204)(143, 201)(144, 202)

MAP           : A4.215
NOTES         : type II, reflexible, isomorphic to A4.211.
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)   : <36, 10>
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)^2, x.4 * x.1 * x.5 * x.2, (x.5 * x.3^-1)^2, (x.2 * x.1)^2, (x.3 * x.4^-1)^3, x.2 * x.5 * x.4^-1 * x.1 * x.4^-1 * x.1 * x.2 * x.5 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 257)(38, 255)(39, 274)(40, 273)(41, 276)(42, 275)(43, 263)(44, 261)(45, 268)(46, 267)(47, 270)(48, 269)(49, 264)(50, 262)(51, 266)(52, 260)(53, 265)(54, 259)(55, 258)(56, 256)(57, 272)(58, 254)(59, 271)(60, 253)(61, 288)(62, 286)(63, 278)(64, 284)(65, 277)(66, 283)(67, 287)(68, 285)(69, 280)(70, 279)(71, 282)(72, 281)(73, 99)(74, 101)(75, 89)(76, 90)(77, 87)(78, 88)(79, 106)(80, 108)(81, 84)(82, 83)(85, 105)(86, 107)(91, 100)(92, 102)(93, 96)(94, 95)(97, 104)(98, 103)(109, 203)(110, 201)(111, 184)(112, 183)(113, 186)(114, 185)(115, 209)(116, 207)(117, 214)(118, 213)(119, 216)(120, 215)(121, 210)(122, 208)(123, 212)(124, 206)(125, 211)(126, 205)(127, 204)(128, 202)(129, 182)(130, 200)(131, 181)(132, 199)(133, 198)(134, 196)(135, 188)(136, 194)(137, 187)(138, 193)(139, 197)(140, 195)(141, 190)(142, 189)(143, 192)(144, 191)(217, 218)(219, 223)(220, 229)(221, 224)(222, 230)(225, 227)(226, 228)(231, 252)(232, 251)(233, 250)(234, 249)(235, 236)(237, 241)(238, 247)(239, 242)(240, 248)(243, 245)(244, 246)

MAP           : A4.216
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
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.3 * x.4^-1)^2, (x.4 * x.1^-1)^3, x.4^-1 * x.2 * x.4 * x.2 * x.4 * x.2 * x.4^-1 * x.2 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 254)(38, 253)(39, 259)(40, 265)(41, 260)(42, 266)(43, 255)(44, 257)(45, 263)(46, 264)(47, 261)(48, 262)(49, 256)(50, 258)(51, 288)(52, 287)(53, 286)(54, 285)(55, 272)(56, 271)(57, 277)(58, 283)(59, 278)(60, 284)(61, 273)(62, 275)(63, 281)(64, 282)(65, 279)(66, 280)(67, 274)(68, 276)(69, 270)(70, 269)(71, 268)(72, 267)(73, 228)(74, 226)(75, 230)(76, 224)(77, 229)(78, 223)(79, 222)(80, 220)(81, 236)(82, 218)(83, 235)(84, 217)(85, 221)(86, 219)(87, 238)(88, 237)(89, 240)(90, 239)(91, 227)(92, 225)(93, 232)(94, 231)(95, 234)(96, 233)(97, 251)(98, 249)(99, 244)(100, 243)(101, 246)(102, 245)(103, 252)(104, 250)(105, 242)(106, 248)(107, 241)(108, 247)(109, 185)(110, 183)(111, 202)(112, 201)(113, 204)(114, 203)(115, 191)(116, 189)(117, 196)(118, 195)(119, 198)(120, 197)(121, 192)(122, 190)(123, 194)(124, 188)(125, 193)(126, 187)(127, 186)(128, 184)(129, 200)(130, 182)(131, 199)(132, 181)(133, 216)(134, 214)(135, 206)(136, 212)(137, 205)(138, 211)(139, 215)(140, 213)(141, 208)(142, 207)(143, 210)(144, 209)

MAP           : A4.217
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
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.2 * x.3)^3, x.4 * x.2 * x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.4 * x.2^-1 * x.3, x.4 * x.2 * x.3 * x.4 * x.2 * x.4 * x.2^-1 * x.3 * x.4 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 258)(38, 256)(39, 272)(40, 254)(41, 271)(42, 253)(43, 288)(44, 286)(45, 278)(46, 284)(47, 277)(48, 283)(49, 287)(50, 285)(51, 280)(52, 279)(53, 282)(54, 281)(55, 257)(56, 255)(57, 274)(58, 273)(59, 276)(60, 275)(61, 263)(62, 261)(63, 268)(64, 267)(65, 270)(66, 269)(67, 264)(68, 262)(69, 266)(70, 260)(71, 265)(72, 259)(73, 228)(74, 226)(75, 230)(76, 224)(77, 229)(78, 223)(79, 222)(80, 220)(81, 236)(82, 218)(83, 235)(84, 217)(85, 221)(86, 219)(87, 238)(88, 237)(89, 240)(90, 239)(91, 227)(92, 225)(93, 232)(94, 231)(95, 234)(96, 233)(97, 251)(98, 249)(99, 244)(100, 243)(101, 246)(102, 245)(103, 252)(104, 250)(105, 242)(106, 248)(107, 241)(108, 247)(109, 182)(110, 181)(111, 187)(112, 193)(113, 188)(114, 194)(115, 183)(116, 185)(117, 191)(118, 192)(119, 189)(120, 190)(121, 184)(122, 186)(123, 216)(124, 215)(125, 214)(126, 213)(127, 200)(128, 199)(129, 205)(130, 211)(131, 206)(132, 212)(133, 201)(134, 203)(135, 209)(136, 210)(137, 207)(138, 208)(139, 202)(140, 204)(141, 198)(142, 197)(143, 196)(144, 195)

MAP           : A4.218
NOTES         : type II, reflexible, isomorphic to A4.211.
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)   : <36, 10>
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)^2, x.4 * x.1 * x.5 * x.2, (x.5 * x.3^-1)^2, (x.2 * x.1)^2, (x.3 * x.4^-1)^3, x.2 * x.5 * x.4^-1 * x.1 * x.4^-1 * x.1 * x.2 * x.5 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 257)(38, 255)(39, 274)(40, 273)(41, 276)(42, 275)(43, 263)(44, 261)(45, 268)(46, 267)(47, 270)(48, 269)(49, 264)(50, 262)(51, 266)(52, 260)(53, 265)(54, 259)(55, 258)(56, 256)(57, 272)(58, 254)(59, 271)(60, 253)(61, 288)(62, 286)(63, 278)(64, 284)(65, 277)(66, 283)(67, 287)(68, 285)(69, 280)(70, 279)(71, 282)(72, 281)(73, 74)(75, 79)(76, 85)(77, 80)(78, 86)(81, 83)(82, 84)(87, 108)(88, 107)(89, 106)(90, 105)(91, 92)(93, 97)(94, 103)(95, 98)(96, 104)(99, 101)(100, 102)(109, 197)(110, 195)(111, 190)(112, 189)(113, 192)(114, 191)(115, 203)(116, 201)(117, 184)(118, 183)(119, 186)(120, 185)(121, 204)(122, 202)(123, 182)(124, 200)(125, 181)(126, 199)(127, 198)(128, 196)(129, 188)(130, 194)(131, 187)(132, 193)(133, 210)(134, 208)(135, 212)(136, 206)(137, 211)(138, 205)(139, 209)(140, 207)(141, 214)(142, 213)(143, 216)(144, 215)(217, 243)(218, 245)(219, 233)(220, 234)(221, 231)(222, 232)(223, 250)(224, 252)(225, 228)(226, 227)(229, 249)(230, 251)(235, 244)(236, 246)(237, 240)(238, 239)(241, 248)(242, 247)

MAP           : A4.219
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, (x.4 * x.2)^2, (x.1 * x.2)^2, (x.3^-1 * x.4)^2, (x.2 * x.3^-1)^2, x.4 * x.3 * x.4 * x.3^3, (x.4 * x.1^-1)^3, (x.4^-1 * x.3^-1 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 258)(38, 256)(39, 272)(40, 254)(41, 271)(42, 253)(43, 288)(44, 286)(45, 278)(46, 284)(47, 277)(48, 283)(49, 287)(50, 285)(51, 280)(52, 279)(53, 282)(54, 281)(55, 257)(56, 255)(57, 274)(58, 273)(59, 276)(60, 275)(61, 263)(62, 261)(63, 268)(64, 267)(65, 270)(66, 269)(67, 264)(68, 262)(69, 266)(70, 260)(71, 265)(72, 259)(73, 219)(74, 221)(75, 227)(76, 228)(77, 225)(78, 226)(79, 238)(80, 240)(81, 234)(82, 233)(83, 232)(84, 231)(85, 237)(86, 239)(87, 245)(88, 246)(89, 243)(90, 244)(91, 220)(92, 222)(93, 252)(94, 251)(95, 250)(96, 249)(97, 236)(98, 235)(99, 241)(100, 247)(101, 242)(102, 248)(103, 218)(104, 217)(105, 223)(106, 229)(107, 224)(108, 230)(109, 185)(110, 183)(111, 202)(112, 201)(113, 204)(114, 203)(115, 191)(116, 189)(117, 196)(118, 195)(119, 198)(120, 197)(121, 192)(122, 190)(123, 194)(124, 188)(125, 193)(126, 187)(127, 186)(128, 184)(129, 200)(130, 182)(131, 199)(132, 181)(133, 216)(134, 214)(135, 206)(136, 212)(137, 205)(138, 211)(139, 215)(140, 213)(141, 208)(142, 207)(143, 210)(144, 209)

MAP           : A4.220
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, (x.3 * x.4)^2, (x.4 * x.1^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, x.3^2 * x.2 * x.3^-2 * x.2^-1, x.3^6, (x.2 * x.3^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 279)(38, 281)(39, 269)(40, 270)(41, 267)(42, 268)(43, 286)(44, 288)(45, 264)(46, 263)(47, 262)(48, 261)(49, 285)(50, 287)(51, 257)(52, 258)(53, 255)(54, 256)(55, 280)(56, 282)(57, 276)(58, 275)(59, 274)(60, 273)(61, 284)(62, 283)(63, 253)(64, 271)(65, 254)(66, 272)(67, 278)(68, 277)(69, 265)(70, 259)(71, 266)(72, 260)(73, 242)(74, 241)(75, 229)(76, 223)(77, 230)(78, 224)(79, 243)(80, 245)(81, 233)(82, 234)(83, 231)(84, 232)(85, 244)(86, 246)(87, 240)(88, 239)(89, 238)(90, 237)(91, 248)(92, 247)(93, 217)(94, 235)(95, 218)(96, 236)(97, 249)(98, 251)(99, 221)(100, 222)(101, 219)(102, 220)(103, 250)(104, 252)(105, 228)(106, 227)(107, 226)(108, 225)(109, 182)(110, 181)(111, 187)(112, 193)(113, 188)(114, 194)(115, 183)(116, 185)(117, 191)(118, 192)(119, 189)(120, 190)(121, 184)(122, 186)(123, 216)(124, 215)(125, 214)(126, 213)(127, 200)(128, 199)(129, 205)(130, 211)(131, 206)(132, 212)(133, 201)(134, 203)(135, 209)(136, 210)(137, 207)(138, 208)(139, 202)(140, 204)(141, 198)(142, 197)(143, 196)(144, 195)

MAP           : A4.221
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.3 * x.4^-1)^2, x.3 * x.4^-1 * x.3^-1 * x.2 * x.4^-1 * x.2, (x.4 * x.2 * x.3^-1)^2, x.4 * x.3 * x.2 * x.4 * x.2 * x.3^-1, (x.4^-1 * x.3^-1 * x.4^-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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 254)(38, 253)(39, 259)(40, 265)(41, 260)(42, 266)(43, 255)(44, 257)(45, 263)(46, 264)(47, 261)(48, 262)(49, 256)(50, 258)(51, 288)(52, 287)(53, 286)(54, 285)(55, 272)(56, 271)(57, 277)(58, 283)(59, 278)(60, 284)(61, 273)(62, 275)(63, 281)(64, 282)(65, 279)(66, 280)(67, 274)(68, 276)(69, 270)(70, 269)(71, 268)(72, 267)(73, 220)(74, 222)(75, 252)(76, 251)(77, 250)(78, 249)(79, 236)(80, 235)(81, 241)(82, 247)(83, 242)(84, 248)(85, 218)(86, 217)(87, 223)(88, 229)(89, 224)(90, 230)(91, 219)(92, 221)(93, 227)(94, 228)(95, 225)(96, 226)(97, 238)(98, 240)(99, 234)(100, 233)(101, 232)(102, 231)(103, 237)(104, 239)(105, 245)(106, 246)(107, 243)(108, 244)(109, 185)(110, 183)(111, 202)(112, 201)(113, 204)(114, 203)(115, 191)(116, 189)(117, 196)(118, 195)(119, 198)(120, 197)(121, 192)(122, 190)(123, 194)(124, 188)(125, 193)(126, 187)(127, 186)(128, 184)(129, 200)(130, 182)(131, 199)(132, 181)(133, 216)(134, 214)(135, 206)(136, 212)(137, 205)(138, 211)(139, 215)(140, 213)(141, 208)(142, 207)(143, 210)(144, 209)

MAP           : A4.222
NOTES         : type II, reflexible, isomorphic to A4.211.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, (x.5 * x.4)^2, (x.3 * x.4)^2, (x.2 * x.1)^2, x.4 * x.1 * x.5^-1 * x.2, (x.5 * x.3^-1)^3 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 258)(38, 256)(39, 272)(40, 254)(41, 271)(42, 253)(43, 288)(44, 286)(45, 278)(46, 284)(47, 277)(48, 283)(49, 287)(50, 285)(51, 280)(52, 279)(53, 282)(54, 281)(55, 257)(56, 255)(57, 274)(58, 273)(59, 276)(60, 275)(61, 263)(62, 261)(63, 268)(64, 267)(65, 270)(66, 269)(67, 264)(68, 262)(69, 266)(70, 260)(71, 265)(72, 259)(73, 82)(74, 84)(75, 78)(76, 77)(79, 86)(80, 85)(81, 91)(83, 92)(87, 103)(88, 97)(89, 104)(90, 98)(93, 107)(94, 108)(95, 105)(96, 106)(99, 102)(100, 101)(109, 204)(110, 202)(111, 182)(112, 200)(113, 181)(114, 199)(115, 198)(116, 196)(117, 188)(118, 194)(119, 187)(120, 193)(121, 197)(122, 195)(123, 190)(124, 189)(125, 192)(126, 191)(127, 203)(128, 201)(129, 184)(130, 183)(131, 186)(132, 185)(133, 209)(134, 207)(135, 214)(136, 213)(137, 216)(138, 215)(139, 210)(140, 208)(141, 212)(142, 206)(143, 211)(144, 205)(217, 218)(219, 223)(220, 229)(221, 224)(222, 230)(225, 227)(226, 228)(231, 252)(232, 251)(233, 250)(234, 249)(235, 236)(237, 241)(238, 247)(239, 242)(240, 248)(243, 245)(244, 246)

MAP           : A4.223
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.3 * x.4)^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^3, x.2^-1 * x.4 * x.2 * x.4 * x.2 * x.4 * x.2^-1 * x.4 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 257)(38, 255)(39, 274)(40, 273)(41, 276)(42, 275)(43, 263)(44, 261)(45, 268)(46, 267)(47, 270)(48, 269)(49, 264)(50, 262)(51, 266)(52, 260)(53, 265)(54, 259)(55, 258)(56, 256)(57, 272)(58, 254)(59, 271)(60, 253)(61, 288)(62, 286)(63, 278)(64, 284)(65, 277)(66, 283)(67, 287)(68, 285)(69, 280)(70, 279)(71, 282)(72, 281)(73, 222)(74, 220)(75, 236)(76, 218)(77, 235)(78, 217)(79, 252)(80, 250)(81, 242)(82, 248)(83, 241)(84, 247)(85, 251)(86, 249)(87, 244)(88, 243)(89, 246)(90, 245)(91, 221)(92, 219)(93, 238)(94, 237)(95, 240)(96, 239)(97, 227)(98, 225)(99, 232)(100, 231)(101, 234)(102, 233)(103, 228)(104, 226)(105, 230)(106, 224)(107, 229)(108, 223)(109, 196)(110, 198)(111, 210)(112, 209)(113, 208)(114, 207)(115, 188)(116, 187)(117, 211)(118, 205)(119, 212)(120, 206)(121, 194)(122, 193)(123, 199)(124, 181)(125, 200)(126, 182)(127, 195)(128, 197)(129, 203)(130, 204)(131, 201)(132, 202)(133, 190)(134, 192)(135, 186)(136, 185)(137, 184)(138, 183)(139, 189)(140, 191)(141, 215)(142, 216)(143, 213)(144, 214)

MAP           : A4.224
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.3 * x.4)^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^3, x.2^-1 * x.4 * x.2 * x.4 * x.2 * x.4 * x.2^-1 * x.4 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 257)(38, 255)(39, 274)(40, 273)(41, 276)(42, 275)(43, 263)(44, 261)(45, 268)(46, 267)(47, 270)(48, 269)(49, 264)(50, 262)(51, 266)(52, 260)(53, 265)(54, 259)(55, 258)(56, 256)(57, 272)(58, 254)(59, 271)(60, 253)(61, 288)(62, 286)(63, 278)(64, 284)(65, 277)(66, 283)(67, 287)(68, 285)(69, 280)(70, 279)(71, 282)(72, 281)(73, 222)(74, 220)(75, 236)(76, 218)(77, 235)(78, 217)(79, 252)(80, 250)(81, 242)(82, 248)(83, 241)(84, 247)(85, 251)(86, 249)(87, 244)(88, 243)(89, 246)(90, 245)(91, 221)(92, 219)(93, 238)(94, 237)(95, 240)(96, 239)(97, 227)(98, 225)(99, 232)(100, 231)(101, 234)(102, 233)(103, 228)(104, 226)(105, 230)(106, 224)(107, 229)(108, 223)(109, 207)(110, 209)(111, 197)(112, 198)(113, 195)(114, 196)(115, 214)(116, 216)(117, 192)(118, 191)(119, 190)(120, 189)(121, 213)(122, 215)(123, 185)(124, 186)(125, 183)(126, 184)(127, 208)(128, 210)(129, 204)(130, 203)(131, 202)(132, 201)(133, 212)(134, 211)(135, 181)(136, 199)(137, 182)(138, 200)(139, 206)(140, 205)(141, 193)(142, 187)(143, 194)(144, 188)

MAP           : A4.225
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, (x.4 * x.1^-1)^2, (x.3 * x.4)^2, (x.1 * x.2^-1)^2, x.3 * x.4 * x.2 * x.4 * x.3^-1 * x.2^-1, x.3^-1 * x.2 * x.3^2 * x.2^-1 * x.3^-1, (x.2 * x.3^-1)^3, x.3^6, x.4 * x.2 * x.4 * 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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 279)(38, 281)(39, 269)(40, 270)(41, 267)(42, 268)(43, 286)(44, 288)(45, 264)(46, 263)(47, 262)(48, 261)(49, 285)(50, 287)(51, 257)(52, 258)(53, 255)(54, 256)(55, 280)(56, 282)(57, 276)(58, 275)(59, 274)(60, 273)(61, 284)(62, 283)(63, 253)(64, 271)(65, 254)(66, 272)(67, 278)(68, 277)(69, 265)(70, 259)(71, 266)(72, 260)(73, 242)(74, 241)(75, 229)(76, 223)(77, 230)(78, 224)(79, 243)(80, 245)(81, 233)(82, 234)(83, 231)(84, 232)(85, 244)(86, 246)(87, 240)(88, 239)(89, 238)(90, 237)(91, 248)(92, 247)(93, 217)(94, 235)(95, 218)(96, 236)(97, 249)(98, 251)(99, 221)(100, 222)(101, 219)(102, 220)(103, 250)(104, 252)(105, 228)(106, 227)(107, 226)(108, 225)(109, 192)(110, 190)(111, 194)(112, 188)(113, 193)(114, 187)(115, 186)(116, 184)(117, 200)(118, 182)(119, 199)(120, 181)(121, 185)(122, 183)(123, 202)(124, 201)(125, 204)(126, 203)(127, 191)(128, 189)(129, 196)(130, 195)(131, 198)(132, 197)(133, 215)(134, 213)(135, 208)(136, 207)(137, 210)(138, 209)(139, 216)(140, 214)(141, 206)(142, 212)(143, 205)(144, 211)

MAP           : A4.226
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.4^4, x.2^4, (x.4^-1 * x.2)^2, x.3 * x.4^-2 * x.3^-1 * x.4 * x.2^-1, (x.3 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 81)(38, 88)(39, 73)(40, 95)(41, 102)(42, 104)(43, 75)(44, 94)(45, 79)(46, 89)(47, 108)(48, 98)(49, 90)(50, 93)(51, 86)(52, 80)(53, 76)(54, 91)(55, 96)(56, 87)(57, 92)(58, 74)(59, 82)(60, 85)(61, 100)(62, 78)(63, 101)(64, 103)(65, 105)(66, 83)(67, 106)(68, 84)(69, 107)(70, 97)(71, 99)(72, 77)(109, 182)(110, 185)(111, 190)(112, 189)(113, 181)(114, 184)(115, 191)(116, 187)(117, 186)(118, 192)(119, 188)(120, 183)(121, 194)(122, 197)(123, 214)(124, 213)(125, 193)(126, 196)(127, 203)(128, 199)(129, 210)(130, 204)(131, 200)(132, 207)(133, 206)(134, 209)(135, 202)(136, 201)(137, 205)(138, 208)(139, 215)(140, 211)(141, 198)(142, 216)(143, 212)(144, 195)(217, 288)(218, 255)(219, 284)(220, 278)(221, 274)(222, 253)(223, 268)(224, 282)(225, 269)(226, 259)(227, 261)(228, 275)(229, 262)(230, 276)(231, 263)(232, 265)(233, 267)(234, 281)(235, 273)(236, 256)(237, 277)(238, 287)(239, 270)(240, 260)(241, 279)(242, 286)(243, 271)(244, 257)(245, 264)(246, 266)(247, 258)(248, 285)(249, 254)(250, 272)(251, 280)(252, 283)

MAP           : A4.227
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, (x.2 * x.3^-1)^2, (x.4 * x.1^-1)^2, (x.3 * x.4)^2, x.4 * x.3^-2 * x.2 * x.4 * x.2^-1, (x.4 * x.2^-1 * x.3^-1)^2, (x.1 * x.2^-1)^3, x.2^-1 * x.3^-3 * x.2^-1 * x.3^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 257)(38, 255)(39, 274)(40, 273)(41, 276)(42, 275)(43, 263)(44, 261)(45, 268)(46, 267)(47, 270)(48, 269)(49, 264)(50, 262)(51, 266)(52, 260)(53, 265)(54, 259)(55, 258)(56, 256)(57, 272)(58, 254)(59, 271)(60, 253)(61, 288)(62, 286)(63, 278)(64, 284)(65, 277)(66, 283)(67, 287)(68, 285)(69, 280)(70, 279)(71, 282)(72, 281)(73, 220)(74, 222)(75, 252)(76, 251)(77, 250)(78, 249)(79, 236)(80, 235)(81, 241)(82, 247)(83, 242)(84, 248)(85, 218)(86, 217)(87, 223)(88, 229)(89, 224)(90, 230)(91, 219)(92, 221)(93, 227)(94, 228)(95, 225)(96, 226)(97, 238)(98, 240)(99, 234)(100, 233)(101, 232)(102, 231)(103, 237)(104, 239)(105, 245)(106, 246)(107, 243)(108, 244)(109, 182)(110, 181)(111, 187)(112, 193)(113, 188)(114, 194)(115, 183)(116, 185)(117, 191)(118, 192)(119, 189)(120, 190)(121, 184)(122, 186)(123, 216)(124, 215)(125, 214)(126, 213)(127, 200)(128, 199)(129, 205)(130, 211)(131, 206)(132, 212)(133, 201)(134, 203)(135, 209)(136, 210)(137, 207)(138, 208)(139, 202)(140, 204)(141, 198)(142, 197)(143, 196)(144, 195)

MAP           : A4.228
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, (x.4 * x.1^-1)^2, (x.3 * x.2^-1)^2, (x.3 * x.4)^2, (x.4 * x.2^-1)^2, x.3^-1 * x.2^-1 * x.3^3 * x.2^-1, x.3^6, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 257)(38, 255)(39, 274)(40, 273)(41, 276)(42, 275)(43, 263)(44, 261)(45, 268)(46, 267)(47, 270)(48, 269)(49, 264)(50, 262)(51, 266)(52, 260)(53, 265)(54, 259)(55, 258)(56, 256)(57, 272)(58, 254)(59, 271)(60, 253)(61, 288)(62, 286)(63, 278)(64, 284)(65, 277)(66, 283)(67, 287)(68, 285)(69, 280)(70, 279)(71, 282)(72, 281)(73, 220)(74, 222)(75, 252)(76, 251)(77, 250)(78, 249)(79, 236)(80, 235)(81, 241)(82, 247)(83, 242)(84, 248)(85, 218)(86, 217)(87, 223)(88, 229)(89, 224)(90, 230)(91, 219)(92, 221)(93, 227)(94, 228)(95, 225)(96, 226)(97, 238)(98, 240)(99, 234)(100, 233)(101, 232)(102, 231)(103, 237)(104, 239)(105, 245)(106, 246)(107, 243)(108, 244)(109, 186)(110, 184)(111, 200)(112, 182)(113, 199)(114, 181)(115, 216)(116, 214)(117, 206)(118, 212)(119, 205)(120, 211)(121, 215)(122, 213)(123, 208)(124, 207)(125, 210)(126, 209)(127, 185)(128, 183)(129, 202)(130, 201)(131, 204)(132, 203)(133, 191)(134, 189)(135, 196)(136, 195)(137, 198)(138, 197)(139, 192)(140, 190)(141, 194)(142, 188)(143, 193)(144, 187)

MAP           : A4.229
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, x.1^6, x.1^-1 * x.2 * x.1^2 * x.2^-2 * x.1 * x.2^-1, (x.2 * x.1^-1 * x.2 * x.1^-2)^2 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 73, 145, 217)(2, 74, 146, 218)(3, 75, 147, 219)(4, 76, 148, 220)(5, 77, 149, 221)(6, 78, 150, 222)(7, 79, 151, 223)(8, 80, 152, 224)(9, 81, 153, 225)(10, 82, 154, 226)(11, 83, 155, 227)(12, 84, 156, 228)(13, 85, 157, 229)(14, 86, 158, 230)(15, 87, 159, 231)(16, 88, 160, 232)(17, 89, 161, 233)(18, 90, 162, 234)(19, 91, 163, 235)(20, 92, 164, 236)(21, 93, 165, 237)(22, 94, 166, 238)(23, 95, 167, 239)(24, 96, 168, 240)(25, 97, 169, 241)(26, 98, 170, 242)(27, 99, 171, 243)(28, 100, 172, 244)(29, 101, 173, 245)(30, 102, 174, 246)(31, 103, 175, 247)(32, 104, 176, 248)(33, 105, 177, 249)(34, 106, 178, 250)(35, 107, 179, 251)(36, 108, 180, 252)(37, 109, 181, 253)(38, 110, 182, 254)(39, 111, 183, 255)(40, 112, 184, 256)(41, 113, 185, 257)(42, 114, 186, 258)(43, 115, 187, 259)(44, 116, 188, 260)(45, 117, 189, 261)(46, 118, 190, 262)(47, 119, 191, 263)(48, 120, 192, 264)(49, 121, 193, 265)(50, 122, 194, 266)(51, 123, 195, 267)(52, 124, 196, 268)(53, 125, 197, 269)(54, 126, 198, 270)(55, 127, 199, 271)(56, 128, 200, 272)(57, 129, 201, 273)(58, 130, 202, 274)(59, 131, 203, 275)(60, 132, 204, 276)(61, 133, 205, 277)(62, 134, 206, 278)(63, 135, 207, 279)(64, 136, 208, 280)(65, 137, 209, 281)(66, 138, 210, 282)(67, 139, 211, 283)(68, 140, 212, 284)(69, 141, 213, 285)(70, 142, 214, 286)(71, 143, 215, 287)(72, 144, 216, 288)
L = (1, 74)(2, 77)(3, 80)(4, 75)(5, 138)(6, 81)(7, 128)(8, 131)(9, 134)(10, 129)(11, 84)(12, 135)(13, 132)(14, 123)(15, 126)(16, 137)(17, 118)(18, 89)(19, 78)(20, 105)(21, 108)(22, 83)(23, 100)(24, 143)(25, 76)(26, 103)(27, 106)(28, 91)(29, 104)(30, 97)(31, 94)(32, 85)(33, 88)(34, 73)(35, 86)(36, 79)(37, 114)(38, 141)(39, 144)(40, 119)(41, 136)(42, 107)(43, 112)(44, 139)(45, 142)(46, 127)(47, 140)(48, 133)(49, 130)(50, 121)(51, 124)(52, 109)(53, 122)(54, 115)(55, 110)(56, 113)(57, 116)(58, 111)(59, 102)(60, 117)(61, 92)(62, 95)(63, 98)(64, 93)(65, 120)(66, 99)(67, 96)(68, 87)(69, 90)(70, 101)(71, 82)(72, 125)(145, 220)(146, 247)(147, 250)(148, 235)(149, 248)(150, 241)(151, 222)(152, 249)(153, 252)(154, 227)(155, 244)(156, 287)(157, 218)(158, 221)(159, 224)(160, 219)(161, 282)(162, 225)(163, 238)(164, 229)(165, 232)(166, 217)(167, 230)(168, 223)(169, 240)(170, 231)(171, 234)(172, 245)(173, 226)(174, 269)(175, 236)(176, 239)(177, 242)(178, 237)(179, 264)(180, 243)(181, 274)(182, 265)(183, 268)(184, 253)(185, 266)(186, 259)(187, 276)(188, 267)(189, 270)(190, 281)(191, 262)(192, 233)(193, 272)(194, 275)(195, 278)(196, 273)(197, 228)(198, 279)(199, 256)(200, 283)(201, 286)(202, 271)(203, 284)(204, 277)(205, 258)(206, 285)(207, 288)(208, 263)(209, 280)(210, 251)(211, 254)(212, 257)(213, 260)(214, 255)(215, 246)(216, 261)

MAP           : A4.230
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, x.1^6, x.1^-1 * x.2 * x.1^2 * x.2^-2 * x.1 * x.2^-1, (x.2 * x.1^-1 * x.2 * x.1^-2)^2 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 73, 145, 217)(2, 74, 146, 218)(3, 75, 147, 219)(4, 76, 148, 220)(5, 77, 149, 221)(6, 78, 150, 222)(7, 79, 151, 223)(8, 80, 152, 224)(9, 81, 153, 225)(10, 82, 154, 226)(11, 83, 155, 227)(12, 84, 156, 228)(13, 85, 157, 229)(14, 86, 158, 230)(15, 87, 159, 231)(16, 88, 160, 232)(17, 89, 161, 233)(18, 90, 162, 234)(19, 91, 163, 235)(20, 92, 164, 236)(21, 93, 165, 237)(22, 94, 166, 238)(23, 95, 167, 239)(24, 96, 168, 240)(25, 97, 169, 241)(26, 98, 170, 242)(27, 99, 171, 243)(28, 100, 172, 244)(29, 101, 173, 245)(30, 102, 174, 246)(31, 103, 175, 247)(32, 104, 176, 248)(33, 105, 177, 249)(34, 106, 178, 250)(35, 107, 179, 251)(36, 108, 180, 252)(37, 109, 181, 253)(38, 110, 182, 254)(39, 111, 183, 255)(40, 112, 184, 256)(41, 113, 185, 257)(42, 114, 186, 258)(43, 115, 187, 259)(44, 116, 188, 260)(45, 117, 189, 261)(46, 118, 190, 262)(47, 119, 191, 263)(48, 120, 192, 264)(49, 121, 193, 265)(50, 122, 194, 266)(51, 123, 195, 267)(52, 124, 196, 268)(53, 125, 197, 269)(54, 126, 198, 270)(55, 127, 199, 271)(56, 128, 200, 272)(57, 129, 201, 273)(58, 130, 202, 274)(59, 131, 203, 275)(60, 132, 204, 276)(61, 133, 205, 277)(62, 134, 206, 278)(63, 135, 207, 279)(64, 136, 208, 280)(65, 137, 209, 281)(66, 138, 210, 282)(67, 139, 211, 283)(68, 140, 212, 284)(69, 141, 213, 285)(70, 142, 214, 286)(71, 143, 215, 287)(72, 144, 216, 288)
L = (1, 83)(2, 132)(3, 137)(4, 74)(5, 123)(6, 128)(7, 143)(8, 126)(9, 89)(10, 104)(11, 129)(12, 122)(13, 105)(14, 100)(15, 103)(16, 108)(17, 133)(18, 106)(19, 75)(20, 94)(21, 73)(22, 78)(23, 85)(24, 76)(25, 81)(26, 88)(27, 79)(28, 84)(29, 91)(30, 82)(31, 77)(32, 138)(33, 131)(34, 80)(35, 99)(36, 134)(37, 119)(38, 96)(39, 101)(40, 110)(41, 87)(42, 92)(43, 107)(44, 90)(45, 125)(46, 140)(47, 93)(48, 86)(49, 141)(50, 136)(51, 139)(52, 144)(53, 97)(54, 142)(55, 111)(56, 130)(57, 109)(58, 114)(59, 121)(60, 112)(61, 117)(62, 124)(63, 115)(64, 120)(65, 127)(66, 118)(67, 113)(68, 102)(69, 95)(70, 116)(71, 135)(72, 98)(145, 286)(146, 253)(147, 256)(148, 277)(149, 254)(150, 271)(151, 288)(152, 255)(153, 258)(154, 251)(155, 274)(156, 263)(157, 284)(158, 287)(159, 248)(160, 285)(161, 270)(162, 249)(163, 280)(164, 241)(165, 244)(166, 283)(167, 242)(168, 247)(169, 282)(170, 243)(171, 246)(172, 275)(173, 250)(174, 239)(175, 278)(176, 281)(177, 272)(178, 279)(179, 222)(180, 273)(181, 232)(182, 235)(183, 238)(184, 223)(185, 236)(186, 217)(187, 234)(188, 237)(189, 240)(190, 269)(191, 220)(192, 245)(193, 230)(194, 233)(195, 266)(196, 231)(197, 252)(198, 267)(199, 226)(200, 259)(201, 262)(202, 229)(203, 260)(204, 265)(205, 228)(206, 261)(207, 264)(208, 221)(209, 268)(210, 257)(211, 224)(212, 227)(213, 218)(214, 225)(215, 276)(216, 219)

MAP           : A4.231
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2 | x.1^4, (x.1 * x.2)^2, x.2^6, x.2 * x.1 * x.2^-1 * x.1^2 * x.2^-2 * x.1^-1, (x.2^2 * x.1^-1 * x.2 * x.1^-1)^2 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 73, 145, 217)(2, 74, 146, 218)(3, 75, 147, 219)(4, 76, 148, 220)(5, 77, 149, 221)(6, 78, 150, 222)(7, 79, 151, 223)(8, 80, 152, 224)(9, 81, 153, 225)(10, 82, 154, 226)(11, 83, 155, 227)(12, 84, 156, 228)(13, 85, 157, 229)(14, 86, 158, 230)(15, 87, 159, 231)(16, 88, 160, 232)(17, 89, 161, 233)(18, 90, 162, 234)(19, 91, 163, 235)(20, 92, 164, 236)(21, 93, 165, 237)(22, 94, 166, 238)(23, 95, 167, 239)(24, 96, 168, 240)(25, 97, 169, 241)(26, 98, 170, 242)(27, 99, 171, 243)(28, 100, 172, 244)(29, 101, 173, 245)(30, 102, 174, 246)(31, 103, 175, 247)(32, 104, 176, 248)(33, 105, 177, 249)(34, 106, 178, 250)(35, 107, 179, 251)(36, 108, 180, 252)(37, 109, 181, 253)(38, 110, 182, 254)(39, 111, 183, 255)(40, 112, 184, 256)(41, 113, 185, 257)(42, 114, 186, 258)(43, 115, 187, 259)(44, 116, 188, 260)(45, 117, 189, 261)(46, 118, 190, 262)(47, 119, 191, 263)(48, 120, 192, 264)(49, 121, 193, 265)(50, 122, 194, 266)(51, 123, 195, 267)(52, 124, 196, 268)(53, 125, 197, 269)(54, 126, 198, 270)(55, 127, 199, 271)(56, 128, 200, 272)(57, 129, 201, 273)(58, 130, 202, 274)(59, 131, 203, 275)(60, 132, 204, 276)(61, 133, 205, 277)(62, 134, 206, 278)(63, 135, 207, 279)(64, 136, 208, 280)(65, 137, 209, 281)(66, 138, 210, 282)(67, 139, 211, 283)(68, 140, 212, 284)(69, 141, 213, 285)(70, 142, 214, 286)(71, 143, 215, 287)(72, 144, 216, 288)
L = (1, 76)(2, 103)(3, 106)(4, 91)(5, 104)(6, 97)(7, 78)(8, 105)(9, 108)(10, 83)(11, 100)(12, 143)(13, 74)(14, 77)(15, 80)(16, 75)(17, 138)(18, 81)(19, 94)(20, 85)(21, 88)(22, 73)(23, 86)(24, 79)(25, 96)(26, 87)(27, 90)(28, 101)(29, 82)(30, 125)(31, 92)(32, 95)(33, 98)(34, 93)(35, 120)(36, 99)(37, 130)(38, 121)(39, 124)(40, 109)(41, 122)(42, 115)(43, 132)(44, 123)(45, 126)(46, 137)(47, 118)(48, 89)(49, 128)(50, 131)(51, 134)(52, 129)(53, 84)(54, 135)(55, 112)(56, 139)(57, 142)(58, 127)(59, 140)(60, 133)(61, 114)(62, 141)(63, 144)(64, 119)(65, 136)(66, 107)(67, 110)(68, 113)(69, 116)(70, 111)(71, 102)(72, 117)(145, 218)(146, 221)(147, 224)(148, 219)(149, 282)(150, 225)(151, 272)(152, 275)(153, 278)(154, 273)(155, 228)(156, 279)(157, 276)(158, 267)(159, 270)(160, 281)(161, 262)(162, 233)(163, 222)(164, 249)(165, 252)(166, 227)(167, 244)(168, 287)(169, 220)(170, 247)(171, 250)(172, 235)(173, 248)(174, 241)(175, 238)(176, 229)(177, 232)(178, 217)(179, 230)(180, 223)(181, 258)(182, 285)(183, 288)(184, 263)(185, 280)(186, 251)(187, 256)(188, 283)(189, 286)(190, 271)(191, 284)(192, 277)(193, 274)(194, 265)(195, 268)(196, 253)(197, 266)(198, 259)(199, 254)(200, 257)(201, 260)(202, 255)(203, 246)(204, 261)(205, 236)(206, 239)(207, 242)(208, 237)(209, 264)(210, 243)(211, 240)(212, 231)(213, 234)(214, 245)(215, 226)(216, 269)

MAP           : A4.232
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <72, 40>
CTG (fp)      : < x.1, x.2 | x.1^4, (x.1 * x.2)^2, x.2^6, x.2 * x.1 * x.2^-1 * x.1^2 * x.2^-2 * x.1^-1, (x.2^2 * x.1^-1 * x.2 * x.1^-1)^2 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 73, 145, 217)(2, 74, 146, 218)(3, 75, 147, 219)(4, 76, 148, 220)(5, 77, 149, 221)(6, 78, 150, 222)(7, 79, 151, 223)(8, 80, 152, 224)(9, 81, 153, 225)(10, 82, 154, 226)(11, 83, 155, 227)(12, 84, 156, 228)(13, 85, 157, 229)(14, 86, 158, 230)(15, 87, 159, 231)(16, 88, 160, 232)(17, 89, 161, 233)(18, 90, 162, 234)(19, 91, 163, 235)(20, 92, 164, 236)(21, 93, 165, 237)(22, 94, 166, 238)(23, 95, 167, 239)(24, 96, 168, 240)(25, 97, 169, 241)(26, 98, 170, 242)(27, 99, 171, 243)(28, 100, 172, 244)(29, 101, 173, 245)(30, 102, 174, 246)(31, 103, 175, 247)(32, 104, 176, 248)(33, 105, 177, 249)(34, 106, 178, 250)(35, 107, 179, 251)(36, 108, 180, 252)(37, 109, 181, 253)(38, 110, 182, 254)(39, 111, 183, 255)(40, 112, 184, 256)(41, 113, 185, 257)(42, 114, 186, 258)(43, 115, 187, 259)(44, 116, 188, 260)(45, 117, 189, 261)(46, 118, 190, 262)(47, 119, 191, 263)(48, 120, 192, 264)(49, 121, 193, 265)(50, 122, 194, 266)(51, 123, 195, 267)(52, 124, 196, 268)(53, 125, 197, 269)(54, 126, 198, 270)(55, 127, 199, 271)(56, 128, 200, 272)(57, 129, 201, 273)(58, 130, 202, 274)(59, 131, 203, 275)(60, 132, 204, 276)(61, 133, 205, 277)(62, 134, 206, 278)(63, 135, 207, 279)(64, 136, 208, 280)(65, 137, 209, 281)(66, 138, 210, 282)(67, 139, 211, 283)(68, 140, 212, 284)(69, 141, 213, 285)(70, 142, 214, 286)(71, 143, 215, 287)(72, 144, 216, 288)
L = (1, 76)(2, 103)(3, 106)(4, 91)(5, 104)(6, 97)(7, 78)(8, 105)(9, 108)(10, 83)(11, 100)(12, 143)(13, 74)(14, 77)(15, 80)(16, 75)(17, 138)(18, 81)(19, 94)(20, 85)(21, 88)(22, 73)(23, 86)(24, 79)(25, 96)(26, 87)(27, 90)(28, 101)(29, 82)(30, 125)(31, 92)(32, 95)(33, 98)(34, 93)(35, 120)(36, 99)(37, 130)(38, 121)(39, 124)(40, 109)(41, 122)(42, 115)(43, 132)(44, 123)(45, 126)(46, 137)(47, 118)(48, 89)(49, 128)(50, 131)(51, 134)(52, 129)(53, 84)(54, 135)(55, 112)(56, 139)(57, 142)(58, 127)(59, 140)(60, 133)(61, 114)(62, 141)(63, 144)(64, 119)(65, 136)(66, 107)(67, 110)(68, 113)(69, 116)(70, 111)(71, 102)(72, 117)(145, 233)(146, 252)(147, 287)(148, 266)(149, 219)(150, 248)(151, 281)(152, 222)(153, 227)(154, 272)(155, 249)(156, 218)(157, 273)(158, 256)(159, 271)(160, 276)(161, 283)(162, 274)(163, 267)(164, 262)(165, 265)(166, 270)(167, 223)(168, 268)(169, 231)(170, 226)(171, 229)(172, 234)(173, 259)(174, 232)(175, 269)(176, 288)(177, 251)(178, 230)(179, 255)(180, 284)(181, 239)(182, 264)(183, 257)(184, 242)(185, 225)(186, 260)(187, 275)(188, 228)(189, 221)(190, 278)(191, 261)(192, 224)(193, 279)(194, 286)(195, 277)(196, 282)(197, 253)(198, 280)(199, 243)(200, 250)(201, 241)(202, 246)(203, 217)(204, 244)(205, 237)(206, 220)(207, 235)(208, 240)(209, 247)(210, 238)(211, 245)(212, 258)(213, 263)(214, 236)(215, 285)(216, 254)

MAP           : A4.233
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, (x.4 * x.2)^2, (x.1 * x.2)^2, (x.3^-1 * x.4)^2, (x.2 * x.3^-1)^2, x.4 * x.3 * x.4 * x.3^3, (x.4 * x.1^-1)^3, (x.4^-1 * x.3^-1 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 258)(38, 256)(39, 272)(40, 254)(41, 271)(42, 253)(43, 288)(44, 286)(45, 278)(46, 284)(47, 277)(48, 283)(49, 287)(50, 285)(51, 280)(52, 279)(53, 282)(54, 281)(55, 257)(56, 255)(57, 274)(58, 273)(59, 276)(60, 275)(61, 263)(62, 261)(63, 268)(64, 267)(65, 270)(66, 269)(67, 264)(68, 262)(69, 266)(70, 260)(71, 265)(72, 259)(73, 220)(74, 222)(75, 252)(76, 251)(77, 250)(78, 249)(79, 236)(80, 235)(81, 241)(82, 247)(83, 242)(84, 248)(85, 218)(86, 217)(87, 223)(88, 229)(89, 224)(90, 230)(91, 219)(92, 221)(93, 227)(94, 228)(95, 225)(96, 226)(97, 238)(98, 240)(99, 234)(100, 233)(101, 232)(102, 231)(103, 237)(104, 239)(105, 245)(106, 246)(107, 243)(108, 244)(109, 185)(110, 183)(111, 202)(112, 201)(113, 204)(114, 203)(115, 191)(116, 189)(117, 196)(118, 195)(119, 198)(120, 197)(121, 192)(122, 190)(123, 194)(124, 188)(125, 193)(126, 187)(127, 186)(128, 184)(129, 200)(130, 182)(131, 199)(132, 181)(133, 216)(134, 214)(135, 206)(136, 212)(137, 205)(138, 211)(139, 215)(140, 213)(141, 208)(142, 207)(143, 210)(144, 209)

MAP           : A4.234
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.4^4, x.2^4, (x.4^-1 * x.2)^2, x.3 * x.4^-2 * x.3^-1 * x.4 * x.2^-1, (x.3 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 75)(38, 94)(39, 79)(40, 89)(41, 108)(42, 98)(43, 81)(44, 88)(45, 73)(46, 95)(47, 102)(48, 104)(49, 96)(50, 87)(51, 92)(52, 74)(53, 82)(54, 85)(55, 90)(56, 93)(57, 86)(58, 80)(59, 76)(60, 91)(61, 106)(62, 84)(63, 107)(64, 97)(65, 99)(66, 77)(67, 100)(68, 78)(69, 101)(70, 103)(71, 105)(72, 83)(109, 182)(110, 185)(111, 190)(112, 189)(113, 181)(114, 184)(115, 191)(116, 187)(117, 186)(118, 192)(119, 188)(120, 183)(121, 194)(122, 197)(123, 214)(124, 213)(125, 193)(126, 196)(127, 203)(128, 199)(129, 210)(130, 204)(131, 200)(132, 207)(133, 206)(134, 209)(135, 202)(136, 201)(137, 205)(138, 208)(139, 215)(140, 211)(141, 198)(142, 216)(143, 212)(144, 195)(217, 282)(218, 261)(219, 278)(220, 284)(221, 268)(222, 259)(223, 274)(224, 288)(225, 275)(226, 253)(227, 255)(228, 269)(229, 256)(230, 270)(231, 257)(232, 271)(233, 273)(234, 287)(235, 267)(236, 262)(237, 283)(238, 281)(239, 276)(240, 254)(241, 285)(242, 280)(243, 265)(244, 263)(245, 258)(246, 272)(247, 264)(248, 279)(249, 260)(250, 266)(251, 286)(252, 277)

MAP           : A4.235
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, (x.4 * x.1^-1)^2, (x.3 * x.2^-1)^2, (x.3 * x.4)^2, (x.4 * x.2^-1)^2, x.3^-1 * x.2^-1 * x.3^3 * x.2^-1, x.3^6, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 257)(38, 255)(39, 274)(40, 273)(41, 276)(42, 275)(43, 263)(44, 261)(45, 268)(46, 267)(47, 270)(48, 269)(49, 264)(50, 262)(51, 266)(52, 260)(53, 265)(54, 259)(55, 258)(56, 256)(57, 272)(58, 254)(59, 271)(60, 253)(61, 288)(62, 286)(63, 278)(64, 284)(65, 277)(66, 283)(67, 287)(68, 285)(69, 280)(70, 279)(71, 282)(72, 281)(73, 219)(74, 221)(75, 227)(76, 228)(77, 225)(78, 226)(79, 238)(80, 240)(81, 234)(82, 233)(83, 232)(84, 231)(85, 237)(86, 239)(87, 245)(88, 246)(89, 243)(90, 244)(91, 220)(92, 222)(93, 252)(94, 251)(95, 250)(96, 249)(97, 236)(98, 235)(99, 241)(100, 247)(101, 242)(102, 248)(103, 218)(104, 217)(105, 223)(106, 229)(107, 224)(108, 230)(109, 186)(110, 184)(111, 200)(112, 182)(113, 199)(114, 181)(115, 216)(116, 214)(117, 206)(118, 212)(119, 205)(120, 211)(121, 215)(122, 213)(123, 208)(124, 207)(125, 210)(126, 209)(127, 185)(128, 183)(129, 202)(130, 201)(131, 204)(132, 203)(133, 191)(134, 189)(135, 196)(136, 195)(137, 198)(138, 197)(139, 192)(140, 190)(141, 194)(142, 188)(143, 193)(144, 187)

MAP           : A4.236
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.4^4, x.2^4, (x.4^-1 * x.2)^2, x.3 * x.4^-2 * x.3^-1 * x.4 * x.2^-1, (x.3 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 75)(38, 94)(39, 79)(40, 89)(41, 108)(42, 98)(43, 81)(44, 88)(45, 73)(46, 95)(47, 102)(48, 104)(49, 96)(50, 87)(51, 92)(52, 74)(53, 82)(54, 85)(55, 90)(56, 93)(57, 86)(58, 80)(59, 76)(60, 91)(61, 106)(62, 84)(63, 107)(64, 97)(65, 99)(66, 77)(67, 100)(68, 78)(69, 101)(70, 103)(71, 105)(72, 83)(109, 193)(110, 194)(111, 195)(112, 196)(113, 197)(114, 198)(115, 211)(116, 212)(117, 213)(118, 214)(119, 215)(120, 216)(121, 205)(122, 206)(123, 207)(124, 208)(125, 209)(126, 210)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(217, 280)(218, 258)(219, 281)(220, 283)(221, 285)(222, 263)(223, 276)(224, 267)(225, 272)(226, 254)(227, 262)(228, 265)(229, 261)(230, 268)(231, 253)(232, 275)(233, 282)(234, 284)(235, 286)(236, 264)(237, 287)(238, 277)(239, 279)(240, 257)(241, 270)(242, 273)(243, 266)(244, 260)(245, 256)(246, 271)(247, 255)(248, 274)(249, 259)(250, 269)(251, 288)(252, 278)

MAP           : A4.237
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.2 * x.4 * x.3, x.4^4, x.2^4, (x.4^-1 * x.2)^2, x.3 * x.4^-2 * x.3^-1 * x.4 * x.2^-1, (x.3 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 81)(38, 88)(39, 73)(40, 95)(41, 102)(42, 104)(43, 75)(44, 94)(45, 79)(46, 89)(47, 108)(48, 98)(49, 90)(50, 93)(51, 86)(52, 80)(53, 76)(54, 91)(55, 96)(56, 87)(57, 92)(58, 74)(59, 82)(60, 85)(61, 100)(62, 78)(63, 101)(64, 103)(65, 105)(66, 83)(67, 106)(68, 84)(69, 107)(70, 97)(71, 99)(72, 77)(109, 193)(110, 194)(111, 195)(112, 196)(113, 197)(114, 198)(115, 211)(116, 212)(117, 213)(118, 214)(119, 215)(120, 216)(121, 205)(122, 206)(123, 207)(124, 208)(125, 209)(126, 210)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(217, 286)(218, 264)(219, 287)(220, 277)(221, 279)(222, 257)(223, 270)(224, 273)(225, 266)(226, 260)(227, 256)(228, 271)(229, 255)(230, 274)(231, 259)(232, 269)(233, 288)(234, 278)(235, 280)(236, 258)(237, 281)(238, 283)(239, 285)(240, 263)(241, 276)(242, 267)(243, 272)(244, 254)(245, 262)(246, 265)(247, 261)(248, 268)(249, 253)(250, 275)(251, 282)(252, 284)

MAP           : A4.238
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, (x.2 * x.3^-1)^2, (x.4 * x.1^-1)^2, (x.3 * x.4)^2, x.4 * x.3^-2 * x.2 * x.4 * x.2^-1, (x.4 * x.2^-1 * x.3^-1)^2, (x.1 * x.2^-1)^3, x.2^-1 * x.3^-3 * x.2^-1 * x.3^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 257)(38, 255)(39, 274)(40, 273)(41, 276)(42, 275)(43, 263)(44, 261)(45, 268)(46, 267)(47, 270)(48, 269)(49, 264)(50, 262)(51, 266)(52, 260)(53, 265)(54, 259)(55, 258)(56, 256)(57, 272)(58, 254)(59, 271)(60, 253)(61, 288)(62, 286)(63, 278)(64, 284)(65, 277)(66, 283)(67, 287)(68, 285)(69, 280)(70, 279)(71, 282)(72, 281)(73, 219)(74, 221)(75, 227)(76, 228)(77, 225)(78, 226)(79, 238)(80, 240)(81, 234)(82, 233)(83, 232)(84, 231)(85, 237)(86, 239)(87, 245)(88, 246)(89, 243)(90, 244)(91, 220)(92, 222)(93, 252)(94, 251)(95, 250)(96, 249)(97, 236)(98, 235)(99, 241)(100, 247)(101, 242)(102, 248)(103, 218)(104, 217)(105, 223)(106, 229)(107, 224)(108, 230)(109, 207)(110, 209)(111, 197)(112, 198)(113, 195)(114, 196)(115, 214)(116, 216)(117, 192)(118, 191)(119, 190)(120, 189)(121, 213)(122, 215)(123, 185)(124, 186)(125, 183)(126, 184)(127, 208)(128, 210)(129, 204)(130, 203)(131, 202)(132, 201)(133, 212)(134, 211)(135, 181)(136, 199)(137, 182)(138, 200)(139, 206)(140, 205)(141, 193)(142, 187)(143, 194)(144, 188)

MAP           : A4.239
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, (x.3 * x.2)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^3, x.4 * x.2 * x.4 * x.2 * x.3 * x.4^-1 * x.2 * x.4^-1 * x.2 * x.3, x.4 * x.2 * x.3 * x.4 * x.2 * x.4^-1 * x.2 * x.3 * x.4^-1 * x.2 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 279)(38, 281)(39, 269)(40, 270)(41, 267)(42, 268)(43, 286)(44, 288)(45, 264)(46, 263)(47, 262)(48, 261)(49, 285)(50, 287)(51, 257)(52, 258)(53, 255)(54, 256)(55, 280)(56, 282)(57, 276)(58, 275)(59, 274)(60, 273)(61, 284)(62, 283)(63, 253)(64, 271)(65, 254)(66, 272)(67, 278)(68, 277)(69, 265)(70, 259)(71, 266)(72, 260)(73, 222)(74, 220)(75, 236)(76, 218)(77, 235)(78, 217)(79, 252)(80, 250)(81, 242)(82, 248)(83, 241)(84, 247)(85, 251)(86, 249)(87, 244)(88, 243)(89, 246)(90, 245)(91, 221)(92, 219)(93, 238)(94, 237)(95, 240)(96, 239)(97, 227)(98, 225)(99, 232)(100, 231)(101, 234)(102, 233)(103, 228)(104, 226)(105, 230)(106, 224)(107, 229)(108, 223)(109, 192)(110, 190)(111, 194)(112, 188)(113, 193)(114, 187)(115, 186)(116, 184)(117, 200)(118, 182)(119, 199)(120, 181)(121, 185)(122, 183)(123, 202)(124, 201)(125, 204)(126, 203)(127, 191)(128, 189)(129, 196)(130, 195)(131, 198)(132, 197)(133, 215)(134, 213)(135, 208)(136, 207)(137, 210)(138, 209)(139, 216)(140, 214)(141, 206)(142, 212)(143, 205)(144, 211)

MAP           : A4.240
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.1 * x.2)^2, (x.3 * x.2)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^3, x.4 * x.2 * x.4 * x.2 * x.3 * x.4^-1 * x.2 * x.4^-1 * x.2 * x.3, x.4 * x.2 * x.3 * x.4 * x.2 * x.4^-1 * x.2 * x.3 * x.4^-1 * x.2 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 254)(38, 253)(39, 259)(40, 265)(41, 260)(42, 266)(43, 255)(44, 257)(45, 263)(46, 264)(47, 261)(48, 262)(49, 256)(50, 258)(51, 288)(52, 287)(53, 286)(54, 285)(55, 272)(56, 271)(57, 277)(58, 283)(59, 278)(60, 284)(61, 273)(62, 275)(63, 281)(64, 282)(65, 279)(66, 280)(67, 274)(68, 276)(69, 270)(70, 269)(71, 268)(72, 267)(73, 228)(74, 226)(75, 230)(76, 224)(77, 229)(78, 223)(79, 222)(80, 220)(81, 236)(82, 218)(83, 235)(84, 217)(85, 221)(86, 219)(87, 238)(88, 237)(89, 240)(90, 239)(91, 227)(92, 225)(93, 232)(94, 231)(95, 234)(96, 233)(97, 251)(98, 249)(99, 244)(100, 243)(101, 246)(102, 245)(103, 252)(104, 250)(105, 242)(106, 248)(107, 241)(108, 247)(109, 186)(110, 184)(111, 200)(112, 182)(113, 199)(114, 181)(115, 216)(116, 214)(117, 206)(118, 212)(119, 205)(120, 211)(121, 215)(122, 213)(123, 208)(124, 207)(125, 210)(126, 209)(127, 185)(128, 183)(129, 202)(130, 201)(131, 204)(132, 203)(133, 191)(134, 189)(135, 196)(136, 195)(137, 198)(138, 197)(139, 192)(140, 190)(141, 194)(142, 188)(143, 193)(144, 187)

MAP           : A4.241
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.4 * x.2 * x.4^-1 * x.2, (x.4 * x.1^-1)^2, (x.1 * x.2)^2, (x.2 * x.3^-1)^2, (x.3 * x.4^-1)^3, x.4 * x.3^2 * x.4^-1 * x.3^-2, x.3^6 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 254)(38, 253)(39, 259)(40, 265)(41, 260)(42, 266)(43, 255)(44, 257)(45, 263)(46, 264)(47, 261)(48, 262)(49, 256)(50, 258)(51, 288)(52, 287)(53, 286)(54, 285)(55, 272)(56, 271)(57, 277)(58, 283)(59, 278)(60, 284)(61, 273)(62, 275)(63, 281)(64, 282)(65, 279)(66, 280)(67, 274)(68, 276)(69, 270)(70, 269)(71, 268)(72, 267)(73, 220)(74, 222)(75, 252)(76, 251)(77, 250)(78, 249)(79, 236)(80, 235)(81, 241)(82, 247)(83, 242)(84, 248)(85, 218)(86, 217)(87, 223)(88, 229)(89, 224)(90, 230)(91, 219)(92, 221)(93, 227)(94, 228)(95, 225)(96, 226)(97, 238)(98, 240)(99, 234)(100, 233)(101, 232)(102, 231)(103, 237)(104, 239)(105, 245)(106, 246)(107, 243)(108, 244)(109, 190)(110, 192)(111, 186)(112, 185)(113, 184)(114, 183)(115, 194)(116, 193)(117, 199)(118, 181)(119, 200)(120, 182)(121, 188)(122, 187)(123, 211)(124, 205)(125, 212)(126, 206)(127, 189)(128, 191)(129, 215)(130, 216)(131, 213)(132, 214)(133, 196)(134, 198)(135, 210)(136, 209)(137, 208)(138, 207)(139, 195)(140, 197)(141, 203)(142, 204)(143, 201)(144, 202)

MAP           : A4.242
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.3 * x.4^-1)^2, x.3 * x.4^-1 * x.3^-1 * x.2 * x.4^-1 * x.2, (x.4 * x.2 * x.3^-1)^2, x.4 * x.3 * x.2 * x.4 * x.2 * x.3^-1, (x.4^-1 * x.3^-1 * x.4^-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        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 279)(38, 281)(39, 269)(40, 270)(41, 267)(42, 268)(43, 286)(44, 288)(45, 264)(46, 263)(47, 262)(48, 261)(49, 285)(50, 287)(51, 257)(52, 258)(53, 255)(54, 256)(55, 280)(56, 282)(57, 276)(58, 275)(59, 274)(60, 273)(61, 284)(62, 283)(63, 253)(64, 271)(65, 254)(66, 272)(67, 278)(68, 277)(69, 265)(70, 259)(71, 266)(72, 260)(73, 219)(74, 221)(75, 227)(76, 228)(77, 225)(78, 226)(79, 238)(80, 240)(81, 234)(82, 233)(83, 232)(84, 231)(85, 237)(86, 239)(87, 245)(88, 246)(89, 243)(90, 244)(91, 220)(92, 222)(93, 252)(94, 251)(95, 250)(96, 249)(97, 236)(98, 235)(99, 241)(100, 247)(101, 242)(102, 248)(103, 218)(104, 217)(105, 223)(106, 229)(107, 224)(108, 230)(109, 185)(110, 183)(111, 202)(112, 201)(113, 204)(114, 203)(115, 191)(116, 189)(117, 196)(118, 195)(119, 198)(120, 197)(121, 192)(122, 190)(123, 194)(124, 188)(125, 193)(126, 187)(127, 186)(128, 184)(129, 200)(130, 182)(131, 199)(132, 181)(133, 216)(134, 214)(135, 206)(136, 212)(137, 205)(138, 211)(139, 215)(140, 213)(141, 208)(142, 207)(143, 210)(144, 209)

MAP           : A4.243
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.4 * x.2 * x.3^-1 * x.4^-1 * x.2, x.3 * x.4 * x.3^-2 * x.4^-1 * x.3, (x.3 * x.4^-1)^3, x.3^6 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 258)(38, 256)(39, 272)(40, 254)(41, 271)(42, 253)(43, 288)(44, 286)(45, 278)(46, 284)(47, 277)(48, 283)(49, 287)(50, 285)(51, 280)(52, 279)(53, 282)(54, 281)(55, 257)(56, 255)(57, 274)(58, 273)(59, 276)(60, 275)(61, 263)(62, 261)(63, 268)(64, 267)(65, 270)(66, 269)(67, 264)(68, 262)(69, 266)(70, 260)(71, 265)(72, 259)(73, 220)(74, 222)(75, 252)(76, 251)(77, 250)(78, 249)(79, 236)(80, 235)(81, 241)(82, 247)(83, 242)(84, 248)(85, 218)(86, 217)(87, 223)(88, 229)(89, 224)(90, 230)(91, 219)(92, 221)(93, 227)(94, 228)(95, 225)(96, 226)(97, 238)(98, 240)(99, 234)(100, 233)(101, 232)(102, 231)(103, 237)(104, 239)(105, 245)(106, 246)(107, 243)(108, 244)(109, 190)(110, 192)(111, 186)(112, 185)(113, 184)(114, 183)(115, 194)(116, 193)(117, 199)(118, 181)(119, 200)(120, 182)(121, 188)(122, 187)(123, 211)(124, 205)(125, 212)(126, 206)(127, 189)(128, 191)(129, 215)(130, 216)(131, 213)(132, 214)(133, 196)(134, 198)(135, 210)(136, 209)(137, 208)(138, 207)(139, 195)(140, 197)(141, 203)(142, 204)(143, 201)(144, 202)

MAP           : A4.244
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.4 * x.2 * x.4^-1 * x.2, (x.4 * x.1^-1)^2, (x.1 * x.2)^2, (x.2 * x.3^-1)^2, (x.3 * x.4^-1)^3, x.4 * x.3^2 * x.4^-1 * x.3^-2, x.3^6 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 279)(38, 281)(39, 269)(40, 270)(41, 267)(42, 268)(43, 286)(44, 288)(45, 264)(46, 263)(47, 262)(48, 261)(49, 285)(50, 287)(51, 257)(52, 258)(53, 255)(54, 256)(55, 280)(56, 282)(57, 276)(58, 275)(59, 274)(60, 273)(61, 284)(62, 283)(63, 253)(64, 271)(65, 254)(66, 272)(67, 278)(68, 277)(69, 265)(70, 259)(71, 266)(72, 260)(73, 219)(74, 221)(75, 227)(76, 228)(77, 225)(78, 226)(79, 238)(80, 240)(81, 234)(82, 233)(83, 232)(84, 231)(85, 237)(86, 239)(87, 245)(88, 246)(89, 243)(90, 244)(91, 220)(92, 222)(93, 252)(94, 251)(95, 250)(96, 249)(97, 236)(98, 235)(99, 241)(100, 247)(101, 242)(102, 248)(103, 218)(104, 217)(105, 223)(106, 229)(107, 224)(108, 230)(109, 182)(110, 181)(111, 187)(112, 193)(113, 188)(114, 194)(115, 183)(116, 185)(117, 191)(118, 192)(119, 189)(120, 190)(121, 184)(122, 186)(123, 216)(124, 215)(125, 214)(126, 213)(127, 200)(128, 199)(129, 205)(130, 211)(131, 206)(132, 212)(133, 201)(134, 203)(135, 209)(136, 210)(137, 207)(138, 208)(139, 202)(140, 204)(141, 198)(142, 197)(143, 196)(144, 195)

MAP           : A4.245
NOTES         : type II, reflexible, isomorphic to A4.213.
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)   : <36, 10>
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.3 * x.4^-1)^2, (x.4 * x.1^-1)^3, x.4^-1 * x.2 * x.4 * x.2 * x.4 * x.2 * x.4^-1 * x.2 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 279)(38, 281)(39, 269)(40, 270)(41, 267)(42, 268)(43, 286)(44, 288)(45, 264)(46, 263)(47, 262)(48, 261)(49, 285)(50, 287)(51, 257)(52, 258)(53, 255)(54, 256)(55, 280)(56, 282)(57, 276)(58, 275)(59, 274)(60, 273)(61, 284)(62, 283)(63, 253)(64, 271)(65, 254)(66, 272)(67, 278)(68, 277)(69, 265)(70, 259)(71, 266)(72, 260)(73, 222)(74, 220)(75, 236)(76, 218)(77, 235)(78, 217)(79, 252)(80, 250)(81, 242)(82, 248)(83, 241)(84, 247)(85, 251)(86, 249)(87, 244)(88, 243)(89, 246)(90, 245)(91, 221)(92, 219)(93, 238)(94, 237)(95, 240)(96, 239)(97, 227)(98, 225)(99, 232)(100, 231)(101, 234)(102, 233)(103, 228)(104, 226)(105, 230)(106, 224)(107, 229)(108, 223)(109, 185)(110, 183)(111, 202)(112, 201)(113, 204)(114, 203)(115, 191)(116, 189)(117, 196)(118, 195)(119, 198)(120, 197)(121, 192)(122, 190)(123, 194)(124, 188)(125, 193)(126, 187)(127, 186)(128, 184)(129, 200)(130, 182)(131, 199)(132, 181)(133, 216)(134, 214)(135, 206)(136, 212)(137, 205)(138, 211)(139, 215)(140, 213)(141, 208)(142, 207)(143, 210)(144, 209)

MAP           : A4.246
NOTES         : type I, reflexible, isomorphic to Med2({4,6}), isomorphic to A4.209.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, (x.3 * x.2)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.3^-1 * x.4 * x.2 * x.3^-1 * x.4^-1 * x.2, x.3 * x.4 * x.3^-2 * x.4^-1 * x.3, (x.3 * x.4^-1)^3, x.3^6 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 6)
#DARTS        : 288
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)(145, 181, 217, 253)(146, 182, 218, 254)(147, 183, 219, 255)(148, 184, 220, 256)(149, 185, 221, 257)(150, 186, 222, 258)(151, 187, 223, 259)(152, 188, 224, 260)(153, 189, 225, 261)(154, 190, 226, 262)(155, 191, 227, 263)(156, 192, 228, 264)(157, 193, 229, 265)(158, 194, 230, 266)(159, 195, 231, 267)(160, 196, 232, 268)(161, 197, 233, 269)(162, 198, 234, 270)(163, 199, 235, 271)(164, 200, 236, 272)(165, 201, 237, 273)(166, 202, 238, 274)(167, 203, 239, 275)(168, 204, 240, 276)(169, 205, 241, 277)(170, 206, 242, 278)(171, 207, 243, 279)(172, 208, 244, 280)(173, 209, 245, 281)(174, 210, 246, 282)(175, 211, 247, 283)(176, 212, 248, 284)(177, 213, 249, 285)(178, 214, 250, 286)(179, 215, 251, 287)(180, 216, 252, 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, 258)(38, 256)(39, 272)(40, 254)(41, 271)(42, 253)(43, 288)(44, 286)(45, 278)(46, 284)(47, 277)(48, 283)(49, 287)(50, 285)(51, 280)(52, 279)(53, 282)(54, 281)(55, 257)(56, 255)(57, 274)(58, 273)(59, 276)(60, 275)(61, 263)(62, 261)(63, 268)(64, 267)(65, 270)(66, 269)(67, 264)(68, 262)(69, 266)(70, 260)(71, 265)(72, 259)(73, 219)(74, 221)(75, 227)(76, 228)(77, 225)(78, 226)(79, 238)(80, 240)(81, 234)(82, 233)(83, 232)(84, 231)(85, 237)(86, 239)(87, 245)(88, 246)(89, 243)(90, 244)(91, 220)(92, 222)(93, 252)(94, 251)(95, 250)(96, 249)(97, 236)(98, 235)(99, 241)(100, 247)(101, 242)(102, 248)(103, 218)(104, 217)(105, 223)(106, 229)(107, 224)(108, 230)(109, 182)(110, 181)(111, 187)(112, 193)(113, 188)(114, 194)(115, 183)(116, 185)(117, 191)(118, 192)(119, 189)(120, 190)(121, 184)(122, 186)(123, 216)(124, 215)(125, 214)(126, 213)(127, 200)(128, 199)(129, 205)(130, 211)(131, 206)(132, 212)(133, 201)(134, 203)(135, 209)(136, 210)(137, 207)(138, 208)(139, 202)(140, 204)(141, 198)(142, 197)(143, 196)(144, 195)

MAP           : A4.247
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: [ 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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.4^2, x.3^3, (x.1 * x.2)^2, (x.2 * x.4)^2, (x.4 * x.1^-1)^2, (x.2 * x.3^-1)^2, x.2 * x.3 * x.4 * x.3^-1 * x.4 * x.3 * x.4, (x.3 * x.4)^4 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 8)
#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, 188)(27, 185)(28, 187)(29, 183)(30, 181)(31, 184)(32, 182)(33, 192)(34, 191)(35, 190)(36, 189)(37, 174)(38, 176)(39, 173)(40, 175)(41, 171)(42, 169)(43, 172)(44, 170)(45, 180)(46, 179)(47, 178)(48, 177)(49, 158)(50, 160)(51, 157)(52, 159)(53, 163)(54, 161)(55, 164)(56, 162)(57, 148)(58, 147)(59, 146)(60, 145)(61, 154)(62, 156)(63, 153)(64, 155)(65, 167)(66, 165)(67, 168)(68, 166)(69, 152)(70, 151)(71, 150)(72, 149)(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           : A4.248
NOTES         : type II, reflexible, isomorphic to A4.247.
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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, (x.2 * x.3)^2, (x.1 * x.2)^2, (x.4 * x.1^-1)^2, x.4 * x.2 * x.4 * x.2 * x.4^-1 * x.2, (x.3 * x.4^-1)^4, 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, 8)
#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, 188)(27, 185)(28, 187)(29, 183)(30, 181)(31, 184)(32, 182)(33, 192)(34, 191)(35, 190)(36, 189)(37, 174)(38, 176)(39, 173)(40, 175)(41, 171)(42, 169)(43, 172)(44, 170)(45, 180)(46, 179)(47, 178)(48, 177)(49, 150)(50, 152)(51, 149)(52, 151)(53, 147)(54, 145)(55, 148)(56, 146)(57, 156)(58, 155)(59, 154)(60, 153)(61, 162)(62, 164)(63, 161)(64, 163)(65, 159)(66, 157)(67, 160)(68, 158)(69, 168)(70, 167)(71, 166)(72, 165)(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           : A4.249
NOTES         : type II, reflexible, isomorphic to A4.247.
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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, x.4^4, (x.4^-1 * x.3)^2, (x.2 * x.3)^2, (x.1 * x.2)^2, (x.4^-1 * x.2)^3, x.3 * x.2 * x.4^2 * x.2 * x.4^-2, (x.4 * x.1^-1)^4 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 8)
#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, 188)(27, 185)(28, 187)(29, 183)(30, 181)(31, 184)(32, 182)(33, 192)(34, 191)(35, 190)(36, 189)(37, 174)(38, 176)(39, 173)(40, 175)(41, 171)(42, 169)(43, 172)(44, 170)(45, 180)(46, 179)(47, 178)(48, 177)(49, 150)(50, 152)(51, 149)(52, 151)(53, 147)(54, 145)(55, 148)(56, 146)(57, 156)(58, 155)(59, 154)(60, 153)(61, 162)(62, 164)(63, 161)(64, 163)(65, 159)(66, 157)(67, 160)(68, 158)(69, 168)(70, 167)(71, 166)(72, 165)(73, 122)(74, 124)(75, 121)(76, 123)(77, 127)(78, 125)(79, 128)(80, 126)(81, 136)(82, 135)(83, 134)(84, 133)(85, 142)(86, 144)(87, 141)(88, 143)(89, 131)(90, 129)(91, 132)(92, 130)(93, 140)(94, 139)(95, 138)(96, 137)

MAP           : A4.250
NOTES         : type II, reflexible, isomorphic to A4.247.
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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.3^2, (x.2^-1 * x.3)^2, (x.3 * x.4)^2, (x.4 * x.1^-1)^2, (x.4 * x.2^-1)^3, x.3 * x.2^-2 * x.4 * x.2^-2 * x.4, (x.1 * x.2^-1)^4 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 8)
#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, 172)(27, 169)(28, 171)(29, 175)(30, 173)(31, 176)(32, 174)(33, 184)(34, 183)(35, 182)(36, 181)(37, 190)(38, 192)(39, 189)(40, 191)(41, 179)(42, 177)(43, 180)(44, 178)(45, 188)(46, 187)(47, 186)(48, 185)(49, 150)(50, 152)(51, 149)(52, 151)(53, 147)(54, 145)(55, 148)(56, 146)(57, 156)(58, 155)(59, 154)(60, 153)(61, 162)(62, 164)(63, 161)(64, 163)(65, 159)(66, 157)(67, 160)(68, 158)(69, 168)(70, 167)(71, 166)(72, 165)(73, 138)(74, 140)(75, 137)(76, 139)(77, 135)(78, 133)(79, 136)(80, 134)(81, 144)(82, 143)(83, 142)(84, 141)(85, 126)(86, 128)(87, 125)(88, 127)(89, 123)(90, 121)(91, 124)(92, 122)(93, 132)(94, 131)(95, 130)(96, 129)

MAP           : A4.251
NOTES         : type II, reflexible, isomorphic to A4.247.
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)   : <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 * x.4 * x.3^-1 * x.2 * x.3 * x.2^-1 * x.3^-1, (x.2 * x.3^-1)^4 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 8)
#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, 188)(27, 185)(28, 187)(29, 183)(30, 181)(31, 184)(32, 182)(33, 192)(34, 191)(35, 190)(36, 189)(37, 174)(38, 176)(39, 173)(40, 175)(41, 171)(42, 169)(43, 172)(44, 170)(45, 180)(46, 179)(47, 178)(48, 177)(49, 153)(50, 154)(51, 155)(52, 156)(53, 165)(54, 166)(55, 167)(56, 168)(57, 161)(58, 162)(59, 163)(60, 164)(61, 149)(62, 150)(63, 151)(64, 152)(65, 145)(66, 146)(67, 147)(68, 148)(69, 157)(70, 158)(71, 159)(72, 160)(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           : A4.252
NOTES         : type II, reflexible, isomorphic to A4.247.
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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^3, x.2^4, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^2, (x.2 * x.3^-1)^2, x.2^-1 * x.4 * x.3^-1 * x.2^-1 * x.3^-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        : 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, 172)(27, 169)(28, 171)(29, 175)(30, 173)(31, 176)(32, 174)(33, 184)(34, 183)(35, 182)(36, 181)(37, 190)(38, 192)(39, 189)(40, 191)(41, 179)(42, 177)(43, 180)(44, 178)(45, 188)(46, 187)(47, 186)(48, 185)(49, 158)(50, 160)(51, 157)(52, 159)(53, 163)(54, 161)(55, 164)(56, 162)(57, 148)(58, 147)(59, 146)(60, 145)(61, 154)(62, 156)(63, 153)(64, 155)(65, 167)(66, 165)(67, 168)(68, 166)(69, 152)(70, 151)(71, 150)(72, 149)(73, 128)(74, 127)(75, 126)(76, 125)(77, 124)(78, 123)(79, 122)(80, 121)(81, 139)(82, 137)(83, 140)(84, 138)(85, 143)(86, 141)(87, 144)(88, 142)(89, 130)(90, 132)(91, 129)(92, 131)(93, 134)(94, 136)(95, 133)(96, 135)

MAP           : A4.253
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: [ 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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.4^2, x.1^2, x.2^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.4, x.5^-1 * x.1 * x.5 * x.4, x.4 * x.1 * x.5^-1 * x.2, (x.2 * x.1)^2, (x.2 * x.5)^3, (x.5 * x.3^-1)^4 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 8)
#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, 188)(27, 185)(28, 187)(29, 183)(30, 181)(31, 184)(32, 182)(33, 192)(34, 191)(35, 190)(36, 189)(37, 174)(38, 176)(39, 173)(40, 175)(41, 171)(42, 169)(43, 172)(44, 170)(45, 180)(46, 179)(47, 178)(48, 177)(49, 69)(50, 70)(51, 71)(52, 72)(53, 57)(54, 58)(55, 59)(56, 60)(61, 65)(62, 66)(63, 67)(64, 68)(73, 123)(74, 121)(75, 124)(76, 122)(77, 126)(78, 128)(79, 125)(80, 127)(81, 138)(82, 140)(83, 137)(84, 139)(85, 132)(86, 131)(87, 130)(88, 129)(89, 144)(90, 143)(91, 142)(92, 141)(93, 135)(94, 133)(95, 136)(96, 134)(145, 155)(146, 153)(147, 156)(148, 154)(149, 166)(150, 168)(151, 165)(152, 167)(157, 164)(158, 163)(159, 162)(160, 161)

MAP           : A4.254
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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^-1 * x.1 * x.4 * x.2, x.5 * x.4^-1 * x.5^-1 * x.4^-1, (x.5 * x.3^-1)^2, x.4 * x.1 * x.5^-1 * x.2, x.5 * x.1 * x.2 * x.5^-1 * x.4^-1 * x.1, (x.2 * x.1)^3, (x.3 * x.4^-1)^4 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 8)
#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, 172)(27, 169)(28, 171)(29, 175)(30, 173)(31, 176)(32, 174)(33, 184)(34, 183)(35, 182)(36, 181)(37, 190)(38, 192)(39, 189)(40, 191)(41, 179)(42, 177)(43, 180)(44, 178)(45, 188)(46, 187)(47, 186)(48, 185)(49, 66)(50, 68)(51, 65)(52, 67)(53, 63)(54, 61)(55, 64)(56, 62)(57, 72)(58, 71)(59, 70)(60, 69)(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)(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           : A4.255
NOTES         : type II, reflexible, isomorphic to A4.253.
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)   : <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^-1 * x.1 * x.4 * x.5, x.4 * x.1 * x.5 * x.2, x.5 * x.4 * x.2 * x.4^-1, (x.5 * x.3^-1)^2, (x.2 * x.1)^2, x.2 * x.4 * x.5 * x.1 * x.5 * x.1, (x.3 * x.4^-1)^4 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 8)
#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, 172)(27, 169)(28, 171)(29, 175)(30, 173)(31, 176)(32, 174)(33, 184)(34, 183)(35, 182)(36, 181)(37, 190)(38, 192)(39, 189)(40, 191)(41, 179)(42, 177)(43, 180)(44, 178)(45, 188)(46, 187)(47, 186)(48, 185)(49, 66)(50, 68)(51, 65)(52, 67)(53, 63)(54, 61)(55, 64)(56, 62)(57, 72)(58, 71)(59, 70)(60, 69)(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)(145, 157)(146, 158)(147, 159)(148, 160)(149, 161)(150, 162)(151, 163)(152, 164)(153, 165)(154, 166)(155, 167)(156, 168)

MAP           : A4.256
NOTES         : type II, reflexible, isomorphic to A4.247.
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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.3 * x.4)^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.4 * x.2 * x.4 * x.2^-1 * x.4 * x.2^-1, (x.2 * x.3)^4, x.4 * x.3 * x.2 * x.4 * x.3 * x.2^-1 * x.4 * x.3 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 8)
#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, 188)(27, 185)(28, 187)(29, 183)(30, 181)(31, 184)(32, 182)(33, 192)(34, 191)(35, 190)(36, 189)(37, 174)(38, 176)(39, 173)(40, 175)(41, 171)(42, 169)(43, 172)(44, 170)(45, 180)(46, 179)(47, 178)(48, 177)(49, 151)(50, 149)(51, 152)(52, 150)(53, 146)(54, 148)(55, 145)(56, 147)(57, 166)(58, 168)(59, 165)(60, 167)(61, 160)(62, 159)(63, 158)(64, 157)(65, 164)(66, 163)(67, 162)(68, 161)(69, 155)(70, 153)(71, 156)(72, 154)(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           : A4.257
NOTES         : type II, reflexible, isomorphic to A4.254.
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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.4 * x.5 * x.4^-1, x.5^-1 * x.1 * x.5 * x.2, (x.3 * x.4^-1)^2, x.4 * x.1 * x.5^-1 * x.2, x.1 * x.4 * x.1 * x.4 * x.5^-1 * x.2, (x.2 * x.1)^3, (x.5 * x.3^-1)^4 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 8)
#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, 188)(27, 185)(28, 187)(29, 183)(30, 181)(31, 184)(32, 182)(33, 192)(34, 191)(35, 190)(36, 189)(37, 174)(38, 176)(39, 173)(40, 175)(41, 171)(42, 169)(43, 172)(44, 170)(45, 180)(46, 179)(47, 178)(48, 177)(49, 69)(50, 70)(51, 71)(52, 72)(53, 57)(54, 58)(55, 59)(56, 60)(61, 65)(62, 66)(63, 67)(64, 68)(73, 136)(74, 135)(75, 134)(76, 133)(77, 140)(78, 139)(79, 138)(80, 137)(81, 131)(82, 129)(83, 132)(84, 130)(85, 127)(86, 125)(87, 128)(88, 126)(89, 122)(90, 124)(91, 121)(92, 123)(93, 142)(94, 144)(95, 141)(96, 143)(145, 149)(146, 150)(147, 151)(148, 152)(153, 157)(154, 158)(155, 159)(156, 160)(161, 165)(162, 166)(163, 167)(164, 168)

MAP           : A4.258
NOTES         : type II, reflexible, isomorphic to A4.247.
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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.3^3, x.4^4, (x.3 * x.4^-1)^2, (x.1 * x.2)^2, (x.4^-1 * x.2)^2, (x.2 * x.3^-1)^2, x.3^-1 * x.2 * x.4 * x.3 * x.4^2, (x.4 * x.1^-1)^4 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 8)
#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, 188)(27, 185)(28, 187)(29, 183)(30, 181)(31, 184)(32, 182)(33, 192)(34, 191)(35, 190)(36, 189)(37, 174)(38, 176)(39, 173)(40, 175)(41, 171)(42, 169)(43, 172)(44, 170)(45, 180)(46, 179)(47, 178)(48, 177)(49, 158)(50, 160)(51, 157)(52, 159)(53, 163)(54, 161)(55, 164)(56, 162)(57, 148)(58, 147)(59, 146)(60, 145)(61, 154)(62, 156)(63, 153)(64, 155)(65, 167)(66, 165)(67, 168)(68, 166)(69, 152)(70, 151)(71, 150)(72, 149)(73, 139)(74, 137)(75, 140)(76, 138)(77, 134)(78, 136)(79, 133)(80, 135)(81, 130)(82, 132)(83, 129)(84, 131)(85, 124)(86, 123)(87, 122)(88, 121)(89, 128)(90, 127)(91, 126)(92, 125)(93, 143)(94, 141)(95, 144)(96, 142)

MAP           : A4.259
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), representative.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 10, 2 ]
UNIGROUP      : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^10 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 41, 81, 121)(2, 42, 82, 122)(3, 43, 83, 123)(4, 44, 84, 124)(5, 45, 85, 125)(6, 46, 86, 126)(7, 47, 87, 127)(8, 48, 88, 128)(9, 49, 89, 129)(10, 50, 90, 130)(11, 51, 91, 131)(12, 52, 92, 132)(13, 53, 93, 133)(14, 54, 94, 134)(15, 55, 95, 135)(16, 56, 96, 136)(17, 57, 97, 137)(18, 58, 98, 138)(19, 59, 99, 139)(20, 60, 100, 140)(21, 61, 101, 141)(22, 62, 102, 142)(23, 63, 103, 143)(24, 64, 104, 144)(25, 65, 105, 145)(26, 66, 106, 146)(27, 67, 107, 147)(28, 68, 108, 148)(29, 69, 109, 149)(30, 70, 110, 150)(31, 71, 111, 151)(32, 72, 112, 152)(33, 73, 113, 153)(34, 74, 114, 154)(35, 75, 115, 155)(36, 76, 116, 156)(37, 77, 117, 157)(38, 78, 118, 158)(39, 79, 119, 159)(40, 80, 120, 160)
L = (1, 43)(2, 48)(3, 67)(4, 47)(5, 52)(6, 71)(7, 66)(8, 63)(9, 46)(10, 56)(11, 75)(12, 68)(13, 51)(14, 60)(15, 79)(16, 72)(17, 55)(18, 59)(19, 80)(20, 76)(21, 44)(22, 41)(23, 65)(24, 49)(25, 42)(26, 61)(27, 62)(28, 70)(29, 53)(30, 45)(31, 64)(32, 74)(33, 57)(34, 50)(35, 69)(36, 78)(37, 58)(38, 54)(39, 73)(40, 77)(81, 122)(82, 125)(83, 141)(84, 121)(85, 130)(86, 149)(87, 144)(88, 142)(89, 124)(90, 134)(91, 153)(92, 145)(93, 129)(94, 138)(95, 157)(96, 150)(97, 133)(98, 137)(99, 158)(100, 154)(101, 126)(102, 127)(103, 148)(104, 131)(105, 123)(106, 147)(107, 143)(108, 152)(109, 135)(110, 128)(111, 146)(112, 156)(113, 139)(114, 132)(115, 151)(116, 160)(117, 140)(118, 136)(119, 155)(120, 159)

MAP           : A4.260
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 10, 2 ]
UNIGROUP      : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^10 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 41, 81, 121)(2, 42, 82, 122)(3, 43, 83, 123)(4, 44, 84, 124)(5, 45, 85, 125)(6, 46, 86, 126)(7, 47, 87, 127)(8, 48, 88, 128)(9, 49, 89, 129)(10, 50, 90, 130)(11, 51, 91, 131)(12, 52, 92, 132)(13, 53, 93, 133)(14, 54, 94, 134)(15, 55, 95, 135)(16, 56, 96, 136)(17, 57, 97, 137)(18, 58, 98, 138)(19, 59, 99, 139)(20, 60, 100, 140)(21, 61, 101, 141)(22, 62, 102, 142)(23, 63, 103, 143)(24, 64, 104, 144)(25, 65, 105, 145)(26, 66, 106, 146)(27, 67, 107, 147)(28, 68, 108, 148)(29, 69, 109, 149)(30, 70, 110, 150)(31, 71, 111, 151)(32, 72, 112, 152)(33, 73, 113, 153)(34, 74, 114, 154)(35, 75, 115, 155)(36, 76, 116, 156)(37, 77, 117, 157)(38, 78, 118, 158)(39, 79, 119, 159)(40, 80, 120, 160)
L = (1, 43)(2, 48)(3, 67)(4, 47)(5, 52)(6, 71)(7, 66)(8, 63)(9, 46)(10, 56)(11, 75)(12, 68)(13, 51)(14, 60)(15, 79)(16, 72)(17, 55)(18, 59)(19, 80)(20, 76)(21, 44)(22, 41)(23, 65)(24, 49)(25, 42)(26, 61)(27, 62)(28, 70)(29, 53)(30, 45)(31, 64)(32, 74)(33, 57)(34, 50)(35, 69)(36, 78)(37, 58)(38, 54)(39, 73)(40, 77)(81, 124)(82, 121)(83, 145)(84, 129)(85, 122)(86, 141)(87, 142)(88, 150)(89, 133)(90, 125)(91, 144)(92, 154)(93, 137)(94, 130)(95, 149)(96, 158)(97, 138)(98, 134)(99, 153)(100, 157)(101, 123)(102, 128)(103, 147)(104, 127)(105, 132)(106, 151)(107, 146)(108, 143)(109, 126)(110, 136)(111, 155)(112, 148)(113, 131)(114, 140)(115, 159)(116, 152)(117, 135)(118, 139)(119, 160)(120, 156)

MAP           : A4.261
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 53)(22, 54)(23, 50)(24, 57)(25, 58)(26, 49)(27, 44)(28, 45)(29, 60)(30, 59)(31, 42)(32, 41)(33, 55)(34, 56)(35, 46)(36, 43)(37, 52)(38, 51)(39, 48)(40, 47)(61, 102)(62, 101)(63, 106)(64, 105)(65, 104)(66, 103)(67, 108)(68, 107)(69, 110)(70, 109)(71, 112)(72, 111)(73, 114)(74, 113)(75, 116)(76, 115)(77, 118)(78, 117)(79, 120)(80, 119)(121, 151)(122, 152)(123, 155)(124, 148)(125, 147)(126, 156)(127, 159)(128, 160)(129, 143)(130, 146)(131, 157)(132, 158)(133, 142)(134, 141)(135, 154)(136, 153)(137, 145)(138, 144)(139, 149)(140, 150)

MAP           : A4.262
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 10, 2 ]
UNIGROUP      : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^10 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 41, 81, 121)(2, 42, 82, 122)(3, 43, 83, 123)(4, 44, 84, 124)(5, 45, 85, 125)(6, 46, 86, 126)(7, 47, 87, 127)(8, 48, 88, 128)(9, 49, 89, 129)(10, 50, 90, 130)(11, 51, 91, 131)(12, 52, 92, 132)(13, 53, 93, 133)(14, 54, 94, 134)(15, 55, 95, 135)(16, 56, 96, 136)(17, 57, 97, 137)(18, 58, 98, 138)(19, 59, 99, 139)(20, 60, 100, 140)(21, 61, 101, 141)(22, 62, 102, 142)(23, 63, 103, 143)(24, 64, 104, 144)(25, 65, 105, 145)(26, 66, 106, 146)(27, 67, 107, 147)(28, 68, 108, 148)(29, 69, 109, 149)(30, 70, 110, 150)(31, 71, 111, 151)(32, 72, 112, 152)(33, 73, 113, 153)(34, 74, 114, 154)(35, 75, 115, 155)(36, 76, 116, 156)(37, 77, 117, 157)(38, 78, 118, 158)(39, 79, 119, 159)(40, 80, 120, 160)
L = (1, 43)(2, 48)(3, 67)(4, 47)(5, 52)(6, 71)(7, 66)(8, 63)(9, 46)(10, 56)(11, 75)(12, 68)(13, 51)(14, 60)(15, 79)(16, 72)(17, 55)(18, 59)(19, 80)(20, 76)(21, 44)(22, 41)(23, 65)(24, 49)(25, 42)(26, 61)(27, 62)(28, 70)(29, 53)(30, 45)(31, 64)(32, 74)(33, 57)(34, 50)(35, 69)(36, 78)(37, 58)(38, 54)(39, 73)(40, 77)(81, 130)(82, 134)(83, 149)(84, 125)(85, 138)(86, 157)(87, 153)(88, 144)(89, 122)(90, 137)(91, 158)(92, 141)(93, 121)(94, 133)(95, 154)(96, 142)(97, 124)(98, 129)(99, 150)(100, 145)(101, 135)(102, 131)(103, 156)(104, 139)(105, 126)(106, 148)(107, 152)(108, 160)(109, 140)(110, 127)(111, 143)(112, 159)(113, 136)(114, 123)(115, 147)(116, 155)(117, 132)(118, 128)(119, 146)(120, 151)

MAP           : A4.263
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 10, 2 ]
UNIGROUP      : < u.1, u.2 | u.1^4, (u.1^-1 * u.2^-1)^2, u.2^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2 | x.1^4, (x.1^-1 * x.2^-1)^2, (x.2^-1 * x.1)^2, x.2^10 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 41, 81, 121)(2, 42, 82, 122)(3, 43, 83, 123)(4, 44, 84, 124)(5, 45, 85, 125)(6, 46, 86, 126)(7, 47, 87, 127)(8, 48, 88, 128)(9, 49, 89, 129)(10, 50, 90, 130)(11, 51, 91, 131)(12, 52, 92, 132)(13, 53, 93, 133)(14, 54, 94, 134)(15, 55, 95, 135)(16, 56, 96, 136)(17, 57, 97, 137)(18, 58, 98, 138)(19, 59, 99, 139)(20, 60, 100, 140)(21, 61, 101, 141)(22, 62, 102, 142)(23, 63, 103, 143)(24, 64, 104, 144)(25, 65, 105, 145)(26, 66, 106, 146)(27, 67, 107, 147)(28, 68, 108, 148)(29, 69, 109, 149)(30, 70, 110, 150)(31, 71, 111, 151)(32, 72, 112, 152)(33, 73, 113, 153)(34, 74, 114, 154)(35, 75, 115, 155)(36, 76, 116, 156)(37, 77, 117, 157)(38, 78, 118, 158)(39, 79, 119, 159)(40, 80, 120, 160)
L = (1, 43)(2, 48)(3, 67)(4, 47)(5, 52)(6, 71)(7, 66)(8, 63)(9, 46)(10, 56)(11, 75)(12, 68)(13, 51)(14, 60)(15, 79)(16, 72)(17, 55)(18, 59)(19, 80)(20, 76)(21, 44)(22, 41)(23, 65)(24, 49)(25, 42)(26, 61)(27, 62)(28, 70)(29, 53)(30, 45)(31, 64)(32, 74)(33, 57)(34, 50)(35, 69)(36, 78)(37, 58)(38, 54)(39, 73)(40, 77)(81, 133)(82, 129)(83, 154)(84, 137)(85, 124)(86, 145)(87, 150)(88, 158)(89, 138)(90, 121)(91, 142)(92, 157)(93, 134)(94, 122)(95, 141)(96, 153)(97, 130)(98, 125)(99, 144)(100, 149)(101, 132)(102, 136)(103, 151)(104, 128)(105, 140)(106, 159)(107, 155)(108, 146)(109, 123)(110, 139)(111, 160)(112, 147)(113, 127)(114, 135)(115, 156)(116, 143)(117, 126)(118, 131)(119, 152)(120, 148)

MAP           : A4.264
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 10, 4, 2 ]
UNIGROUP      : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^10 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 41, 81, 121)(2, 42, 82, 122)(3, 43, 83, 123)(4, 44, 84, 124)(5, 45, 85, 125)(6, 46, 86, 126)(7, 47, 87, 127)(8, 48, 88, 128)(9, 49, 89, 129)(10, 50, 90, 130)(11, 51, 91, 131)(12, 52, 92, 132)(13, 53, 93, 133)(14, 54, 94, 134)(15, 55, 95, 135)(16, 56, 96, 136)(17, 57, 97, 137)(18, 58, 98, 138)(19, 59, 99, 139)(20, 60, 100, 140)(21, 61, 101, 141)(22, 62, 102, 142)(23, 63, 103, 143)(24, 64, 104, 144)(25, 65, 105, 145)(26, 66, 106, 146)(27, 67, 107, 147)(28, 68, 108, 148)(29, 69, 109, 149)(30, 70, 110, 150)(31, 71, 111, 151)(32, 72, 112, 152)(33, 73, 113, 153)(34, 74, 114, 154)(35, 75, 115, 155)(36, 76, 116, 156)(37, 77, 117, 157)(38, 78, 118, 158)(39, 79, 119, 159)(40, 80, 120, 160)
L = (1, 53)(2, 49)(3, 74)(4, 57)(5, 44)(6, 65)(7, 70)(8, 78)(9, 58)(10, 41)(11, 62)(12, 77)(13, 54)(14, 42)(15, 61)(16, 73)(17, 50)(18, 45)(19, 64)(20, 69)(21, 52)(22, 56)(23, 71)(24, 48)(25, 60)(26, 79)(27, 75)(28, 66)(29, 43)(30, 59)(31, 80)(32, 67)(33, 47)(34, 55)(35, 76)(36, 63)(37, 46)(38, 51)(39, 72)(40, 68)(81, 123)(82, 128)(83, 147)(84, 127)(85, 132)(86, 151)(87, 146)(88, 143)(89, 126)(90, 136)(91, 155)(92, 148)(93, 131)(94, 140)(95, 159)(96, 152)(97, 135)(98, 139)(99, 160)(100, 156)(101, 124)(102, 121)(103, 145)(104, 129)(105, 122)(106, 141)(107, 142)(108, 150)(109, 133)(110, 125)(111, 144)(112, 154)(113, 137)(114, 130)(115, 149)(116, 158)(117, 138)(118, 134)(119, 153)(120, 157)

MAP           : A4.265
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 10, 4, 2 ]
UNIGROUP      : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^10 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 41, 81, 121)(2, 42, 82, 122)(3, 43, 83, 123)(4, 44, 84, 124)(5, 45, 85, 125)(6, 46, 86, 126)(7, 47, 87, 127)(8, 48, 88, 128)(9, 49, 89, 129)(10, 50, 90, 130)(11, 51, 91, 131)(12, 52, 92, 132)(13, 53, 93, 133)(14, 54, 94, 134)(15, 55, 95, 135)(16, 56, 96, 136)(17, 57, 97, 137)(18, 58, 98, 138)(19, 59, 99, 139)(20, 60, 100, 140)(21, 61, 101, 141)(22, 62, 102, 142)(23, 63, 103, 143)(24, 64, 104, 144)(25, 65, 105, 145)(26, 66, 106, 146)(27, 67, 107, 147)(28, 68, 108, 148)(29, 69, 109, 149)(30, 70, 110, 150)(31, 71, 111, 151)(32, 72, 112, 152)(33, 73, 113, 153)(34, 74, 114, 154)(35, 75, 115, 155)(36, 76, 116, 156)(37, 77, 117, 157)(38, 78, 118, 158)(39, 79, 119, 159)(40, 80, 120, 160)
L = (1, 44)(2, 41)(3, 65)(4, 49)(5, 42)(6, 61)(7, 62)(8, 70)(9, 53)(10, 45)(11, 64)(12, 74)(13, 57)(14, 50)(15, 69)(16, 78)(17, 58)(18, 54)(19, 73)(20, 77)(21, 43)(22, 48)(23, 67)(24, 47)(25, 52)(26, 71)(27, 66)(28, 63)(29, 46)(30, 56)(31, 75)(32, 68)(33, 51)(34, 60)(35, 79)(36, 72)(37, 55)(38, 59)(39, 80)(40, 76)(81, 123)(82, 128)(83, 147)(84, 127)(85, 132)(86, 151)(87, 146)(88, 143)(89, 126)(90, 136)(91, 155)(92, 148)(93, 131)(94, 140)(95, 159)(96, 152)(97, 135)(98, 139)(99, 160)(100, 156)(101, 124)(102, 121)(103, 145)(104, 129)(105, 122)(106, 141)(107, 142)(108, 150)(109, 133)(110, 125)(111, 144)(112, 154)(113, 137)(114, 130)(115, 149)(116, 158)(117, 138)(118, 134)(119, 153)(120, 157)

MAP           : A4.266
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 51)(22, 52)(23, 55)(24, 48)(25, 47)(26, 56)(27, 59)(28, 60)(29, 43)(30, 46)(31, 57)(32, 58)(33, 42)(34, 41)(35, 54)(36, 53)(37, 45)(38, 44)(39, 49)(40, 50)(61, 102)(62, 101)(63, 106)(64, 105)(65, 104)(66, 103)(67, 108)(68, 107)(69, 110)(70, 109)(71, 112)(72, 111)(73, 114)(74, 113)(75, 116)(76, 115)(77, 118)(78, 117)(79, 120)(80, 119)(121, 153)(122, 154)(123, 150)(124, 157)(125, 158)(126, 149)(127, 144)(128, 145)(129, 160)(130, 159)(131, 142)(132, 141)(133, 155)(134, 156)(135, 146)(136, 143)(137, 152)(138, 151)(139, 148)(140, 147)

MAP           : A4.267
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 54)(22, 53)(23, 49)(24, 58)(25, 57)(26, 50)(27, 45)(28, 44)(29, 59)(30, 60)(31, 41)(32, 42)(33, 56)(34, 55)(35, 43)(36, 46)(37, 51)(38, 52)(39, 47)(40, 48)(61, 102)(62, 101)(63, 106)(64, 105)(65, 104)(66, 103)(67, 108)(68, 107)(69, 110)(70, 109)(71, 112)(72, 111)(73, 114)(74, 113)(75, 116)(76, 115)(77, 118)(78, 117)(79, 120)(80, 119)(121, 152)(122, 151)(123, 156)(124, 147)(125, 148)(126, 155)(127, 160)(128, 159)(129, 146)(130, 143)(131, 158)(132, 157)(133, 141)(134, 142)(135, 153)(136, 154)(137, 144)(138, 145)(139, 150)(140, 149)

MAP           : A4.268
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 45)(22, 44)(23, 41)(24, 50)(25, 49)(26, 42)(27, 43)(28, 46)(29, 54)(30, 53)(31, 47)(32, 48)(33, 58)(34, 57)(35, 51)(36, 52)(37, 59)(38, 60)(39, 55)(40, 56)(61, 102)(62, 101)(63, 106)(64, 105)(65, 104)(66, 103)(67, 108)(68, 107)(69, 110)(70, 109)(71, 112)(72, 111)(73, 114)(74, 113)(75, 116)(76, 115)(77, 118)(78, 117)(79, 120)(80, 119)(121, 146)(122, 143)(123, 148)(124, 141)(125, 142)(126, 147)(127, 152)(128, 151)(129, 144)(130, 145)(131, 156)(132, 155)(133, 149)(134, 150)(135, 160)(136, 159)(137, 153)(138, 154)(139, 158)(140, 157)

MAP           : A4.269
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 44)(22, 45)(23, 42)(24, 49)(25, 50)(26, 41)(27, 46)(28, 43)(29, 53)(30, 54)(31, 48)(32, 47)(33, 57)(34, 58)(35, 52)(36, 51)(37, 60)(38, 59)(39, 56)(40, 55)(61, 102)(62, 101)(63, 106)(64, 105)(65, 104)(66, 103)(67, 108)(68, 107)(69, 110)(70, 109)(71, 112)(72, 111)(73, 114)(74, 113)(75, 116)(76, 115)(77, 118)(78, 117)(79, 120)(80, 119)(121, 143)(122, 146)(123, 147)(124, 142)(125, 141)(126, 148)(127, 151)(128, 152)(129, 145)(130, 144)(131, 155)(132, 156)(133, 150)(134, 149)(135, 159)(136, 160)(137, 154)(138, 153)(139, 157)(140, 158)

MAP           : A4.270
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 51)(22, 52)(23, 55)(24, 48)(25, 47)(26, 56)(27, 59)(28, 60)(29, 43)(30, 46)(31, 57)(32, 58)(33, 42)(34, 41)(35, 54)(36, 53)(37, 45)(38, 44)(39, 49)(40, 50)(61, 120)(62, 119)(63, 118)(64, 115)(65, 116)(66, 117)(67, 113)(68, 114)(69, 112)(70, 111)(71, 110)(72, 109)(73, 107)(74, 108)(75, 104)(76, 105)(77, 106)(78, 103)(79, 102)(80, 101)(121, 148)(122, 147)(123, 152)(124, 143)(125, 146)(126, 151)(127, 156)(128, 155)(129, 142)(130, 141)(131, 160)(132, 159)(133, 145)(134, 144)(135, 158)(136, 157)(137, 150)(138, 149)(139, 153)(140, 154)

MAP           : A4.271
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 54)(22, 53)(23, 49)(24, 58)(25, 57)(26, 50)(27, 45)(28, 44)(29, 59)(30, 60)(31, 41)(32, 42)(33, 56)(34, 55)(35, 43)(36, 46)(37, 51)(38, 52)(39, 47)(40, 48)(61, 120)(62, 119)(63, 118)(64, 115)(65, 116)(66, 117)(67, 113)(68, 114)(69, 112)(70, 111)(71, 110)(72, 109)(73, 107)(74, 108)(75, 104)(76, 105)(77, 106)(78, 103)(79, 102)(80, 101)(121, 150)(122, 149)(123, 144)(124, 154)(125, 153)(126, 145)(127, 142)(128, 141)(129, 158)(130, 157)(131, 146)(132, 143)(133, 159)(134, 160)(135, 148)(136, 147)(137, 156)(138, 155)(139, 152)(140, 151)

MAP           : A4.272
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 45)(22, 44)(23, 41)(24, 50)(25, 49)(26, 42)(27, 43)(28, 46)(29, 54)(30, 53)(31, 47)(32, 48)(33, 58)(34, 57)(35, 51)(36, 52)(37, 59)(38, 60)(39, 55)(40, 56)(61, 120)(62, 119)(63, 118)(64, 115)(65, 116)(66, 117)(67, 113)(68, 114)(69, 112)(70, 111)(71, 110)(72, 109)(73, 107)(74, 108)(75, 104)(76, 105)(77, 106)(78, 103)(79, 102)(80, 101)(121, 158)(122, 157)(123, 153)(124, 159)(125, 160)(126, 154)(127, 150)(128, 149)(129, 156)(130, 155)(131, 144)(132, 145)(133, 151)(134, 152)(135, 142)(136, 141)(137, 148)(138, 147)(139, 146)(140, 143)

MAP           : A4.273
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 10, 4, 2 ]
UNIGROUP      : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^10 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 41, 81, 121)(2, 42, 82, 122)(3, 43, 83, 123)(4, 44, 84, 124)(5, 45, 85, 125)(6, 46, 86, 126)(7, 47, 87, 127)(8, 48, 88, 128)(9, 49, 89, 129)(10, 50, 90, 130)(11, 51, 91, 131)(12, 52, 92, 132)(13, 53, 93, 133)(14, 54, 94, 134)(15, 55, 95, 135)(16, 56, 96, 136)(17, 57, 97, 137)(18, 58, 98, 138)(19, 59, 99, 139)(20, 60, 100, 140)(21, 61, 101, 141)(22, 62, 102, 142)(23, 63, 103, 143)(24, 64, 104, 144)(25, 65, 105, 145)(26, 66, 106, 146)(27, 67, 107, 147)(28, 68, 108, 148)(29, 69, 109, 149)(30, 70, 110, 150)(31, 71, 111, 151)(32, 72, 112, 152)(33, 73, 113, 153)(34, 74, 114, 154)(35, 75, 115, 155)(36, 76, 116, 156)(37, 77, 117, 157)(38, 78, 118, 158)(39, 79, 119, 159)(40, 80, 120, 160)
L = (1, 50)(2, 54)(3, 69)(4, 45)(5, 58)(6, 77)(7, 73)(8, 64)(9, 42)(10, 57)(11, 78)(12, 61)(13, 41)(14, 53)(15, 74)(16, 62)(17, 44)(18, 49)(19, 70)(20, 65)(21, 55)(22, 51)(23, 76)(24, 59)(25, 46)(26, 68)(27, 72)(28, 80)(29, 60)(30, 47)(31, 63)(32, 79)(33, 56)(34, 43)(35, 67)(36, 75)(37, 52)(38, 48)(39, 66)(40, 71)(81, 123)(82, 128)(83, 147)(84, 127)(85, 132)(86, 151)(87, 146)(88, 143)(89, 126)(90, 136)(91, 155)(92, 148)(93, 131)(94, 140)(95, 159)(96, 152)(97, 135)(98, 139)(99, 160)(100, 156)(101, 124)(102, 121)(103, 145)(104, 129)(105, 122)(106, 141)(107, 142)(108, 150)(109, 133)(110, 125)(111, 144)(112, 154)(113, 137)(114, 130)(115, 149)(116, 158)(117, 138)(118, 134)(119, 153)(120, 157)

MAP           : A4.274
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 48)(22, 47)(23, 52)(24, 43)(25, 46)(26, 51)(27, 56)(28, 55)(29, 42)(30, 41)(31, 60)(32, 59)(33, 45)(34, 44)(35, 58)(36, 57)(37, 50)(38, 49)(39, 53)(40, 54)(61, 119)(62, 120)(63, 117)(64, 116)(65, 115)(66, 118)(67, 114)(68, 113)(69, 111)(70, 112)(71, 109)(72, 110)(73, 108)(74, 107)(75, 105)(76, 104)(77, 103)(78, 106)(79, 101)(80, 102)(121, 152)(122, 151)(123, 156)(124, 147)(125, 148)(126, 155)(127, 160)(128, 159)(129, 146)(130, 143)(131, 158)(132, 157)(133, 141)(134, 142)(135, 153)(136, 154)(137, 144)(138, 145)(139, 150)(140, 149)

MAP           : A4.275
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 58)(22, 57)(23, 53)(24, 59)(25, 60)(26, 54)(27, 50)(28, 49)(29, 56)(30, 55)(31, 44)(32, 45)(33, 51)(34, 52)(35, 42)(36, 41)(37, 48)(38, 47)(39, 46)(40, 43)(61, 119)(62, 120)(63, 117)(64, 116)(65, 115)(66, 118)(67, 114)(68, 113)(69, 111)(70, 112)(71, 109)(72, 110)(73, 108)(74, 107)(75, 105)(76, 104)(77, 103)(78, 106)(79, 101)(80, 102)(121, 144)(122, 145)(123, 142)(124, 149)(125, 150)(126, 141)(127, 146)(128, 143)(129, 153)(130, 154)(131, 148)(132, 147)(133, 157)(134, 158)(135, 152)(136, 151)(137, 160)(138, 159)(139, 156)(140, 155)

MAP           : A4.276
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 56)(22, 55)(23, 60)(24, 51)(25, 52)(26, 59)(27, 58)(28, 57)(29, 48)(30, 47)(31, 53)(32, 54)(33, 43)(34, 46)(35, 50)(36, 49)(37, 42)(38, 41)(39, 44)(40, 45)(61, 119)(62, 120)(63, 117)(64, 116)(65, 115)(66, 118)(67, 114)(68, 113)(69, 111)(70, 112)(71, 109)(72, 110)(73, 108)(74, 107)(75, 105)(76, 104)(77, 103)(78, 106)(79, 101)(80, 102)(121, 146)(122, 143)(123, 148)(124, 141)(125, 142)(126, 147)(127, 152)(128, 151)(129, 144)(130, 145)(131, 156)(132, 155)(133, 149)(134, 150)(135, 160)(136, 159)(137, 153)(138, 154)(139, 158)(140, 157)

MAP           : A4.277
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 50)(22, 49)(23, 44)(24, 54)(25, 53)(26, 45)(27, 42)(28, 41)(29, 58)(30, 57)(31, 46)(32, 43)(33, 59)(34, 60)(35, 48)(36, 47)(37, 56)(38, 55)(39, 52)(40, 51)(61, 119)(62, 120)(63, 117)(64, 116)(65, 115)(66, 118)(67, 114)(68, 113)(69, 111)(70, 112)(71, 109)(72, 110)(73, 108)(74, 107)(75, 105)(76, 104)(77, 103)(78, 106)(79, 101)(80, 102)(121, 153)(122, 154)(123, 150)(124, 157)(125, 158)(126, 149)(127, 144)(128, 145)(129, 160)(130, 159)(131, 142)(132, 141)(133, 155)(134, 156)(135, 146)(136, 143)(137, 152)(138, 151)(139, 148)(140, 147)

MAP           : A4.278
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 43)(22, 46)(23, 47)(24, 42)(25, 41)(26, 48)(27, 51)(28, 52)(29, 45)(30, 44)(31, 55)(32, 56)(33, 50)(34, 49)(35, 59)(36, 60)(37, 54)(38, 53)(39, 57)(40, 58)(61, 120)(62, 119)(63, 118)(64, 115)(65, 116)(66, 117)(67, 113)(68, 114)(69, 112)(70, 111)(71, 110)(72, 109)(73, 107)(74, 108)(75, 104)(76, 105)(77, 106)(78, 103)(79, 102)(80, 101)(121, 156)(122, 155)(123, 160)(124, 151)(125, 152)(126, 159)(127, 158)(128, 157)(129, 148)(130, 147)(131, 153)(132, 154)(133, 143)(134, 146)(135, 150)(136, 149)(137, 142)(138, 141)(139, 144)(140, 145)

MAP           : A4.279
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, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2^-1 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 147)(22, 150)(23, 149)(24, 160)(25, 143)(26, 158)(27, 145)(28, 156)(29, 141)(30, 154)(31, 159)(32, 148)(33, 155)(34, 146)(35, 157)(36, 144)(37, 151)(38, 142)(39, 153)(40, 152)(41, 124)(42, 135)(43, 132)(44, 121)(45, 128)(46, 131)(47, 136)(48, 125)(49, 140)(50, 133)(51, 126)(52, 123)(53, 130)(54, 139)(55, 122)(56, 127)(57, 138)(58, 137)(59, 134)(60, 129)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)

MAP           : A4.280
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 147)(22, 150)(23, 149)(24, 160)(25, 143)(26, 158)(27, 145)(28, 156)(29, 141)(30, 154)(31, 159)(32, 148)(33, 155)(34, 146)(35, 157)(36, 144)(37, 151)(38, 142)(39, 153)(40, 152)(41, 124)(42, 135)(43, 132)(44, 121)(45, 128)(46, 131)(47, 136)(48, 125)(49, 140)(50, 133)(51, 126)(52, 123)(53, 130)(54, 139)(55, 122)(56, 127)(57, 138)(58, 137)(59, 134)(60, 129)(61, 115)(62, 104)(63, 111)(64, 102)(65, 119)(66, 112)(67, 113)(68, 114)(69, 117)(70, 116)(71, 103)(72, 106)(73, 107)(74, 108)(75, 101)(76, 110)(77, 109)(78, 120)(79, 105)(80, 118)

MAP           : A4.281
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2^-1 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 147)(22, 150)(23, 149)(24, 160)(25, 143)(26, 158)(27, 145)(28, 156)(29, 141)(30, 154)(31, 159)(32, 148)(33, 155)(34, 146)(35, 157)(36, 144)(37, 151)(38, 142)(39, 153)(40, 152)(41, 131)(42, 132)(43, 133)(44, 134)(45, 135)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)

MAP           : A4.282
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {5, 4, 4})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 4, 5, 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)^5 >
CTG (small)   : <20, 1>
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.4^-2 * x.2^2, x.2^2 * x.4^2, x.3^2 * x.4^-1 * x.3^-2 * x.2^-1, (x.3 * x.1^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 43)(22, 47)(23, 51)(24, 42)(25, 49)(26, 41)(27, 52)(28, 56)(29, 54)(30, 45)(31, 46)(32, 44)(33, 48)(34, 50)(35, 57)(36, 59)(37, 60)(38, 55)(39, 53)(40, 58)(61, 102)(62, 108)(63, 109)(64, 106)(65, 101)(66, 110)(67, 103)(68, 115)(69, 117)(70, 118)(71, 112)(72, 119)(73, 104)(74, 111)(75, 105)(76, 107)(77, 116)(78, 113)(79, 120)(80, 114)(121, 150)(122, 146)(123, 142)(124, 159)(125, 158)(126, 152)(127, 148)(128, 144)(129, 141)(130, 151)(131, 149)(132, 143)(133, 160)(134, 157)(135, 153)(136, 155)(137, 145)(138, 154)(139, 147)(140, 156)

MAP           : A4.283
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {5, 4, 4})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 4, 5, 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)^5 >
CTG (small)   : <20, 1>
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.4^-2 * x.2^2, x.2^2 * x.4^2, x.3^2 * x.4^-1 * x.3^-2 * x.2^-1, (x.3 * x.1^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 46)(22, 44)(23, 41)(24, 52)(25, 50)(26, 51)(27, 42)(28, 53)(29, 45)(30, 54)(31, 43)(32, 47)(33, 59)(34, 49)(35, 58)(36, 48)(37, 55)(38, 60)(39, 56)(40, 57)(61, 102)(62, 108)(63, 109)(64, 106)(65, 101)(66, 110)(67, 103)(68, 115)(69, 117)(70, 118)(71, 112)(72, 119)(73, 104)(74, 111)(75, 105)(76, 107)(77, 116)(78, 113)(79, 120)(80, 114)(121, 149)(122, 143)(123, 152)(124, 148)(125, 157)(126, 142)(127, 159)(128, 147)(129, 151)(130, 141)(131, 150)(132, 146)(133, 155)(134, 158)(135, 156)(136, 160)(137, 154)(138, 145)(139, 144)(140, 153)

MAP           : A4.284
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {5, 4, 4})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 4, 5, 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)^5 >
CTG (small)   : <20, 1>
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.4^-2 * x.2^2, x.2^2 * x.4^2, x.3^2 * x.4^-1 * x.3^-2 * x.2^-1, (x.3 * x.1^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 43)(22, 47)(23, 51)(24, 42)(25, 49)(26, 41)(27, 52)(28, 56)(29, 54)(30, 45)(31, 46)(32, 44)(33, 48)(34, 50)(35, 57)(36, 59)(37, 60)(38, 55)(39, 53)(40, 58)(61, 108)(62, 115)(63, 117)(64, 110)(65, 102)(66, 118)(67, 109)(68, 105)(69, 116)(70, 113)(71, 119)(72, 120)(73, 106)(74, 112)(75, 101)(76, 103)(77, 107)(78, 104)(79, 114)(80, 111)(121, 158)(122, 150)(123, 148)(124, 160)(125, 153)(126, 159)(127, 155)(128, 146)(129, 142)(130, 152)(131, 157)(132, 149)(133, 154)(134, 156)(135, 144)(136, 145)(137, 141)(138, 151)(139, 143)(140, 147)

MAP           : A4.285
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {5, 4, 4})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 4, 5, 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)^5 >
CTG (small)   : <20, 1>
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.4^-2 * x.2^2, x.2^2 * x.4^2, x.3^2 * x.4^-1 * x.3^-2 * x.2^-1, (x.3 * x.1^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 46)(22, 44)(23, 41)(24, 52)(25, 50)(26, 51)(27, 42)(28, 53)(29, 45)(30, 54)(31, 43)(32, 47)(33, 59)(34, 49)(35, 58)(36, 48)(37, 55)(38, 60)(39, 56)(40, 57)(61, 108)(62, 115)(63, 117)(64, 110)(65, 102)(66, 118)(67, 109)(68, 105)(69, 116)(70, 113)(71, 119)(72, 120)(73, 106)(74, 112)(75, 101)(76, 103)(77, 107)(78, 104)(79, 114)(80, 111)(121, 157)(122, 149)(123, 159)(124, 155)(125, 156)(126, 148)(127, 160)(128, 143)(129, 152)(130, 142)(131, 158)(132, 150)(133, 145)(134, 153)(135, 147)(136, 154)(137, 151)(138, 141)(139, 146)(140, 144)

MAP           : A4.286
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, {5, 4, 4})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 4, 5, 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)^5 >
CTG (small)   : <20, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^-1 * x.3 * x.2^-1 * x.3, x.1 * x.2^-1 * x.3^-1 * x.4^-1, x.2^4, x.4^4, x.2^-1 * x.4^-1 * x.3^-2, (x.4 * x.2^-1)^2, (x.3 * x.1^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 43)(22, 54)(23, 52)(24, 45)(25, 57)(26, 42)(27, 48)(28, 60)(29, 47)(30, 41)(31, 44)(32, 50)(33, 59)(34, 58)(35, 53)(36, 55)(37, 51)(38, 46)(39, 56)(40, 49)(61, 102)(62, 108)(63, 120)(64, 107)(65, 101)(66, 104)(67, 110)(68, 119)(69, 118)(70, 113)(71, 115)(72, 111)(73, 106)(74, 116)(75, 109)(76, 103)(77, 114)(78, 112)(79, 105)(80, 117)(121, 144)(122, 150)(123, 159)(124, 158)(125, 153)(126, 155)(127, 151)(128, 146)(129, 156)(130, 149)(131, 143)(132, 154)(133, 152)(134, 145)(135, 157)(136, 142)(137, 148)(138, 160)(139, 147)(140, 141)

MAP           : A4.287
NOTES         : type II, reflexible, isomorphic to A4.286.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {5, 4, 4})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 4, 4, 5, 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)^5 >
CTG (small)   : <20, 3>
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^-1 * x.3 * x.4^-1 * x.3^-1, x.2^4, x.4^4, x.4 * x.2 * x.3^-2, (x.4^-1 * x.2)^2, (x.3 * x.1^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 50)(22, 46)(23, 41)(24, 51)(25, 44)(26, 58)(27, 49)(28, 47)(29, 60)(30, 52)(31, 57)(32, 43)(33, 55)(34, 42)(35, 56)(36, 59)(37, 45)(38, 54)(39, 53)(40, 48)(61, 102)(62, 108)(63, 120)(64, 107)(65, 101)(66, 104)(67, 110)(68, 119)(69, 118)(70, 113)(71, 115)(72, 111)(73, 106)(74, 116)(75, 109)(76, 103)(77, 114)(78, 112)(79, 105)(80, 117)(121, 157)(122, 143)(123, 155)(124, 142)(125, 156)(126, 159)(127, 145)(128, 154)(129, 153)(130, 148)(131, 150)(132, 146)(133, 141)(134, 151)(135, 144)(136, 158)(137, 149)(138, 147)(139, 160)(140, 152)

MAP           : A4.288
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 43)(22, 46)(23, 47)(24, 42)(25, 41)(26, 48)(27, 51)(28, 52)(29, 45)(30, 44)(31, 55)(32, 56)(33, 50)(34, 49)(35, 59)(36, 60)(37, 54)(38, 53)(39, 57)(40, 58)(61, 102)(62, 101)(63, 106)(64, 105)(65, 104)(66, 103)(67, 108)(68, 107)(69, 110)(70, 109)(71, 112)(72, 111)(73, 114)(74, 113)(75, 116)(76, 115)(77, 118)(78, 117)(79, 120)(80, 119)(121, 144)(122, 145)(123, 142)(124, 149)(125, 150)(126, 141)(127, 146)(128, 143)(129, 153)(130, 154)(131, 148)(132, 147)(133, 157)(134, 158)(135, 152)(136, 151)(137, 160)(138, 159)(139, 156)(140, 155)

MAP           : A4.289
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 5 ]
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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4^-1 * x.3)^2, (x.2 * x.3)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 144)(22, 155)(23, 152)(24, 141)(25, 148)(26, 151)(27, 156)(28, 145)(29, 160)(30, 153)(31, 146)(32, 143)(33, 150)(34, 159)(35, 142)(36, 147)(37, 158)(38, 157)(39, 154)(40, 149)(41, 135)(42, 124)(43, 131)(44, 122)(45, 139)(46, 132)(47, 133)(48, 134)(49, 137)(50, 136)(51, 123)(52, 126)(53, 127)(54, 128)(55, 121)(56, 130)(57, 129)(58, 140)(59, 125)(60, 138)(61, 103)(62, 106)(63, 107)(64, 108)(65, 101)(66, 110)(67, 109)(68, 120)(69, 105)(70, 118)(71, 115)(72, 104)(73, 111)(74, 102)(75, 119)(76, 112)(77, 113)(78, 114)(79, 117)(80, 116)

MAP           : A4.290
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 5 ]
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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4^-1 * x.3)^2, (x.2 * x.3)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 144)(22, 155)(23, 152)(24, 141)(25, 148)(26, 151)(27, 156)(28, 145)(29, 160)(30, 153)(31, 146)(32, 143)(33, 150)(34, 159)(35, 142)(36, 147)(37, 158)(38, 157)(39, 154)(40, 149)(41, 135)(42, 124)(43, 131)(44, 122)(45, 139)(46, 132)(47, 133)(48, 134)(49, 137)(50, 136)(51, 123)(52, 126)(53, 127)(54, 128)(55, 121)(56, 130)(57, 129)(58, 140)(59, 125)(60, 138)(61, 107)(62, 110)(63, 109)(64, 120)(65, 103)(66, 118)(67, 105)(68, 116)(69, 101)(70, 114)(71, 119)(72, 108)(73, 115)(74, 106)(75, 117)(76, 104)(77, 111)(78, 102)(79, 113)(80, 112)

MAP           : A4.291
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 5 ]
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)^5 >
CTG (small)   : <20, 4>
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.3^-1 * x.4)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, x.3^3 * x.4 * x.3, (x.4 * x.1^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 144)(22, 155)(23, 152)(24, 141)(25, 148)(26, 151)(27, 156)(28, 145)(29, 160)(30, 153)(31, 146)(32, 143)(33, 150)(34, 159)(35, 142)(36, 147)(37, 158)(38, 157)(39, 154)(40, 149)(41, 126)(42, 123)(43, 130)(44, 139)(45, 122)(46, 127)(47, 138)(48, 137)(49, 134)(50, 129)(51, 124)(52, 135)(53, 132)(54, 121)(55, 128)(56, 131)(57, 136)(58, 125)(59, 140)(60, 133)(61, 103)(62, 106)(63, 107)(64, 108)(65, 101)(66, 110)(67, 109)(68, 120)(69, 105)(70, 118)(71, 115)(72, 104)(73, 111)(74, 102)(75, 119)(76, 112)(77, 113)(78, 114)(79, 117)(80, 116)

MAP           : A4.292
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 5 ]
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)^5 >
CTG (small)   : <20, 4>
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.3^-1 * x.4)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, x.3^3 * x.4 * x.3, (x.4 * x.1^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 144)(22, 155)(23, 152)(24, 141)(25, 148)(26, 151)(27, 156)(28, 145)(29, 160)(30, 153)(31, 146)(32, 143)(33, 150)(34, 159)(35, 142)(36, 147)(37, 158)(38, 157)(39, 154)(40, 149)(41, 138)(42, 129)(43, 134)(44, 133)(45, 130)(46, 125)(47, 122)(48, 131)(49, 126)(50, 121)(51, 140)(52, 137)(53, 128)(54, 127)(55, 136)(56, 139)(57, 124)(58, 123)(59, 132)(60, 135)(61, 109)(62, 118)(63, 105)(64, 116)(65, 107)(66, 114)(67, 101)(68, 112)(69, 103)(70, 102)(71, 117)(72, 120)(73, 119)(74, 110)(75, 113)(76, 108)(77, 115)(78, 106)(79, 111)(80, 104)

MAP           : A4.293
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 5 ]
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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4^-1 * x.3)^2, (x.2 * x.3)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 151)(22, 152)(23, 153)(24, 154)(25, 155)(26, 156)(27, 157)(28, 158)(29, 159)(30, 160)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 132)(42, 131)(43, 136)(44, 125)(45, 124)(46, 133)(47, 140)(48, 129)(49, 128)(50, 137)(51, 122)(52, 121)(53, 126)(54, 135)(55, 134)(56, 123)(57, 130)(58, 139)(59, 138)(60, 127)(61, 103)(62, 106)(63, 107)(64, 108)(65, 101)(66, 110)(67, 109)(68, 120)(69, 105)(70, 118)(71, 115)(72, 104)(73, 111)(74, 102)(75, 119)(76, 112)(77, 113)(78, 114)(79, 117)(80, 116)

MAP           : A4.294
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 52)(22, 51)(23, 56)(24, 47)(25, 48)(26, 55)(27, 60)(28, 59)(29, 46)(30, 43)(31, 58)(32, 57)(33, 41)(34, 42)(35, 53)(36, 54)(37, 44)(38, 45)(39, 50)(40, 49)(61, 102)(62, 101)(63, 106)(64, 105)(65, 104)(66, 103)(67, 108)(68, 107)(69, 110)(70, 109)(71, 112)(72, 111)(73, 114)(74, 113)(75, 116)(76, 115)(77, 118)(78, 117)(79, 120)(80, 119)(121, 154)(122, 153)(123, 149)(124, 158)(125, 157)(126, 150)(127, 145)(128, 144)(129, 159)(130, 160)(131, 141)(132, 142)(133, 156)(134, 155)(135, 143)(136, 146)(137, 151)(138, 152)(139, 147)(140, 148)

MAP           : A4.295
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 46)(22, 43)(23, 48)(24, 41)(25, 42)(26, 47)(27, 52)(28, 51)(29, 44)(30, 45)(31, 56)(32, 55)(33, 49)(34, 50)(35, 60)(36, 59)(37, 53)(38, 54)(39, 58)(40, 57)(61, 102)(62, 101)(63, 106)(64, 105)(65, 104)(66, 103)(67, 108)(68, 107)(69, 110)(70, 109)(71, 112)(72, 111)(73, 114)(74, 113)(75, 116)(76, 115)(77, 118)(78, 117)(79, 120)(80, 119)(121, 145)(122, 144)(123, 141)(124, 150)(125, 149)(126, 142)(127, 143)(128, 146)(129, 154)(130, 153)(131, 147)(132, 148)(133, 158)(134, 157)(135, 151)(136, 152)(137, 159)(138, 160)(139, 155)(140, 156)

MAP           : A4.296
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 44)(22, 45)(23, 42)(24, 49)(25, 50)(26, 41)(27, 46)(28, 43)(29, 53)(30, 54)(31, 48)(32, 47)(33, 57)(34, 58)(35, 52)(36, 51)(37, 60)(38, 59)(39, 56)(40, 55)(61, 119)(62, 120)(63, 117)(64, 116)(65, 115)(66, 118)(67, 114)(68, 113)(69, 111)(70, 112)(71, 109)(72, 110)(73, 108)(74, 107)(75, 105)(76, 104)(77, 103)(78, 106)(79, 101)(80, 102)(121, 158)(122, 157)(123, 153)(124, 159)(125, 160)(126, 154)(127, 150)(128, 149)(129, 156)(130, 155)(131, 144)(132, 145)(133, 151)(134, 152)(135, 142)(136, 141)(137, 148)(138, 147)(139, 146)(140, 143)

MAP           : A4.297
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 53)(22, 54)(23, 50)(24, 57)(25, 58)(26, 49)(27, 44)(28, 45)(29, 60)(30, 59)(31, 42)(32, 41)(33, 55)(34, 56)(35, 46)(36, 43)(37, 52)(38, 51)(39, 48)(40, 47)(61, 119)(62, 120)(63, 117)(64, 116)(65, 115)(66, 118)(67, 114)(68, 113)(69, 111)(70, 112)(71, 109)(72, 110)(73, 108)(74, 107)(75, 105)(76, 104)(77, 103)(78, 106)(79, 101)(80, 102)(121, 150)(122, 149)(123, 144)(124, 154)(125, 153)(126, 145)(127, 142)(128, 141)(129, 158)(130, 157)(131, 146)(132, 143)(133, 159)(134, 160)(135, 148)(136, 147)(137, 156)(138, 155)(139, 152)(140, 151)

MAP           : A4.298
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^2, (x.3, x.2^-1), (x.3 * x.4^-1)^2, x.3 * x.2^-1 * x.3^4, x.3^2 * x.2 * x.3^2 * x.2^2 * x.3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 126)(42, 123)(43, 130)(44, 139)(45, 122)(46, 127)(47, 138)(48, 137)(49, 134)(50, 129)(51, 124)(52, 135)(53, 132)(54, 121)(55, 128)(56, 131)(57, 136)(58, 125)(59, 140)(60, 133)(61, 111)(62, 112)(63, 113)(64, 114)(65, 115)(66, 116)(67, 117)(68, 118)(69, 119)(70, 120)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)

MAP           : A4.299
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 10, 4, 2 ]
UNIGROUP      : < u.1, u.2 | u.2^4, (u.1^-1 * u.2^-1)^2, u.1^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2 | x.2^4, (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^10 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 41, 81, 121)(2, 42, 82, 122)(3, 43, 83, 123)(4, 44, 84, 124)(5, 45, 85, 125)(6, 46, 86, 126)(7, 47, 87, 127)(8, 48, 88, 128)(9, 49, 89, 129)(10, 50, 90, 130)(11, 51, 91, 131)(12, 52, 92, 132)(13, 53, 93, 133)(14, 54, 94, 134)(15, 55, 95, 135)(16, 56, 96, 136)(17, 57, 97, 137)(18, 58, 98, 138)(19, 59, 99, 139)(20, 60, 100, 140)(21, 61, 101, 141)(22, 62, 102, 142)(23, 63, 103, 143)(24, 64, 104, 144)(25, 65, 105, 145)(26, 66, 106, 146)(27, 67, 107, 147)(28, 68, 108, 148)(29, 69, 109, 149)(30, 70, 110, 150)(31, 71, 111, 151)(32, 72, 112, 152)(33, 73, 113, 153)(34, 74, 114, 154)(35, 75, 115, 155)(36, 76, 116, 156)(37, 77, 117, 157)(38, 78, 118, 158)(39, 79, 119, 159)(40, 80, 120, 160)
L = (1, 42)(2, 45)(3, 61)(4, 41)(5, 50)(6, 69)(7, 64)(8, 62)(9, 44)(10, 54)(11, 73)(12, 65)(13, 49)(14, 58)(15, 77)(16, 70)(17, 53)(18, 57)(19, 78)(20, 74)(21, 46)(22, 47)(23, 68)(24, 51)(25, 43)(26, 67)(27, 63)(28, 72)(29, 55)(30, 48)(31, 66)(32, 76)(33, 59)(34, 52)(35, 71)(36, 80)(37, 60)(38, 56)(39, 75)(40, 79)(81, 123)(82, 128)(83, 147)(84, 127)(85, 132)(86, 151)(87, 146)(88, 143)(89, 126)(90, 136)(91, 155)(92, 148)(93, 131)(94, 140)(95, 159)(96, 152)(97, 135)(98, 139)(99, 160)(100, 156)(101, 124)(102, 121)(103, 145)(104, 129)(105, 122)(106, 141)(107, 142)(108, 150)(109, 133)(110, 125)(111, 144)(112, 154)(113, 137)(114, 130)(115, 149)(116, 158)(117, 138)(118, 134)(119, 153)(120, 157)

MAP           : A4.300
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 46)(22, 43)(23, 48)(24, 41)(25, 42)(26, 47)(27, 52)(28, 51)(29, 44)(30, 45)(31, 56)(32, 55)(33, 49)(34, 50)(35, 60)(36, 59)(37, 53)(38, 54)(39, 58)(40, 57)(61, 119)(62, 120)(63, 117)(64, 116)(65, 115)(66, 118)(67, 114)(68, 113)(69, 111)(70, 112)(71, 109)(72, 110)(73, 108)(74, 107)(75, 105)(76, 104)(77, 103)(78, 106)(79, 101)(80, 102)(121, 156)(122, 155)(123, 160)(124, 151)(125, 152)(126, 159)(127, 158)(128, 157)(129, 148)(130, 147)(131, 153)(132, 154)(133, 143)(134, 146)(135, 150)(136, 149)(137, 142)(138, 141)(139, 144)(140, 145)

MAP           : A4.301
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^2, (x.3, x.2^-1), (x.3 * x.4^-1)^2, x.3 * x.2^-1 * x.3^4, x.3^2 * x.2 * x.3^2 * x.2^2 * x.3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 138)(42, 129)(43, 134)(44, 133)(45, 130)(46, 125)(47, 122)(48, 131)(49, 126)(50, 121)(51, 140)(52, 137)(53, 128)(54, 127)(55, 136)(56, 139)(57, 124)(58, 123)(59, 132)(60, 135)(61, 111)(62, 112)(63, 113)(64, 114)(65, 115)(66, 116)(67, 117)(68, 118)(69, 119)(70, 120)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)

MAP           : A4.302
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
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.4^-1, x.2^-1), (x.1 * x.2^-1)^2, (x.2 * x.3)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 144)(22, 155)(23, 152)(24, 141)(25, 148)(26, 151)(27, 156)(28, 145)(29, 160)(30, 153)(31, 146)(32, 143)(33, 150)(34, 159)(35, 142)(36, 147)(37, 158)(38, 157)(39, 154)(40, 149)(41, 136)(42, 133)(43, 140)(44, 129)(45, 132)(46, 137)(47, 128)(48, 127)(49, 124)(50, 139)(51, 134)(52, 125)(53, 122)(54, 131)(55, 138)(56, 121)(57, 126)(58, 135)(59, 130)(60, 123)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)

MAP           : A4.303
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
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.2 * x.4 * x.2)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2^-1 * x.4 * x.2^-1 * x.4 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 144)(22, 155)(23, 152)(24, 141)(25, 148)(26, 151)(27, 156)(28, 145)(29, 160)(30, 153)(31, 146)(32, 143)(33, 150)(34, 159)(35, 142)(36, 147)(37, 158)(38, 157)(39, 154)(40, 149)(41, 136)(42, 133)(43, 140)(44, 129)(45, 132)(46, 137)(47, 128)(48, 127)(49, 124)(50, 139)(51, 134)(52, 125)(53, 122)(54, 131)(55, 138)(56, 121)(57, 126)(58, 135)(59, 130)(60, 123)(61, 113)(62, 116)(63, 117)(64, 118)(65, 111)(66, 120)(67, 119)(68, 110)(69, 115)(70, 108)(71, 105)(72, 114)(73, 101)(74, 112)(75, 109)(76, 102)(77, 103)(78, 104)(79, 107)(80, 106)

MAP           : A4.304
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
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.4^-1, x.2^-1), (x.1 * x.2^-1)^2, (x.2 * x.3)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 144)(22, 155)(23, 152)(24, 141)(25, 148)(26, 151)(27, 156)(28, 145)(29, 160)(30, 153)(31, 146)(32, 143)(33, 150)(34, 159)(35, 142)(36, 147)(37, 158)(38, 157)(39, 154)(40, 149)(41, 128)(42, 139)(43, 124)(44, 123)(45, 140)(46, 135)(47, 132)(48, 121)(49, 136)(50, 131)(51, 130)(52, 127)(53, 138)(54, 137)(55, 126)(56, 129)(57, 134)(58, 133)(59, 122)(60, 125)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)

MAP           : A4.305
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
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.2 * x.4 * x.2)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2^-1 * x.4 * x.2^-1 * x.4 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 144)(22, 155)(23, 152)(24, 141)(25, 148)(26, 151)(27, 156)(28, 145)(29, 160)(30, 153)(31, 146)(32, 143)(33, 150)(34, 159)(35, 142)(36, 147)(37, 158)(38, 157)(39, 154)(40, 149)(41, 128)(42, 139)(43, 124)(44, 123)(45, 140)(46, 135)(47, 132)(48, 121)(49, 136)(50, 131)(51, 130)(52, 127)(53, 138)(54, 137)(55, 126)(56, 129)(57, 134)(58, 133)(59, 122)(60, 125)(61, 119)(62, 108)(63, 115)(64, 106)(65, 117)(66, 104)(67, 111)(68, 102)(69, 113)(70, 112)(71, 107)(72, 110)(73, 109)(74, 120)(75, 103)(76, 118)(77, 105)(78, 116)(79, 101)(80, 114)

MAP           : A4.306
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
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.4^-1, x.2^-1), (x.1 * x.2^-1)^2, (x.2 * x.3)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 151)(22, 152)(23, 153)(24, 154)(25, 155)(26, 156)(27, 157)(28, 158)(29, 159)(30, 160)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 137)(42, 140)(43, 139)(44, 130)(45, 133)(46, 128)(47, 135)(48, 126)(49, 131)(50, 124)(51, 129)(52, 138)(53, 125)(54, 136)(55, 127)(56, 134)(57, 121)(58, 132)(59, 123)(60, 122)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)

MAP           : A4.307
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
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.2 * x.4 * x.2)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2^-1 * x.4 * x.2^-1 * x.4 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 151)(22, 152)(23, 153)(24, 154)(25, 155)(26, 156)(27, 157)(28, 158)(29, 159)(30, 160)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 137)(42, 140)(43, 139)(44, 130)(45, 133)(46, 128)(47, 135)(48, 126)(49, 131)(50, 124)(51, 129)(52, 138)(53, 125)(54, 136)(55, 127)(56, 134)(57, 121)(58, 132)(59, 123)(60, 122)(61, 120)(62, 117)(63, 108)(64, 107)(65, 116)(66, 119)(67, 104)(68, 103)(69, 112)(70, 115)(71, 118)(72, 109)(73, 114)(74, 113)(75, 110)(76, 105)(77, 102)(78, 111)(79, 106)(80, 101)

MAP           : A4.308
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
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.4^-1, x.2^-1), (x.1 * x.2^-1)^2, (x.2 * x.3)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 151)(22, 152)(23, 153)(24, 154)(25, 155)(26, 156)(27, 157)(28, 158)(29, 159)(30, 160)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 135)(42, 124)(43, 131)(44, 122)(45, 139)(46, 132)(47, 133)(48, 134)(49, 137)(50, 136)(51, 123)(52, 126)(53, 127)(54, 128)(55, 121)(56, 130)(57, 129)(58, 140)(59, 125)(60, 138)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)

MAP           : A4.309
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 48)(22, 47)(23, 52)(24, 43)(25, 46)(26, 51)(27, 56)(28, 55)(29, 42)(30, 41)(31, 60)(32, 59)(33, 45)(34, 44)(35, 58)(36, 57)(37, 50)(38, 49)(39, 53)(40, 54)(61, 120)(62, 119)(63, 118)(64, 115)(65, 116)(66, 117)(67, 113)(68, 114)(69, 112)(70, 111)(71, 110)(72, 109)(73, 107)(74, 108)(75, 104)(76, 105)(77, 106)(78, 103)(79, 102)(80, 101)(121, 151)(122, 152)(123, 155)(124, 148)(125, 147)(126, 156)(127, 159)(128, 160)(129, 143)(130, 146)(131, 157)(132, 158)(133, 142)(134, 141)(135, 154)(136, 153)(137, 145)(138, 144)(139, 149)(140, 150)

MAP           : A4.310
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 58)(22, 57)(23, 53)(24, 59)(25, 60)(26, 54)(27, 50)(28, 49)(29, 56)(30, 55)(31, 44)(32, 45)(33, 51)(34, 52)(35, 42)(36, 41)(37, 48)(38, 47)(39, 46)(40, 43)(61, 120)(62, 119)(63, 118)(64, 115)(65, 116)(66, 117)(67, 113)(68, 114)(69, 112)(70, 111)(71, 110)(72, 109)(73, 107)(74, 108)(75, 104)(76, 105)(77, 106)(78, 103)(79, 102)(80, 101)(121, 145)(122, 144)(123, 141)(124, 150)(125, 149)(126, 142)(127, 143)(128, 146)(129, 154)(130, 153)(131, 147)(132, 148)(133, 158)(134, 157)(135, 151)(136, 152)(137, 159)(138, 160)(139, 155)(140, 156)

MAP           : A4.311
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 56)(22, 55)(23, 60)(24, 51)(25, 52)(26, 59)(27, 58)(28, 57)(29, 48)(30, 47)(31, 53)(32, 54)(33, 43)(34, 46)(35, 50)(36, 49)(37, 42)(38, 41)(39, 44)(40, 45)(61, 120)(62, 119)(63, 118)(64, 115)(65, 116)(66, 117)(67, 113)(68, 114)(69, 112)(70, 111)(71, 110)(72, 109)(73, 107)(74, 108)(75, 104)(76, 105)(77, 106)(78, 103)(79, 102)(80, 101)(121, 143)(122, 146)(123, 147)(124, 142)(125, 141)(126, 148)(127, 151)(128, 152)(129, 145)(130, 144)(131, 155)(132, 156)(133, 150)(134, 149)(135, 159)(136, 160)(137, 154)(138, 153)(139, 157)(140, 158)

MAP           : A4.312
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 50)(22, 49)(23, 44)(24, 54)(25, 53)(26, 45)(27, 42)(28, 41)(29, 58)(30, 57)(31, 46)(32, 43)(33, 59)(34, 60)(35, 48)(36, 47)(37, 56)(38, 55)(39, 52)(40, 51)(61, 120)(62, 119)(63, 118)(64, 115)(65, 116)(66, 117)(67, 113)(68, 114)(69, 112)(70, 111)(71, 110)(72, 109)(73, 107)(74, 108)(75, 104)(76, 105)(77, 106)(78, 103)(79, 102)(80, 101)(121, 154)(122, 153)(123, 149)(124, 158)(125, 157)(126, 150)(127, 145)(128, 144)(129, 159)(130, 160)(131, 141)(132, 142)(133, 156)(134, 155)(135, 143)(136, 146)(137, 151)(138, 152)(139, 147)(140, 148)

MAP           : A4.313
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, x.4 * x.2 * x.4^-1 * x.2, (x.1 * x.2)^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 131)(42, 132)(43, 133)(44, 134)(45, 135)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 115)(62, 104)(63, 111)(64, 102)(65, 119)(66, 112)(67, 113)(68, 114)(69, 117)(70, 116)(71, 103)(72, 106)(73, 107)(74, 108)(75, 101)(76, 110)(77, 109)(78, 120)(79, 105)(80, 118)

MAP           : A4.314
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2^-1 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 143)(22, 146)(23, 147)(24, 148)(25, 141)(26, 150)(27, 149)(28, 160)(29, 145)(30, 158)(31, 155)(32, 144)(33, 151)(34, 142)(35, 159)(36, 152)(37, 153)(38, 154)(39, 157)(40, 156)(41, 124)(42, 135)(43, 132)(44, 121)(45, 128)(46, 131)(47, 136)(48, 125)(49, 140)(50, 133)(51, 126)(52, 123)(53, 130)(54, 139)(55, 122)(56, 127)(57, 138)(58, 137)(59, 134)(60, 129)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)

MAP           : A4.315
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 143)(22, 146)(23, 147)(24, 148)(25, 141)(26, 150)(27, 149)(28, 160)(29, 145)(30, 158)(31, 155)(32, 144)(33, 151)(34, 142)(35, 159)(36, 152)(37, 153)(38, 154)(39, 157)(40, 156)(41, 124)(42, 135)(43, 132)(44, 121)(45, 128)(46, 131)(47, 136)(48, 125)(49, 140)(50, 133)(51, 126)(52, 123)(53, 130)(54, 139)(55, 122)(56, 127)(57, 138)(58, 137)(59, 134)(60, 129)(61, 115)(62, 104)(63, 111)(64, 102)(65, 119)(66, 112)(67, 113)(68, 114)(69, 117)(70, 116)(71, 103)(72, 106)(73, 107)(74, 108)(75, 101)(76, 110)(77, 109)(78, 120)(79, 105)(80, 118)

MAP           : A4.316
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2^-1 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 143)(22, 146)(23, 147)(24, 148)(25, 141)(26, 150)(27, 149)(28, 160)(29, 145)(30, 158)(31, 155)(32, 144)(33, 151)(34, 142)(35, 159)(36, 152)(37, 153)(38, 154)(39, 157)(40, 156)(41, 131)(42, 132)(43, 133)(44, 134)(45, 135)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)

MAP           : A4.317
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 143)(22, 146)(23, 147)(24, 148)(25, 141)(26, 150)(27, 149)(28, 160)(29, 145)(30, 158)(31, 155)(32, 144)(33, 151)(34, 142)(35, 159)(36, 152)(37, 153)(38, 154)(39, 157)(40, 156)(41, 131)(42, 132)(43, 133)(44, 134)(45, 135)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 112)(62, 111)(63, 116)(64, 105)(65, 104)(66, 113)(67, 120)(68, 109)(69, 108)(70, 117)(71, 102)(72, 101)(73, 106)(74, 115)(75, 114)(76, 103)(77, 110)(78, 119)(79, 118)(80, 107)

MAP           : A4.318
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2 * x.2^-2, (x.4 * x.1^-1)^2, (x.3 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.2^-1 * x.4 * x.2^-1 * x.4^-1, x.2^5, (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 143)(22, 146)(23, 147)(24, 148)(25, 141)(26, 150)(27, 149)(28, 160)(29, 145)(30, 158)(31, 155)(32, 144)(33, 151)(34, 142)(35, 159)(36, 152)(37, 153)(38, 154)(39, 157)(40, 156)(41, 126)(42, 123)(43, 130)(44, 139)(45, 122)(46, 127)(47, 138)(48, 137)(49, 134)(50, 129)(51, 124)(52, 135)(53, 132)(54, 121)(55, 128)(56, 131)(57, 136)(58, 125)(59, 140)(60, 133)(61, 104)(62, 115)(63, 112)(64, 101)(65, 108)(66, 111)(67, 116)(68, 105)(69, 120)(70, 113)(71, 106)(72, 103)(73, 110)(74, 119)(75, 102)(76, 107)(77, 118)(78, 117)(79, 114)(80, 109)

MAP           : A4.319
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2 * x.2^-2, (x.4 * x.1^-1)^2, (x.3 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.2^-1 * x.4 * x.2^-1 * x.4^-1, x.2^5, (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 143)(22, 146)(23, 147)(24, 148)(25, 141)(26, 150)(27, 149)(28, 160)(29, 145)(30, 158)(31, 155)(32, 144)(33, 151)(34, 142)(35, 159)(36, 152)(37, 153)(38, 154)(39, 157)(40, 156)(41, 126)(42, 123)(43, 130)(44, 139)(45, 122)(46, 127)(47, 138)(48, 137)(49, 134)(50, 129)(51, 124)(52, 135)(53, 132)(54, 121)(55, 128)(56, 131)(57, 136)(58, 125)(59, 140)(60, 133)(61, 111)(62, 112)(63, 113)(64, 114)(65, 115)(66, 116)(67, 117)(68, 118)(69, 119)(70, 120)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)

MAP           : A4.320
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, (x.4^-1, x.3^-1), x.4 * x.3^-5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 151)(22, 152)(23, 153)(24, 154)(25, 155)(26, 156)(27, 157)(28, 158)(29, 159)(30, 160)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 126)(42, 123)(43, 130)(44, 139)(45, 122)(46, 127)(47, 138)(48, 137)(49, 134)(50, 129)(51, 124)(52, 135)(53, 132)(54, 121)(55, 128)(56, 131)(57, 136)(58, 125)(59, 140)(60, 133)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)

MAP           : A4.321
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, (x.4^-1, x.3^-1), x.4 * x.3^-5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 151)(22, 152)(23, 153)(24, 154)(25, 155)(26, 156)(27, 157)(28, 158)(29, 159)(30, 160)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 138)(42, 129)(43, 134)(44, 133)(45, 130)(46, 125)(47, 122)(48, 131)(49, 126)(50, 121)(51, 140)(52, 137)(53, 128)(54, 127)(55, 136)(56, 139)(57, 124)(58, 123)(59, 132)(60, 135)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)

MAP           : A4.322
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 147)(22, 150)(23, 149)(24, 160)(25, 143)(26, 158)(27, 145)(28, 156)(29, 141)(30, 154)(31, 159)(32, 148)(33, 155)(34, 146)(35, 157)(36, 144)(37, 151)(38, 142)(39, 153)(40, 152)(41, 131)(42, 132)(43, 133)(44, 134)(45, 135)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 112)(62, 111)(63, 116)(64, 105)(65, 104)(66, 113)(67, 120)(68, 109)(69, 108)(70, 117)(71, 102)(72, 101)(73, 106)(74, 115)(75, 114)(76, 103)(77, 110)(78, 119)(79, 118)(80, 107)

MAP           : A4.323
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2 * x.2^-2, (x.4 * x.1^-1)^2, (x.3 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.2^-1 * x.4 * x.2^-1 * x.4^-1, x.2^5, (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 147)(22, 150)(23, 149)(24, 160)(25, 143)(26, 158)(27, 145)(28, 156)(29, 141)(30, 154)(31, 159)(32, 148)(33, 155)(34, 146)(35, 157)(36, 144)(37, 151)(38, 142)(39, 153)(40, 152)(41, 130)(42, 127)(43, 138)(44, 137)(45, 126)(46, 129)(47, 134)(48, 133)(49, 122)(50, 125)(51, 128)(52, 139)(53, 124)(54, 123)(55, 140)(56, 135)(57, 132)(58, 121)(59, 136)(60, 131)(61, 104)(62, 115)(63, 112)(64, 101)(65, 108)(66, 111)(67, 116)(68, 105)(69, 120)(70, 113)(71, 106)(72, 103)(73, 110)(74, 119)(75, 102)(76, 107)(77, 118)(78, 117)(79, 114)(80, 109)

MAP           : A4.324
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2 * x.2^-2, (x.4 * x.1^-1)^2, (x.3 * x.2^-1)^2, (x.3 * x.4^-1)^2, x.2^-1 * x.4 * x.2^-1 * x.4^-1, x.2^5, (x.1 * x.2^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 147)(22, 150)(23, 149)(24, 160)(25, 143)(26, 158)(27, 145)(28, 156)(29, 141)(30, 154)(31, 159)(32, 148)(33, 155)(34, 146)(35, 157)(36, 144)(37, 151)(38, 142)(39, 153)(40, 152)(41, 130)(42, 127)(43, 138)(44, 137)(45, 126)(46, 129)(47, 134)(48, 133)(49, 122)(50, 125)(51, 128)(52, 139)(53, 124)(54, 123)(55, 140)(56, 135)(57, 132)(58, 121)(59, 136)(60, 131)(61, 111)(62, 112)(63, 113)(64, 114)(65, 115)(66, 116)(67, 117)(68, 118)(69, 119)(70, 120)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)

MAP           : A4.325
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 5 ]
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)^5 >
CTG (small)   : <20, 4>
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)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 124)(42, 135)(43, 132)(44, 121)(45, 128)(46, 131)(47, 136)(48, 125)(49, 140)(50, 133)(51, 126)(52, 123)(53, 130)(54, 139)(55, 122)(56, 127)(57, 138)(58, 137)(59, 134)(60, 129)(61, 103)(62, 106)(63, 107)(64, 108)(65, 101)(66, 110)(67, 109)(68, 120)(69, 105)(70, 118)(71, 115)(72, 104)(73, 111)(74, 102)(75, 119)(76, 112)(77, 113)(78, 114)(79, 117)(80, 116)

MAP           : A4.326
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 5 ]
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)^5 >
CTG (small)   : <20, 4>
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)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 124)(42, 135)(43, 132)(44, 121)(45, 128)(46, 131)(47, 136)(48, 125)(49, 140)(50, 133)(51, 126)(52, 123)(53, 130)(54, 139)(55, 122)(56, 127)(57, 138)(58, 137)(59, 134)(60, 129)(61, 107)(62, 110)(63, 109)(64, 120)(65, 103)(66, 118)(67, 105)(68, 116)(69, 101)(70, 114)(71, 119)(72, 108)(73, 115)(74, 106)(75, 117)(76, 104)(77, 111)(78, 102)(79, 113)(80, 112)

MAP           : A4.327
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 5 ]
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)^5 >
CTG (small)   : <20, 4>
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)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 131)(42, 132)(43, 133)(44, 134)(45, 135)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 103)(62, 106)(63, 107)(64, 108)(65, 101)(66, 110)(67, 109)(68, 120)(69, 105)(70, 118)(71, 115)(72, 104)(73, 111)(74, 102)(75, 119)(76, 112)(77, 113)(78, 114)(79, 117)(80, 116)

MAP           : A4.328
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 5 ]
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)^5 >
CTG (small)   : <20, 4>
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)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 131)(42, 132)(43, 133)(44, 134)(45, 135)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 107)(62, 110)(63, 109)(64, 120)(65, 103)(66, 118)(67, 105)(68, 116)(69, 101)(70, 114)(71, 119)(72, 108)(73, 115)(74, 106)(75, 117)(76, 104)(77, 111)(78, 102)(79, 113)(80, 112)

MAP           : A4.329
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, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.5^-1 * x.1, x.5 * x.2 * x.5^-1 * x.2, x.4^-1 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^2, x.4 * x.5^-1 * x.1 * x.2, (x.3 * x.4^-1)^5 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 147)(22, 150)(23, 149)(24, 160)(25, 143)(26, 158)(27, 145)(28, 156)(29, 141)(30, 154)(31, 159)(32, 148)(33, 155)(34, 146)(35, 157)(36, 144)(37, 151)(38, 142)(39, 153)(40, 152)(41, 51)(42, 52)(43, 53)(44, 54)(45, 55)(46, 56)(47, 57)(48, 58)(49, 59)(50, 60)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)(121, 128)(122, 139)(123, 124)(125, 140)(126, 135)(127, 132)(129, 136)(130, 131)(133, 138)(134, 137)

MAP           : A4.330
NOTES         : type II, reflexible, isomorphic to A4.329.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, x.5^-1 * x.2 * x.4 * x.1, (x.3 * x.4)^2, x.5^-1 * x.4 * x.2 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.3^-1)^5 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 44)(42, 55)(43, 52)(45, 48)(46, 51)(47, 56)(49, 60)(50, 53)(54, 59)(57, 58)(61, 105)(62, 114)(63, 101)(64, 112)(65, 109)(66, 102)(67, 103)(68, 104)(69, 107)(70, 106)(71, 113)(72, 116)(73, 117)(74, 118)(75, 111)(76, 120)(77, 119)(78, 110)(79, 115)(80, 108)(121, 131)(122, 132)(123, 133)(124, 134)(125, 135)(126, 136)(127, 137)(128, 138)(129, 139)(130, 140)

MAP           : A4.331
NOTES         : type II, reflexible, isomorphic to A4.329.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, x.5^-1 * x.2 * x.4 * x.1, (x.3 * x.4)^2, x.5^-1 * x.4 * x.2 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.3^-1)^5 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 44)(42, 55)(43, 52)(45, 48)(46, 51)(47, 56)(49, 60)(50, 53)(54, 59)(57, 58)(61, 107)(62, 110)(63, 109)(64, 120)(65, 103)(66, 118)(67, 105)(68, 116)(69, 101)(70, 114)(71, 119)(72, 108)(73, 115)(74, 106)(75, 117)(76, 104)(77, 111)(78, 102)(79, 113)(80, 112)(121, 137)(122, 140)(123, 139)(124, 130)(125, 133)(126, 128)(127, 135)(129, 131)(132, 138)(134, 136)

MAP           : A4.332
NOTES         : type II, reflexible, isomorphic to A4.329.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, x.5^-1 * x.2 * x.4 * x.1, (x.3 * x.4)^2, x.5^-1 * x.4 * x.2 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.3^-1)^5 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 51)(42, 52)(43, 53)(44, 54)(45, 55)(46, 56)(47, 57)(48, 58)(49, 59)(50, 60)(61, 103)(62, 106)(63, 107)(64, 108)(65, 101)(66, 110)(67, 109)(68, 120)(69, 105)(70, 118)(71, 115)(72, 104)(73, 111)(74, 102)(75, 119)(76, 112)(77, 113)(78, 114)(79, 117)(80, 116)(121, 124)(122, 135)(123, 132)(125, 128)(126, 131)(127, 136)(129, 140)(130, 133)(134, 139)(137, 138)

MAP           : A4.333
NOTES         : type II, reflexible, isomorphic to A4.329.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^2, x.5^-1 * x.2 * x.4 * x.1, (x.3 * x.4)^2, x.5^-1 * x.4 * x.2 * x.1, x.5 * x.4 * x.1 * x.2, (x.5 * x.3^-1)^5 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 51)(42, 52)(43, 53)(44, 54)(45, 55)(46, 56)(47, 57)(48, 58)(49, 59)(50, 60)(61, 107)(62, 110)(63, 109)(64, 120)(65, 103)(66, 118)(67, 105)(68, 116)(69, 101)(70, 114)(71, 119)(72, 108)(73, 115)(74, 106)(75, 117)(76, 104)(77, 111)(78, 102)(79, 113)(80, 112)(121, 128)(122, 139)(123, 124)(125, 140)(126, 135)(127, 132)(129, 136)(130, 131)(133, 138)(134, 137)

MAP           : A4.334
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 5 ]
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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4^-1 * x.3)^2, (x.2 * x.3)^2, x.4^-1 * x.2 * x.4^-1 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 151)(22, 152)(23, 153)(24, 154)(25, 155)(26, 156)(27, 157)(28, 158)(29, 159)(30, 160)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 132)(42, 131)(43, 136)(44, 125)(45, 124)(46, 133)(47, 140)(48, 129)(49, 128)(50, 137)(51, 122)(52, 121)(53, 126)(54, 135)(55, 134)(56, 123)(57, 130)(58, 139)(59, 138)(60, 127)(61, 107)(62, 110)(63, 109)(64, 120)(65, 103)(66, 118)(67, 105)(68, 116)(69, 101)(70, 114)(71, 119)(72, 108)(73, 115)(74, 106)(75, 117)(76, 104)(77, 111)(78, 102)(79, 113)(80, 112)

MAP           : A4.335
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 5 ]
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)^5 >
CTG (small)   : <20, 4>
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.3^-1 * x.4)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, x.3^3 * x.4 * x.3, (x.4 * x.1^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 151)(22, 152)(23, 153)(24, 154)(25, 155)(26, 156)(27, 157)(28, 158)(29, 159)(30, 160)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 126)(42, 123)(43, 130)(44, 139)(45, 122)(46, 127)(47, 138)(48, 137)(49, 134)(50, 129)(51, 124)(52, 135)(53, 132)(54, 121)(55, 128)(56, 131)(57, 136)(58, 125)(59, 140)(60, 133)(61, 103)(62, 106)(63, 107)(64, 108)(65, 101)(66, 110)(67, 109)(68, 120)(69, 105)(70, 118)(71, 115)(72, 104)(73, 111)(74, 102)(75, 119)(76, 112)(77, 113)(78, 114)(79, 117)(80, 116)

MAP           : A4.336
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 5 ]
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)^5 >
CTG (small)   : <20, 4>
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.3^-1 * x.4)^2, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, x.3^3 * x.4 * x.3, (x.4 * x.1^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 151)(22, 152)(23, 153)(24, 154)(25, 155)(26, 156)(27, 157)(28, 158)(29, 159)(30, 160)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 138)(42, 129)(43, 134)(44, 133)(45, 130)(46, 125)(47, 122)(48, 131)(49, 126)(50, 121)(51, 140)(52, 137)(53, 128)(54, 127)(55, 136)(56, 139)(57, 124)(58, 123)(59, 132)(60, 135)(61, 109)(62, 118)(63, 105)(64, 116)(65, 107)(66, 114)(67, 101)(68, 112)(69, 103)(70, 102)(71, 117)(72, 120)(73, 119)(74, 110)(75, 113)(76, 108)(77, 115)(78, 106)(79, 111)(80, 104)

MAP           : A4.337
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^2, (x.3, x.2^-1), (x.3 * x.4^-1)^2, x.3 * x.2^-1 * x.3^4, x.3^2 * x.2 * x.3^2 * x.2^2 * x.3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 126)(42, 123)(43, 130)(44, 139)(45, 122)(46, 127)(47, 138)(48, 137)(49, 134)(50, 129)(51, 124)(52, 135)(53, 132)(54, 121)(55, 128)(56, 131)(57, 136)(58, 125)(59, 140)(60, 133)(61, 104)(62, 115)(63, 112)(64, 101)(65, 108)(66, 111)(67, 116)(68, 105)(69, 120)(70, 113)(71, 106)(72, 103)(73, 110)(74, 119)(75, 102)(76, 107)(77, 118)(78, 117)(79, 114)(80, 109)

MAP           : A4.338
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, x.4 * x.2 * x.4^-1 * x.2, (x.1 * x.2)^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 124)(42, 135)(43, 132)(44, 121)(45, 128)(46, 131)(47, 136)(48, 125)(49, 140)(50, 133)(51, 126)(52, 123)(53, 130)(54, 139)(55, 122)(56, 127)(57, 138)(58, 137)(59, 134)(60, 129)(61, 108)(62, 119)(63, 104)(64, 103)(65, 120)(66, 115)(67, 112)(68, 101)(69, 116)(70, 111)(71, 110)(72, 107)(73, 118)(74, 117)(75, 106)(76, 109)(77, 114)(78, 113)(79, 102)(80, 105)

MAP           : A4.339
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {10, 10, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 10, 10, 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.2^10, u.4^10 >
CTG (small)   : <20, 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.2^10, x.4^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 52)(22, 51)(23, 56)(24, 47)(25, 48)(26, 55)(27, 60)(28, 59)(29, 46)(30, 43)(31, 58)(32, 57)(33, 41)(34, 42)(35, 53)(36, 54)(37, 44)(38, 45)(39, 50)(40, 49)(61, 119)(62, 120)(63, 117)(64, 116)(65, 115)(66, 118)(67, 114)(68, 113)(69, 111)(70, 112)(71, 109)(72, 110)(73, 108)(74, 107)(75, 105)(76, 104)(77, 103)(78, 106)(79, 101)(80, 102)(121, 148)(122, 147)(123, 152)(124, 143)(125, 146)(126, 151)(127, 156)(128, 155)(129, 142)(130, 141)(131, 160)(132, 159)(133, 145)(134, 144)(135, 158)(136, 157)(137, 150)(138, 149)(139, 153)(140, 154)

MAP           : A4.340
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, (x.4 * x.1^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^2, (x.3, x.2^-1), (x.3 * x.4^-1)^2, x.3 * x.2^-1 * x.3^4, x.3^2 * x.2 * x.3^2 * x.2^2 * x.3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 138)(42, 129)(43, 134)(44, 133)(45, 130)(46, 125)(47, 122)(48, 131)(49, 126)(50, 121)(51, 140)(52, 137)(53, 128)(54, 127)(55, 136)(56, 139)(57, 124)(58, 123)(59, 132)(60, 135)(61, 104)(62, 115)(63, 112)(64, 101)(65, 108)(66, 111)(67, 116)(68, 105)(69, 120)(70, 113)(71, 106)(72, 103)(73, 110)(74, 119)(75, 102)(76, 107)(77, 118)(78, 117)(79, 114)(80, 109)

MAP           : A4.341
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 5, 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)^5 >
CTG (small)   : <20, 4>
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.2 * x.4^-1 * x.3 * x.4^-1 * x.2 * x.4^-1 * 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, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 144)(22, 155)(23, 152)(24, 141)(25, 148)(26, 151)(27, 156)(28, 145)(29, 160)(30, 153)(31, 146)(32, 143)(33, 150)(34, 159)(35, 142)(36, 147)(37, 158)(38, 157)(39, 154)(40, 149)(41, 135)(42, 124)(43, 131)(44, 122)(45, 139)(46, 132)(47, 133)(48, 134)(49, 137)(50, 136)(51, 123)(52, 126)(53, 127)(54, 128)(55, 121)(56, 130)(57, 129)(58, 140)(59, 125)(60, 138)(61, 111)(62, 112)(63, 113)(64, 114)(65, 115)(66, 116)(67, 117)(68, 118)(69, 119)(70, 120)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)

MAP           : A4.342
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 5, 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)^5 >
CTG (small)   : <20, 4>
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.2 * x.4^-1 * x.3 * x.4^-1 * x.2 * x.4^-1 * 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, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 144)(22, 155)(23, 152)(24, 141)(25, 148)(26, 151)(27, 156)(28, 145)(29, 160)(30, 153)(31, 146)(32, 143)(33, 150)(34, 159)(35, 142)(36, 147)(37, 158)(38, 157)(39, 154)(40, 149)(41, 135)(42, 124)(43, 131)(44, 122)(45, 139)(46, 132)(47, 133)(48, 134)(49, 137)(50, 136)(51, 123)(52, 126)(53, 127)(54, 128)(55, 121)(56, 130)(57, 129)(58, 140)(59, 125)(60, 138)(61, 117)(62, 120)(63, 119)(64, 110)(65, 113)(66, 108)(67, 115)(68, 106)(69, 111)(70, 104)(71, 109)(72, 118)(73, 105)(74, 116)(75, 107)(76, 114)(77, 101)(78, 112)(79, 103)(80, 102)

MAP           : A4.343
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, (x.4^-1, x.3^-1), x.4 * x.3^-5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 144)(22, 155)(23, 152)(24, 141)(25, 148)(26, 151)(27, 156)(28, 145)(29, 160)(30, 153)(31, 146)(32, 143)(33, 150)(34, 159)(35, 142)(36, 147)(37, 158)(38, 157)(39, 154)(40, 149)(41, 126)(42, 123)(43, 130)(44, 139)(45, 122)(46, 127)(47, 138)(48, 137)(49, 134)(50, 129)(51, 124)(52, 135)(53, 132)(54, 121)(55, 128)(56, 131)(57, 136)(58, 125)(59, 140)(60, 133)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)

MAP           : A4.344
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^4, (x.4 * x.1^-1)^2, (x.4^-1, x.2^-1), (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, (x.4^-1, x.3^-1), x.4 * x.3^-5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 144)(22, 155)(23, 152)(24, 141)(25, 148)(26, 151)(27, 156)(28, 145)(29, 160)(30, 153)(31, 146)(32, 143)(33, 150)(34, 159)(35, 142)(36, 147)(37, 158)(38, 157)(39, 154)(40, 149)(41, 138)(42, 129)(43, 134)(44, 133)(45, 130)(46, 125)(47, 122)(48, 131)(49, 126)(50, 121)(51, 140)(52, 137)(53, 128)(54, 127)(55, 136)(56, 139)(57, 124)(58, 123)(59, 132)(60, 135)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)

MAP           : A4.345
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 5, 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)^5 >
CTG (small)   : <20, 4>
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.2 * x.4^-1 * x.3 * x.4^-1 * x.2 * x.4^-1 * 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, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 151)(22, 152)(23, 153)(24, 154)(25, 155)(26, 156)(27, 157)(28, 158)(29, 159)(30, 160)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 132)(42, 131)(43, 136)(44, 125)(45, 124)(46, 133)(47, 140)(48, 129)(49, 128)(50, 137)(51, 122)(52, 121)(53, 126)(54, 135)(55, 134)(56, 123)(57, 130)(58, 139)(59, 138)(60, 127)(61, 104)(62, 115)(63, 112)(64, 101)(65, 108)(66, 111)(67, 116)(68, 105)(69, 120)(70, 113)(71, 106)(72, 103)(73, 110)(74, 119)(75, 102)(76, 107)(77, 118)(78, 117)(79, 114)(80, 109)

MAP           : A4.346
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 5, 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)^5 >
CTG (small)   : <20, 4>
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.2 * x.4^-1 * x.3 * x.4^-1 * x.2 * x.4^-1 * 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, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 151)(22, 152)(23, 153)(24, 154)(25, 155)(26, 156)(27, 157)(28, 158)(29, 159)(30, 160)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 132)(42, 131)(43, 136)(44, 125)(45, 124)(46, 133)(47, 140)(48, 129)(49, 128)(50, 137)(51, 122)(52, 121)(53, 126)(54, 135)(55, 134)(56, 123)(57, 130)(58, 139)(59, 138)(60, 127)(61, 108)(62, 119)(63, 104)(64, 103)(65, 120)(66, 115)(67, 112)(68, 101)(69, 116)(70, 111)(71, 110)(72, 107)(73, 118)(74, 117)(75, 106)(76, 109)(77, 114)(78, 113)(79, 102)(80, 105)

MAP           : A4.347
NOTES         : type II, reflexible, isomorphic to A4.329.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.5^-1 * x.1, x.5 * x.2 * x.5^-1 * x.2, x.4^-1 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^2, x.4 * x.5^-1 * x.1 * x.2, (x.3 * x.4^-1)^5 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 147)(22, 150)(23, 149)(24, 160)(25, 143)(26, 158)(27, 145)(28, 156)(29, 141)(30, 154)(31, 159)(32, 148)(33, 155)(34, 146)(35, 157)(36, 144)(37, 151)(38, 142)(39, 153)(40, 152)(41, 44)(42, 55)(43, 52)(45, 48)(46, 51)(47, 56)(49, 60)(50, 53)(54, 59)(57, 58)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)(121, 137)(122, 140)(123, 139)(124, 130)(125, 133)(126, 128)(127, 135)(129, 131)(132, 138)(134, 136)

MAP           : A4.348
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, x.4 * x.2 * x.4^-1 * x.2, (x.1 * x.2)^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 131)(42, 132)(43, 133)(44, 134)(45, 135)(46, 136)(47, 137)(48, 138)(49, 139)(50, 140)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 117)(62, 120)(63, 119)(64, 110)(65, 113)(66, 108)(67, 115)(68, 106)(69, 111)(70, 104)(71, 109)(72, 118)(73, 105)(74, 116)(75, 107)(76, 114)(77, 101)(78, 112)(79, 103)(80, 102)

MAP           : A4.349
NOTES         : type II, reflexible, isomorphic to A4.279.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 5, 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)^5 >
CTG (small)   : <20, 4>
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.2 * x.4 * x.2)^2, x.4 * x.2 * x.3 * x.4 * x.2^-1 * x.3, x.2^-1 * x.4 * x.2^-1 * x.4 * x.2 * x.3 * x.2 * x.3 * x.2 * x.3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 151)(22, 152)(23, 153)(24, 154)(25, 155)(26, 156)(27, 157)(28, 158)(29, 159)(30, 160)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 135)(42, 124)(43, 131)(44, 122)(45, 139)(46, 132)(47, 133)(48, 134)(49, 137)(50, 136)(51, 123)(52, 126)(53, 127)(54, 128)(55, 121)(56, 130)(57, 129)(58, 140)(59, 125)(60, 138)(61, 104)(62, 115)(63, 112)(64, 101)(65, 108)(66, 111)(67, 116)(68, 105)(69, 120)(70, 113)(71, 106)(72, 103)(73, 110)(74, 119)(75, 102)(76, 107)(77, 118)(78, 117)(79, 114)(80, 109)

MAP           : A4.350
NOTES         : type I, reflexible, isomorphic to Med2({4,10}), isomorphic to A4.259.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.2^2, x.4 * x.2 * x.4^-1 * x.2, (x.1 * x.2)^2, (x.2 * x.3)^2, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^5 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 142)(22, 141)(23, 146)(24, 155)(25, 154)(26, 143)(27, 150)(28, 159)(29, 158)(30, 147)(31, 152)(32, 151)(33, 156)(34, 145)(35, 144)(36, 153)(37, 160)(38, 149)(39, 148)(40, 157)(41, 124)(42, 135)(43, 132)(44, 121)(45, 128)(46, 131)(47, 136)(48, 125)(49, 140)(50, 133)(51, 126)(52, 123)(53, 130)(54, 139)(55, 122)(56, 127)(57, 138)(58, 137)(59, 134)(60, 129)(61, 116)(62, 113)(63, 120)(64, 109)(65, 112)(66, 117)(67, 108)(68, 107)(69, 104)(70, 119)(71, 114)(72, 105)(73, 102)(74, 111)(75, 118)(76, 101)(77, 106)(78, 115)(79, 110)(80, 103)

MAP           : A4.351
NOTES         : type II, reflexible, isomorphic to A4.329.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.5^-1 * x.1, x.5 * x.2 * x.5^-1 * x.2, x.4^-1 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^2, x.4 * x.5^-1 * x.1 * x.2, (x.3 * x.4^-1)^5 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 143)(22, 146)(23, 147)(24, 148)(25, 141)(26, 150)(27, 149)(28, 160)(29, 145)(30, 158)(31, 155)(32, 144)(33, 151)(34, 142)(35, 159)(36, 152)(37, 153)(38, 154)(39, 157)(40, 156)(41, 44)(42, 55)(43, 52)(45, 48)(46, 51)(47, 56)(49, 60)(50, 53)(54, 59)(57, 58)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)(121, 139)(122, 128)(123, 135)(124, 126)(125, 137)(127, 131)(129, 133)(130, 132)(134, 140)(136, 138)

MAP           : A4.352
NOTES         : type II, reflexible, isomorphic to A4.329.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 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)^5 >
CTG (small)   : <20, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^-1 * x.2 * x.5^-1 * x.1, x.5 * x.2 * x.5^-1 * x.2, x.4^-1 * x.5 * x.2 * x.1, (x.5 * x.3^-1)^2, x.4 * x.5^-1 * x.1 * x.2, (x.3 * x.4^-1)^5 >
SCHREIER VEC. : (x.3, x.4, x.1, x.5)
LOCAL TYPE    : (4, 4, 4, 10)
#DARTS        : 160
R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)(81, 101, 121, 141)(82, 102, 122, 142)(83, 103, 123, 143)(84, 104, 124, 144)(85, 105, 125, 145)(86, 106, 126, 146)(87, 107, 127, 147)(88, 108, 128, 148)(89, 109, 129, 149)(90, 110, 130, 150)(91, 111, 131, 151)(92, 112, 132, 152)(93, 113, 133, 153)(94, 114, 134, 154)(95, 115, 135, 155)(96, 116, 136, 156)(97, 117, 137, 157)(98, 118, 138, 158)(99, 119, 139, 159)(100, 120, 140, 160)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 143)(22, 146)(23, 147)(24, 148)(25, 141)(26, 150)(27, 149)(28, 160)(29, 145)(30, 158)(31, 155)(32, 144)(33, 151)(34, 142)(35, 159)(36, 152)(37, 153)(38, 154)(39, 157)(40, 156)(41, 51)(42, 52)(43, 53)(44, 54)(45, 55)(46, 56)(47, 57)(48, 58)(49, 59)(50, 60)(61, 102)(62, 101)(63, 106)(64, 115)(65, 114)(66, 103)(67, 110)(68, 119)(69, 118)(70, 107)(71, 112)(72, 111)(73, 116)(74, 105)(75, 104)(76, 113)(77, 120)(78, 109)(79, 108)(80, 117)(121, 124)(122, 135)(123, 132)(125, 128)(126, 131)(127, 136)(129, 140)(130, 133)(134, 139)(137, 138)

MAP           : A4.353
NOTES         : type I, 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, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 126)(38, 112)(39, 121)(40, 120)(41, 116)(42, 113)(43, 117)(44, 114)(45, 118)(46, 115)(47, 111)(48, 110)(49, 119)(50, 123)(51, 125)(52, 109)(53, 122)(54, 124)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.354
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 110)(38, 113)(39, 115)(40, 116)(41, 109)(42, 124)(43, 123)(44, 126)(45, 125)(46, 122)(47, 118)(48, 114)(49, 117)(50, 119)(51, 111)(52, 120)(53, 121)(54, 112)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.355
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 116)(38, 126)(39, 125)(40, 124)(41, 112)(42, 110)(43, 121)(44, 120)(45, 119)(46, 111)(47, 123)(48, 109)(49, 122)(50, 115)(51, 117)(52, 113)(53, 118)(54, 114)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.356
NOTES         : type I, 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, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.2^3, x.3^3, (x.3 * x.4)^2, (x.4 * x.1^-1)^2, (x.3^-1, x.2^-1), x.2 * x.3^-1 * x.4 * x.2^-1 * x.4, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 127)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 134)(33, 135)(34, 136)(35, 137)(36, 138)(37, 118)(38, 111)(39, 120)(40, 119)(41, 115)(42, 122)(43, 124)(44, 117)(45, 126)(46, 125)(47, 121)(48, 110)(49, 112)(50, 123)(51, 114)(52, 113)(53, 109)(54, 116)(55, 92)(56, 91)(57, 107)(58, 105)(59, 108)(60, 103)(61, 99)(62, 106)(63, 97)(64, 102)(65, 104)(66, 100)(67, 96)(68, 101)(69, 94)(70, 98)(71, 93)(72, 95)

MAP           : A4.357
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, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 2 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.2^3, x.3^3, (x.4 * x.3^-1)^2, (x.4 * x.1^-1)^2, (x.3^-1, x.2^-1), x.2 * x.4 * x.3^-1 * x.2^-1 * x.4, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 127)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 134)(33, 135)(34, 136)(35, 137)(36, 138)(37, 125)(38, 120)(39, 110)(40, 121)(41, 124)(42, 123)(43, 113)(44, 126)(45, 116)(46, 109)(47, 112)(48, 111)(49, 119)(50, 114)(51, 122)(52, 115)(53, 118)(54, 117)(55, 92)(56, 91)(57, 107)(58, 105)(59, 108)(60, 103)(61, 99)(62, 106)(63, 97)(64, 102)(65, 104)(66, 100)(67, 96)(68, 101)(69, 94)(70, 98)(71, 93)(72, 95)

MAP           : A4.358
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3 * x.2 * x.3, (x.4 * x.3^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3^-1)^2, (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 141)(21, 132)(22, 131)(23, 127)(24, 134)(25, 136)(26, 129)(27, 138)(28, 137)(29, 133)(30, 140)(31, 142)(32, 135)(33, 144)(34, 143)(35, 139)(36, 128)(37, 114)(38, 119)(39, 112)(40, 116)(41, 111)(42, 113)(43, 110)(44, 109)(45, 125)(46, 123)(47, 126)(48, 121)(49, 117)(50, 124)(51, 115)(52, 120)(53, 122)(54, 118)(55, 103)(56, 104)(57, 105)(58, 106)(59, 107)(60, 108)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)

MAP           : A4.359
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3 * x.2 * x.3, (x.4 * x.3^-1)^2, (x.4^-1, x.2^-1), (x.2 * x.3^-1)^2, (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 131)(20, 144)(21, 134)(22, 127)(23, 130)(24, 129)(25, 137)(26, 132)(27, 140)(28, 133)(29, 136)(30, 135)(31, 143)(32, 138)(33, 128)(34, 139)(35, 142)(36, 141)(37, 116)(38, 115)(39, 113)(40, 111)(41, 114)(42, 109)(43, 123)(44, 112)(45, 121)(46, 126)(47, 110)(48, 124)(49, 120)(50, 125)(51, 118)(52, 122)(53, 117)(54, 119)(55, 97)(56, 98)(57, 99)(58, 100)(59, 101)(60, 102)(61, 103)(62, 104)(63, 105)(64, 106)(65, 107)(66, 108)(67, 91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96)

MAP           : A4.360
NOTES         : type I, reflexible, isomorphic to A4.356.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.4^3, x.3^3, (x.1 * x.2)^2, (x.2 * x.3^-1)^2, (x.4, x.3^-1), x.2 * x.3^-1 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 118)(38, 111)(39, 120)(40, 119)(41, 115)(42, 122)(43, 124)(44, 117)(45, 126)(46, 125)(47, 121)(48, 110)(49, 112)(50, 123)(51, 114)(52, 113)(53, 109)(54, 116)(55, 106)(56, 99)(57, 108)(58, 107)(59, 103)(60, 92)(61, 94)(62, 105)(63, 96)(64, 95)(65, 91)(66, 98)(67, 100)(68, 93)(69, 102)(70, 101)(71, 97)(72, 104)

MAP           : A4.361
NOTES         : type I, reflexible, isomorphic to A4.356.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.4^3, x.3^3, (x.1 * x.2)^2, (x.2 * x.3^-1)^2, (x.4, x.3^-1), x.2 * x.3^-1 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 118)(38, 111)(39, 120)(40, 119)(41, 115)(42, 122)(43, 124)(44, 117)(45, 126)(46, 125)(47, 121)(48, 110)(49, 112)(50, 123)(51, 114)(52, 113)(53, 109)(54, 116)(55, 103)(56, 104)(57, 105)(58, 106)(59, 107)(60, 108)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)

MAP           : A4.362
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.4^3, x.3^3, (x.1 * x.2)^2, (x.3, x.4^-1), (x.2 * x.3^-1)^2, x.2 * x.3^-1 * x.4^-1 * x.2 * x.4, (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 118)(38, 111)(39, 120)(40, 119)(41, 115)(42, 122)(43, 124)(44, 117)(45, 126)(46, 125)(47, 121)(48, 110)(49, 112)(50, 123)(51, 114)(52, 113)(53, 109)(54, 116)(55, 101)(56, 96)(57, 104)(58, 97)(59, 100)(60, 99)(61, 107)(62, 102)(63, 92)(64, 103)(65, 106)(66, 105)(67, 95)(68, 108)(69, 98)(70, 91)(71, 94)(72, 93)

MAP           : A4.363
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)

MAP           : A4.364
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)

MAP           : A4.365
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 108)(56, 94)(57, 103)(58, 102)(59, 98)(60, 95)(61, 99)(62, 96)(63, 100)(64, 97)(65, 93)(66, 92)(67, 101)(68, 105)(69, 107)(70, 91)(71, 104)(72, 106)

MAP           : A4.366
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.2 * x.3^3, x.3^-3 * x.2, (x.4 * x.1^-1)^2, (x.1 * x.2)^2, x.3 * x.4 * x.3^2 * x.4^-1 * x.2, x.4 * x.2 * x.4 * x.2 * x.4^-1 * x.2, (x.3 * x.4^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 123)(38, 112)(39, 121)(40, 126)(41, 110)(42, 124)(43, 120)(44, 125)(45, 118)(46, 122)(47, 117)(48, 119)(49, 116)(50, 115)(51, 113)(52, 111)(53, 114)(54, 109)(55, 102)(56, 107)(57, 100)(58, 104)(59, 99)(60, 101)(61, 98)(62, 97)(63, 95)(64, 93)(65, 96)(66, 91)(67, 105)(68, 94)(69, 103)(70, 108)(71, 92)(72, 106)

MAP           : A4.367
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.2^3, x.3^3, (x.4 * x.3^-1)^2, (x.4 * x.1^-1)^2, (x.3^-1, x.2^-1), x.2 * x.4 * x.3^-1 * x.2^-1 * x.4, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 118)(38, 111)(39, 120)(40, 119)(41, 115)(42, 122)(43, 124)(44, 117)(45, 126)(46, 125)(47, 121)(48, 110)(49, 112)(50, 123)(51, 114)(52, 113)(53, 109)(54, 116)(55, 92)(56, 91)(57, 107)(58, 105)(59, 108)(60, 103)(61, 99)(62, 106)(63, 97)(64, 102)(65, 104)(66, 100)(67, 96)(68, 101)(69, 94)(70, 98)(71, 93)(72, 95)

MAP           : A4.368
NOTES         : type I, reflexible, isomorphic to A4.356.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.2^3, x.3^3, (x.3 * x.4)^2, (x.4 * x.1^-1)^2, (x.3^-1, x.2^-1), x.2 * x.3^-1 * x.4 * x.2^-1 * x.4, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 125)(38, 120)(39, 110)(40, 121)(41, 124)(42, 123)(43, 113)(44, 126)(45, 116)(46, 109)(47, 112)(48, 111)(49, 119)(50, 114)(51, 122)(52, 115)(53, 118)(54, 117)(55, 92)(56, 91)(57, 107)(58, 105)(59, 108)(60, 103)(61, 99)(62, 106)(63, 97)(64, 102)(65, 104)(66, 100)(67, 96)(68, 101)(69, 94)(70, 98)(71, 93)(72, 95)

MAP           : A4.369
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 96)(56, 106)(57, 104)(58, 91)(59, 102)(60, 94)(61, 101)(62, 92)(63, 93)(64, 103)(65, 107)(66, 108)(67, 105)(68, 99)(69, 100)(70, 98)(71, 97)(72, 95)

MAP           : A4.370
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 112)(38, 116)(39, 117)(40, 114)(41, 126)(42, 109)(43, 125)(44, 124)(45, 122)(46, 123)(47, 115)(48, 113)(49, 118)(50, 111)(51, 121)(52, 110)(53, 119)(54, 120)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.371
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 114)(38, 124)(39, 122)(40, 109)(41, 120)(42, 112)(43, 119)(44, 110)(45, 111)(46, 121)(47, 125)(48, 126)(49, 123)(50, 117)(51, 118)(52, 116)(53, 115)(54, 113)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.372
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 116)(38, 126)(39, 125)(40, 124)(41, 112)(42, 110)(43, 121)(44, 120)(45, 119)(46, 111)(47, 123)(48, 109)(49, 122)(50, 115)(51, 117)(52, 113)(53, 118)(54, 114)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.373
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 120)(38, 114)(39, 118)(40, 113)(41, 124)(42, 126)(43, 122)(44, 109)(45, 123)(46, 125)(47, 117)(48, 116)(49, 115)(50, 121)(51, 119)(52, 112)(53, 111)(54, 110)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.374
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 124)(38, 120)(39, 119)(40, 110)(41, 114)(42, 116)(43, 118)(44, 113)(45, 115)(46, 117)(47, 121)(48, 112)(49, 111)(50, 125)(51, 122)(52, 126)(53, 123)(54, 109)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.375
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 126)(38, 112)(39, 121)(40, 120)(41, 116)(42, 113)(43, 117)(44, 114)(45, 118)(46, 115)(47, 111)(48, 110)(49, 119)(50, 123)(51, 125)(52, 109)(53, 122)(54, 124)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.376
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 110)(38, 113)(39, 115)(40, 116)(41, 109)(42, 124)(43, 123)(44, 126)(45, 125)(46, 122)(47, 118)(48, 114)(49, 117)(50, 119)(51, 111)(52, 120)(53, 121)(54, 112)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.377
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 113)(38, 109)(39, 123)(40, 126)(41, 110)(42, 120)(43, 111)(44, 112)(45, 121)(46, 119)(47, 122)(48, 124)(49, 125)(50, 118)(51, 115)(52, 114)(53, 117)(54, 116)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.378
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 115)(38, 111)(39, 110)(40, 119)(41, 123)(42, 125)(43, 109)(44, 122)(45, 124)(46, 126)(47, 112)(48, 121)(49, 120)(50, 116)(51, 113)(52, 117)(53, 114)(54, 118)(55, 99)(56, 103)(57, 94)(58, 93)(59, 107)(60, 104)(61, 108)(62, 105)(63, 91)(64, 106)(65, 102)(66, 101)(67, 92)(68, 96)(69, 98)(70, 100)(71, 95)(72, 97)

MAP           : A4.379
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 115)(38, 111)(39, 110)(40, 119)(41, 123)(42, 125)(43, 109)(44, 122)(45, 124)(46, 126)(47, 112)(48, 121)(49, 120)(50, 116)(51, 113)(52, 117)(53, 114)(54, 118)(55, 107)(56, 99)(57, 98)(58, 97)(59, 103)(60, 101)(61, 94)(62, 93)(63, 92)(64, 102)(65, 96)(66, 100)(67, 95)(68, 106)(69, 108)(70, 104)(71, 91)(72, 105)

MAP           : A4.380
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 120)(38, 114)(39, 118)(40, 113)(41, 124)(42, 126)(43, 122)(44, 109)(45, 123)(46, 125)(47, 117)(48, 116)(49, 115)(50, 121)(51, 119)(52, 112)(53, 111)(54, 110)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.381
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 124)(38, 120)(39, 119)(40, 110)(41, 114)(42, 116)(43, 118)(44, 113)(45, 115)(46, 117)(47, 121)(48, 112)(49, 111)(50, 125)(51, 122)(52, 126)(53, 123)(54, 109)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.382
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 126)(38, 112)(39, 121)(40, 120)(41, 116)(42, 113)(43, 117)(44, 114)(45, 118)(46, 115)(47, 111)(48, 110)(49, 119)(50, 123)(51, 125)(52, 109)(53, 122)(54, 124)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.383
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 110)(38, 113)(39, 115)(40, 116)(41, 109)(42, 124)(43, 123)(44, 126)(45, 125)(46, 122)(47, 118)(48, 114)(49, 117)(50, 119)(51, 111)(52, 120)(53, 121)(54, 112)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.384
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 113)(38, 109)(39, 123)(40, 126)(41, 110)(42, 120)(43, 111)(44, 112)(45, 121)(46, 119)(47, 122)(48, 124)(49, 125)(50, 118)(51, 115)(52, 114)(53, 117)(54, 116)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.385
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 112)(38, 116)(39, 117)(40, 114)(41, 126)(42, 109)(43, 125)(44, 124)(45, 122)(46, 123)(47, 115)(48, 113)(49, 118)(50, 111)(51, 121)(52, 110)(53, 119)(54, 120)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.386
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 114)(38, 124)(39, 122)(40, 109)(41, 120)(42, 112)(43, 119)(44, 110)(45, 111)(46, 121)(47, 125)(48, 126)(49, 123)(50, 117)(51, 118)(52, 116)(53, 115)(54, 113)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.387
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 124)(38, 120)(39, 119)(40, 110)(41, 114)(42, 116)(43, 118)(44, 113)(45, 115)(46, 117)(47, 121)(48, 112)(49, 111)(50, 125)(51, 122)(52, 126)(53, 123)(54, 109)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.388
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2 * x.4, (x.2 * x.3^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 116)(38, 115)(39, 113)(40, 111)(41, 114)(42, 109)(43, 123)(44, 112)(45, 121)(46, 126)(47, 110)(48, 124)(49, 120)(50, 125)(51, 118)(52, 122)(53, 117)(54, 119)(55, 95)(56, 108)(57, 98)(58, 91)(59, 94)(60, 93)(61, 101)(62, 96)(63, 104)(64, 97)(65, 100)(66, 99)(67, 107)(68, 102)(69, 92)(70, 103)(71, 106)(72, 105)

MAP           : A4.389
NOTES         : type I, reflexible, isomorphic to A4.356.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, (x.2 * x.3^-1)^2, x.2^-1 * x.3^-1 * x.4 * x.3, x.3^-1 * x.2 * x.3 * x.4^-1, (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 116)(38, 115)(39, 113)(40, 111)(41, 114)(42, 109)(43, 123)(44, 112)(45, 121)(46, 126)(47, 110)(48, 124)(49, 120)(50, 125)(51, 118)(52, 122)(53, 117)(54, 119)(55, 106)(56, 99)(57, 108)(58, 107)(59, 103)(60, 92)(61, 94)(62, 105)(63, 96)(64, 95)(65, 91)(66, 98)(67, 100)(68, 93)(69, 102)(70, 101)(71, 97)(72, 104)

MAP           : A4.390
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 113)(38, 109)(39, 123)(40, 126)(41, 110)(42, 120)(43, 111)(44, 112)(45, 121)(46, 119)(47, 122)(48, 124)(49, 125)(50, 118)(51, 115)(52, 114)(53, 117)(54, 116)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.391
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 112)(38, 116)(39, 117)(40, 114)(41, 126)(42, 109)(43, 125)(44, 124)(45, 122)(46, 123)(47, 115)(48, 113)(49, 118)(50, 111)(51, 121)(52, 110)(53, 119)(54, 120)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.392
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 114)(38, 124)(39, 122)(40, 109)(41, 120)(42, 112)(43, 119)(44, 110)(45, 111)(46, 121)(47, 125)(48, 126)(49, 123)(50, 117)(51, 118)(52, 116)(53, 115)(54, 113)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.393
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 116)(38, 126)(39, 125)(40, 124)(41, 112)(42, 110)(43, 121)(44, 120)(45, 119)(46, 111)(47, 123)(48, 109)(49, 122)(50, 115)(51, 117)(52, 113)(53, 118)(54, 114)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.394
NOTES         : type I, reflexible, isomorphic to A4.356.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2 * x.2^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3 * x.4^-1, x.4 * x.3 * x.2^-1 * x.3^-1, x.3 * x.2 * x.3 * x.2 * x.3 * x.2^-1, x.3 * x.4^-1 * x.2^-2 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 116)(38, 115)(39, 113)(40, 111)(41, 114)(42, 109)(43, 123)(44, 112)(45, 121)(46, 126)(47, 110)(48, 124)(49, 120)(50, 125)(51, 118)(52, 122)(53, 117)(54, 119)(55, 102)(56, 107)(57, 100)(58, 104)(59, 99)(60, 101)(61, 98)(62, 97)(63, 95)(64, 93)(65, 96)(66, 91)(67, 105)(68, 94)(69, 103)(70, 108)(71, 92)(72, 106)

MAP           : A4.395
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.3^-3 * x.4, x.3^2 * x.4 * x.3, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.3 * x.2 * x.3^2 * x.2^-1 * x.4, x.4 * x.3^-1 * x.2 * x.4 * x.3 * x.2^-1, x.4 * x.2 * x.4 * x.2^-1 * x.4 * x.2^-1, (x.2 * x.3^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 116)(38, 115)(39, 113)(40, 111)(41, 114)(42, 109)(43, 123)(44, 112)(45, 121)(46, 126)(47, 110)(48, 124)(49, 120)(50, 125)(51, 118)(52, 122)(53, 117)(54, 119)(55, 93)(56, 100)(57, 91)(58, 96)(59, 98)(60, 94)(61, 108)(62, 95)(63, 106)(64, 92)(65, 105)(66, 107)(67, 104)(68, 103)(69, 101)(70, 99)(71, 102)(72, 97)

MAP           : A4.396
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.2 * x.3^3, x.3^-3 * x.2, (x.4 * x.1^-1)^2, (x.1 * x.2)^2, x.3 * x.4 * x.3^2 * x.4^-1 * x.2, x.4 * x.2 * x.4 * x.2 * x.4^-1 * x.2, (x.3 * x.4^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 126)(38, 113)(39, 124)(40, 110)(41, 123)(42, 125)(43, 122)(44, 121)(45, 119)(46, 117)(47, 120)(48, 115)(49, 111)(50, 118)(51, 109)(52, 114)(53, 116)(54, 112)(55, 102)(56, 107)(57, 100)(58, 104)(59, 99)(60, 101)(61, 98)(62, 97)(63, 95)(64, 93)(65, 96)(66, 91)(67, 105)(68, 94)(69, 103)(70, 108)(71, 92)(72, 106)

MAP           : A4.397
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.4, x.3^-1), (x.1 * x.2^-1)^2, (x.4, x.2^-1), (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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 118)(38, 111)(39, 120)(40, 119)(41, 115)(42, 122)(43, 124)(44, 117)(45, 126)(46, 125)(47, 121)(48, 110)(49, 112)(50, 123)(51, 114)(52, 113)(53, 109)(54, 116)(55, 94)(56, 105)(57, 96)(58, 95)(59, 91)(60, 98)(61, 100)(62, 93)(63, 102)(64, 101)(65, 97)(66, 104)(67, 106)(68, 99)(69, 108)(70, 107)(71, 103)(72, 92)

MAP           : A4.398
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.4, x.3^-1), (x.1 * x.2^-1)^2, (x.4, x.2^-1), (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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 118)(38, 111)(39, 120)(40, 119)(41, 115)(42, 122)(43, 124)(44, 117)(45, 126)(46, 125)(47, 121)(48, 110)(49, 112)(50, 123)(51, 114)(52, 113)(53, 109)(54, 116)(55, 95)(56, 108)(57, 98)(58, 91)(59, 94)(60, 93)(61, 101)(62, 96)(63, 104)(64, 97)(65, 100)(66, 99)(67, 107)(68, 102)(69, 92)(70, 103)(71, 106)(72, 105)

MAP           : A4.399
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.4^3, x.3^3, (x.1 * x.2)^2, (x.3, x.4^-1), (x.2 * x.3^-1)^2, x.2 * x.3^-1 * x.4^-1 * x.2 * x.4, (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 118)(38, 111)(39, 120)(40, 119)(41, 115)(42, 122)(43, 124)(44, 117)(45, 126)(46, 125)(47, 121)(48, 110)(49, 112)(50, 123)(51, 114)(52, 113)(53, 109)(54, 116)(55, 97)(56, 98)(57, 99)(58, 100)(59, 101)(60, 102)(61, 103)(62, 104)(63, 105)(64, 106)(65, 107)(66, 108)(67, 91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96)

MAP           : A4.400
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 108)(56, 94)(57, 103)(58, 102)(59, 98)(60, 95)(61, 99)(62, 96)(63, 100)(64, 97)(65, 93)(66, 92)(67, 101)(68, 105)(69, 107)(70, 91)(71, 104)(72, 106)

MAP           : A4.401
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)

MAP           : A4.402
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 95)(56, 91)(57, 105)(58, 108)(59, 92)(60, 102)(61, 93)(62, 94)(63, 103)(64, 101)(65, 104)(66, 106)(67, 107)(68, 100)(69, 97)(70, 96)(71, 99)(72, 98)

MAP           : A4.403
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 119)(38, 122)(39, 124)(40, 125)(41, 118)(42, 115)(43, 114)(44, 117)(45, 116)(46, 113)(47, 109)(48, 123)(49, 126)(50, 110)(51, 120)(52, 111)(53, 112)(54, 121)(55, 100)(56, 101)(57, 102)(58, 103)(59, 104)(60, 105)(61, 106)(62, 107)(63, 108)(64, 91)(65, 92)(66, 93)(67, 94)(68, 95)(69, 96)(70, 97)(71, 98)(72, 99)

MAP           : A4.404
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 110)(38, 113)(39, 115)(40, 116)(41, 109)(42, 124)(43, 123)(44, 126)(45, 125)(46, 122)(47, 118)(48, 114)(49, 117)(50, 119)(51, 111)(52, 120)(53, 121)(54, 112)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)

MAP           : A4.405
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 102)(56, 96)(57, 100)(58, 95)(59, 106)(60, 108)(61, 104)(62, 91)(63, 105)(64, 107)(65, 99)(66, 98)(67, 97)(68, 103)(69, 101)(70, 94)(71, 93)(72, 92)

MAP           : A4.406
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)

MAP           : A4.407
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 95)(56, 91)(57, 105)(58, 108)(59, 92)(60, 102)(61, 93)(62, 94)(63, 103)(64, 101)(65, 104)(66, 106)(67, 107)(68, 100)(69, 97)(70, 96)(71, 99)(72, 98)

MAP           : A4.408
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)

MAP           : A4.409
NOTES         : type I, reflexible, isomorphic to A4.353.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^2 * x.1 * x.3^-2 * x.1, (x.3 * x.1)^3, x.3^6 >
SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 75)(2, 77)(3, 83)(4, 84)(5, 81)(6, 82)(7, 94)(8, 96)(9, 90)(10, 89)(11, 88)(12, 87)(13, 93)(14, 95)(15, 101)(16, 102)(17, 99)(18, 100)(19, 76)(20, 78)(21, 108)(22, 107)(23, 106)(24, 105)(25, 92)(26, 91)(27, 97)(28, 103)(29, 98)(30, 104)(31, 74)(32, 73)(33, 79)(34, 85)(35, 80)(36, 86)(37, 38)(39, 43)(40, 49)(41, 44)(42, 50)(45, 47)(46, 48)(51, 72)(52, 71)(53, 70)(54, 69)(55, 56)(57, 61)(58, 67)(59, 62)(60, 68)(63, 65)(64, 66)(109, 135)(110, 137)(111, 125)(112, 126)(113, 123)(114, 124)(115, 142)(116, 144)(117, 120)(118, 119)(121, 141)(122, 143)(127, 136)(128, 138)(129, 132)(130, 131)(133, 140)(134, 139)

MAP           : A4.410
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)

MAP           : A4.411
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 108)(56, 94)(57, 103)(58, 102)(59, 98)(60, 95)(61, 99)(62, 96)(63, 100)(64, 97)(65, 93)(66, 92)(67, 101)(68, 105)(69, 107)(70, 91)(71, 104)(72, 106)

MAP           : A4.412
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)

MAP           : A4.413
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 95)(56, 91)(57, 105)(58, 108)(59, 92)(60, 102)(61, 93)(62, 94)(63, 103)(64, 101)(65, 104)(66, 106)(67, 107)(68, 100)(69, 97)(70, 96)(71, 99)(72, 98)

MAP           : A4.414
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)

MAP           : A4.415
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 96)(56, 106)(57, 104)(58, 91)(59, 102)(60, 94)(61, 101)(62, 92)(63, 93)(64, 103)(65, 107)(66, 108)(67, 105)(68, 99)(69, 100)(70, 98)(71, 97)(72, 95)

MAP           : A4.416
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)

MAP           : A4.417
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 102)(56, 96)(57, 100)(58, 95)(59, 106)(60, 108)(61, 104)(62, 91)(63, 105)(64, 107)(65, 99)(66, 98)(67, 97)(68, 103)(69, 101)(70, 94)(71, 93)(72, 92)

MAP           : A4.418
NOTES         : type I, reflexible, isomorphic to A4.353.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.2 * x.1, (x.4, x.5^-1), x.4 * x.2 * x.5^-1 * x.1, 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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 106)(56, 99)(57, 108)(58, 107)(59, 103)(60, 92)(61, 94)(62, 105)(63, 96)(64, 95)(65, 91)(66, 98)(67, 100)(68, 93)(69, 102)(70, 101)(71, 97)(72, 104)(109, 110)(111, 125)(112, 123)(113, 126)(114, 121)(115, 117)(116, 124)(118, 120)(119, 122)

MAP           : A4.419
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, 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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^-1 * x.5 * x.2 * x.1, x.4^-1 * x.2 * x.1 * x.5, x.5^-1 * x.1 * x.5 * x.1, x.4^-1 * x.1 * x.4 * 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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 95)(56, 108)(57, 98)(58, 91)(59, 94)(60, 93)(61, 101)(62, 96)(63, 104)(64, 97)(65, 100)(66, 99)(67, 107)(68, 102)(69, 92)(70, 103)(71, 106)(72, 105)(109, 111)(110, 118)(112, 114)(113, 116)(115, 126)(117, 124)(119, 123)(120, 125)(121, 122)

MAP           : A4.420
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 141)(21, 132)(22, 131)(23, 127)(24, 134)(25, 136)(26, 129)(27, 138)(28, 137)(29, 133)(30, 140)(31, 142)(32, 135)(33, 144)(34, 143)(35, 139)(36, 128)(37, 118)(38, 111)(39, 120)(40, 119)(41, 115)(42, 122)(43, 124)(44, 117)(45, 126)(46, 125)(47, 121)(48, 110)(49, 112)(50, 123)(51, 114)(52, 113)(53, 109)(54, 116)(55, 92)(56, 91)(57, 107)(58, 105)(59, 108)(60, 103)(61, 99)(62, 106)(63, 97)(64, 102)(65, 104)(66, 100)(67, 96)(68, 101)(69, 94)(70, 98)(71, 93)(72, 95)

MAP           : A4.421
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 131)(20, 144)(21, 134)(22, 127)(23, 130)(24, 129)(25, 137)(26, 132)(27, 140)(28, 133)(29, 136)(30, 135)(31, 143)(32, 138)(33, 128)(34, 139)(35, 142)(36, 141)(37, 118)(38, 111)(39, 120)(40, 119)(41, 115)(42, 122)(43, 124)(44, 117)(45, 126)(46, 125)(47, 121)(48, 110)(49, 112)(50, 123)(51, 114)(52, 113)(53, 109)(54, 116)(55, 92)(56, 91)(57, 107)(58, 105)(59, 108)(60, 103)(61, 99)(62, 106)(63, 97)(64, 102)(65, 104)(66, 100)(67, 96)(68, 101)(69, 94)(70, 98)(71, 93)(72, 95)

MAP           : A4.422
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 124)(38, 120)(39, 119)(40, 110)(41, 114)(42, 116)(43, 118)(44, 113)(45, 115)(46, 117)(47, 121)(48, 112)(49, 111)(50, 125)(51, 122)(52, 126)(53, 123)(54, 109)(55, 95)(56, 91)(57, 105)(58, 108)(59, 92)(60, 102)(61, 93)(62, 94)(63, 103)(64, 101)(65, 104)(66, 106)(67, 107)(68, 100)(69, 97)(70, 96)(71, 99)(72, 98)

MAP           : A4.423
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 124)(38, 120)(39, 119)(40, 110)(41, 114)(42, 116)(43, 118)(44, 113)(45, 115)(46, 117)(47, 121)(48, 112)(49, 111)(50, 125)(51, 122)(52, 126)(53, 123)(54, 109)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)

MAP           : A4.424
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 124)(38, 120)(39, 119)(40, 110)(41, 114)(42, 116)(43, 118)(44, 113)(45, 115)(46, 117)(47, 121)(48, 112)(49, 111)(50, 125)(51, 122)(52, 126)(53, 123)(54, 109)(55, 96)(56, 106)(57, 104)(58, 91)(59, 102)(60, 94)(61, 101)(62, 92)(63, 93)(64, 103)(65, 107)(66, 108)(67, 105)(68, 99)(69, 100)(70, 98)(71, 97)(72, 95)

MAP           : A4.425
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 124)(38, 120)(39, 119)(40, 110)(41, 114)(42, 116)(43, 118)(44, 113)(45, 115)(46, 117)(47, 121)(48, 112)(49, 111)(50, 125)(51, 122)(52, 126)(53, 123)(54, 109)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)

MAP           : A4.426
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 124)(38, 120)(39, 119)(40, 110)(41, 114)(42, 116)(43, 118)(44, 113)(45, 115)(46, 117)(47, 121)(48, 112)(49, 111)(50, 125)(51, 122)(52, 126)(53, 123)(54, 109)(55, 102)(56, 96)(57, 100)(58, 95)(59, 106)(60, 108)(61, 104)(62, 91)(63, 105)(64, 107)(65, 99)(66, 98)(67, 97)(68, 103)(69, 101)(70, 94)(71, 93)(72, 92)

MAP           : A4.427
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 117)(38, 121)(39, 112)(40, 111)(41, 125)(42, 122)(43, 126)(44, 123)(45, 109)(46, 124)(47, 120)(48, 119)(49, 110)(50, 114)(51, 116)(52, 118)(53, 113)(54, 115)(55, 107)(56, 99)(57, 98)(58, 97)(59, 103)(60, 101)(61, 94)(62, 93)(63, 92)(64, 102)(65, 96)(66, 100)(67, 95)(68, 106)(69, 108)(70, 104)(71, 91)(72, 105)

MAP           : A4.428
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 117)(38, 121)(39, 112)(40, 111)(41, 125)(42, 122)(43, 126)(44, 123)(45, 109)(46, 124)(47, 120)(48, 119)(49, 110)(50, 114)(51, 116)(52, 118)(53, 113)(54, 115)(55, 105)(56, 97)(57, 95)(58, 100)(59, 93)(60, 103)(61, 92)(62, 101)(63, 102)(64, 94)(65, 98)(66, 99)(67, 96)(68, 108)(69, 91)(70, 107)(71, 106)(72, 104)

MAP           : A4.429
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 117)(38, 121)(39, 112)(40, 111)(41, 125)(42, 122)(43, 126)(44, 123)(45, 109)(46, 124)(47, 120)(48, 119)(49, 110)(50, 114)(51, 116)(52, 118)(53, 113)(54, 115)(55, 101)(56, 104)(57, 106)(58, 107)(59, 100)(60, 97)(61, 96)(62, 99)(63, 98)(64, 95)(65, 91)(66, 105)(67, 108)(68, 92)(69, 102)(70, 93)(71, 94)(72, 103)

MAP           : A4.430
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2 * x.4, (x.2 * x.3^-1)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 127)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 134)(33, 135)(34, 136)(35, 137)(36, 138)(37, 114)(38, 119)(39, 112)(40, 116)(41, 111)(42, 113)(43, 110)(44, 109)(45, 125)(46, 123)(47, 126)(48, 121)(49, 117)(50, 124)(51, 115)(52, 120)(53, 122)(54, 118)(55, 94)(56, 105)(57, 96)(58, 95)(59, 91)(60, 98)(61, 100)(62, 93)(63, 102)(64, 101)(65, 97)(66, 104)(67, 106)(68, 99)(69, 108)(70, 107)(71, 103)(72, 92)

MAP           : A4.431
NOTES         : type I, reflexible, isomorphic to A4.356.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, (x.2 * x.3^-1)^2, x.2^-1 * x.3^-1 * x.4 * x.3, x.3^-1 * x.2 * x.3 * x.4^-1, (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 127)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 134)(33, 135)(34, 136)(35, 137)(36, 138)(37, 114)(38, 119)(39, 112)(40, 116)(41, 111)(42, 113)(43, 110)(44, 109)(45, 125)(46, 123)(47, 126)(48, 121)(49, 117)(50, 124)(51, 115)(52, 120)(53, 122)(54, 118)(55, 101)(56, 96)(57, 104)(58, 97)(59, 100)(60, 99)(61, 107)(62, 102)(63, 92)(64, 103)(65, 106)(66, 105)(67, 95)(68, 108)(69, 98)(70, 91)(71, 94)(72, 93)

MAP           : A4.432
NOTES         : type I, reflexible, isomorphic to A4.356.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2 * x.2^2, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.3^-1 * x.2 * x.3 * x.4^-1, x.4 * x.3 * x.2^-1 * x.3^-1, x.3 * x.2 * x.3 * x.2 * x.3 * x.2^-1, x.3 * x.4^-1 * x.2^-2 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 114)(38, 119)(39, 112)(40, 116)(41, 111)(42, 113)(43, 110)(44, 109)(45, 125)(46, 123)(47, 126)(48, 121)(49, 117)(50, 124)(51, 115)(52, 120)(53, 122)(54, 118)(55, 102)(56, 107)(57, 100)(58, 104)(59, 99)(60, 101)(61, 98)(62, 97)(63, 95)(64, 93)(65, 96)(66, 91)(67, 105)(68, 94)(69, 103)(70, 108)(71, 92)(72, 106)

MAP           : A4.433
NOTES         : type II, reflexible, isomorphic to A4.357.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.3^-3 * x.4, x.3^2 * x.4 * x.3, (x.4 * x.1^-1)^2, (x.1 * x.2^-1)^2, x.3 * x.2 * x.3^2 * x.2^-1 * x.4, x.4 * x.3^-1 * x.2 * x.4 * x.3 * x.2^-1, x.4 * x.2 * x.4 * x.2^-1 * x.4 * x.2^-1, (x.2 * x.3^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 114)(38, 119)(39, 112)(40, 116)(41, 111)(42, 113)(43, 110)(44, 109)(45, 125)(46, 123)(47, 126)(48, 121)(49, 117)(50, 124)(51, 115)(52, 120)(53, 122)(54, 118)(55, 93)(56, 100)(57, 91)(58, 96)(59, 98)(60, 94)(61, 108)(62, 95)(63, 106)(64, 92)(65, 105)(66, 107)(67, 104)(68, 103)(69, 101)(70, 99)(71, 102)(72, 97)

MAP           : A4.434
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 125)(38, 117)(39, 116)(40, 115)(41, 121)(42, 119)(43, 112)(44, 111)(45, 110)(46, 120)(47, 114)(48, 118)(49, 113)(50, 124)(51, 126)(52, 122)(53, 109)(54, 123)(55, 105)(56, 97)(57, 95)(58, 100)(59, 93)(60, 103)(61, 92)(62, 101)(63, 102)(64, 94)(65, 98)(66, 99)(67, 96)(68, 108)(69, 91)(70, 107)(71, 106)(72, 104)

MAP           : A4.435
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
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.4 * u.1^-1)^2, (u.3 * u.4^-1)^2, (u.1 * u.2^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^3, x.3^3, (x.4 * x.1^-1)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3, x.2^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 120)(38, 114)(39, 118)(40, 113)(41, 124)(42, 126)(43, 122)(44, 109)(45, 123)(46, 125)(47, 117)(48, 116)(49, 115)(50, 121)(51, 119)(52, 112)(53, 111)(54, 110)(55, 93)(56, 105)(57, 91)(58, 104)(59, 97)(60, 99)(61, 95)(62, 100)(63, 96)(64, 98)(65, 108)(66, 107)(67, 106)(68, 94)(69, 92)(70, 103)(71, 102)(72, 101)

MAP           : A4.436
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)

MAP           : A4.437
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 96)(56, 106)(57, 104)(58, 91)(59, 102)(60, 94)(61, 101)(62, 92)(63, 93)(64, 103)(65, 107)(66, 108)(67, 105)(68, 99)(69, 100)(70, 98)(71, 97)(72, 95)

MAP           : A4.438
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)

MAP           : A4.439
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 102)(56, 96)(57, 100)(58, 95)(59, 106)(60, 108)(61, 104)(62, 91)(63, 105)(64, 107)(65, 99)(66, 98)(67, 97)(68, 103)(69, 101)(70, 94)(71, 93)(72, 92)

MAP           : A4.440
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.2 * u.3^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.1 * u.2^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.2 * x.3)^2, (x.3 * x.4^-1)^2, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)

MAP           : A4.441
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 119)(38, 122)(39, 124)(40, 125)(41, 118)(42, 115)(43, 114)(44, 117)(45, 116)(46, 113)(47, 109)(48, 123)(49, 126)(50, 110)(51, 120)(52, 111)(53, 112)(54, 121)(55, 105)(56, 97)(57, 95)(58, 100)(59, 93)(60, 103)(61, 92)(62, 101)(63, 102)(64, 94)(65, 98)(66, 99)(67, 96)(68, 108)(69, 91)(70, 107)(71, 106)(72, 104)

MAP           : A4.442
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 119)(38, 122)(39, 124)(40, 125)(41, 118)(42, 115)(43, 114)(44, 117)(45, 116)(46, 113)(47, 109)(48, 123)(49, 126)(50, 110)(51, 120)(52, 111)(53, 112)(54, 121)(55, 104)(56, 100)(57, 96)(58, 99)(59, 101)(60, 93)(61, 102)(62, 103)(63, 94)(64, 92)(65, 95)(66, 97)(67, 98)(68, 91)(69, 106)(70, 105)(71, 108)(72, 107)

MAP           : A4.443
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 96)(56, 106)(57, 104)(58, 91)(59, 102)(60, 94)(61, 101)(62, 92)(63, 93)(64, 103)(65, 107)(66, 108)(67, 105)(68, 99)(69, 100)(70, 98)(71, 97)(72, 95)(109, 125)(110, 117)(111, 116)(112, 115)(113, 121)(114, 119)(118, 120)(122, 124)(123, 126)

MAP           : A4.444
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)(109, 123)(110, 115)(111, 113)(112, 118)(114, 121)(116, 119)(117, 120)(122, 126)(124, 125)

MAP           : A4.445
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 110)(38, 113)(39, 115)(40, 116)(41, 109)(42, 124)(43, 123)(44, 126)(45, 125)(46, 122)(47, 118)(48, 114)(49, 117)(50, 119)(51, 111)(52, 120)(53, 121)(54, 112)(55, 96)(56, 106)(57, 104)(58, 91)(59, 102)(60, 94)(61, 101)(62, 92)(63, 93)(64, 103)(65, 107)(66, 108)(67, 105)(68, 99)(69, 100)(70, 98)(71, 97)(72, 95)

MAP           : A4.446
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)(109, 118)(110, 119)(111, 120)(112, 121)(113, 122)(114, 123)(115, 124)(116, 125)(117, 126)

MAP           : A4.447
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 110)(38, 113)(39, 115)(40, 116)(41, 109)(42, 124)(43, 123)(44, 126)(45, 125)(46, 122)(47, 118)(48, 114)(49, 117)(50, 119)(51, 111)(52, 120)(53, 121)(54, 112)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)

MAP           : A4.448
NOTES         : type I, reflexible, isomorphic to A4.353.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3^-1 * x.2)^2, (x.2 * x.1)^2, x.3^2 * x.1 * x.3^-2 * x.1, (x.3 * x.1)^3, x.3^6 >
SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 76)(2, 78)(3, 108)(4, 107)(5, 106)(6, 105)(7, 92)(8, 91)(9, 97)(10, 103)(11, 98)(12, 104)(13, 74)(14, 73)(15, 79)(16, 85)(17, 80)(18, 86)(19, 75)(20, 77)(21, 83)(22, 84)(23, 81)(24, 82)(25, 94)(26, 96)(27, 90)(28, 89)(29, 88)(30, 87)(31, 93)(32, 95)(33, 101)(34, 102)(35, 99)(36, 100)(37, 46)(38, 48)(39, 42)(40, 41)(43, 50)(44, 49)(45, 55)(47, 56)(51, 67)(52, 61)(53, 68)(54, 62)(57, 71)(58, 72)(59, 69)(60, 70)(63, 66)(64, 65)(109, 110)(111, 115)(112, 121)(113, 116)(114, 122)(117, 119)(118, 120)(123, 144)(124, 143)(125, 142)(126, 141)(127, 128)(129, 133)(130, 139)(131, 134)(132, 140)(135, 137)(136, 138)

MAP           : A4.449
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 110)(38, 113)(39, 115)(40, 116)(41, 109)(42, 124)(43, 123)(44, 126)(45, 125)(46, 122)(47, 118)(48, 114)(49, 117)(50, 119)(51, 111)(52, 120)(53, 121)(54, 112)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)

MAP           : A4.450
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.2 * x.3)^2, (x.3 * x.1 * x.2)^2, x.3^-1 * x.1 * x.3^2 * x.1 * x.3^-1, (x.3 * x.1)^3, x.3^6 >
SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 75)(2, 77)(3, 83)(4, 84)(5, 81)(6, 82)(7, 94)(8, 96)(9, 90)(10, 89)(11, 88)(12, 87)(13, 93)(14, 95)(15, 101)(16, 102)(17, 99)(18, 100)(19, 76)(20, 78)(21, 108)(22, 107)(23, 106)(24, 105)(25, 92)(26, 91)(27, 97)(28, 103)(29, 98)(30, 104)(31, 74)(32, 73)(33, 79)(34, 85)(35, 80)(36, 86)(37, 38)(39, 43)(40, 49)(41, 44)(42, 50)(45, 47)(46, 48)(51, 72)(52, 71)(53, 70)(54, 69)(55, 56)(57, 61)(58, 67)(59, 62)(60, 68)(63, 65)(64, 66)(109, 114)(110, 112)(111, 128)(113, 127)(115, 144)(116, 142)(117, 134)(118, 140)(119, 133)(120, 139)(121, 143)(122, 141)(123, 136)(124, 135)(125, 138)(126, 137)(129, 130)(131, 132)

MAP           : A4.451
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.2 * x.3)^2, (x.3 * x.1 * x.2)^2, x.3^-1 * x.1 * x.3^2 * x.1 * x.3^-1, (x.3 * x.1)^3, x.3^6 >
SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 76)(2, 78)(3, 108)(4, 107)(5, 106)(6, 105)(7, 92)(8, 91)(9, 97)(10, 103)(11, 98)(12, 104)(13, 74)(14, 73)(15, 79)(16, 85)(17, 80)(18, 86)(19, 75)(20, 77)(21, 83)(22, 84)(23, 81)(24, 82)(25, 94)(26, 96)(27, 90)(28, 89)(29, 88)(30, 87)(31, 93)(32, 95)(33, 101)(34, 102)(35, 99)(36, 100)(37, 46)(38, 48)(39, 42)(40, 41)(43, 50)(44, 49)(45, 55)(47, 56)(51, 67)(52, 61)(53, 68)(54, 62)(57, 71)(58, 72)(59, 69)(60, 70)(63, 66)(64, 65)(109, 114)(110, 112)(111, 128)(113, 127)(115, 144)(116, 142)(117, 134)(118, 140)(119, 133)(120, 139)(121, 143)(122, 141)(123, 136)(124, 135)(125, 138)(126, 137)(129, 130)(131, 132)

MAP           : A4.452
NOTES         : type I, reflexible, isomorphic to A4.353.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3 * x.1)^2, (x.2 * x.1)^2, x.3^2 * x.2 * x.3^-2 * x.2, (x.3^-1 * x.2)^3, x.3^6 >
SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 75)(2, 77)(3, 83)(4, 84)(5, 81)(6, 82)(7, 94)(8, 96)(9, 90)(10, 89)(11, 88)(12, 87)(13, 93)(14, 95)(15, 101)(16, 102)(17, 99)(18, 100)(19, 76)(20, 78)(21, 108)(22, 107)(23, 106)(24, 105)(25, 92)(26, 91)(27, 97)(28, 103)(29, 98)(30, 104)(31, 74)(32, 73)(33, 79)(34, 85)(35, 80)(36, 86)(37, 63)(38, 65)(39, 53)(40, 54)(41, 51)(42, 52)(43, 70)(44, 72)(45, 48)(46, 47)(49, 69)(50, 71)(55, 64)(56, 66)(57, 60)(58, 59)(61, 68)(62, 67)(109, 110)(111, 115)(112, 121)(113, 116)(114, 122)(117, 119)(118, 120)(123, 144)(124, 143)(125, 142)(126, 141)(127, 128)(129, 133)(130, 139)(131, 134)(132, 140)(135, 137)(136, 138)

MAP           : A4.453
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3 * x.1)^2, (x.2 * x.3^-1 * x.1)^2, (x.1 * x.3^-1 * x.2)^2, (x.3^-1 * x.2)^3, x.3^6 >
SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 75)(2, 77)(3, 83)(4, 84)(5, 81)(6, 82)(7, 94)(8, 96)(9, 90)(10, 89)(11, 88)(12, 87)(13, 93)(14, 95)(15, 101)(16, 102)(17, 99)(18, 100)(19, 76)(20, 78)(21, 108)(22, 107)(23, 106)(24, 105)(25, 92)(26, 91)(27, 97)(28, 103)(29, 98)(30, 104)(31, 74)(32, 73)(33, 79)(34, 85)(35, 80)(36, 86)(37, 42)(38, 40)(39, 56)(41, 55)(43, 72)(44, 70)(45, 62)(46, 68)(47, 61)(48, 67)(49, 71)(50, 69)(51, 64)(52, 63)(53, 66)(54, 65)(57, 58)(59, 60)(109, 110)(111, 115)(112, 121)(113, 116)(114, 122)(117, 119)(118, 120)(123, 144)(124, 143)(125, 142)(126, 141)(127, 128)(129, 133)(130, 139)(131, 134)(132, 140)(135, 137)(136, 138)

MAP           : A4.454
NOTES         : type I, reflexible, isomorphic to A4.353.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3 * x.1)^2, (x.2 * x.1)^2, x.3^2 * x.2 * x.3^-2 * x.2, (x.3^-1 * x.2)^3, x.3^6 >
SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 98)(2, 97)(3, 85)(4, 79)(5, 86)(6, 80)(7, 99)(8, 101)(9, 89)(10, 90)(11, 87)(12, 88)(13, 100)(14, 102)(15, 96)(16, 95)(17, 94)(18, 93)(19, 104)(20, 103)(21, 73)(22, 91)(23, 74)(24, 92)(25, 105)(26, 107)(27, 77)(28, 78)(29, 75)(30, 76)(31, 106)(32, 108)(33, 84)(34, 83)(35, 82)(36, 81)(37, 38)(39, 43)(40, 49)(41, 44)(42, 50)(45, 47)(46, 48)(51, 72)(52, 71)(53, 70)(54, 69)(55, 56)(57, 61)(58, 67)(59, 62)(60, 68)(63, 65)(64, 66)(109, 135)(110, 137)(111, 125)(112, 126)(113, 123)(114, 124)(115, 142)(116, 144)(117, 120)(118, 119)(121, 141)(122, 143)(127, 136)(128, 138)(129, 132)(130, 131)(133, 140)(134, 139)

MAP           : A4.455
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.2^2, (x.3 * x.1)^2, (x.2 * x.3^-1 * x.1)^2, (x.1 * x.3^-1 * x.2)^2, (x.3^-1 * x.2)^3, x.3^6 >
SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 98)(2, 97)(3, 85)(4, 79)(5, 86)(6, 80)(7, 99)(8, 101)(9, 89)(10, 90)(11, 87)(12, 88)(13, 100)(14, 102)(15, 96)(16, 95)(17, 94)(18, 93)(19, 104)(20, 103)(21, 73)(22, 91)(23, 74)(24, 92)(25, 105)(26, 107)(27, 77)(28, 78)(29, 75)(30, 76)(31, 106)(32, 108)(33, 84)(34, 83)(35, 82)(36, 81)(37, 48)(38, 46)(39, 50)(40, 44)(41, 49)(42, 43)(45, 56)(47, 55)(51, 58)(52, 57)(53, 60)(54, 59)(61, 71)(62, 69)(63, 64)(65, 66)(67, 72)(68, 70)(109, 135)(110, 137)(111, 125)(112, 126)(113, 123)(114, 124)(115, 142)(116, 144)(117, 120)(118, 119)(121, 141)(122, 143)(127, 136)(128, 138)(129, 132)(130, 131)(133, 140)(134, 139)

MAP           : A4.456
NOTES         : type II, reflexible, isomorphic to A4.419.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.2 * x.4^-1 * x.2, x.5 * x.1 * x.2 * x.4^-1, x.4 * x.1 * x.4^-1 * x.1, x.4^-1 * x.2 * x.5 * x.1, x.5 * x.2 * x.5^-1 * x.1, (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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 141)(21, 132)(22, 131)(23, 127)(24, 134)(25, 136)(26, 129)(27, 138)(28, 137)(29, 133)(30, 140)(31, 142)(32, 135)(33, 144)(34, 143)(35, 139)(36, 128)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 103)(56, 104)(57, 105)(58, 106)(59, 107)(60, 108)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)(109, 120)(110, 125)(111, 118)(112, 122)(113, 117)(114, 119)(115, 116)(121, 123)(124, 126)

MAP           : A4.457
NOTES         : type II, reflexible, isomorphic to A4.419.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4 * x.2 * x.4^-1 * x.2, x.5 * x.1 * x.2 * x.4^-1, x.4 * x.1 * x.4^-1 * x.1, x.4^-1 * x.2 * x.5 * x.1, x.5 * x.2 * x.5^-1 * x.1, (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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 131)(20, 144)(21, 134)(22, 127)(23, 130)(24, 129)(25, 137)(26, 132)(27, 140)(28, 133)(29, 136)(30, 135)(31, 143)(32, 138)(33, 128)(34, 139)(35, 142)(36, 141)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 106)(56, 99)(57, 108)(58, 107)(59, 103)(60, 92)(61, 94)(62, 105)(63, 96)(64, 95)(65, 91)(66, 98)(67, 100)(68, 93)(69, 102)(70, 101)(71, 97)(72, 104)(109, 120)(110, 125)(111, 118)(112, 122)(113, 117)(114, 119)(115, 116)(121, 123)(124, 126)

MAP           : A4.458
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 116)(38, 126)(39, 125)(40, 124)(41, 112)(42, 110)(43, 121)(44, 120)(45, 119)(46, 111)(47, 123)(48, 109)(49, 122)(50, 115)(51, 117)(52, 113)(53, 118)(54, 114)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)

MAP           : A4.459
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 116)(38, 126)(39, 125)(40, 124)(41, 112)(42, 110)(43, 121)(44, 120)(45, 119)(46, 111)(47, 123)(48, 109)(49, 122)(50, 115)(51, 117)(52, 113)(53, 118)(54, 114)(55, 96)(56, 106)(57, 104)(58, 91)(59, 102)(60, 94)(61, 101)(62, 92)(63, 93)(64, 103)(65, 107)(66, 108)(67, 105)(68, 99)(69, 100)(70, 98)(71, 97)(72, 95)

MAP           : A4.460
NOTES         : type I, reflexible, isomorphic to A4.353.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.2 * x.1, (x.4, x.5^-1), x.4 * x.2 * x.5^-1 * x.1, 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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 127)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 134)(33, 135)(34, 136)(35, 137)(36, 138)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 101)(56, 96)(57, 104)(58, 97)(59, 100)(60, 99)(61, 107)(62, 102)(63, 92)(64, 103)(65, 106)(66, 105)(67, 95)(68, 108)(69, 98)(70, 91)(71, 94)(72, 93)(109, 110)(111, 125)(112, 123)(113, 126)(114, 121)(115, 117)(116, 124)(118, 120)(119, 122)

MAP           : A4.461
NOTES         : type II, reflexible, isomorphic to A4.419.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^-1 * x.5 * x.2 * x.1, x.4^-1 * x.2 * x.1 * x.5, x.5^-1 * x.1 * x.5 * x.1, x.4^-1 * x.1 * x.4 * 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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 127)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 134)(33, 135)(34, 136)(35, 137)(36, 138)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 94)(56, 105)(57, 96)(58, 95)(59, 91)(60, 98)(61, 100)(62, 93)(63, 102)(64, 101)(65, 97)(66, 104)(67, 106)(68, 99)(69, 108)(70, 107)(71, 103)(72, 92)(109, 120)(110, 125)(111, 118)(112, 122)(113, 117)(114, 119)(115, 116)(121, 123)(124, 126)

MAP           : A4.462
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 115)(38, 111)(39, 110)(40, 119)(41, 123)(42, 125)(43, 109)(44, 122)(45, 124)(46, 126)(47, 112)(48, 121)(49, 120)(50, 116)(51, 113)(52, 117)(53, 114)(54, 118)(55, 104)(56, 100)(57, 96)(58, 99)(59, 101)(60, 93)(61, 102)(62, 103)(63, 94)(64, 92)(65, 95)(66, 97)(67, 98)(68, 91)(69, 106)(70, 105)(71, 108)(72, 107)

MAP           : A4.463
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 115)(38, 111)(39, 110)(40, 119)(41, 123)(42, 125)(43, 109)(44, 122)(45, 124)(46, 126)(47, 112)(48, 121)(49, 120)(50, 116)(51, 113)(52, 117)(53, 114)(54, 118)(55, 101)(56, 104)(57, 106)(58, 107)(59, 100)(60, 97)(61, 96)(62, 99)(63, 98)(64, 95)(65, 91)(66, 105)(67, 108)(68, 92)(69, 102)(70, 93)(71, 94)(72, 103)

MAP           : A4.464
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 115)(38, 111)(39, 110)(40, 119)(41, 123)(42, 125)(43, 109)(44, 122)(45, 124)(46, 126)(47, 112)(48, 121)(49, 120)(50, 116)(51, 113)(52, 117)(53, 114)(54, 118)(55, 103)(56, 107)(57, 108)(58, 105)(59, 99)(60, 100)(61, 98)(62, 97)(63, 95)(64, 96)(65, 106)(66, 104)(67, 91)(68, 102)(69, 94)(70, 101)(71, 92)(72, 93)

MAP           : A4.465
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 115)(38, 111)(39, 110)(40, 119)(41, 123)(42, 125)(43, 109)(44, 122)(45, 124)(46, 126)(47, 112)(48, 121)(49, 120)(50, 116)(51, 113)(52, 117)(53, 114)(54, 118)(55, 100)(56, 101)(57, 102)(58, 103)(59, 104)(60, 105)(61, 106)(62, 107)(63, 108)(64, 91)(65, 92)(66, 93)(67, 94)(68, 95)(69, 96)(70, 97)(71, 98)(72, 99)

MAP           : A4.466
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 117)(38, 121)(39, 112)(40, 111)(41, 125)(42, 122)(43, 126)(44, 123)(45, 109)(46, 124)(47, 120)(48, 119)(49, 110)(50, 114)(51, 116)(52, 118)(53, 113)(54, 115)(55, 97)(56, 93)(57, 92)(58, 101)(59, 105)(60, 107)(61, 91)(62, 104)(63, 106)(64, 108)(65, 94)(66, 103)(67, 102)(68, 98)(69, 95)(70, 99)(71, 96)(72, 100)

MAP           : A4.467
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)(109, 121)(110, 125)(111, 126)(112, 123)(113, 117)(114, 118)(115, 116)(119, 124)(120, 122)

MAP           : A4.468
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)(109, 118)(110, 119)(111, 120)(112, 121)(113, 122)(114, 123)(115, 124)(116, 125)(117, 126)

MAP           : A4.469
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)(109, 115)(110, 111)(112, 119)(113, 123)(114, 125)(116, 122)(117, 124)(118, 126)(120, 121)

MAP           : A4.470
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 117)(38, 121)(39, 112)(40, 111)(41, 125)(42, 122)(43, 126)(44, 123)(45, 109)(46, 124)(47, 120)(48, 119)(49, 110)(50, 114)(51, 116)(52, 118)(53, 113)(54, 115)(55, 103)(56, 107)(57, 108)(58, 105)(59, 99)(60, 100)(61, 98)(62, 97)(63, 95)(64, 96)(65, 106)(66, 104)(67, 91)(68, 102)(69, 94)(70, 101)(71, 92)(72, 93)

MAP           : A4.471
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 117)(38, 121)(39, 112)(40, 111)(41, 125)(42, 122)(43, 126)(44, 123)(45, 109)(46, 124)(47, 120)(48, 119)(49, 110)(50, 114)(51, 116)(52, 118)(53, 113)(54, 115)(55, 100)(56, 101)(57, 102)(58, 103)(59, 104)(60, 105)(61, 106)(62, 107)(63, 108)(64, 91)(65, 92)(66, 93)(67, 94)(68, 95)(69, 96)(70, 97)(71, 98)(72, 99)

MAP           : A4.472
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 125)(38, 117)(39, 116)(40, 115)(41, 121)(42, 119)(43, 112)(44, 111)(45, 110)(46, 120)(47, 114)(48, 118)(49, 113)(50, 124)(51, 126)(52, 122)(53, 109)(54, 123)(55, 97)(56, 93)(57, 92)(58, 101)(59, 105)(60, 107)(61, 91)(62, 104)(63, 106)(64, 108)(65, 94)(66, 103)(67, 102)(68, 98)(69, 95)(70, 99)(71, 96)(72, 100)

MAP           : A4.473
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 125)(38, 117)(39, 116)(40, 115)(41, 121)(42, 119)(43, 112)(44, 111)(45, 110)(46, 120)(47, 114)(48, 118)(49, 113)(50, 124)(51, 126)(52, 122)(53, 109)(54, 123)(55, 99)(56, 103)(57, 94)(58, 93)(59, 107)(60, 104)(61, 108)(62, 105)(63, 91)(64, 106)(65, 102)(66, 101)(67, 92)(68, 96)(69, 98)(70, 100)(71, 95)(72, 97)

MAP           : A4.474
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 108)(56, 94)(57, 103)(58, 102)(59, 98)(60, 95)(61, 99)(62, 96)(63, 100)(64, 97)(65, 93)(66, 92)(67, 101)(68, 105)(69, 107)(70, 91)(71, 104)(72, 106)(109, 118)(110, 119)(111, 120)(112, 121)(113, 122)(114, 123)(115, 124)(116, 125)(117, 126)

MAP           : A4.475
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 125)(38, 117)(39, 116)(40, 115)(41, 121)(42, 119)(43, 112)(44, 111)(45, 110)(46, 120)(47, 114)(48, 118)(49, 113)(50, 124)(51, 126)(52, 122)(53, 109)(54, 123)(55, 104)(56, 100)(57, 96)(58, 99)(59, 101)(60, 93)(61, 102)(62, 103)(63, 94)(64, 92)(65, 95)(66, 97)(67, 98)(68, 91)(69, 106)(70, 105)(71, 108)(72, 107)

MAP           : A4.476
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 125)(38, 117)(39, 116)(40, 115)(41, 121)(42, 119)(43, 112)(44, 111)(45, 110)(46, 120)(47, 114)(48, 118)(49, 113)(50, 124)(51, 126)(52, 122)(53, 109)(54, 123)(55, 101)(56, 104)(57, 106)(58, 107)(59, 100)(60, 97)(61, 96)(62, 99)(63, 98)(64, 95)(65, 91)(66, 105)(67, 108)(68, 92)(69, 102)(70, 93)(71, 94)(72, 103)

MAP           : A4.477
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 125)(38, 117)(39, 116)(40, 115)(41, 121)(42, 119)(43, 112)(44, 111)(45, 110)(46, 120)(47, 114)(48, 118)(49, 113)(50, 124)(51, 126)(52, 122)(53, 109)(54, 123)(55, 103)(56, 107)(57, 108)(58, 105)(59, 99)(60, 100)(61, 98)(62, 97)(63, 95)(64, 96)(65, 106)(66, 104)(67, 91)(68, 102)(69, 94)(70, 101)(71, 92)(72, 93)

MAP           : A4.478
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 119)(38, 122)(39, 124)(40, 125)(41, 118)(42, 115)(43, 114)(44, 117)(45, 116)(46, 113)(47, 109)(48, 123)(49, 126)(50, 110)(51, 120)(52, 111)(53, 112)(54, 121)(55, 97)(56, 93)(57, 92)(58, 101)(59, 105)(60, 107)(61, 91)(62, 104)(63, 106)(64, 108)(65, 94)(66, 103)(67, 102)(68, 98)(69, 95)(70, 99)(71, 96)(72, 100)

MAP           : A4.479
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 119)(38, 122)(39, 124)(40, 125)(41, 118)(42, 115)(43, 114)(44, 117)(45, 116)(46, 113)(47, 109)(48, 123)(49, 126)(50, 110)(51, 120)(52, 111)(53, 112)(54, 121)(55, 99)(56, 103)(57, 94)(58, 93)(59, 107)(60, 104)(61, 108)(62, 105)(63, 91)(64, 106)(65, 102)(66, 101)(67, 92)(68, 96)(69, 98)(70, 100)(71, 95)(72, 97)

MAP           : A4.480
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 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)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
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.4 * x.2 * x.3 * x.4^-1 * x.2^-1 * x.3, (x.2 * x.3)^3, x.4 * x.3 * x.2 * x.4^-1 * x.3 * x.2^-1, (x.3 * x.4^-1)^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, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 119)(38, 122)(39, 124)(40, 125)(41, 118)(42, 115)(43, 114)(44, 117)(45, 116)(46, 113)(47, 109)(48, 123)(49, 126)(50, 110)(51, 120)(52, 111)(53, 112)(54, 121)(55, 107)(56, 99)(57, 98)(58, 97)(59, 103)(60, 101)(61, 94)(62, 93)(63, 92)(64, 102)(65, 96)(66, 100)(67, 95)(68, 106)(69, 108)(70, 104)(71, 91)(72, 105)

MAP           : A4.481
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)(109, 115)(110, 111)(112, 119)(113, 123)(114, 125)(116, 122)(117, 124)(118, 126)(120, 121)

MAP           : A4.482
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 102)(56, 96)(57, 100)(58, 95)(59, 106)(60, 108)(61, 104)(62, 91)(63, 105)(64, 107)(65, 99)(66, 98)(67, 97)(68, 103)(69, 101)(70, 94)(71, 93)(72, 92)(109, 117)(110, 121)(111, 112)(113, 125)(114, 122)(115, 126)(116, 123)(118, 124)(119, 120)

MAP           : A4.483
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 112)(38, 116)(39, 117)(40, 114)(41, 126)(42, 109)(43, 125)(44, 124)(45, 122)(46, 123)(47, 115)(48, 113)(49, 118)(50, 111)(51, 121)(52, 110)(53, 119)(54, 120)(55, 108)(56, 94)(57, 103)(58, 102)(59, 98)(60, 95)(61, 99)(62, 96)(63, 100)(64, 97)(65, 93)(66, 92)(67, 101)(68, 105)(69, 107)(70, 91)(71, 104)(72, 106)

MAP           : A4.484
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 116)(38, 126)(39, 125)(40, 124)(41, 112)(42, 110)(43, 121)(44, 120)(45, 119)(46, 111)(47, 123)(48, 109)(49, 122)(50, 115)(51, 117)(52, 113)(53, 118)(54, 114)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)

MAP           : A4.485
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 95)(56, 91)(57, 105)(58, 108)(59, 92)(60, 102)(61, 93)(62, 94)(63, 103)(64, 101)(65, 104)(66, 106)(67, 107)(68, 100)(69, 97)(70, 96)(71, 99)(72, 98)(109, 122)(110, 118)(111, 114)(112, 117)(113, 119)(115, 120)(116, 121)(123, 124)(125, 126)

MAP           : A4.486
NOTES         : type I, reflexible, isomorphic to A4.353.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.2 * x.1, x.3 * x.4^-1 * x.3^-1 * x.5^-1, (x.5 * x.2)^3, (x.4 * x.1)^3, x.5^2 * x.1 * x.5^-2 * x.1, x.5 * x.1 * x.4 * x.5^-1 * x.1 * x.4^-1, x.5^3 * x.4^-3, x.4^2 * x.1 * x.4^-2 * x.1 >
SCHREIER VEC. : (x.3, x.4, x.1, x.4^-1)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 60)(20, 65)(21, 58)(22, 62)(23, 57)(24, 59)(25, 56)(26, 55)(27, 71)(28, 69)(29, 72)(30, 67)(31, 63)(32, 70)(33, 61)(34, 66)(35, 68)(36, 64)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(91, 134)(92, 133)(93, 131)(94, 129)(95, 132)(96, 127)(97, 141)(98, 130)(99, 139)(100, 144)(101, 128)(102, 142)(103, 138)(104, 143)(105, 136)(106, 140)(107, 135)(108, 137)(109, 110)(111, 125)(112, 123)(113, 126)(114, 121)(115, 117)(116, 124)(118, 120)(119, 122)

MAP           : A4.487
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 116)(38, 126)(39, 125)(40, 124)(41, 112)(42, 110)(43, 121)(44, 120)(45, 119)(46, 111)(47, 123)(48, 109)(49, 122)(50, 115)(51, 117)(52, 113)(53, 118)(54, 114)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)

MAP           : A4.488
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 110)(38, 113)(39, 115)(40, 116)(41, 109)(42, 124)(43, 123)(44, 126)(45, 125)(46, 122)(47, 118)(48, 114)(49, 117)(50, 119)(51, 111)(52, 120)(53, 121)(54, 112)(55, 102)(56, 96)(57, 100)(58, 95)(59, 106)(60, 108)(61, 104)(62, 91)(63, 105)(64, 107)(65, 99)(66, 98)(67, 97)(68, 103)(69, 101)(70, 94)(71, 93)(72, 92)

MAP           : A4.489
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 124)(38, 120)(39, 119)(40, 110)(41, 114)(42, 116)(43, 118)(44, 113)(45, 115)(46, 117)(47, 121)(48, 112)(49, 111)(50, 125)(51, 122)(52, 126)(53, 123)(54, 109)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)

MAP           : A4.490
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 110)(38, 113)(39, 115)(40, 116)(41, 109)(42, 124)(43, 123)(44, 126)(45, 125)(46, 122)(47, 118)(48, 114)(49, 117)(50, 119)(51, 111)(52, 120)(53, 121)(54, 112)(55, 108)(56, 94)(57, 103)(58, 102)(59, 98)(60, 95)(61, 99)(62, 96)(63, 100)(64, 97)(65, 93)(66, 92)(67, 101)(68, 105)(69, 107)(70, 91)(71, 104)(72, 106)

MAP           : A4.491
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 112)(38, 116)(39, 117)(40, 114)(41, 126)(42, 109)(43, 125)(44, 124)(45, 122)(46, 123)(47, 115)(48, 113)(49, 118)(50, 111)(51, 121)(52, 110)(53, 119)(54, 120)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)

MAP           : A4.492
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 112)(38, 116)(39, 117)(40, 114)(41, 126)(42, 109)(43, 125)(44, 124)(45, 122)(46, 123)(47, 115)(48, 113)(49, 118)(50, 111)(51, 121)(52, 110)(53, 119)(54, 120)(55, 95)(56, 91)(57, 105)(58, 108)(59, 92)(60, 102)(61, 93)(62, 94)(63, 103)(64, 101)(65, 104)(66, 106)(67, 107)(68, 100)(69, 97)(70, 96)(71, 99)(72, 98)

MAP           : A4.493
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 112)(38, 116)(39, 117)(40, 114)(41, 126)(42, 109)(43, 125)(44, 124)(45, 122)(46, 123)(47, 115)(48, 113)(49, 118)(50, 111)(51, 121)(52, 110)(53, 119)(54, 120)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)

MAP           : A4.494
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 112)(38, 116)(39, 117)(40, 114)(41, 126)(42, 109)(43, 125)(44, 124)(45, 122)(46, 123)(47, 115)(48, 113)(49, 118)(50, 111)(51, 121)(52, 110)(53, 119)(54, 120)(55, 102)(56, 96)(57, 100)(58, 95)(59, 106)(60, 108)(61, 104)(62, 91)(63, 105)(64, 107)(65, 99)(66, 98)(67, 97)(68, 103)(69, 101)(70, 94)(71, 93)(72, 92)

MAP           : A4.495
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 112)(38, 116)(39, 117)(40, 114)(41, 126)(42, 109)(43, 125)(44, 124)(45, 122)(46, 123)(47, 115)(48, 113)(49, 118)(50, 111)(51, 121)(52, 110)(53, 119)(54, 120)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)

MAP           : A4.496
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 95)(56, 91)(57, 105)(58, 108)(59, 92)(60, 102)(61, 93)(62, 94)(63, 103)(64, 101)(65, 104)(66, 106)(67, 107)(68, 100)(69, 97)(70, 96)(71, 99)(72, 98)(109, 121)(110, 125)(111, 126)(112, 123)(113, 117)(114, 118)(115, 116)(119, 124)(120, 122)

MAP           : A4.497
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)(109, 125)(110, 117)(111, 116)(112, 115)(113, 121)(114, 119)(118, 120)(122, 124)(123, 126)

MAP           : A4.498
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 116)(38, 126)(39, 125)(40, 124)(41, 112)(42, 110)(43, 121)(44, 120)(45, 119)(46, 111)(47, 123)(48, 109)(49, 122)(50, 115)(51, 117)(52, 113)(53, 118)(54, 114)(55, 95)(56, 91)(57, 105)(58, 108)(59, 92)(60, 102)(61, 93)(62, 94)(63, 103)(64, 101)(65, 104)(66, 106)(67, 107)(68, 100)(69, 97)(70, 96)(71, 99)(72, 98)

MAP           : A4.499
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)(109, 119)(110, 122)(111, 124)(112, 125)(113, 118)(114, 115)(116, 117)(120, 123)(121, 126)

MAP           : A4.500
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)(109, 125)(110, 117)(111, 116)(112, 115)(113, 121)(114, 119)(118, 120)(122, 124)(123, 126)

MAP           : A4.501
NOTES         : type I, reflexible, isomorphic to A4.353.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 3, 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.4 * u.1^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^3, x.3^3, (x.2 * x.3^-1)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.3, x.4^-1), (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 116)(38, 126)(39, 125)(40, 124)(41, 112)(42, 110)(43, 121)(44, 120)(45, 119)(46, 111)(47, 123)(48, 109)(49, 122)(50, 115)(51, 117)(52, 113)(53, 118)(54, 114)(55, 108)(56, 94)(57, 103)(58, 102)(59, 98)(60, 95)(61, 99)(62, 96)(63, 100)(64, 97)(65, 93)(66, 92)(67, 101)(68, 105)(69, 107)(70, 91)(71, 104)(72, 106)

MAP           : A4.502
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 96)(56, 106)(57, 104)(58, 91)(59, 102)(60, 94)(61, 101)(62, 92)(63, 93)(64, 103)(65, 107)(66, 108)(67, 105)(68, 99)(69, 100)(70, 98)(71, 97)(72, 95)(109, 115)(110, 111)(112, 119)(113, 123)(114, 125)(116, 122)(117, 124)(118, 126)(120, 121)

MAP           : A4.503
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 108)(56, 94)(57, 103)(58, 102)(59, 98)(60, 95)(61, 99)(62, 96)(63, 100)(64, 97)(65, 93)(66, 92)(67, 101)(68, 105)(69, 107)(70, 91)(71, 104)(72, 106)(109, 117)(110, 121)(111, 112)(113, 125)(114, 122)(115, 126)(116, 123)(118, 124)(119, 120)

MAP           : A4.504
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 95)(56, 91)(57, 105)(58, 108)(59, 92)(60, 102)(61, 93)(62, 94)(63, 103)(64, 101)(65, 104)(66, 106)(67, 107)(68, 100)(69, 97)(70, 96)(71, 99)(72, 98)(109, 117)(110, 121)(111, 112)(113, 125)(114, 122)(115, 126)(116, 123)(118, 124)(119, 120)

MAP           : A4.505
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 102)(56, 96)(57, 100)(58, 95)(59, 106)(60, 108)(61, 104)(62, 91)(63, 105)(64, 107)(65, 99)(66, 98)(67, 97)(68, 103)(69, 101)(70, 94)(71, 93)(72, 92)(109, 122)(110, 118)(111, 114)(112, 117)(113, 119)(115, 120)(116, 121)(123, 124)(125, 126)

MAP           : A4.506
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 96)(56, 106)(57, 104)(58, 91)(59, 102)(60, 94)(61, 101)(62, 92)(63, 93)(64, 103)(65, 107)(66, 108)(67, 105)(68, 99)(69, 100)(70, 98)(71, 97)(72, 95)(109, 119)(110, 122)(111, 124)(112, 125)(113, 118)(114, 115)(116, 117)(120, 123)(121, 126)

MAP           : A4.507
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)(109, 121)(110, 125)(111, 126)(112, 123)(113, 117)(114, 118)(115, 116)(119, 124)(120, 122)

MAP           : A4.508
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)(109, 123)(110, 115)(111, 113)(112, 118)(114, 121)(116, 119)(117, 120)(122, 126)(124, 125)

MAP           : A4.509
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^-1 * x.5^-2 * x.4^-1, x.3 * x.4^-1 * x.3^-1 * x.5^-1, x.4 * x.1 * x.4^-1 * x.2, x.5 * x.1 * x.5^-1 * x.2, x.5 * x.2 * x.5^-1 * x.1, x.4 * x.2 * x.4^-1 * x.1, (x.4 * x.1)^3, (x.5 * x.2)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.4, x.1, x.4^-1)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 60)(20, 65)(21, 58)(22, 62)(23, 57)(24, 59)(25, 56)(26, 55)(27, 71)(28, 69)(29, 72)(30, 67)(31, 63)(32, 70)(33, 61)(34, 66)(35, 68)(36, 64)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(91, 134)(92, 133)(93, 131)(94, 129)(95, 132)(96, 127)(97, 141)(98, 130)(99, 139)(100, 144)(101, 128)(102, 142)(103, 138)(104, 143)(105, 136)(106, 140)(107, 135)(108, 137)(109, 120)(110, 125)(111, 118)(112, 122)(113, 117)(114, 119)(115, 116)(121, 123)(124, 126)

MAP           : A4.510
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 102)(56, 96)(57, 100)(58, 95)(59, 106)(60, 108)(61, 104)(62, 91)(63, 105)(64, 107)(65, 99)(66, 98)(67, 97)(68, 103)(69, 101)(70, 94)(71, 93)(72, 92)(109, 123)(110, 115)(111, 113)(112, 118)(114, 121)(116, 119)(117, 120)(122, 126)(124, 125)

MAP           : A4.511
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.4^-1 * x.5^-2 * x.4^-1, x.3 * x.4^-1 * x.3^-1 * x.5^-1, x.4 * x.1 * x.4^-1 * x.2, x.5 * x.1 * x.5^-1 * x.2, x.5 * x.2 * x.5^-1 * x.1, x.4 * x.2 * x.4^-1 * x.1, (x.4 * x.1)^3, (x.5 * x.2)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.4, x.1, x.4^-1)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 62)(20, 61)(21, 59)(22, 57)(23, 60)(24, 55)(25, 69)(26, 58)(27, 67)(28, 72)(29, 56)(30, 70)(31, 66)(32, 71)(33, 64)(34, 68)(35, 63)(36, 65)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(91, 132)(92, 137)(93, 130)(94, 134)(95, 129)(96, 131)(97, 128)(98, 127)(99, 143)(100, 141)(101, 144)(102, 139)(103, 135)(104, 142)(105, 133)(106, 138)(107, 140)(108, 136)(109, 120)(110, 125)(111, 118)(112, 122)(113, 117)(114, 119)(115, 116)(121, 123)(124, 126)

MAP           : A4.512
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 108)(56, 94)(57, 103)(58, 102)(59, 98)(60, 95)(61, 99)(62, 96)(63, 100)(64, 97)(65, 93)(66, 92)(67, 101)(68, 105)(69, 107)(70, 91)(71, 104)(72, 106)(109, 122)(110, 118)(111, 114)(112, 117)(113, 119)(115, 120)(116, 121)(123, 124)(125, 126)

MAP           : A4.513
NOTES         : type I, reflexible, isomorphic to A4.353.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.2 * x.1, x.3 * x.4^-1 * x.3^-1 * x.5^-1, (x.5 * x.2)^3, (x.4 * x.1)^3, x.5^2 * x.1 * x.5^-2 * x.1, x.5 * x.1 * x.4 * x.5^-1 * x.1 * x.4^-1, x.5^3 * x.4^-3, x.4^2 * x.1 * x.4^-2 * x.1 >
SCHREIER VEC. : (x.3, x.4, x.1, x.4^-1)
LOCAL TYPE    : (4, 4, 6, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 62)(20, 61)(21, 59)(22, 57)(23, 60)(24, 55)(25, 69)(26, 58)(27, 67)(28, 72)(29, 56)(30, 70)(31, 66)(32, 71)(33, 64)(34, 68)(35, 63)(36, 65)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(91, 132)(92, 137)(93, 130)(94, 134)(95, 129)(96, 131)(97, 128)(98, 127)(99, 143)(100, 141)(101, 144)(102, 139)(103, 135)(104, 142)(105, 133)(106, 138)(107, 140)(108, 136)(109, 110)(111, 125)(112, 123)(113, 126)(114, 121)(115, 117)(116, 124)(118, 120)(119, 122)

MAP           : A4.514
NOTES         : type I, reflexible, isomorphic to A4.356.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.3, x.1^2, x.2^2, x.5 * x.1 * x.4^-1 * x.2, (x.5^-1 * x.1)^2, x.1 * x.4^-1 * x.5^-1 * x.2, (x.1 * x.4^-1)^2, (x.2 * x.4)^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        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)(109, 119)(110, 122)(111, 124)(112, 125)(113, 118)(114, 115)(116, 117)(120, 123)(121, 126)

MAP           : A4.515
NOTES         : type I, chiral, representative.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 3)
ORBIFOLD      : O(0, {4, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3^-1 * u.2)^2, (u.3 * u.1)^4 >
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)^2, x.2 * x.1 * x.2 * x.3 * x.1 * x.3^-1, (x.1 * x.2)^3 >
SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2)
LOCAL TYPE    : (4, 4, 8, 8)
#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, 64)(3, 61)(4, 63)(5, 67)(6, 65)(7, 68)(8, 66)(9, 52)(10, 51)(11, 50)(12, 49)(13, 58)(14, 60)(15, 57)(16, 59)(17, 71)(18, 69)(19, 72)(20, 70)(21, 56)(22, 55)(23, 54)(24, 53)(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, 92)(75, 89)(76, 91)(77, 87)(78, 85)(79, 88)(80, 86)(81, 96)(82, 95)(83, 94)(84, 93)

MAP           : A4.516
NOTES         : type I, chiral, isomorphic to A4.515.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 3)
ORBIFOLD      : O(0, {4, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3^-1 * u.2)^2, (u.3 * u.1)^4 >
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.1 * x.2 * x.3^-1)^2, x.1 * x.3^-1 * x.1 * x.3 * x.1 * x.2 >
SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2)
LOCAL TYPE    : (4, 4, 8, 8)
#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, 64)(3, 61)(4, 63)(5, 67)(6, 65)(7, 68)(8, 66)(9, 52)(10, 51)(11, 50)(12, 49)(13, 58)(14, 60)(15, 57)(16, 59)(17, 71)(18, 69)(19, 72)(20, 70)(21, 56)(22, 55)(23, 54)(24, 53)(25, 35)(26, 33)(27, 36)(28, 34)(29, 46)(30, 48)(31, 45)(32, 47)(37, 44)(38, 43)(39, 42)(40, 41)(73, 90)(74, 92)(75, 89)(76, 91)(77, 87)(78, 85)(79, 88)(80, 86)(81, 96)(82, 95)(83, 94)(84, 93)

MAP           : A4.517
NOTES         : type I, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 3)
ORBIFOLD      : O(0, {4, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 2, 4 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3 * u.1)^2, (u.3^-1 * u.2)^4 >
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.1 * x.2)^2, x.2 * x.3 * x.2 * x.3^-1 * x.1 * x.2 * x.3^-1, (x.3^-1 * x.2)^4 >
SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2)
LOCAL TYPE    : (4, 4, 8, 8)
#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, 57)(2, 58)(3, 59)(4, 60)(5, 69)(6, 70)(7, 71)(8, 72)(9, 65)(10, 66)(11, 67)(12, 68)(13, 53)(14, 54)(15, 55)(16, 56)(17, 49)(18, 50)(19, 51)(20, 52)(21, 61)(22, 62)(23, 63)(24, 64)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)(73, 90)(74, 92)(75, 89)(76, 91)(77, 87)(78, 85)(79, 88)(80, 86)(81, 96)(82, 95)(83, 94)(84, 93)

MAP           : A4.518
NOTES         : type I, reflexible, isomorphic to A4.517.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 3)
ORBIFOLD      : O(0, {4, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3^-1 * u.2)^2, (u.3 * u.1)^4 >
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.2 * x.3 * x.1 * x.3^-1 * x.1 * x.3 * x.1, (x.3 * x.1)^4 >
SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2)
LOCAL TYPE    : (4, 4, 8, 8)
#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, 64)(3, 61)(4, 63)(5, 67)(6, 65)(7, 68)(8, 66)(9, 52)(10, 51)(11, 50)(12, 49)(13, 58)(14, 60)(15, 57)(16, 59)(17, 71)(18, 69)(19, 72)(20, 70)(21, 56)(22, 55)(23, 54)(24, 53)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)(73, 90)(74, 92)(75, 89)(76, 91)(77, 87)(78, 85)(79, 88)(80, 86)(81, 96)(82, 95)(83, 94)(84, 93)

MAP           : A4.519
NOTES         : type I, chiral, isomorphic to A4.515.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 3)
ORBIFOLD      : O(0, {4, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 2, 4 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3 * u.1)^2, (u.3^-1 * u.2)^4 >
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.1 * x.2 * x.1 * x.3^-1 * x.2 * x.3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2)
LOCAL TYPE    : (4, 4, 8, 8)
#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, 57)(2, 58)(3, 59)(4, 60)(5, 69)(6, 70)(7, 71)(8, 72)(9, 65)(10, 66)(11, 67)(12, 68)(13, 53)(14, 54)(15, 55)(16, 56)(17, 49)(18, 50)(19, 51)(20, 52)(21, 61)(22, 62)(23, 63)(24, 64)(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, 90)(74, 92)(75, 89)(76, 91)(77, 87)(78, 85)(79, 88)(80, 86)(81, 96)(82, 95)(83, 94)(84, 93)

MAP           : A4.520
NOTES         : type I, chiral, isomorphic to A4.515.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 3)
ORBIFOLD      : O(0, {4, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 2, 4 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.2^2, (u.3 * u.1)^2, (u.3^-1 * u.2)^4 >
CTG (small)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.2^2, x.3^3, (x.1 * x.3^-1)^2, (x.2 * x.1 * x.3)^2, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.3^-1, x.2)
LOCAL TYPE    : (4, 4, 8, 8)
#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, 57)(2, 58)(3, 59)(4, 60)(5, 69)(6, 70)(7, 71)(8, 72)(9, 65)(10, 66)(11, 67)(12, 68)(13, 53)(14, 54)(15, 55)(16, 56)(17, 49)(18, 50)(19, 51)(20, 52)(21, 61)(22, 62)(23, 63)(24, 64)(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, 92)(75, 89)(76, 91)(77, 87)(78, 85)(79, 88)(80, 86)(81, 96)(82, 95)(83, 94)(84, 93)

MAP           : A4.521
NOTES         : type I, non-Cayley, reflexible, isomorphic to Med({4,5}), representative.
QUOTIENT      : R = (1, 2) L = (1, 2)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 2 ], faces: [ 5, 4 ]
UNIGROUP      : < u.1, u.2 | u.2^2, u.1^4, (u.1 * u.2)^5 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2 | x.2^2, x.1^4, (x.2 * x.1)^5, (x.2 * x.1^-1 * x.2 * x.1)^3, x.2 * x.1^-2 * x.2 * x.1^-1 * x.2 * x.1 * x.2 * x.1 * x.2 * x.1^-1 * x.2 * x.1^-2 * x.2 * x.1^-1 >
SCHREIER VEC. : (x.1, x.1^-1)^2
LOCAL TYPE    : (4, 5, 4, 5)
#DARTS        : 240
R = (1, 122, 2, 121)(3, 127, 7, 123)(4, 134, 14, 124)(5, 133, 13, 125)(6, 128, 8, 126)(9, 136, 16, 129)(10, 222, 102, 130)(11, 219, 99, 131)(12, 137, 17, 132)(15, 239, 119, 135)(18, 238, 118, 138)(19, 174, 54, 139)(20, 171, 51, 140)(21, 210, 90, 141)(22, 169, 49, 142)(23, 170, 50, 143)(24, 207, 87, 144)(25, 160, 40, 145)(26, 161, 41, 146)(27, 158, 38, 147)(28, 197, 77, 148)(29, 196, 76, 149)(30, 157, 37, 150)(31, 231, 111, 151)(32, 234, 114, 152)(33, 220, 100, 153)(34, 186, 66, 154)(35, 183, 63, 155)(36, 221, 101, 156)(39, 162, 42, 159)(43, 230, 110, 163)(44, 229, 109, 164)(45, 235, 115, 165)(46, 218, 98, 166)(47, 217, 97, 167)(48, 236, 116, 168)(52, 173, 53, 172)(55, 233, 113, 175)(56, 232, 112, 176)(57, 203, 83, 177)(58, 237, 117, 178)(59, 240, 120, 179)(60, 202, 82, 180)(61, 191, 71, 181)(62, 190, 70, 182)(64, 201, 81, 184)(65, 204, 84, 185)(67, 188, 68, 187)(69, 199, 79, 189)(72, 200, 80, 192)(73, 226, 106, 193)(74, 227, 107, 194)(75, 224, 104, 195)(78, 223, 103, 198)(85, 216, 96, 205)(86, 213, 93, 206)(88, 211, 91, 208)(89, 212, 92, 209)(94, 215, 95, 214)(105, 228, 108, 225)
L = (1, 123)(2, 126)(3, 136)(4, 222)(5, 219)(6, 137)(7, 174)(8, 171)(9, 210)(10, 169)(11, 170)(12, 207)(13, 122)(14, 121)(15, 127)(16, 134)(17, 133)(18, 128)(19, 160)(20, 161)(21, 158)(22, 197)(23, 196)(24, 157)(25, 125)(26, 124)(27, 239)(28, 129)(29, 132)(30, 238)(31, 233)(32, 232)(33, 203)(34, 237)(35, 240)(36, 202)(37, 230)(38, 229)(39, 235)(40, 218)(41, 217)(42, 236)(43, 142)(44, 143)(45, 140)(46, 173)(47, 172)(48, 139)(49, 231)(50, 234)(51, 220)(52, 186)(53, 183)(54, 221)(55, 150)(56, 147)(57, 162)(58, 145)(59, 146)(60, 159)(61, 226)(62, 227)(63, 224)(64, 149)(65, 148)(66, 223)(67, 191)(68, 190)(69, 155)(70, 201)(71, 204)(72, 154)(73, 216)(74, 213)(75, 144)(76, 211)(77, 212)(78, 141)(79, 188)(80, 187)(81, 199)(82, 182)(83, 181)(84, 200)(85, 189)(86, 192)(87, 184)(88, 180)(89, 177)(90, 185)(91, 164)(92, 163)(93, 151)(94, 176)(95, 175)(96, 152)(97, 165)(98, 168)(99, 178)(100, 138)(101, 135)(102, 179)(103, 167)(104, 166)(105, 131)(106, 153)(107, 156)(108, 130)(109, 198)(110, 195)(111, 228)(112, 193)(113, 194)(114, 225)(115, 208)(116, 209)(117, 206)(118, 215)(119, 214)(120, 205)

MAP           : A4.522
NOTES         : type I, reflexible, isomorphic to Med({4,5}), isomorphic to A4.521.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 5, 2 ]
UNIGROUP      : < u.1, u.2 | (u.1^-1 * u.2^-1)^2, u.1^5, u.2^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2 | (x.1^-1 * x.2^-1)^2, x.1^5, x.2^5, (x.1^-1 * x.2)^3, (x.1^-1 * x.2^2 * x.1^-1)^2 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 5, 4, 5)
#DARTS        : 240
R = (1, 61, 121, 181)(2, 62, 122, 182)(3, 63, 123, 183)(4, 64, 124, 184)(5, 65, 125, 185)(6, 66, 126, 186)(7, 67, 127, 187)(8, 68, 128, 188)(9, 69, 129, 189)(10, 70, 130, 190)(11, 71, 131, 191)(12, 72, 132, 192)(13, 73, 133, 193)(14, 74, 134, 194)(15, 75, 135, 195)(16, 76, 136, 196)(17, 77, 137, 197)(18, 78, 138, 198)(19, 79, 139, 199)(20, 80, 140, 200)(21, 81, 141, 201)(22, 82, 142, 202)(23, 83, 143, 203)(24, 84, 144, 204)(25, 85, 145, 205)(26, 86, 146, 206)(27, 87, 147, 207)(28, 88, 148, 208)(29, 89, 149, 209)(30, 90, 150, 210)(31, 91, 151, 211)(32, 92, 152, 212)(33, 93, 153, 213)(34, 94, 154, 214)(35, 95, 155, 215)(36, 96, 156, 216)(37, 97, 157, 217)(38, 98, 158, 218)(39, 99, 159, 219)(40, 100, 160, 220)(41, 101, 161, 221)(42, 102, 162, 222)(43, 103, 163, 223)(44, 104, 164, 224)(45, 105, 165, 225)(46, 106, 166, 226)(47, 107, 167, 227)(48, 108, 168, 228)(49, 109, 169, 229)(50, 110, 170, 230)(51, 111, 171, 231)(52, 112, 172, 232)(53, 113, 173, 233)(54, 114, 174, 234)(55, 115, 175, 235)(56, 116, 176, 236)(57, 117, 177, 237)(58, 118, 178, 238)(59, 119, 179, 239)(60, 120, 180, 240)
L = (1, 65)(2, 78)(3, 101)(4, 62)(5, 64)(6, 94)(7, 74)(8, 77)(9, 79)(10, 73)(11, 90)(12, 89)(13, 87)(14, 63)(15, 100)(16, 99)(17, 111)(18, 61)(19, 88)(20, 85)(21, 72)(22, 114)(23, 86)(24, 116)(25, 102)(26, 112)(27, 98)(28, 113)(29, 109)(30, 75)(31, 71)(32, 96)(33, 83)(34, 68)(35, 70)(36, 76)(37, 92)(38, 95)(39, 97)(40, 91)(41, 108)(42, 107)(43, 105)(44, 69)(45, 82)(46, 81)(47, 117)(48, 67)(49, 106)(50, 103)(51, 66)(52, 120)(53, 104)(54, 110)(55, 84)(56, 118)(57, 80)(58, 119)(59, 115)(60, 93)(121, 189)(122, 237)(123, 226)(124, 225)(125, 213)(126, 235)(127, 190)(128, 187)(129, 210)(130, 216)(131, 188)(132, 182)(133, 228)(134, 214)(135, 224)(136, 215)(137, 211)(138, 201)(139, 198)(140, 184)(141, 194)(142, 185)(143, 181)(144, 231)(145, 220)(146, 217)(147, 240)(148, 186)(149, 218)(150, 212)(151, 200)(152, 203)(153, 193)(154, 199)(155, 192)(156, 191)(157, 239)(158, 204)(159, 227)(160, 236)(161, 238)(162, 232)(163, 209)(164, 234)(165, 197)(166, 206)(167, 208)(168, 202)(169, 230)(170, 233)(171, 223)(172, 229)(173, 222)(174, 221)(175, 219)(176, 207)(177, 196)(178, 195)(179, 183)(180, 205)

MAP           : A4.523
NOTES         : type I, reflexible, isomorphic to Med({4,5}), isomorphic to A4.521.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 5, 2 ]
UNIGROUP      : < u.1, u.2 | (u.1^-1 * u.2^-1)^2, u.1^5, u.2^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2 | (x.1^-1 * x.2^-1)^2, x.1^5, x.2^5, (x.1^-1 * x.2)^3, (x.1^-1 * x.2^2 * x.1^-1)^2 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 5, 4, 5)
#DARTS        : 240
R = (1, 61, 121, 181)(2, 62, 122, 182)(3, 63, 123, 183)(4, 64, 124, 184)(5, 65, 125, 185)(6, 66, 126, 186)(7, 67, 127, 187)(8, 68, 128, 188)(9, 69, 129, 189)(10, 70, 130, 190)(11, 71, 131, 191)(12, 72, 132, 192)(13, 73, 133, 193)(14, 74, 134, 194)(15, 75, 135, 195)(16, 76, 136, 196)(17, 77, 137, 197)(18, 78, 138, 198)(19, 79, 139, 199)(20, 80, 140, 200)(21, 81, 141, 201)(22, 82, 142, 202)(23, 83, 143, 203)(24, 84, 144, 204)(25, 85, 145, 205)(26, 86, 146, 206)(27, 87, 147, 207)(28, 88, 148, 208)(29, 89, 149, 209)(30, 90, 150, 210)(31, 91, 151, 211)(32, 92, 152, 212)(33, 93, 153, 213)(34, 94, 154, 214)(35, 95, 155, 215)(36, 96, 156, 216)(37, 97, 157, 217)(38, 98, 158, 218)(39, 99, 159, 219)(40, 100, 160, 220)(41, 101, 161, 221)(42, 102, 162, 222)(43, 103, 163, 223)(44, 104, 164, 224)(45, 105, 165, 225)(46, 106, 166, 226)(47, 107, 167, 227)(48, 108, 168, 228)(49, 109, 169, 229)(50, 110, 170, 230)(51, 111, 171, 231)(52, 112, 172, 232)(53, 113, 173, 233)(54, 114, 174, 234)(55, 115, 175, 235)(56, 116, 176, 236)(57, 117, 177, 237)(58, 118, 178, 238)(59, 119, 179, 239)(60, 120, 180, 240)
L = (1, 62)(2, 65)(3, 67)(4, 61)(5, 78)(6, 77)(7, 101)(8, 66)(9, 113)(10, 98)(11, 100)(12, 106)(13, 95)(14, 108)(15, 71)(16, 92)(17, 94)(18, 64)(19, 104)(20, 107)(21, 109)(22, 103)(23, 120)(24, 119)(25, 117)(26, 93)(27, 70)(28, 69)(29, 81)(30, 91)(31, 75)(32, 99)(33, 112)(34, 111)(35, 87)(36, 97)(37, 76)(38, 73)(39, 96)(40, 90)(41, 74)(42, 80)(43, 114)(44, 88)(45, 110)(46, 89)(47, 85)(48, 63)(49, 72)(50, 82)(51, 68)(52, 83)(53, 79)(54, 105)(55, 118)(56, 115)(57, 102)(58, 84)(59, 116)(60, 86)(121, 210)(122, 196)(123, 206)(124, 197)(125, 193)(126, 219)(127, 216)(128, 190)(129, 212)(130, 191)(131, 187)(132, 237)(133, 202)(134, 199)(135, 234)(136, 192)(137, 200)(138, 194)(139, 201)(140, 225)(141, 214)(142, 213)(143, 189)(144, 223)(145, 236)(146, 239)(147, 205)(148, 235)(149, 204)(150, 203)(151, 184)(152, 181)(153, 228)(154, 198)(155, 182)(156, 188)(157, 183)(158, 231)(159, 208)(160, 207)(161, 195)(162, 229)(163, 218)(164, 221)(165, 211)(166, 217)(167, 186)(168, 185)(169, 233)(170, 222)(171, 209)(172, 230)(173, 232)(174, 238)(175, 227)(176, 240)(177, 215)(178, 224)(179, 226)(180, 220)

MAP           : A4.524
NOTES         : type I, non-Cayley, reflexible, isomorphic to Med({4,5}), isomorphic to A4.521.
QUOTIENT      : R = (1, 2) L = (1, 2)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 2 ], faces: [ 4, 5 ]
UNIGROUP      : < u.1, u.2 | u.2^2, u.1^5, (u.1 * u.2)^4 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2 | x.2^2, x.1^5, (x.1 * x.2)^4, (x.2 * x.1^2 * x.2 * x.1^-2)^2, (x.2 * x.1 * x.2 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1)^2
LOCAL TYPE    : (4, 5, 4, 5)
#DARTS        : 240
R = (1, 122, 2, 121)(3, 127, 7, 123)(4, 134, 14, 124)(5, 133, 13, 125)(6, 128, 8, 126)(9, 136, 16, 129)(10, 222, 102, 130)(11, 219, 99, 131)(12, 137, 17, 132)(15, 239, 119, 135)(18, 238, 118, 138)(19, 174, 54, 139)(20, 171, 51, 140)(21, 210, 90, 141)(22, 169, 49, 142)(23, 170, 50, 143)(24, 207, 87, 144)(25, 160, 40, 145)(26, 161, 41, 146)(27, 158, 38, 147)(28, 197, 77, 148)(29, 196, 76, 149)(30, 157, 37, 150)(31, 231, 111, 151)(32, 234, 114, 152)(33, 220, 100, 153)(34, 186, 66, 154)(35, 183, 63, 155)(36, 221, 101, 156)(39, 162, 42, 159)(43, 230, 110, 163)(44, 229, 109, 164)(45, 235, 115, 165)(46, 218, 98, 166)(47, 217, 97, 167)(48, 236, 116, 168)(52, 173, 53, 172)(55, 233, 113, 175)(56, 232, 112, 176)(57, 203, 83, 177)(58, 237, 117, 178)(59, 240, 120, 179)(60, 202, 82, 180)(61, 191, 71, 181)(62, 190, 70, 182)(64, 201, 81, 184)(65, 204, 84, 185)(67, 188, 68, 187)(69, 199, 79, 189)(72, 200, 80, 192)(73, 226, 106, 193)(74, 227, 107, 194)(75, 224, 104, 195)(78, 223, 103, 198)(85, 216, 96, 205)(86, 213, 93, 206)(88, 211, 91, 208)(89, 212, 92, 209)(94, 215, 95, 214)(105, 228, 108, 225)
L = (1, 124)(2, 125)(3, 122)(4, 161)(5, 160)(6, 121)(7, 239)(8, 238)(9, 197)(10, 225)(11, 228)(12, 196)(13, 132)(14, 129)(15, 156)(16, 127)(17, 128)(18, 153)(19, 236)(20, 235)(21, 223)(22, 230)(23, 229)(24, 224)(25, 237)(26, 240)(27, 232)(28, 204)(29, 201)(30, 233)(31, 206)(32, 205)(33, 193)(34, 200)(35, 199)(36, 194)(37, 207)(38, 210)(39, 202)(40, 174)(41, 171)(42, 203)(43, 209)(44, 208)(45, 167)(46, 195)(47, 198)(48, 166)(49, 222)(50, 219)(51, 126)(52, 217)(53, 218)(54, 123)(55, 214)(56, 215)(57, 212)(58, 131)(59, 130)(60, 211)(61, 177)(62, 180)(63, 172)(64, 144)(65, 141)(66, 173)(67, 192)(68, 189)(69, 216)(70, 187)(71, 188)(72, 213)(73, 176)(74, 175)(75, 163)(76, 170)(77, 169)(78, 164)(79, 184)(80, 185)(81, 182)(82, 221)(83, 220)(84, 181)(85, 179)(86, 178)(87, 137)(88, 165)(89, 168)(90, 136)(91, 149)(92, 148)(93, 227)(94, 135)(95, 138)(96, 226)(97, 146)(98, 145)(99, 133)(100, 140)(101, 139)(102, 134)(103, 154)(104, 155)(105, 152)(106, 191)(107, 190)(108, 151)(109, 147)(110, 150)(111, 142)(112, 234)(113, 231)(114, 143)(115, 162)(116, 159)(117, 186)(118, 157)(119, 158)(120, 183)

MAP           : A4.525
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), representative.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3 * x.2 * x.3, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^2, (x.2 * x.3^-1)^2, (x.1 * x.2^-1)^3, (x.3 * x.4^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 141)(21, 132)(22, 131)(23, 127)(24, 134)(25, 136)(26, 129)(27, 138)(28, 137)(29, 133)(30, 140)(31, 142)(32, 135)(33, 144)(34, 143)(35, 139)(36, 128)(37, 114)(38, 119)(39, 112)(40, 116)(41, 111)(42, 113)(43, 110)(44, 109)(45, 125)(46, 123)(47, 126)(48, 121)(49, 117)(50, 124)(51, 115)(52, 120)(53, 122)(54, 118)(55, 92)(56, 91)(57, 107)(58, 105)(59, 108)(60, 103)(61, 99)(62, 106)(63, 97)(64, 102)(65, 104)(66, 100)(67, 96)(68, 101)(69, 94)(70, 98)(71, 93)(72, 95)

MAP           : A4.526
NOTES         : type I, reflexible, isomorphic to Med({4,6}), representative.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 99)(56, 103)(57, 94)(58, 93)(59, 107)(60, 104)(61, 108)(62, 105)(63, 91)(64, 106)(65, 102)(66, 101)(67, 92)(68, 96)(69, 98)(70, 100)(71, 95)(72, 97)

MAP           : A4.527
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.3^-3 * x.4, (x.4 * x.1^-1)^2, x.3^-2 * x.4 * x.3^-1, (x.2 * x.3^-1)^2, x.2^-1 * x.4 * x.2^-1 * x.3^-1, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 127)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 134)(33, 135)(34, 136)(35, 137)(36, 138)(37, 114)(38, 119)(39, 112)(40, 116)(41, 111)(42, 113)(43, 110)(44, 109)(45, 125)(46, 123)(47, 126)(48, 121)(49, 117)(50, 124)(51, 115)(52, 120)(53, 122)(54, 118)(55, 93)(56, 100)(57, 91)(58, 96)(59, 98)(60, 94)(61, 108)(62, 95)(63, 106)(64, 92)(65, 105)(66, 107)(67, 104)(68, 103)(69, 101)(70, 99)(71, 102)(72, 97)

MAP           : A4.528
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 107)(56, 99)(57, 98)(58, 97)(59, 103)(60, 101)(61, 94)(62, 93)(63, 92)(64, 102)(65, 96)(66, 100)(67, 95)(68, 106)(69, 108)(70, 104)(71, 91)(72, 105)

MAP           : A4.529
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2 | (u.1^-1 * u.2^-1)^2, u.1^6, u.2^6 >
CTG (small)   : <36, 10>
CTG (fp)      : < x.1, x.2 | (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^6, x.2^6 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 38)(2, 42)(3, 44)(4, 43)(5, 37)(6, 58)(7, 56)(8, 60)(9, 62)(10, 61)(11, 55)(12, 40)(13, 70)(14, 69)(15, 59)(16, 39)(17, 66)(18, 65)(19, 52)(20, 51)(21, 41)(22, 57)(23, 48)(24, 47)(25, 53)(26, 49)(27, 64)(28, 72)(29, 45)(30, 50)(31, 71)(32, 67)(33, 46)(34, 54)(35, 63)(36, 68)(73, 112)(74, 111)(75, 137)(76, 141)(77, 132)(78, 131)(79, 113)(80, 109)(81, 124)(82, 120)(83, 129)(84, 110)(85, 119)(86, 115)(87, 130)(88, 114)(89, 123)(90, 116)(91, 134)(92, 138)(93, 128)(94, 127)(95, 133)(96, 142)(97, 140)(98, 144)(99, 122)(100, 121)(101, 139)(102, 136)(103, 118)(104, 117)(105, 143)(106, 135)(107, 126)(108, 125)

MAP           : A4.530
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.2 * x.3^3, (x.1 * x.2)^2, x.3^-1 * x.4^-1 * x.2 * x.4^-1, x.3^-3 * x.2, (x.3 * x.4^-1)^2, (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 126)(38, 113)(39, 124)(40, 110)(41, 123)(42, 125)(43, 122)(44, 121)(45, 119)(46, 117)(47, 120)(48, 115)(49, 111)(50, 118)(51, 109)(52, 114)(53, 116)(54, 112)(55, 97)(56, 98)(57, 99)(58, 100)(59, 101)(60, 102)(61, 103)(62, 104)(63, 105)(64, 106)(65, 107)(66, 108)(67, 91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96)

MAP           : A4.531
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2 | (u.1^-1 * u.2^-1)^2, u.1^6, u.2^6 >
CTG (small)   : <36, 10>
CTG (fp)      : < x.1, x.2 | (x.1^-1 * x.2^-1)^2, (x.2 * x.1^-1)^2, x.1^6, x.2^6 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 40)(2, 39)(3, 65)(4, 69)(5, 60)(6, 59)(7, 41)(8, 37)(9, 52)(10, 48)(11, 57)(12, 38)(13, 47)(14, 43)(15, 58)(16, 42)(17, 51)(18, 44)(19, 62)(20, 66)(21, 56)(22, 55)(23, 61)(24, 70)(25, 68)(26, 72)(27, 50)(28, 49)(29, 67)(30, 64)(31, 46)(32, 45)(33, 71)(34, 63)(35, 54)(36, 53)(73, 110)(74, 114)(75, 116)(76, 115)(77, 109)(78, 130)(79, 128)(80, 132)(81, 134)(82, 133)(83, 127)(84, 112)(85, 142)(86, 141)(87, 131)(88, 111)(89, 138)(90, 137)(91, 124)(92, 123)(93, 113)(94, 129)(95, 120)(96, 119)(97, 125)(98, 121)(99, 136)(100, 144)(101, 117)(102, 122)(103, 143)(104, 139)(105, 118)(106, 126)(107, 135)(108, 140)

MAP           : A4.532
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2 | (u.1^-1 * u.2^-1)^2, u.1^6, u.2^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2 | (x.1^-1 * x.2^-1)^2, x.2 * x.1^-1 * x.2^3 * x.1^-1, x.2^-3 * x.1 * x.2^-1 * x.1, x.1^6, (x.1 * x.2^-1 * x.1)^2 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 39)(2, 52)(3, 49)(4, 38)(5, 44)(6, 57)(7, 58)(8, 53)(9, 42)(10, 43)(11, 48)(12, 59)(13, 51)(14, 64)(15, 61)(16, 50)(17, 56)(18, 69)(19, 70)(20, 65)(21, 54)(22, 55)(23, 60)(24, 71)(25, 63)(26, 40)(27, 37)(28, 62)(29, 68)(30, 45)(31, 46)(32, 41)(33, 66)(34, 67)(35, 72)(36, 47)(73, 112)(74, 135)(75, 140)(76, 117)(77, 109)(78, 134)(79, 133)(80, 119)(81, 139)(82, 138)(83, 110)(84, 113)(85, 127)(86, 126)(87, 122)(88, 144)(89, 141)(90, 130)(91, 129)(92, 123)(93, 137)(94, 143)(95, 142)(96, 136)(97, 125)(98, 131)(99, 118)(100, 121)(101, 132)(102, 116)(103, 120)(104, 114)(105, 124)(106, 111)(107, 128)(108, 115)

MAP           : A4.533
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2 | (u.1^-1 * u.2^-1)^2, u.1^6, u.2^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2 | (x.1^-1 * x.2^-1)^2, x.2 * x.1^-1 * x.2^3 * x.1^-1, x.2^-3 * x.1 * x.2^-1 * x.1, x.1^6, (x.1 * x.2^-1 * x.1)^2 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 39)(2, 52)(3, 49)(4, 38)(5, 44)(6, 57)(7, 58)(8, 53)(9, 42)(10, 43)(11, 48)(12, 59)(13, 51)(14, 64)(15, 61)(16, 50)(17, 56)(18, 69)(19, 70)(20, 65)(21, 54)(22, 55)(23, 60)(24, 71)(25, 63)(26, 40)(27, 37)(28, 62)(29, 68)(30, 45)(31, 46)(32, 41)(33, 66)(34, 67)(35, 72)(36, 47)(73, 116)(74, 120)(75, 139)(76, 111)(77, 131)(78, 113)(79, 119)(80, 117)(81, 110)(82, 109)(83, 125)(84, 118)(85, 134)(86, 133)(87, 137)(88, 138)(89, 135)(90, 136)(91, 123)(92, 144)(93, 142)(94, 141)(95, 112)(96, 140)(97, 130)(98, 129)(99, 124)(100, 143)(101, 126)(102, 115)(103, 114)(104, 121)(105, 128)(106, 132)(107, 127)(108, 122)

MAP           : A4.534
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2 | (u.1^-1 * u.2^-1)^2, u.1^6, u.2^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2 | (x.1^-1 * x.2^-1)^2, x.2 * x.1^-1 * x.2^3 * x.1^-1, x.2^-3 * x.1 * x.2^-1 * x.1, x.1^6, (x.1 * x.2^-1 * x.1)^2 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 63)(2, 40)(3, 37)(4, 62)(5, 68)(6, 45)(7, 46)(8, 41)(9, 66)(10, 67)(11, 72)(12, 47)(13, 39)(14, 52)(15, 49)(16, 38)(17, 44)(18, 57)(19, 58)(20, 53)(21, 42)(22, 43)(23, 48)(24, 59)(25, 51)(26, 64)(27, 61)(28, 50)(29, 56)(30, 69)(31, 70)(32, 65)(33, 54)(34, 55)(35, 60)(36, 71)(73, 113)(74, 119)(75, 142)(76, 109)(77, 120)(78, 140)(79, 144)(80, 138)(81, 112)(82, 135)(83, 116)(84, 139)(85, 136)(86, 123)(87, 128)(88, 141)(89, 133)(90, 122)(91, 121)(92, 143)(93, 127)(94, 126)(95, 134)(96, 137)(97, 115)(98, 114)(99, 110)(100, 132)(101, 129)(102, 118)(103, 117)(104, 111)(105, 125)(106, 131)(107, 130)(108, 124)

MAP           : A4.535
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2 | (u.1^-1 * u.2^-1)^2, u.1^6, u.2^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2 | (x.1^-1 * x.2^-1)^2, x.2 * x.1^-1 * x.2^3 * x.1^-1, x.2^-3 * x.1 * x.2^-1 * x.1, x.1^6, (x.1 * x.2^-1 * x.1)^2 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 63)(2, 40)(3, 37)(4, 62)(5, 68)(6, 45)(7, 46)(8, 41)(9, 66)(10, 67)(11, 72)(12, 47)(13, 39)(14, 52)(15, 49)(16, 38)(17, 44)(18, 57)(19, 58)(20, 53)(21, 42)(22, 43)(23, 48)(24, 59)(25, 51)(26, 64)(27, 61)(28, 50)(29, 56)(30, 69)(31, 70)(32, 65)(33, 54)(34, 55)(35, 60)(36, 71)(73, 118)(74, 117)(75, 112)(76, 131)(77, 114)(78, 139)(79, 138)(80, 109)(81, 116)(82, 120)(83, 115)(84, 110)(85, 140)(86, 144)(87, 127)(88, 135)(89, 119)(90, 137)(91, 143)(92, 141)(93, 134)(94, 133)(95, 113)(96, 142)(97, 122)(98, 121)(99, 125)(100, 126)(101, 123)(102, 124)(103, 111)(104, 132)(105, 130)(106, 129)(107, 136)(108, 128)

MAP           : A4.536
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2 | (u.1^-1 * u.2^-1)^2, u.1^6, u.2^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2 | (x.1^-1 * x.2^-1)^2, x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^2, x.1^-2 * x.2 * x.1^-1 * x.2 * x.1^-1, (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, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 40)(2, 63)(3, 68)(4, 45)(5, 37)(6, 62)(7, 61)(8, 47)(9, 67)(10, 66)(11, 38)(12, 41)(13, 55)(14, 54)(15, 50)(16, 72)(17, 69)(18, 58)(19, 57)(20, 51)(21, 65)(22, 71)(23, 70)(24, 64)(25, 53)(26, 59)(27, 46)(28, 49)(29, 60)(30, 44)(31, 48)(32, 42)(33, 52)(34, 39)(35, 56)(36, 43)(73, 111)(74, 124)(75, 121)(76, 110)(77, 116)(78, 129)(79, 130)(80, 125)(81, 114)(82, 115)(83, 120)(84, 131)(85, 123)(86, 136)(87, 133)(88, 122)(89, 128)(90, 141)(91, 142)(92, 137)(93, 126)(94, 127)(95, 132)(96, 143)(97, 135)(98, 112)(99, 109)(100, 134)(101, 140)(102, 117)(103, 118)(104, 113)(105, 138)(106, 139)(107, 144)(108, 119)

MAP           : A4.537
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3 * x.2 * x.3, (x.4^-1, x.2^-1), (x.4 * x.1^-1)^2, (x.2 * x.3^-1)^2, (x.1 * x.2^-1)^3, (x.3 * x.4^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 131)(20, 144)(21, 134)(22, 127)(23, 130)(24, 129)(25, 137)(26, 132)(27, 140)(28, 133)(29, 136)(30, 135)(31, 143)(32, 138)(33, 128)(34, 139)(35, 142)(36, 141)(37, 116)(38, 115)(39, 113)(40, 111)(41, 114)(42, 109)(43, 123)(44, 112)(45, 121)(46, 126)(47, 110)(48, 124)(49, 120)(50, 125)(51, 118)(52, 122)(53, 117)(54, 119)(55, 92)(56, 91)(57, 107)(58, 105)(59, 108)(60, 103)(61, 99)(62, 106)(63, 97)(64, 102)(65, 104)(66, 100)(67, 96)(68, 101)(69, 94)(70, 98)(71, 93)(72, 95)

MAP           : A4.538
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.4^2, x.3^-3 * x.4, (x.4 * x.1^-1)^2, x.3^-2 * x.4 * x.3^-1, (x.2 * x.3^-1)^2, x.2^-1 * x.4 * x.2^-1 * x.3^-1, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 116)(38, 115)(39, 113)(40, 111)(41, 114)(42, 109)(43, 123)(44, 112)(45, 121)(46, 126)(47, 110)(48, 124)(49, 120)(50, 125)(51, 118)(52, 122)(53, 117)(54, 119)(55, 93)(56, 100)(57, 91)(58, 96)(59, 98)(60, 94)(61, 108)(62, 95)(63, 106)(64, 92)(65, 105)(66, 107)(67, 104)(68, 103)(69, 101)(70, 99)(71, 102)(72, 97)

MAP           : A4.539
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2 | (u.1^-1 * u.2^-1)^2, u.1^6, u.2^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2 | (x.1^-1 * x.2^-1)^2, x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^2, x.1^-2 * x.2 * x.1^-1 * x.2 * x.1^-1, (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, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 46)(2, 45)(3, 40)(4, 59)(5, 42)(6, 67)(7, 66)(8, 37)(9, 44)(10, 48)(11, 43)(12, 38)(13, 68)(14, 72)(15, 55)(16, 63)(17, 47)(18, 65)(19, 71)(20, 69)(21, 62)(22, 61)(23, 41)(24, 70)(25, 50)(26, 49)(27, 53)(28, 54)(29, 51)(30, 52)(31, 39)(32, 60)(33, 58)(34, 57)(35, 64)(36, 56)(73, 135)(74, 112)(75, 109)(76, 134)(77, 140)(78, 117)(79, 118)(80, 113)(81, 138)(82, 139)(83, 144)(84, 119)(85, 111)(86, 124)(87, 121)(88, 110)(89, 116)(90, 129)(91, 130)(92, 125)(93, 114)(94, 115)(95, 120)(96, 131)(97, 123)(98, 136)(99, 133)(100, 122)(101, 128)(102, 141)(103, 142)(104, 137)(105, 126)(106, 127)(107, 132)(108, 143)

MAP           : A4.540
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3 * x.4 * x.3, (x.2^-1, x.4^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 114)(38, 119)(39, 112)(40, 116)(41, 111)(42, 113)(43, 110)(44, 109)(45, 125)(46, 123)(47, 126)(48, 121)(49, 117)(50, 124)(51, 115)(52, 120)(53, 122)(54, 118)(55, 94)(56, 105)(57, 96)(58, 95)(59, 91)(60, 98)(61, 100)(62, 93)(63, 102)(64, 101)(65, 97)(66, 104)(67, 106)(68, 99)(69, 108)(70, 107)(71, 103)(72, 92)

MAP           : A4.541
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.2^2, x.2 * x.3^3, (x.1 * x.2)^2, x.3^-1 * x.4^-1 * x.2 * x.4^-1, x.3^-3 * x.2, (x.3 * x.4^-1)^2, (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 123)(38, 112)(39, 121)(40, 126)(41, 110)(42, 124)(43, 120)(44, 125)(45, 118)(46, 122)(47, 117)(48, 119)(49, 116)(50, 115)(51, 113)(52, 111)(53, 114)(54, 109)(55, 103)(56, 104)(57, 105)(58, 106)(59, 107)(60, 108)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)

MAP           : A4.542
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3 * x.4 * x.3, (x.2^-1, x.4^-1), (x.3 * x.4^-1)^2, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 127)(21, 143)(22, 141)(23, 144)(24, 139)(25, 135)(26, 142)(27, 133)(28, 138)(29, 140)(30, 136)(31, 132)(32, 137)(33, 130)(34, 134)(35, 129)(36, 131)(37, 116)(38, 115)(39, 113)(40, 111)(41, 114)(42, 109)(43, 123)(44, 112)(45, 121)(46, 126)(47, 110)(48, 124)(49, 120)(50, 125)(51, 118)(52, 122)(53, 117)(54, 119)(55, 95)(56, 108)(57, 98)(58, 91)(59, 94)(60, 93)(61, 101)(62, 96)(63, 104)(64, 97)(65, 100)(66, 99)(67, 107)(68, 102)(69, 92)(70, 103)(71, 106)(72, 105)

MAP           : A4.543
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 125)(38, 117)(39, 116)(40, 115)(41, 121)(42, 119)(43, 112)(44, 111)(45, 110)(46, 120)(47, 114)(48, 118)(49, 113)(50, 124)(51, 126)(52, 122)(53, 109)(54, 123)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)

MAP           : A4.544
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 125)(38, 117)(39, 116)(40, 115)(41, 121)(42, 119)(43, 112)(44, 111)(45, 110)(46, 120)(47, 114)(48, 118)(49, 113)(50, 124)(51, 126)(52, 122)(53, 109)(54, 123)(55, 95)(56, 91)(57, 105)(58, 108)(59, 92)(60, 102)(61, 93)(62, 94)(63, 103)(64, 101)(65, 104)(66, 106)(67, 107)(68, 100)(69, 97)(70, 96)(71, 99)(72, 98)

MAP           : A4.545
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 125)(38, 117)(39, 116)(40, 115)(41, 121)(42, 119)(43, 112)(44, 111)(45, 110)(46, 120)(47, 114)(48, 118)(49, 113)(50, 124)(51, 126)(52, 122)(53, 109)(54, 123)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)

MAP           : A4.546
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 125)(38, 117)(39, 116)(40, 115)(41, 121)(42, 119)(43, 112)(44, 111)(45, 110)(46, 120)(47, 114)(48, 118)(49, 113)(50, 124)(51, 126)(52, 122)(53, 109)(54, 123)(55, 96)(56, 106)(57, 104)(58, 91)(59, 102)(60, 94)(61, 101)(62, 92)(63, 93)(64, 103)(65, 107)(66, 108)(67, 105)(68, 99)(69, 100)(70, 98)(71, 97)(72, 95)

MAP           : A4.547
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 125)(38, 117)(39, 116)(40, 115)(41, 121)(42, 119)(43, 112)(44, 111)(45, 110)(46, 120)(47, 114)(48, 118)(49, 113)(50, 124)(51, 126)(52, 122)(53, 109)(54, 123)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)

MAP           : A4.548
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 125)(38, 117)(39, 116)(40, 115)(41, 121)(42, 119)(43, 112)(44, 111)(45, 110)(46, 120)(47, 114)(48, 118)(49, 113)(50, 124)(51, 126)(52, 122)(53, 109)(54, 123)(55, 108)(56, 94)(57, 103)(58, 102)(59, 98)(60, 95)(61, 99)(62, 96)(63, 100)(64, 97)(65, 93)(66, 92)(67, 101)(68, 105)(69, 107)(70, 91)(71, 104)(72, 106)

MAP           : A4.549
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 119)(38, 122)(39, 124)(40, 125)(41, 118)(42, 115)(43, 114)(44, 117)(45, 116)(46, 113)(47, 109)(48, 123)(49, 126)(50, 110)(51, 120)(52, 111)(53, 112)(54, 121)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)

MAP           : A4.550
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 119)(38, 122)(39, 124)(40, 125)(41, 118)(42, 115)(43, 114)(44, 117)(45, 116)(46, 113)(47, 109)(48, 123)(49, 126)(50, 110)(51, 120)(52, 111)(53, 112)(54, 121)(55, 95)(56, 91)(57, 105)(58, 108)(59, 92)(60, 102)(61, 93)(62, 94)(63, 103)(64, 101)(65, 104)(66, 106)(67, 107)(68, 100)(69, 97)(70, 96)(71, 99)(72, 98)

MAP           : A4.551
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 119)(38, 122)(39, 124)(40, 125)(41, 118)(42, 115)(43, 114)(44, 117)(45, 116)(46, 113)(47, 109)(48, 123)(49, 126)(50, 110)(51, 120)(52, 111)(53, 112)(54, 121)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)

MAP           : A4.552
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 119)(38, 122)(39, 124)(40, 125)(41, 118)(42, 115)(43, 114)(44, 117)(45, 116)(46, 113)(47, 109)(48, 123)(49, 126)(50, 110)(51, 120)(52, 111)(53, 112)(54, 121)(55, 96)(56, 106)(57, 104)(58, 91)(59, 102)(60, 94)(61, 101)(62, 92)(63, 93)(64, 103)(65, 107)(66, 108)(67, 105)(68, 99)(69, 100)(70, 98)(71, 97)(72, 95)

MAP           : A4.553
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 119)(38, 122)(39, 124)(40, 125)(41, 118)(42, 115)(43, 114)(44, 117)(45, 116)(46, 113)(47, 109)(48, 123)(49, 126)(50, 110)(51, 120)(52, 111)(53, 112)(54, 121)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)

MAP           : A4.554
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 119)(38, 122)(39, 124)(40, 125)(41, 118)(42, 115)(43, 114)(44, 117)(45, 116)(46, 113)(47, 109)(48, 123)(49, 126)(50, 110)(51, 120)(52, 111)(53, 112)(54, 121)(55, 102)(56, 96)(57, 100)(58, 95)(59, 106)(60, 108)(61, 104)(62, 91)(63, 105)(64, 107)(65, 99)(66, 98)(67, 97)(68, 103)(69, 101)(70, 94)(71, 93)(72, 92)

MAP           : A4.555
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 105)(56, 97)(57, 95)(58, 100)(59, 93)(60, 103)(61, 92)(62, 101)(63, 102)(64, 94)(65, 98)(66, 99)(67, 96)(68, 108)(69, 91)(70, 107)(71, 106)(72, 104)

MAP           : A4.556
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 101)(56, 104)(57, 106)(58, 107)(59, 100)(60, 97)(61, 96)(62, 99)(63, 98)(64, 95)(65, 91)(66, 105)(67, 108)(68, 92)(69, 102)(70, 93)(71, 94)(72, 103)

MAP           : A4.557
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 103)(56, 107)(57, 108)(58, 105)(59, 99)(60, 100)(61, 98)(62, 97)(63, 95)(64, 96)(65, 106)(66, 104)(67, 91)(68, 102)(69, 94)(70, 101)(71, 92)(72, 93)

MAP           : A4.558
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 100)(56, 101)(57, 102)(58, 103)(59, 104)(60, 105)(61, 106)(62, 107)(63, 108)(64, 91)(65, 92)(66, 93)(67, 94)(68, 95)(69, 96)(70, 97)(71, 98)(72, 99)

MAP           : A4.559
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 97)(56, 93)(57, 92)(58, 101)(59, 105)(60, 107)(61, 91)(62, 104)(63, 106)(64, 108)(65, 94)(66, 103)(67, 102)(68, 98)(69, 95)(70, 99)(71, 96)(72, 100)

MAP           : A4.560
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 99)(56, 103)(57, 94)(58, 93)(59, 107)(60, 104)(61, 108)(62, 105)(63, 91)(64, 106)(65, 102)(66, 101)(67, 92)(68, 96)(69, 98)(70, 100)(71, 95)(72, 97)

MAP           : A4.561
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 105)(56, 97)(57, 95)(58, 100)(59, 93)(60, 103)(61, 92)(62, 101)(63, 102)(64, 94)(65, 98)(66, 99)(67, 96)(68, 108)(69, 91)(70, 107)(71, 106)(72, 104)

MAP           : A4.562
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 104)(56, 100)(57, 96)(58, 99)(59, 101)(60, 93)(61, 102)(62, 103)(63, 94)(64, 92)(65, 95)(66, 97)(67, 98)(68, 91)(69, 106)(70, 105)(71, 108)(72, 107)

MAP           : A4.563
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 101)(56, 104)(57, 106)(58, 107)(59, 100)(60, 97)(61, 96)(62, 99)(63, 98)(64, 95)(65, 91)(66, 105)(67, 108)(68, 92)(69, 102)(70, 93)(71, 94)(72, 103)

MAP           : A4.564
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 134)(20, 144)(21, 143)(22, 142)(23, 130)(24, 128)(25, 139)(26, 138)(27, 137)(28, 129)(29, 141)(30, 127)(31, 140)(32, 133)(33, 135)(34, 131)(35, 136)(36, 132)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 103)(56, 107)(57, 108)(58, 105)(59, 99)(60, 100)(61, 98)(62, 97)(63, 95)(64, 96)(65, 106)(66, 104)(67, 91)(68, 102)(69, 94)(70, 101)(71, 92)(72, 93)

MAP           : A4.565
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 97)(56, 93)(57, 92)(58, 101)(59, 105)(60, 107)(61, 91)(62, 104)(63, 106)(64, 108)(65, 94)(66, 103)(67, 102)(68, 98)(69, 95)(70, 99)(71, 96)(72, 100)

MAP           : A4.566
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 99)(56, 103)(57, 94)(58, 93)(59, 107)(60, 104)(61, 108)(62, 105)(63, 91)(64, 106)(65, 102)(66, 101)(67, 92)(68, 96)(69, 98)(70, 100)(71, 95)(72, 97)

MAP           : A4.567
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 107)(56, 99)(57, 98)(58, 97)(59, 103)(60, 101)(61, 94)(62, 93)(63, 92)(64, 102)(65, 96)(66, 100)(67, 95)(68, 106)(69, 108)(70, 104)(71, 91)(72, 105)

MAP           : A4.568
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 105)(56, 97)(57, 95)(58, 100)(59, 93)(60, 103)(61, 92)(62, 101)(63, 102)(64, 94)(65, 98)(66, 99)(67, 96)(68, 108)(69, 91)(70, 107)(71, 106)(72, 104)

MAP           : A4.569
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 104)(56, 100)(57, 96)(58, 99)(59, 101)(60, 93)(61, 102)(62, 103)(63, 94)(64, 92)(65, 95)(66, 97)(67, 98)(68, 91)(69, 106)(70, 105)(71, 108)(72, 107)

MAP           : A4.570
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 142)(20, 138)(21, 137)(22, 128)(23, 132)(24, 134)(25, 136)(26, 131)(27, 133)(28, 135)(29, 139)(30, 130)(31, 129)(32, 143)(33, 140)(34, 144)(35, 141)(36, 127)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 100)(56, 101)(57, 102)(58, 103)(59, 104)(60, 105)(61, 106)(62, 107)(63, 108)(64, 91)(65, 92)(66, 93)(67, 94)(68, 95)(69, 96)(70, 97)(71, 98)(72, 99)

MAP           : A4.571
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 115)(38, 111)(39, 110)(40, 119)(41, 123)(42, 125)(43, 109)(44, 122)(45, 124)(46, 126)(47, 112)(48, 121)(49, 120)(50, 116)(51, 113)(52, 117)(53, 114)(54, 118)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)

MAP           : A4.572
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 115)(38, 111)(39, 110)(40, 119)(41, 123)(42, 125)(43, 109)(44, 122)(45, 124)(46, 126)(47, 112)(48, 121)(49, 120)(50, 116)(51, 113)(52, 117)(53, 114)(54, 118)(55, 96)(56, 106)(57, 104)(58, 91)(59, 102)(60, 94)(61, 101)(62, 92)(63, 93)(64, 103)(65, 107)(66, 108)(67, 105)(68, 99)(69, 100)(70, 98)(71, 97)(72, 95)

MAP           : A4.573
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 115)(38, 111)(39, 110)(40, 119)(41, 123)(42, 125)(43, 109)(44, 122)(45, 124)(46, 126)(47, 112)(48, 121)(49, 120)(50, 116)(51, 113)(52, 117)(53, 114)(54, 118)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)

MAP           : A4.574
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 115)(38, 111)(39, 110)(40, 119)(41, 123)(42, 125)(43, 109)(44, 122)(45, 124)(46, 126)(47, 112)(48, 121)(49, 120)(50, 116)(51, 113)(52, 117)(53, 114)(54, 118)(55, 102)(56, 96)(57, 100)(58, 95)(59, 106)(60, 108)(61, 104)(62, 91)(63, 105)(64, 107)(65, 99)(66, 98)(67, 97)(68, 103)(69, 101)(70, 94)(71, 93)(72, 92)

MAP           : A4.575
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 115)(38, 111)(39, 110)(40, 119)(41, 123)(42, 125)(43, 109)(44, 122)(45, 124)(46, 126)(47, 112)(48, 121)(49, 120)(50, 116)(51, 113)(52, 117)(53, 114)(54, 118)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)

MAP           : A4.576
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 115)(38, 111)(39, 110)(40, 119)(41, 123)(42, 125)(43, 109)(44, 122)(45, 124)(46, 126)(47, 112)(48, 121)(49, 120)(50, 116)(51, 113)(52, 117)(53, 114)(54, 118)(55, 108)(56, 94)(57, 103)(58, 102)(59, 98)(60, 95)(61, 99)(62, 96)(63, 100)(64, 97)(65, 93)(66, 92)(67, 101)(68, 105)(69, 107)(70, 91)(71, 104)(72, 106)

MAP           : A4.577
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2 | (u.1^-1 * u.2^-1)^2, u.1^6, u.2^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2 | (x.1^-1 * x.2^-1)^2, x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^2, x.1^-2 * x.2 * x.1^-1 * x.2 * x.1^-1, (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, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 41)(2, 47)(3, 70)(4, 37)(5, 48)(6, 68)(7, 72)(8, 66)(9, 40)(10, 63)(11, 44)(12, 67)(13, 64)(14, 51)(15, 56)(16, 69)(17, 61)(18, 50)(19, 49)(20, 71)(21, 55)(22, 54)(23, 62)(24, 65)(25, 43)(26, 42)(27, 38)(28, 60)(29, 57)(30, 46)(31, 45)(32, 39)(33, 53)(34, 59)(35, 58)(36, 52)(73, 135)(74, 112)(75, 109)(76, 134)(77, 140)(78, 117)(79, 118)(80, 113)(81, 138)(82, 139)(83, 144)(84, 119)(85, 111)(86, 124)(87, 121)(88, 110)(89, 116)(90, 129)(91, 130)(92, 125)(93, 114)(94, 115)(95, 120)(96, 131)(97, 123)(98, 136)(99, 133)(100, 122)(101, 128)(102, 141)(103, 142)(104, 137)(105, 126)(106, 127)(107, 132)(108, 143)

MAP           : A4.578
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 2 ]
UNIGROUP      : < u.1, u.2 | (u.1^-1 * u.2^-1)^2, u.1^6, u.2^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2 | (x.1^-1 * x.2^-1)^2, x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^2, x.1^-2 * x.2 * x.1^-1 * x.2 * x.1^-1, (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, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 44)(2, 48)(3, 67)(4, 39)(5, 59)(6, 41)(7, 47)(8, 45)(9, 38)(10, 37)(11, 53)(12, 46)(13, 62)(14, 61)(15, 65)(16, 66)(17, 63)(18, 64)(19, 51)(20, 72)(21, 70)(22, 69)(23, 40)(24, 68)(25, 58)(26, 57)(27, 52)(28, 71)(29, 54)(30, 43)(31, 42)(32, 49)(33, 56)(34, 60)(35, 55)(36, 50)(73, 111)(74, 124)(75, 121)(76, 110)(77, 116)(78, 129)(79, 130)(80, 125)(81, 114)(82, 115)(83, 120)(84, 131)(85, 123)(86, 136)(87, 133)(88, 122)(89, 128)(90, 141)(91, 142)(92, 137)(93, 126)(94, 127)(95, 132)(96, 143)(97, 135)(98, 112)(99, 109)(100, 134)(101, 140)(102, 117)(103, 118)(104, 113)(105, 138)(106, 139)(107, 144)(108, 119)

MAP           : A4.579
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 117)(38, 121)(39, 112)(40, 111)(41, 125)(42, 122)(43, 126)(44, 123)(45, 109)(46, 124)(47, 120)(48, 119)(49, 110)(50, 114)(51, 116)(52, 118)(53, 113)(54, 115)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)

MAP           : A4.580
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 117)(38, 121)(39, 112)(40, 111)(41, 125)(42, 122)(43, 126)(44, 123)(45, 109)(46, 124)(47, 120)(48, 119)(49, 110)(50, 114)(51, 116)(52, 118)(53, 113)(54, 115)(55, 102)(56, 96)(57, 100)(58, 95)(59, 106)(60, 108)(61, 104)(62, 91)(63, 105)(64, 107)(65, 99)(66, 98)(67, 97)(68, 103)(69, 101)(70, 94)(71, 93)(72, 92)

MAP           : A4.581
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 117)(38, 121)(39, 112)(40, 111)(41, 125)(42, 122)(43, 126)(44, 123)(45, 109)(46, 124)(47, 120)(48, 119)(49, 110)(50, 114)(51, 116)(52, 118)(53, 113)(54, 115)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)

MAP           : A4.582
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 117)(38, 121)(39, 112)(40, 111)(41, 125)(42, 122)(43, 126)(44, 123)(45, 109)(46, 124)(47, 120)(48, 119)(49, 110)(50, 114)(51, 116)(52, 118)(53, 113)(54, 115)(55, 108)(56, 94)(57, 103)(58, 102)(59, 98)(60, 95)(61, 99)(62, 96)(63, 100)(64, 97)(65, 93)(66, 92)(67, 101)(68, 105)(69, 107)(70, 91)(71, 104)(72, 106)

MAP           : A4.583
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 38)(20, 44)(21, 43)(22, 42)(23, 37)(24, 45)(25, 46)(26, 52)(27, 51)(28, 53)(29, 39)(30, 47)(31, 40)(32, 41)(33, 54)(34, 50)(35, 48)(36, 49)(55, 102)(56, 101)(57, 103)(58, 106)(59, 107)(60, 104)(61, 94)(62, 93)(63, 95)(64, 96)(65, 108)(66, 105)(67, 98)(68, 100)(69, 91)(70, 97)(71, 99)(72, 92)(109, 135)(110, 141)(111, 128)(112, 129)(113, 132)(114, 133)(115, 134)(116, 144)(117, 136)(118, 142)(119, 127)(120, 131)(121, 137)(122, 130)(123, 143)(124, 139)(125, 140)(126, 138)

MAP           : A4.584
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 41)(20, 37)(21, 47)(22, 49)(23, 50)(24, 40)(25, 39)(26, 38)(27, 42)(28, 43)(29, 48)(30, 53)(31, 54)(32, 52)(33, 45)(34, 44)(35, 46)(36, 51)(55, 102)(56, 101)(57, 103)(58, 106)(59, 107)(60, 104)(61, 94)(62, 93)(63, 95)(64, 96)(65, 108)(66, 105)(67, 98)(68, 100)(69, 91)(70, 97)(71, 99)(72, 92)(109, 144)(110, 139)(111, 142)(112, 136)(113, 141)(114, 143)(115, 140)(116, 130)(117, 138)(118, 131)(119, 134)(120, 128)(121, 133)(122, 135)(123, 137)(124, 132)(125, 127)(126, 129)

MAP           : A4.585
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {4, 4, 3})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 4, 3 ]
UNIGROUP      : < u.1, u.2 | u.1^4, u.2^4, (u.1^-1 * u.2^-1)^3 >
CTG (small)   : <36, 9>
CTG (fp)      : < x.1, x.2 | x.1^4, x.2^4, (x.2 * x.1^-1)^2, (x.1^-1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 39)(2, 58)(3, 43)(4, 53)(5, 72)(6, 62)(7, 45)(8, 52)(9, 37)(10, 59)(11, 66)(12, 68)(13, 60)(14, 51)(15, 56)(16, 38)(17, 46)(18, 49)(19, 54)(20, 57)(21, 50)(22, 44)(23, 40)(24, 55)(25, 70)(26, 48)(27, 71)(28, 61)(29, 63)(30, 41)(31, 64)(32, 42)(33, 65)(34, 67)(35, 69)(36, 47)(73, 126)(74, 129)(75, 122)(76, 116)(77, 112)(78, 127)(79, 142)(80, 120)(81, 143)(82, 133)(83, 135)(84, 113)(85, 136)(86, 114)(87, 137)(88, 139)(89, 141)(90, 119)(91, 111)(92, 130)(93, 115)(94, 125)(95, 144)(96, 134)(97, 117)(98, 124)(99, 109)(100, 131)(101, 138)(102, 140)(103, 132)(104, 123)(105, 128)(106, 110)(107, 118)(108, 121)

MAP           : A4.586
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {4, 4, 3})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 4, 3 ]
UNIGROUP      : < u.1, u.2 | u.1^4, u.2^4, (u.1^-1 * u.2^-1)^3 >
CTG (small)   : <36, 9>
CTG (fp)      : < x.1, x.2 | x.1^4, x.2^4, (x.2 * x.1^-1)^2, (x.1^-1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 39)(2, 58)(3, 43)(4, 53)(5, 72)(6, 62)(7, 45)(8, 52)(9, 37)(10, 59)(11, 66)(12, 68)(13, 60)(14, 51)(15, 56)(16, 38)(17, 46)(18, 49)(19, 54)(20, 57)(21, 50)(22, 44)(23, 40)(24, 55)(25, 70)(26, 48)(27, 71)(28, 61)(29, 63)(30, 41)(31, 64)(32, 42)(33, 65)(34, 67)(35, 69)(36, 47)(73, 114)(74, 141)(75, 110)(76, 128)(77, 136)(78, 139)(79, 118)(80, 132)(81, 119)(82, 121)(83, 123)(84, 137)(85, 124)(86, 138)(87, 125)(88, 115)(89, 117)(90, 131)(91, 135)(92, 142)(93, 127)(94, 113)(95, 120)(96, 122)(97, 129)(98, 112)(99, 133)(100, 143)(101, 126)(102, 116)(103, 144)(104, 111)(105, 140)(106, 134)(107, 130)(108, 109)

MAP           : A4.587
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {4, 4, 3})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 4, 3 ]
UNIGROUP      : < u.1, u.2 | u.1^4, u.2^4, (u.1^-1 * u.2^-1)^3 >
CTG (small)   : <36, 9>
CTG (fp)      : < x.1, x.2 | x.1^4, x.2^4, (x.2 * x.1^-1)^2, (x.1^-1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 45)(2, 52)(3, 37)(4, 59)(5, 66)(6, 68)(7, 39)(8, 58)(9, 43)(10, 53)(11, 72)(12, 62)(13, 54)(14, 57)(15, 50)(16, 44)(17, 40)(18, 55)(19, 60)(20, 51)(21, 56)(22, 38)(23, 46)(24, 49)(25, 64)(26, 42)(27, 65)(28, 67)(29, 69)(30, 47)(31, 70)(32, 48)(33, 71)(34, 61)(35, 63)(36, 41)(73, 135)(74, 142)(75, 127)(76, 113)(77, 120)(78, 122)(79, 129)(80, 112)(81, 133)(82, 143)(83, 126)(84, 116)(85, 144)(86, 111)(87, 140)(88, 134)(89, 130)(90, 109)(91, 114)(92, 141)(93, 110)(94, 128)(95, 136)(96, 139)(97, 118)(98, 132)(99, 119)(100, 121)(101, 123)(102, 137)(103, 124)(104, 138)(105, 125)(106, 115)(107, 117)(108, 131)

MAP           : A4.588
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)(3, 4)
ORBIFOLD      : O(0, {4, 4, 3})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 4, 3 ]
UNIGROUP      : < u.1, u.2 | u.1^4, u.2^4, (u.1^-1 * u.2^-1)^3 >
CTG (small)   : <36, 9>
CTG (fp)      : < x.1, x.2 | x.1^4, x.2^4, (x.2 * x.1^-1)^2, (x.1^-1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 73, 109)(2, 38, 74, 110)(3, 39, 75, 111)(4, 40, 76, 112)(5, 41, 77, 113)(6, 42, 78, 114)(7, 43, 79, 115)(8, 44, 80, 116)(9, 45, 81, 117)(10, 46, 82, 118)(11, 47, 83, 119)(12, 48, 84, 120)(13, 49, 85, 121)(14, 50, 86, 122)(15, 51, 87, 123)(16, 52, 88, 124)(17, 53, 89, 125)(18, 54, 90, 126)(19, 55, 91, 127)(20, 56, 92, 128)(21, 57, 93, 129)(22, 58, 94, 130)(23, 59, 95, 131)(24, 60, 96, 132)(25, 61, 97, 133)(26, 62, 98, 134)(27, 63, 99, 135)(28, 64, 100, 136)(29, 65, 101, 137)(30, 66, 102, 138)(31, 67, 103, 139)(32, 68, 104, 140)(33, 69, 105, 141)(34, 70, 106, 142)(35, 71, 107, 143)(36, 72, 108, 144)
L = (1, 45)(2, 52)(3, 37)(4, 59)(5, 66)(6, 68)(7, 39)(8, 58)(9, 43)(10, 53)(11, 72)(12, 62)(13, 54)(14, 57)(15, 50)(16, 44)(17, 40)(18, 55)(19, 60)(20, 51)(21, 56)(22, 38)(23, 46)(24, 49)(25, 64)(26, 42)(27, 65)(28, 67)(29, 69)(30, 47)(31, 70)(32, 48)(33, 71)(34, 61)(35, 63)(36, 41)(73, 144)(74, 111)(75, 140)(76, 134)(77, 130)(78, 109)(79, 124)(80, 138)(81, 125)(82, 115)(83, 117)(84, 131)(85, 118)(86, 132)(87, 119)(88, 121)(89, 123)(90, 137)(91, 129)(92, 112)(93, 133)(94, 143)(95, 126)(96, 116)(97, 135)(98, 142)(99, 127)(100, 113)(101, 120)(102, 122)(103, 114)(104, 141)(105, 110)(106, 128)(107, 136)(108, 139)

MAP           : A4.589
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 107)(56, 99)(57, 98)(58, 97)(59, 103)(60, 101)(61, 94)(62, 93)(63, 92)(64, 102)(65, 96)(66, 100)(67, 95)(68, 106)(69, 108)(70, 104)(71, 91)(72, 105)

MAP           : A4.590
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 104)(56, 100)(57, 96)(58, 99)(59, 101)(60, 93)(61, 102)(62, 103)(63, 94)(64, 92)(65, 95)(66, 97)(67, 98)(68, 91)(69, 106)(70, 105)(71, 108)(72, 107)

MAP           : A4.591
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 101)(56, 104)(57, 106)(58, 107)(59, 100)(60, 97)(61, 96)(62, 99)(63, 98)(64, 95)(65, 91)(66, 105)(67, 108)(68, 92)(69, 102)(70, 93)(71, 94)(72, 103)

MAP           : A4.592
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 103)(56, 107)(57, 108)(58, 105)(59, 99)(60, 100)(61, 98)(62, 97)(63, 95)(64, 96)(65, 106)(66, 104)(67, 91)(68, 102)(69, 94)(70, 101)(71, 92)(72, 93)

MAP           : A4.593
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 128)(20, 131)(21, 133)(22, 134)(23, 127)(24, 142)(25, 141)(26, 144)(27, 143)(28, 140)(29, 136)(30, 132)(31, 135)(32, 137)(33, 129)(34, 138)(35, 139)(36, 130)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 100)(56, 101)(57, 102)(58, 103)(59, 104)(60, 105)(61, 106)(62, 107)(63, 108)(64, 91)(65, 92)(66, 93)(67, 94)(68, 95)(69, 96)(70, 97)(71, 98)(72, 99)

MAP           : A4.594
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 2, 3, 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.1 * u.2^-1)^3, (u.3 * u.4^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.1^-1)^2, (x.2 * x.3)^2, x.4 * x.2^-1 * x.4^-1 * x.2^-1, (x.3 * x.4^-1)^3, (x.1 * x.2^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 130)(20, 134)(21, 135)(22, 132)(23, 144)(24, 127)(25, 143)(26, 142)(27, 140)(28, 141)(29, 133)(30, 131)(31, 136)(32, 129)(33, 139)(34, 128)(35, 137)(36, 138)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 97)(56, 93)(57, 92)(58, 101)(59, 105)(60, 107)(61, 91)(62, 104)(63, 106)(64, 108)(65, 94)(66, 103)(67, 102)(68, 98)(69, 95)(70, 99)(71, 96)(72, 100)

MAP           : A4.595
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, (x.3^-1 * x.2)^2, x.4^2 * x.2^-2, x.1 * x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.4 * x.3^-2, x.3 * x.2^3 * x.4^-1, x.4^2 * x.2^4, (x.3 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 45)(20, 37)(21, 47)(22, 43)(23, 38)(24, 39)(25, 50)(26, 53)(27, 54)(28, 41)(29, 40)(30, 44)(31, 52)(32, 42)(33, 49)(34, 48)(35, 51)(36, 46)(55, 96)(56, 105)(57, 100)(58, 92)(59, 97)(60, 107)(61, 102)(62, 93)(63, 106)(64, 98)(65, 103)(66, 95)(67, 108)(68, 99)(69, 94)(70, 104)(71, 91)(72, 101)(109, 134)(110, 137)(111, 138)(112, 143)(113, 142)(114, 128)(115, 136)(116, 144)(117, 133)(118, 132)(119, 135)(120, 130)(121, 129)(122, 139)(123, 131)(124, 127)(125, 140)(126, 141)

MAP           : A4.596
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, (x.3^-1 * x.2)^2, x.4^2 * x.2^-2, x.1 * x.2^-1 * x.3^-1 * x.4^-1, x.2 * x.4 * x.3^-2, x.3 * x.2^3 * x.4^-1, x.4^2 * x.2^4, (x.3 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 38)(20, 41)(21, 42)(22, 47)(23, 46)(24, 50)(25, 40)(26, 48)(27, 37)(28, 54)(29, 39)(30, 52)(31, 51)(32, 43)(33, 53)(34, 49)(35, 44)(36, 45)(55, 107)(56, 94)(57, 98)(58, 105)(59, 102)(60, 91)(61, 95)(62, 100)(63, 104)(64, 93)(65, 108)(66, 97)(67, 101)(68, 106)(69, 92)(70, 99)(71, 96)(72, 103)(109, 129)(110, 139)(111, 131)(112, 127)(113, 140)(114, 141)(115, 134)(116, 137)(117, 138)(118, 143)(119, 142)(120, 128)(121, 136)(122, 144)(123, 133)(124, 132)(125, 135)(126, 130)

MAP           : A4.597
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.4 * x.3 * x.2, x.3 * x.2^-1 * x.4^-1, x.3 * x.4^-1 * x.3^-1 * x.2^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 38)(20, 41)(21, 42)(22, 47)(23, 46)(24, 50)(25, 40)(26, 48)(27, 37)(28, 54)(29, 39)(30, 52)(31, 51)(32, 43)(33, 53)(34, 49)(35, 44)(36, 45)(55, 101)(56, 106)(57, 92)(58, 99)(59, 96)(60, 103)(61, 107)(62, 94)(63, 98)(64, 105)(65, 102)(66, 91)(67, 95)(68, 100)(69, 104)(70, 93)(71, 108)(72, 97)(109, 134)(110, 137)(111, 138)(112, 143)(113, 142)(114, 128)(115, 136)(116, 144)(117, 133)(118, 132)(119, 135)(120, 130)(121, 129)(122, 139)(123, 131)(124, 127)(125, 140)(126, 141)

MAP           : A4.598
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.1, x.4 * x.3 * x.2, x.3 * x.2^-1 * x.4^-1, x.3 * x.4^-1 * x.3^-1 * x.2^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 45)(20, 37)(21, 47)(22, 43)(23, 38)(24, 39)(25, 50)(26, 53)(27, 54)(28, 41)(29, 40)(30, 44)(31, 52)(32, 42)(33, 49)(34, 48)(35, 51)(36, 46)(55, 101)(56, 106)(57, 92)(58, 99)(59, 96)(60, 103)(61, 107)(62, 94)(63, 98)(64, 105)(65, 102)(66, 91)(67, 95)(68, 100)(69, 104)(70, 93)(71, 108)(72, 97)(109, 142)(110, 132)(111, 139)(112, 138)(113, 141)(114, 136)(115, 135)(116, 127)(117, 137)(118, 133)(119, 128)(120, 129)(121, 140)(122, 143)(123, 144)(124, 131)(125, 130)(126, 134)

MAP           : A4.599
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 40)(20, 42)(21, 41)(22, 48)(23, 49)(24, 47)(25, 37)(26, 45)(27, 39)(28, 38)(29, 50)(30, 52)(31, 53)(32, 54)(33, 43)(34, 51)(35, 44)(36, 46)(55, 98)(56, 106)(57, 100)(58, 99)(59, 92)(60, 105)(61, 107)(62, 104)(63, 108)(64, 102)(65, 97)(66, 93)(67, 96)(68, 91)(69, 103)(70, 95)(71, 101)(72, 94)(109, 137)(110, 129)(111, 130)(112, 140)(113, 138)(114, 131)(115, 132)(116, 133)(117, 127)(118, 135)(119, 139)(120, 144)(121, 142)(122, 143)(123, 128)(124, 136)(125, 141)(126, 134)

MAP           : A4.600
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 43)(20, 46)(21, 45)(22, 37)(23, 39)(24, 38)(25, 51)(26, 53)(27, 44)(28, 54)(29, 42)(30, 40)(31, 41)(32, 47)(33, 52)(34, 48)(35, 49)(36, 50)(55, 98)(56, 106)(57, 100)(58, 99)(59, 92)(60, 105)(61, 107)(62, 104)(63, 108)(64, 102)(65, 97)(66, 93)(67, 96)(68, 91)(69, 103)(70, 95)(71, 101)(72, 94)(109, 144)(110, 139)(111, 142)(112, 136)(113, 141)(114, 143)(115, 140)(116, 130)(117, 138)(118, 131)(119, 134)(120, 128)(121, 133)(122, 135)(123, 137)(124, 132)(125, 127)(126, 129)

MAP           : A4.601
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 45)(20, 51)(21, 38)(22, 39)(23, 42)(24, 43)(25, 44)(26, 54)(27, 46)(28, 52)(29, 37)(30, 41)(31, 47)(32, 40)(33, 53)(34, 49)(35, 50)(36, 48)(55, 98)(56, 106)(57, 100)(58, 99)(59, 92)(60, 105)(61, 107)(62, 104)(63, 108)(64, 102)(65, 97)(66, 93)(67, 96)(68, 91)(69, 103)(70, 95)(71, 101)(72, 94)(109, 143)(110, 138)(111, 144)(112, 134)(113, 136)(114, 142)(115, 139)(116, 137)(117, 140)(118, 130)(119, 141)(120, 135)(121, 128)(122, 133)(123, 131)(124, 129)(125, 132)(126, 127)

MAP           : A4.602
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 47)(20, 39)(21, 40)(22, 50)(23, 48)(24, 41)(25, 42)(26, 43)(27, 37)(28, 45)(29, 49)(30, 54)(31, 52)(32, 53)(33, 38)(34, 46)(35, 51)(36, 44)(55, 98)(56, 106)(57, 100)(58, 99)(59, 92)(60, 105)(61, 107)(62, 104)(63, 108)(64, 102)(65, 97)(66, 93)(67, 96)(68, 91)(69, 103)(70, 95)(71, 101)(72, 94)(109, 130)(110, 132)(111, 131)(112, 138)(113, 139)(114, 137)(115, 127)(116, 135)(117, 129)(118, 128)(119, 140)(120, 142)(121, 143)(122, 144)(123, 133)(124, 141)(125, 134)(126, 136)

MAP           : A4.603
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 53)(20, 48)(21, 54)(22, 44)(23, 46)(24, 52)(25, 49)(26, 47)(27, 50)(28, 40)(29, 51)(30, 45)(31, 38)(32, 43)(33, 41)(34, 39)(35, 42)(36, 37)(55, 98)(56, 106)(57, 100)(58, 99)(59, 92)(60, 105)(61, 107)(62, 104)(63, 108)(64, 102)(65, 97)(66, 93)(67, 96)(68, 91)(69, 103)(70, 95)(71, 101)(72, 94)(109, 135)(110, 141)(111, 128)(112, 129)(113, 132)(114, 133)(115, 134)(116, 144)(117, 136)(118, 142)(119, 127)(120, 131)(121, 137)(122, 130)(123, 143)(124, 139)(125, 140)(126, 138)

MAP           : A4.604
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 54)(20, 49)(21, 52)(22, 46)(23, 51)(24, 53)(25, 50)(26, 40)(27, 48)(28, 41)(29, 44)(30, 38)(31, 43)(32, 45)(33, 47)(34, 42)(35, 37)(36, 39)(55, 98)(56, 106)(57, 100)(58, 99)(59, 92)(60, 105)(61, 107)(62, 104)(63, 108)(64, 102)(65, 97)(66, 93)(67, 96)(68, 91)(69, 103)(70, 95)(71, 101)(72, 94)(109, 133)(110, 136)(111, 135)(112, 127)(113, 129)(114, 128)(115, 141)(116, 143)(117, 134)(118, 144)(119, 132)(120, 130)(121, 131)(122, 137)(123, 142)(124, 138)(125, 139)(126, 140)

MAP           : A4.605
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 40)(20, 42)(21, 41)(22, 48)(23, 49)(24, 47)(25, 37)(26, 45)(27, 39)(28, 38)(29, 50)(30, 52)(31, 53)(32, 54)(33, 43)(34, 51)(35, 44)(36, 46)(55, 104)(56, 95)(57, 102)(58, 108)(59, 106)(60, 103)(61, 101)(62, 91)(63, 94)(64, 93)(65, 107)(66, 100)(67, 105)(68, 98)(69, 96)(70, 92)(71, 97)(72, 99)(109, 143)(110, 138)(111, 144)(112, 134)(113, 136)(114, 142)(115, 139)(116, 137)(117, 140)(118, 130)(119, 141)(120, 135)(121, 128)(122, 133)(123, 131)(124, 129)(125, 132)(126, 127)

MAP           : A4.606
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 43)(20, 46)(21, 45)(22, 37)(23, 39)(24, 38)(25, 51)(26, 53)(27, 44)(28, 54)(29, 42)(30, 40)(31, 41)(32, 47)(33, 52)(34, 48)(35, 49)(36, 50)(55, 104)(56, 95)(57, 102)(58, 108)(59, 106)(60, 103)(61, 101)(62, 91)(63, 94)(64, 93)(65, 107)(66, 100)(67, 105)(68, 98)(69, 96)(70, 92)(71, 97)(72, 99)(109, 135)(110, 141)(111, 128)(112, 129)(113, 132)(114, 133)(115, 134)(116, 144)(117, 136)(118, 142)(119, 127)(120, 131)(121, 137)(122, 130)(123, 143)(124, 139)(125, 140)(126, 138)

MAP           : A4.607
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 45)(20, 51)(21, 38)(22, 39)(23, 42)(24, 43)(25, 44)(26, 54)(27, 46)(28, 52)(29, 37)(30, 41)(31, 47)(32, 40)(33, 53)(34, 49)(35, 50)(36, 48)(55, 104)(56, 95)(57, 102)(58, 108)(59, 106)(60, 103)(61, 101)(62, 91)(63, 94)(64, 93)(65, 107)(66, 100)(67, 105)(68, 98)(69, 96)(70, 92)(71, 97)(72, 99)(109, 133)(110, 136)(111, 135)(112, 127)(113, 129)(114, 128)(115, 141)(116, 143)(117, 134)(118, 144)(119, 132)(120, 130)(121, 131)(122, 137)(123, 142)(124, 138)(125, 139)(126, 140)

MAP           : A4.608
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 47)(20, 39)(21, 40)(22, 50)(23, 48)(24, 41)(25, 42)(26, 43)(27, 37)(28, 45)(29, 49)(30, 54)(31, 52)(32, 53)(33, 38)(34, 46)(35, 51)(36, 44)(55, 104)(56, 95)(57, 102)(58, 108)(59, 106)(60, 103)(61, 101)(62, 91)(63, 94)(64, 93)(65, 107)(66, 100)(67, 105)(68, 98)(69, 96)(70, 92)(71, 97)(72, 99)(109, 144)(110, 139)(111, 142)(112, 136)(113, 141)(114, 143)(115, 140)(116, 130)(117, 138)(118, 131)(119, 134)(120, 128)(121, 133)(122, 135)(123, 137)(124, 132)(125, 127)(126, 129)

MAP           : A4.609
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 53)(20, 48)(21, 54)(22, 44)(23, 46)(24, 52)(25, 49)(26, 47)(27, 50)(28, 40)(29, 51)(30, 45)(31, 38)(32, 43)(33, 41)(34, 39)(35, 42)(36, 37)(55, 104)(56, 95)(57, 102)(58, 108)(59, 106)(60, 103)(61, 101)(62, 91)(63, 94)(64, 93)(65, 107)(66, 100)(67, 105)(68, 98)(69, 96)(70, 92)(71, 97)(72, 99)(109, 130)(110, 132)(111, 131)(112, 138)(113, 139)(114, 137)(115, 127)(116, 135)(117, 129)(118, 128)(119, 140)(120, 142)(121, 143)(122, 144)(123, 133)(124, 141)(125, 134)(126, 136)

MAP           : A4.610
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 54)(20, 49)(21, 52)(22, 46)(23, 51)(24, 53)(25, 50)(26, 40)(27, 48)(28, 41)(29, 44)(30, 38)(31, 43)(32, 45)(33, 47)(34, 42)(35, 37)(36, 39)(55, 104)(56, 95)(57, 102)(58, 108)(59, 106)(60, 103)(61, 101)(62, 91)(63, 94)(64, 93)(65, 107)(66, 100)(67, 105)(68, 98)(69, 96)(70, 92)(71, 97)(72, 99)(109, 137)(110, 129)(111, 130)(112, 140)(113, 138)(114, 131)(115, 132)(116, 133)(117, 127)(118, 135)(119, 139)(120, 144)(121, 142)(122, 143)(123, 128)(124, 136)(125, 141)(126, 134)

MAP           : A4.611
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 38)(20, 44)(21, 43)(22, 42)(23, 37)(24, 45)(25, 46)(26, 52)(27, 51)(28, 53)(29, 39)(30, 47)(31, 40)(32, 41)(33, 54)(34, 50)(35, 48)(36, 49)(55, 93)(56, 97)(57, 96)(58, 95)(59, 101)(60, 91)(61, 99)(62, 100)(63, 92)(64, 105)(65, 94)(66, 103)(67, 104)(68, 102)(69, 98)(70, 107)(71, 108)(72, 106)(109, 130)(110, 132)(111, 131)(112, 138)(113, 139)(114, 137)(115, 127)(116, 135)(117, 129)(118, 128)(119, 140)(120, 142)(121, 143)(122, 144)(123, 133)(124, 141)(125, 134)(126, 136)

MAP           : A4.612
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 41)(20, 37)(21, 47)(22, 49)(23, 50)(24, 40)(25, 39)(26, 38)(27, 42)(28, 43)(29, 48)(30, 53)(31, 54)(32, 52)(33, 45)(34, 44)(35, 46)(36, 51)(55, 93)(56, 97)(57, 96)(58, 95)(59, 101)(60, 91)(61, 99)(62, 100)(63, 92)(64, 105)(65, 94)(66, 103)(67, 104)(68, 102)(69, 98)(70, 107)(71, 108)(72, 106)(109, 135)(110, 141)(111, 128)(112, 129)(113, 132)(114, 133)(115, 134)(116, 144)(117, 136)(118, 142)(119, 127)(120, 131)(121, 137)(122, 130)(123, 143)(124, 139)(125, 140)(126, 138)

MAP           : A4.613
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 40)(20, 42)(21, 41)(22, 48)(23, 49)(24, 47)(25, 37)(26, 45)(27, 39)(28, 38)(29, 50)(30, 52)(31, 53)(32, 54)(33, 43)(34, 51)(35, 44)(36, 46)(55, 93)(56, 97)(57, 96)(58, 95)(59, 101)(60, 91)(61, 99)(62, 100)(63, 92)(64, 105)(65, 94)(66, 103)(67, 104)(68, 102)(69, 98)(70, 107)(71, 108)(72, 106)(109, 128)(110, 134)(111, 133)(112, 132)(113, 127)(114, 135)(115, 136)(116, 142)(117, 141)(118, 143)(119, 129)(120, 137)(121, 130)(122, 131)(123, 144)(124, 140)(125, 138)(126, 139)

MAP           : A4.614
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 43)(20, 46)(21, 45)(22, 37)(23, 39)(24, 38)(25, 51)(26, 53)(27, 44)(28, 54)(29, 42)(30, 40)(31, 41)(32, 47)(33, 52)(34, 48)(35, 49)(36, 50)(55, 93)(56, 97)(57, 96)(58, 95)(59, 101)(60, 91)(61, 99)(62, 100)(63, 92)(64, 105)(65, 94)(66, 103)(67, 104)(68, 102)(69, 98)(70, 107)(71, 108)(72, 106)(109, 137)(110, 129)(111, 130)(112, 140)(113, 138)(114, 131)(115, 132)(116, 133)(117, 127)(118, 135)(119, 139)(120, 144)(121, 142)(122, 143)(123, 128)(124, 136)(125, 141)(126, 134)

MAP           : A4.615
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 45)(20, 51)(21, 38)(22, 39)(23, 42)(24, 43)(25, 44)(26, 54)(27, 46)(28, 52)(29, 37)(30, 41)(31, 47)(32, 40)(33, 53)(34, 49)(35, 50)(36, 48)(55, 93)(56, 97)(57, 96)(58, 95)(59, 101)(60, 91)(61, 99)(62, 100)(63, 92)(64, 105)(65, 94)(66, 103)(67, 104)(68, 102)(69, 98)(70, 107)(71, 108)(72, 106)(109, 131)(110, 127)(111, 137)(112, 139)(113, 140)(114, 130)(115, 129)(116, 128)(117, 132)(118, 133)(119, 138)(120, 143)(121, 144)(122, 142)(123, 135)(124, 134)(125, 136)(126, 141)

MAP           : A4.616
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 47)(20, 39)(21, 40)(22, 50)(23, 48)(24, 41)(25, 42)(26, 43)(27, 37)(28, 45)(29, 49)(30, 54)(31, 52)(32, 53)(33, 38)(34, 46)(35, 51)(36, 44)(55, 93)(56, 97)(57, 96)(58, 95)(59, 101)(60, 91)(61, 99)(62, 100)(63, 92)(64, 105)(65, 94)(66, 103)(67, 104)(68, 102)(69, 98)(70, 107)(71, 108)(72, 106)(109, 133)(110, 136)(111, 135)(112, 127)(113, 129)(114, 128)(115, 141)(116, 143)(117, 134)(118, 144)(119, 132)(120, 130)(121, 131)(122, 137)(123, 142)(124, 138)(125, 139)(126, 140)

MAP           : A4.617
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 117)(38, 121)(39, 112)(40, 111)(41, 125)(42, 122)(43, 126)(44, 123)(45, 109)(46, 124)(47, 120)(48, 119)(49, 110)(50, 114)(51, 116)(52, 118)(53, 113)(54, 115)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)

MAP           : A4.618
NOTES         : type I, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 8)(3, 7)(4, 6)
ORBIFOLD      : O(0, {3, 3, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 3, 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, (u.1 * u.2^-1)^2, (u.3 * u.4^-1)^2, (u.4 * u.1^-1)^3, (u.2 * u.3^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, (x.4 * x.3)^2, x.4 * x.2 * x.4 * x.2^-1, (x.1 * x.2^-1)^2, (x.4 * x.1^-1)^3, (x.2 * x.3)^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.4)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 129)(20, 141)(21, 127)(22, 140)(23, 133)(24, 135)(25, 131)(26, 136)(27, 132)(28, 134)(29, 144)(30, 143)(31, 142)(32, 130)(33, 128)(34, 139)(35, 138)(36, 137)(37, 117)(38, 121)(39, 112)(40, 111)(41, 125)(42, 122)(43, 126)(44, 123)(45, 109)(46, 124)(47, 120)(48, 119)(49, 110)(50, 114)(51, 116)(52, 118)(53, 113)(54, 115)(55, 95)(56, 91)(57, 105)(58, 108)(59, 92)(60, 102)(61, 93)(62, 94)(63, 103)(64, 101)(65, 104)(66, 106)(67, 107)(68, 100)(69, 97)(70, 96)(71, 99)(72, 98)

MAP           : A4.619
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 40)(20, 42)(21, 41)(22, 48)(23, 49)(24, 47)(25, 37)(26, 45)(27, 39)(28, 38)(29, 50)(30, 52)(31, 53)(32, 54)(33, 43)(34, 51)(35, 44)(36, 46)(55, 96)(56, 99)(57, 91)(58, 101)(59, 94)(60, 93)(61, 92)(62, 105)(63, 97)(64, 98)(65, 95)(66, 104)(67, 102)(68, 103)(69, 100)(70, 108)(71, 106)(72, 107)(109, 135)(110, 141)(111, 128)(112, 129)(113, 132)(114, 133)(115, 134)(116, 144)(117, 136)(118, 142)(119, 127)(120, 131)(121, 137)(122, 130)(123, 143)(124, 139)(125, 140)(126, 138)

MAP           : A4.620
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 43)(20, 46)(21, 45)(22, 37)(23, 39)(24, 38)(25, 51)(26, 53)(27, 44)(28, 54)(29, 42)(30, 40)(31, 41)(32, 47)(33, 52)(34, 48)(35, 49)(36, 50)(55, 96)(56, 99)(57, 91)(58, 101)(59, 94)(60, 93)(61, 92)(62, 105)(63, 97)(64, 98)(65, 95)(66, 104)(67, 102)(68, 103)(69, 100)(70, 108)(71, 106)(72, 107)(109, 131)(110, 127)(111, 137)(112, 139)(113, 140)(114, 130)(115, 129)(116, 128)(117, 132)(118, 133)(119, 138)(120, 143)(121, 144)(122, 142)(123, 135)(124, 134)(125, 136)(126, 141)

MAP           : A4.621
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 45)(20, 51)(21, 38)(22, 39)(23, 42)(24, 43)(25, 44)(26, 54)(27, 46)(28, 52)(29, 37)(30, 41)(31, 47)(32, 40)(33, 53)(34, 49)(35, 50)(36, 48)(55, 96)(56, 99)(57, 91)(58, 101)(59, 94)(60, 93)(61, 92)(62, 105)(63, 97)(64, 98)(65, 95)(66, 104)(67, 102)(68, 103)(69, 100)(70, 108)(71, 106)(72, 107)(109, 130)(110, 132)(111, 131)(112, 138)(113, 139)(114, 137)(115, 127)(116, 135)(117, 129)(118, 128)(119, 140)(120, 142)(121, 143)(122, 144)(123, 133)(124, 141)(125, 134)(126, 136)

MAP           : A4.622
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 47)(20, 39)(21, 40)(22, 50)(23, 48)(24, 41)(25, 42)(26, 43)(27, 37)(28, 45)(29, 49)(30, 54)(31, 52)(32, 53)(33, 38)(34, 46)(35, 51)(36, 44)(55, 96)(56, 99)(57, 91)(58, 101)(59, 94)(60, 93)(61, 92)(62, 105)(63, 97)(64, 98)(65, 95)(66, 104)(67, 102)(68, 103)(69, 100)(70, 108)(71, 106)(72, 107)(109, 128)(110, 134)(111, 133)(112, 132)(113, 127)(114, 135)(115, 136)(116, 142)(117, 141)(118, 143)(119, 129)(120, 137)(121, 130)(122, 131)(123, 144)(124, 140)(125, 138)(126, 139)

MAP           : A4.623
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 41)(20, 37)(21, 47)(22, 49)(23, 50)(24, 40)(25, 39)(26, 38)(27, 42)(28, 43)(29, 48)(30, 53)(31, 54)(32, 52)(33, 45)(34, 44)(35, 46)(36, 51)(55, 100)(56, 107)(57, 105)(58, 92)(59, 97)(60, 98)(61, 108)(62, 102)(63, 106)(64, 103)(65, 99)(66, 96)(67, 91)(68, 93)(69, 104)(70, 101)(71, 94)(72, 95)(109, 130)(110, 132)(111, 131)(112, 138)(113, 139)(114, 137)(115, 127)(116, 135)(117, 129)(118, 128)(119, 140)(120, 142)(121, 143)(122, 144)(123, 133)(124, 141)(125, 134)(126, 136)

MAP           : A4.624
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 40)(20, 42)(21, 41)(22, 48)(23, 49)(24, 47)(25, 37)(26, 45)(27, 39)(28, 38)(29, 50)(30, 52)(31, 53)(32, 54)(33, 43)(34, 51)(35, 44)(36, 46)(55, 100)(56, 107)(57, 105)(58, 92)(59, 97)(60, 98)(61, 108)(62, 102)(63, 106)(64, 103)(65, 99)(66, 96)(67, 91)(68, 93)(69, 104)(70, 101)(71, 94)(72, 95)(109, 131)(110, 127)(111, 137)(112, 139)(113, 140)(114, 130)(115, 129)(116, 128)(117, 132)(118, 133)(119, 138)(120, 143)(121, 144)(122, 142)(123, 135)(124, 134)(125, 136)(126, 141)

MAP           : A4.625
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 45)(20, 51)(21, 38)(22, 39)(23, 42)(24, 43)(25, 44)(26, 54)(27, 46)(28, 52)(29, 37)(30, 41)(31, 47)(32, 40)(33, 53)(34, 49)(35, 50)(36, 48)(55, 102)(56, 101)(57, 103)(58, 106)(59, 107)(60, 104)(61, 94)(62, 93)(63, 95)(64, 96)(65, 108)(66, 105)(67, 98)(68, 100)(69, 91)(70, 97)(71, 99)(72, 92)(109, 128)(110, 134)(111, 133)(112, 132)(113, 127)(114, 135)(115, 136)(116, 142)(117, 141)(118, 143)(119, 129)(120, 137)(121, 130)(122, 131)(123, 144)(124, 140)(125, 138)(126, 139)

MAP           : A4.626
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 47)(20, 39)(21, 40)(22, 50)(23, 48)(24, 41)(25, 42)(26, 43)(27, 37)(28, 45)(29, 49)(30, 54)(31, 52)(32, 53)(33, 38)(34, 46)(35, 51)(36, 44)(55, 102)(56, 101)(57, 103)(58, 106)(59, 107)(60, 104)(61, 94)(62, 93)(63, 95)(64, 96)(65, 108)(66, 105)(67, 98)(68, 100)(69, 91)(70, 97)(71, 99)(72, 92)(109, 143)(110, 138)(111, 144)(112, 134)(113, 136)(114, 142)(115, 139)(116, 137)(117, 140)(118, 130)(119, 141)(120, 135)(121, 128)(122, 133)(123, 131)(124, 129)(125, 132)(126, 127)

MAP           : A4.627
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 53)(20, 48)(21, 54)(22, 44)(23, 46)(24, 52)(25, 49)(26, 47)(27, 50)(28, 40)(29, 51)(30, 45)(31, 38)(32, 43)(33, 41)(34, 39)(35, 42)(36, 37)(55, 102)(56, 101)(57, 103)(58, 106)(59, 107)(60, 104)(61, 94)(62, 93)(63, 95)(64, 96)(65, 108)(66, 105)(67, 98)(68, 100)(69, 91)(70, 97)(71, 99)(72, 92)(109, 137)(110, 129)(111, 130)(112, 140)(113, 138)(114, 131)(115, 132)(116, 133)(117, 127)(118, 135)(119, 139)(120, 144)(121, 142)(122, 143)(123, 128)(124, 136)(125, 141)(126, 134)

MAP           : A4.628
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 54)(20, 49)(21, 52)(22, 46)(23, 51)(24, 53)(25, 50)(26, 40)(27, 48)(28, 41)(29, 44)(30, 38)(31, 43)(32, 45)(33, 47)(34, 42)(35, 37)(36, 39)(55, 102)(56, 101)(57, 103)(58, 106)(59, 107)(60, 104)(61, 94)(62, 93)(63, 95)(64, 96)(65, 108)(66, 105)(67, 98)(68, 100)(69, 91)(70, 97)(71, 99)(72, 92)(109, 131)(110, 127)(111, 137)(112, 139)(113, 140)(114, 130)(115, 129)(116, 128)(117, 132)(118, 133)(119, 138)(120, 143)(121, 144)(122, 142)(123, 135)(124, 134)(125, 136)(126, 141)

MAP           : A4.629
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 38)(20, 44)(21, 43)(22, 42)(23, 37)(24, 45)(25, 46)(26, 52)(27, 51)(28, 53)(29, 39)(30, 47)(31, 40)(32, 41)(33, 54)(34, 50)(35, 48)(36, 49)(55, 105)(56, 108)(57, 98)(58, 97)(59, 99)(60, 100)(61, 106)(62, 103)(63, 107)(64, 104)(65, 92)(66, 91)(67, 93)(68, 96)(69, 102)(70, 94)(71, 95)(72, 101)(109, 143)(110, 138)(111, 144)(112, 134)(113, 136)(114, 142)(115, 139)(116, 137)(117, 140)(118, 130)(119, 141)(120, 135)(121, 128)(122, 133)(123, 131)(124, 129)(125, 132)(126, 127)

MAP           : A4.630
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 41)(20, 37)(21, 47)(22, 49)(23, 50)(24, 40)(25, 39)(26, 38)(27, 42)(28, 43)(29, 48)(30, 53)(31, 54)(32, 52)(33, 45)(34, 44)(35, 46)(36, 51)(55, 105)(56, 108)(57, 98)(58, 97)(59, 99)(60, 100)(61, 106)(62, 103)(63, 107)(64, 104)(65, 92)(66, 91)(67, 93)(68, 96)(69, 102)(70, 94)(71, 95)(72, 101)(109, 137)(110, 129)(111, 130)(112, 140)(113, 138)(114, 131)(115, 132)(116, 133)(117, 127)(118, 135)(119, 139)(120, 144)(121, 142)(122, 143)(123, 128)(124, 136)(125, 141)(126, 134)

MAP           : A4.631
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 45)(20, 51)(21, 38)(22, 39)(23, 42)(24, 43)(25, 44)(26, 54)(27, 46)(28, 52)(29, 37)(30, 41)(31, 47)(32, 40)(33, 53)(34, 49)(35, 50)(36, 48)(55, 105)(56, 108)(57, 98)(58, 97)(59, 99)(60, 100)(61, 106)(62, 103)(63, 107)(64, 104)(65, 92)(66, 91)(67, 93)(68, 96)(69, 102)(70, 94)(71, 95)(72, 101)(109, 144)(110, 139)(111, 142)(112, 136)(113, 141)(114, 143)(115, 140)(116, 130)(117, 138)(118, 131)(119, 134)(120, 128)(121, 133)(122, 135)(123, 137)(124, 132)(125, 127)(126, 129)

MAP           : A4.632
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 47)(20, 39)(21, 40)(22, 50)(23, 48)(24, 41)(25, 42)(26, 43)(27, 37)(28, 45)(29, 49)(30, 54)(31, 52)(32, 53)(33, 38)(34, 46)(35, 51)(36, 44)(55, 105)(56, 108)(57, 98)(58, 97)(59, 99)(60, 100)(61, 106)(62, 103)(63, 107)(64, 104)(65, 92)(66, 91)(67, 93)(68, 96)(69, 102)(70, 94)(71, 95)(72, 101)(109, 131)(110, 127)(111, 137)(112, 139)(113, 140)(114, 130)(115, 129)(116, 128)(117, 132)(118, 133)(119, 138)(120, 143)(121, 144)(122, 142)(123, 135)(124, 134)(125, 136)(126, 141)

MAP           : A4.633
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 53)(20, 48)(21, 54)(22, 44)(23, 46)(24, 52)(25, 49)(26, 47)(27, 50)(28, 40)(29, 51)(30, 45)(31, 38)(32, 43)(33, 41)(34, 39)(35, 42)(36, 37)(55, 105)(56, 108)(57, 98)(58, 97)(59, 99)(60, 100)(61, 106)(62, 103)(63, 107)(64, 104)(65, 92)(66, 91)(67, 93)(68, 96)(69, 102)(70, 94)(71, 95)(72, 101)(109, 128)(110, 134)(111, 133)(112, 132)(113, 127)(114, 135)(115, 136)(116, 142)(117, 141)(118, 143)(119, 129)(120, 137)(121, 130)(122, 131)(123, 144)(124, 140)(125, 138)(126, 139)

MAP           : A4.634
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 54)(20, 49)(21, 52)(22, 46)(23, 51)(24, 53)(25, 50)(26, 40)(27, 48)(28, 41)(29, 44)(30, 38)(31, 43)(32, 45)(33, 47)(34, 42)(35, 37)(36, 39)(55, 105)(56, 108)(57, 98)(58, 97)(59, 99)(60, 100)(61, 106)(62, 103)(63, 107)(64, 104)(65, 92)(66, 91)(67, 93)(68, 96)(69, 102)(70, 94)(71, 95)(72, 101)(109, 135)(110, 141)(111, 128)(112, 129)(113, 132)(114, 133)(115, 134)(116, 144)(117, 136)(118, 142)(119, 127)(120, 131)(121, 137)(122, 130)(123, 143)(124, 139)(125, 140)(126, 138)

MAP           : A4.635
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 38)(20, 44)(21, 43)(22, 42)(23, 37)(24, 45)(25, 46)(26, 52)(27, 51)(28, 53)(29, 39)(30, 47)(31, 40)(32, 41)(33, 54)(34, 50)(35, 48)(36, 49)(55, 100)(56, 107)(57, 105)(58, 92)(59, 97)(60, 98)(61, 108)(62, 102)(63, 106)(64, 103)(65, 99)(66, 96)(67, 91)(68, 93)(69, 104)(70, 101)(71, 94)(72, 95)(109, 144)(110, 139)(111, 142)(112, 136)(113, 141)(114, 143)(115, 140)(116, 130)(117, 138)(118, 131)(119, 134)(120, 128)(121, 133)(122, 135)(123, 137)(124, 132)(125, 127)(126, 129)

MAP           : A4.636
NOTES         : type I, non-biCayley, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2)(3, 4) L = (1, 3)(2, 4)
ORBIFOLD      : O(0, {3, 2, 2, 2})
EMBEDDING     : vertices: [ 2, 2 ], faces: [ 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.3^2, u.4^2, (u.1 * u.2^-1)^2, (u.2 * u.3 * u.1^-1 * u.4)^3 >
CTG (small)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.1 * x.2^-1)^2, x.2 * x.4 * x.2 * x.3 * x.2^-1 * x.4 * x.2^-1 * x.3, x.4 * x.2 * x.3 * x.2 * x.4 * x.2^-1 * x.3 * x.2^-1, (x.2 * x.3 * x.1^-1 * x.4)^3 >
SCHREIER VEC. : (x.1, x.2)^2
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 10, 46)(2, 38, 12, 48)(3, 39, 6, 42)(4, 40, 5, 41)(7, 43, 14, 50)(8, 44, 13, 49)(9, 45, 19, 55)(11, 47, 20, 56)(15, 51, 31, 67)(16, 52, 25, 61)(17, 53, 32, 68)(18, 54, 26, 62)(21, 57, 35, 71)(22, 58, 36, 72)(23, 59, 33, 69)(24, 60, 34, 70)(27, 63, 30, 66)(28, 64, 29, 65)(73, 110, 74, 109)(75, 115, 79, 111)(76, 121, 85, 112)(77, 116, 80, 113)(78, 122, 86, 114)(81, 119, 83, 117)(82, 120, 84, 118)(87, 144, 108, 123)(88, 143, 107, 124)(89, 142, 106, 125)(90, 141, 105, 126)(91, 128, 92, 127)(93, 133, 97, 129)(94, 139, 103, 130)(95, 134, 98, 131)(96, 140, 104, 132)(99, 137, 101, 135)(100, 138, 102, 136)
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, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 114)(38, 112)(39, 128)(40, 110)(41, 127)(42, 109)(43, 144)(44, 142)(45, 134)(46, 140)(47, 133)(48, 139)(49, 143)(50, 141)(51, 136)(52, 135)(53, 138)(54, 137)(55, 113)(56, 111)(57, 130)(58, 129)(59, 132)(60, 131)(61, 119)(62, 117)(63, 124)(64, 123)(65, 126)(66, 125)(67, 120)(68, 118)(69, 122)(70, 116)(71, 121)(72, 115)

MAP           : A4.637
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 38)(20, 44)(21, 43)(22, 42)(23, 37)(24, 45)(25, 46)(26, 52)(27, 51)(28, 53)(29, 39)(30, 47)(31, 40)(32, 41)(33, 54)(34, 50)(35, 48)(36, 49)(55, 103)(56, 94)(57, 104)(58, 107)(59, 108)(60, 102)(61, 95)(62, 96)(63, 101)(64, 91)(65, 106)(66, 98)(67, 100)(68, 105)(69, 93)(70, 99)(71, 92)(72, 97)(109, 133)(110, 136)(111, 135)(112, 127)(113, 129)(114, 128)(115, 141)(116, 143)(117, 134)(118, 144)(119, 132)(120, 130)(121, 131)(122, 137)(123, 142)(124, 138)(125, 139)(126, 140)

MAP           : A4.638
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 43)(20, 46)(21, 45)(22, 37)(23, 39)(24, 38)(25, 51)(26, 53)(27, 44)(28, 54)(29, 42)(30, 40)(31, 41)(32, 47)(33, 52)(34, 48)(35, 49)(36, 50)(55, 100)(56, 107)(57, 105)(58, 92)(59, 97)(60, 98)(61, 108)(62, 102)(63, 106)(64, 103)(65, 99)(66, 96)(67, 91)(68, 93)(69, 104)(70, 101)(71, 94)(72, 95)(109, 143)(110, 138)(111, 144)(112, 134)(113, 136)(114, 142)(115, 139)(116, 137)(117, 140)(118, 130)(119, 141)(120, 135)(121, 128)(122, 133)(123, 131)(124, 129)(125, 132)(126, 127)

MAP           : A4.639
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 53)(20, 48)(21, 54)(22, 44)(23, 46)(24, 52)(25, 49)(26, 47)(27, 50)(28, 40)(29, 51)(30, 45)(31, 38)(32, 43)(33, 41)(34, 39)(35, 42)(36, 37)(55, 100)(56, 107)(57, 105)(58, 92)(59, 97)(60, 98)(61, 108)(62, 102)(63, 106)(64, 103)(65, 99)(66, 96)(67, 91)(68, 93)(69, 104)(70, 101)(71, 94)(72, 95)(109, 133)(110, 136)(111, 135)(112, 127)(113, 129)(114, 128)(115, 141)(116, 143)(117, 134)(118, 144)(119, 132)(120, 130)(121, 131)(122, 137)(123, 142)(124, 138)(125, 139)(126, 140)

MAP           : A4.640
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 54)(20, 49)(21, 52)(22, 46)(23, 51)(24, 53)(25, 50)(26, 40)(27, 48)(28, 41)(29, 44)(30, 38)(31, 43)(32, 45)(33, 47)(34, 42)(35, 37)(36, 39)(55, 100)(56, 107)(57, 105)(58, 92)(59, 97)(60, 98)(61, 108)(62, 102)(63, 106)(64, 103)(65, 99)(66, 96)(67, 91)(68, 93)(69, 104)(70, 101)(71, 94)(72, 95)(109, 128)(110, 134)(111, 133)(112, 132)(113, 127)(114, 135)(115, 136)(116, 142)(117, 141)(118, 143)(119, 129)(120, 137)(121, 130)(122, 131)(123, 144)(124, 140)(125, 138)(126, 139)

MAP           : A4.641
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 53)(20, 48)(21, 54)(22, 44)(23, 46)(24, 52)(25, 49)(26, 47)(27, 50)(28, 40)(29, 51)(30, 45)(31, 38)(32, 43)(33, 41)(34, 39)(35, 42)(36, 37)(55, 103)(56, 94)(57, 104)(58, 107)(59, 108)(60, 102)(61, 95)(62, 96)(63, 101)(64, 91)(65, 106)(66, 98)(67, 100)(68, 105)(69, 93)(70, 99)(71, 92)(72, 97)(109, 131)(110, 127)(111, 137)(112, 139)(113, 140)(114, 130)(115, 129)(116, 128)(117, 132)(118, 133)(119, 138)(120, 143)(121, 144)(122, 142)(123, 135)(124, 134)(125, 136)(126, 141)

MAP           : A4.642
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 41)(20, 37)(21, 47)(22, 49)(23, 50)(24, 40)(25, 39)(26, 38)(27, 42)(28, 43)(29, 48)(30, 53)(31, 54)(32, 52)(33, 45)(34, 44)(35, 46)(36, 51)(55, 103)(56, 94)(57, 104)(58, 107)(59, 108)(60, 102)(61, 95)(62, 96)(63, 101)(64, 91)(65, 106)(66, 98)(67, 100)(68, 105)(69, 93)(70, 99)(71, 92)(72, 97)(109, 143)(110, 138)(111, 144)(112, 134)(113, 136)(114, 142)(115, 139)(116, 137)(117, 140)(118, 130)(119, 141)(120, 135)(121, 128)(122, 133)(123, 131)(124, 129)(125, 132)(126, 127)

MAP           : A4.643
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 40)(20, 42)(21, 41)(22, 48)(23, 49)(24, 47)(25, 37)(26, 45)(27, 39)(28, 38)(29, 50)(30, 52)(31, 53)(32, 54)(33, 43)(34, 51)(35, 44)(36, 46)(55, 103)(56, 94)(57, 104)(58, 107)(59, 108)(60, 102)(61, 95)(62, 96)(63, 101)(64, 91)(65, 106)(66, 98)(67, 100)(68, 105)(69, 93)(70, 99)(71, 92)(72, 97)(109, 144)(110, 139)(111, 142)(112, 136)(113, 141)(114, 143)(115, 140)(116, 130)(117, 138)(118, 131)(119, 134)(120, 128)(121, 133)(122, 135)(123, 137)(124, 132)(125, 127)(126, 129)

MAP           : A4.644
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 43)(20, 46)(21, 45)(22, 37)(23, 39)(24, 38)(25, 51)(26, 53)(27, 44)(28, 54)(29, 42)(30, 40)(31, 41)(32, 47)(33, 52)(34, 48)(35, 49)(36, 50)(55, 103)(56, 94)(57, 104)(58, 107)(59, 108)(60, 102)(61, 95)(62, 96)(63, 101)(64, 91)(65, 106)(66, 98)(67, 100)(68, 105)(69, 93)(70, 99)(71, 92)(72, 97)(109, 128)(110, 134)(111, 133)(112, 132)(113, 127)(114, 135)(115, 136)(116, 142)(117, 141)(118, 143)(119, 129)(120, 137)(121, 130)(122, 131)(123, 144)(124, 140)(125, 138)(126, 139)

MAP           : A4.645
NOTES         : type I, non-Cayley, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2) L = (1, 2)
ORBIFOLD      : O(0, {6, 4, 2})
EMBEDDING     : vertices: [ 2 ], faces: [ 6, 4 ]
UNIGROUP      : < u.1, u.2 | u.2^2, u.1^4, (u.1 * u.2)^6 >
CTG (small)   : <72, 40>
CTG (fp)      : < x.1, x.2 | x.2^2, x.1^4, (x.2 * x.1^-1 * x.2 * x.1)^2, (x.1 * x.2)^6 >
SCHREIER VEC. : (x.1, x.1^-1)^2
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 138, 66, 73)(2, 99, 27, 74)(3, 102, 30, 75)(4, 131, 59, 76)(5, 106, 34, 77)(6, 95, 23, 78)(7, 136, 64, 79)(8, 97, 25, 80)(9, 100, 28, 81)(10, 139, 67, 82)(11, 98, 26, 83)(12, 103, 31, 84)(13, 142, 70, 85)(14, 109, 37, 86)(15, 112, 40, 87)(16, 133, 61, 88)(17, 110, 38, 89)(18, 127, 55, 90)(19, 134, 62, 91)(20, 137, 65, 92)(21, 128, 56, 93)(22, 135, 63, 94)(24, 129, 57, 96)(29, 132, 60, 101)(32, 117, 45, 104)(33, 120, 48, 105)(35, 124, 52, 107)(36, 113, 41, 108)(39, 122, 50, 111)(42, 123, 51, 114)(43, 140, 68, 115)(44, 143, 71, 116)(46, 141, 69, 118)(47, 126, 54, 119)(49, 144, 72, 121)(53, 130, 58, 125)
L = (1, 76)(2, 103)(3, 106)(4, 91)(5, 104)(6, 97)(7, 78)(8, 105)(9, 108)(10, 83)(11, 100)(12, 143)(13, 74)(14, 77)(15, 80)(16, 75)(17, 138)(18, 81)(19, 94)(20, 85)(21, 88)(22, 73)(23, 86)(24, 79)(25, 96)(26, 87)(27, 90)(28, 101)(29, 82)(30, 125)(31, 92)(32, 95)(33, 98)(34, 93)(35, 120)(36, 99)(37, 130)(38, 121)(39, 124)(40, 109)(41, 122)(42, 115)(43, 132)(44, 123)(45, 126)(46, 137)(47, 118)(48, 89)(49, 128)(50, 131)(51, 134)(52, 129)(53, 84)(54, 135)(55, 112)(56, 139)(57, 142)(58, 127)(59, 140)(60, 133)(61, 114)(62, 141)(63, 144)(64, 119)(65, 136)(66, 107)(67, 110)(68, 113)(69, 116)(70, 111)(71, 102)(72, 117)

MAP           : A4.646
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 54)(20, 49)(21, 52)(22, 46)(23, 51)(24, 53)(25, 50)(26, 40)(27, 48)(28, 41)(29, 44)(30, 38)(31, 43)(32, 45)(33, 47)(34, 42)(35, 37)(36, 39)(55, 103)(56, 94)(57, 104)(58, 107)(59, 108)(60, 102)(61, 95)(62, 96)(63, 101)(64, 91)(65, 106)(66, 98)(67, 100)(68, 105)(69, 93)(70, 99)(71, 92)(72, 97)(109, 130)(110, 132)(111, 131)(112, 138)(113, 139)(114, 137)(115, 127)(116, 135)(117, 129)(118, 128)(119, 140)(120, 142)(121, 143)(122, 144)(123, 133)(124, 141)(125, 134)(126, 136)

MAP           : A4.647
NOTES         : type I, non-biCayley, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2)(3, 4) L = (1, 3)(2, 4)
ORBIFOLD      : O(0, {3, 2, 2, 2})
EMBEDDING     : vertices: [ 2, 2 ], faces: [ 3, 2 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.3^2, u.4^2, (u.1 * u.2^-1)^3, (u.2 * u.3 * u.1^-1 * u.4)^2 >
CTG (small)   : <36, 10>
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.2 * x.4 * x.3 * x.2 * x.3, (x.1 * x.2^-1)^3, x.2 * x.3 * x.1^-1 * x.3 * x.2^-1 * x.4 * x.1^-1 * x.4, x.2^-1 * x.4 * x.2 * x.4 * x.2 * x.3 * x.2 * x.3 >
SCHREIER VEC. : (x.1, x.2)^2
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 27, 63)(2, 38, 29, 65)(3, 39, 17, 53)(4, 40, 18, 54)(5, 41, 15, 51)(6, 42, 16, 52)(7, 43, 34, 70)(8, 44, 36, 72)(9, 45, 12, 48)(10, 46, 11, 47)(13, 49, 33, 69)(14, 50, 35, 71)(19, 55, 28, 64)(20, 56, 30, 66)(21, 57, 24, 60)(22, 58, 23, 59)(25, 61, 32, 68)(26, 62, 31, 67)(73, 110, 74, 109)(75, 115, 79, 111)(76, 121, 85, 112)(77, 116, 80, 113)(78, 122, 86, 114)(81, 119, 83, 117)(82, 120, 84, 118)(87, 144, 108, 123)(88, 143, 107, 124)(89, 142, 106, 125)(90, 141, 105, 126)(91, 128, 92, 127)(93, 133, 97, 129)(94, 139, 103, 130)(95, 134, 98, 131)(96, 140, 104, 132)(99, 137, 101, 135)(100, 138, 102, 136)
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, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 113)(38, 111)(39, 130)(40, 129)(41, 132)(42, 131)(43, 119)(44, 117)(45, 124)(46, 123)(47, 126)(48, 125)(49, 120)(50, 118)(51, 122)(52, 116)(53, 121)(54, 115)(55, 114)(56, 112)(57, 128)(58, 110)(59, 127)(60, 109)(61, 144)(62, 142)(63, 134)(64, 140)(65, 133)(66, 139)(67, 143)(68, 141)(69, 136)(70, 135)(71, 138)(72, 137)

MAP           : A4.648
NOTES         : type I, non-biCayley, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2)(3, 4) L = (1, 3)(2, 4)
ORBIFOLD      : O(0, {3, 2, 2, 2})
EMBEDDING     : vertices: [ 2, 2 ], faces: [ 2, 3 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.3^2, u.4^2, (u.1 * u.2^-1)^2, (u.2 * u.3 * u.1^-1 * u.4)^3 >
CTG (small)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1, x.3^2, x.4^2, (x.4 * x.3)^2, (x.1 * x.2^-1)^2, x.2 * x.4 * x.2 * x.3 * x.2^-1 * x.4 * x.2^-1 * x.3, x.4 * x.2 * x.3 * x.2 * x.4 * x.2^-1 * x.3 * x.2^-1, (x.2 * x.3 * x.1^-1 * x.4)^3 >
SCHREIER VEC. : (x.1, x.2)^2
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 13, 49)(5, 41, 8, 44)(6, 42, 14, 50)(9, 45, 11, 47)(10, 46, 12, 48)(15, 51, 36, 72)(16, 52, 35, 71)(17, 53, 34, 70)(18, 54, 33, 69)(19, 55, 20, 56)(21, 57, 25, 61)(22, 58, 31, 67)(23, 59, 26, 62)(24, 60, 32, 68)(27, 63, 29, 65)(28, 64, 30, 66)(73, 118, 82, 109)(74, 120, 84, 110)(75, 114, 78, 111)(76, 113, 77, 112)(79, 122, 86, 115)(80, 121, 85, 116)(81, 127, 91, 117)(83, 128, 92, 119)(87, 139, 103, 123)(88, 133, 97, 124)(89, 140, 104, 125)(90, 134, 98, 126)(93, 143, 107, 129)(94, 144, 108, 130)(95, 141, 105, 131)(96, 142, 106, 132)(99, 138, 102, 135)(100, 137, 101, 136)
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, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 114)(38, 112)(39, 128)(40, 110)(41, 127)(42, 109)(43, 144)(44, 142)(45, 134)(46, 140)(47, 133)(48, 139)(49, 143)(50, 141)(51, 136)(52, 135)(53, 138)(54, 137)(55, 113)(56, 111)(57, 130)(58, 129)(59, 132)(60, 131)(61, 119)(62, 117)(63, 124)(64, 123)(65, 126)(66, 125)(67, 120)(68, 118)(69, 122)(70, 116)(71, 121)(72, 115)

MAP           : A4.649
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 38)(20, 44)(21, 43)(22, 42)(23, 37)(24, 45)(25, 46)(26, 52)(27, 51)(28, 53)(29, 39)(30, 47)(31, 40)(32, 41)(33, 54)(34, 50)(35, 48)(36, 49)(55, 96)(56, 99)(57, 91)(58, 101)(59, 94)(60, 93)(61, 92)(62, 105)(63, 97)(64, 98)(65, 95)(66, 104)(67, 102)(68, 103)(69, 100)(70, 108)(71, 106)(72, 107)(109, 137)(110, 129)(111, 130)(112, 140)(113, 138)(114, 131)(115, 132)(116, 133)(117, 127)(118, 135)(119, 139)(120, 144)(121, 142)(122, 143)(123, 128)(124, 136)(125, 141)(126, 134)

MAP           : A4.650
NOTES         : type I, non-Cayley, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2) L = (1, 2)
ORBIFOLD      : O(0, {6, 4, 2})
EMBEDDING     : vertices: [ 2 ], faces: [ 6, 4 ]
UNIGROUP      : < u.1, u.2 | u.2^2, u.1^4, (u.1 * u.2)^6 >
CTG (small)   : <72, 40>
CTG (fp)      : < x.1, x.2 | x.2^2, x.1^4, (x.2 * x.1^-1 * x.2 * x.1)^2, (x.1 * x.2)^6 >
SCHREIER VEC. : (x.1, x.1^-1)^2
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 75, 3, 73)(2, 94, 22, 74)(4, 78, 6, 76)(5, 85, 13, 77)(7, 81, 9, 79)(8, 88, 16, 80)(10, 84, 12, 82)(11, 91, 19, 83)(14, 138, 66, 86)(15, 131, 59, 87)(17, 99, 27, 89)(18, 134, 62, 90)(20, 132, 60, 92)(21, 137, 65, 93)(23, 123, 51, 95)(24, 128, 56, 96)(25, 143, 71, 97)(26, 126, 54, 98)(28, 104, 32, 100)(29, 129, 57, 101)(30, 122, 50, 102)(31, 105, 33, 103)(34, 108, 36, 106)(35, 133, 61, 107)(37, 111, 39, 109)(38, 130, 58, 110)(40, 114, 42, 112)(41, 121, 49, 113)(43, 117, 45, 115)(44, 124, 52, 116)(46, 120, 48, 118)(47, 127, 55, 119)(53, 135, 63, 125)(64, 140, 68, 136)(67, 141, 69, 139)(70, 144, 72, 142)
L = (1, 76)(2, 103)(3, 106)(4, 91)(5, 104)(6, 97)(7, 78)(8, 105)(9, 108)(10, 83)(11, 100)(12, 143)(13, 74)(14, 77)(15, 80)(16, 75)(17, 138)(18, 81)(19, 94)(20, 85)(21, 88)(22, 73)(23, 86)(24, 79)(25, 96)(26, 87)(27, 90)(28, 101)(29, 82)(30, 125)(31, 92)(32, 95)(33, 98)(34, 93)(35, 120)(36, 99)(37, 130)(38, 121)(39, 124)(40, 109)(41, 122)(42, 115)(43, 132)(44, 123)(45, 126)(46, 137)(47, 118)(48, 89)(49, 128)(50, 131)(51, 134)(52, 129)(53, 84)(54, 135)(55, 112)(56, 139)(57, 142)(58, 127)(59, 140)(60, 133)(61, 114)(62, 141)(63, 144)(64, 119)(65, 136)(66, 107)(67, 110)(68, 113)(69, 116)(70, 111)(71, 102)(72, 117)

MAP           : A4.651
NOTES         : type I, non-Cayley, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2) L = (1, 2)
ORBIFOLD      : O(0, {6, 4, 2})
EMBEDDING     : vertices: [ 2 ], faces: [ 4, 6 ]
UNIGROUP      : < u.1, u.2 | u.2^2, u.1^6, (u.1 * u.2)^4 >
CTG (small)   : <72, 40>
CTG (fp)      : < x.1, x.2 | x.2^2, x.1^6, (x.1 * x.2)^4, (x.2 * x.1 * x.2 * x.1^-1)^2, x.1^-2 * x.2 * x.1^-2 * x.2 * x.1^2 * x.2 * x.1^2 * x.2 >
SCHREIER VEC. : (x.1, x.1^-1)^2
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 75, 3, 73)(2, 94, 22, 74)(4, 78, 6, 76)(5, 85, 13, 77)(7, 81, 9, 79)(8, 88, 16, 80)(10, 84, 12, 82)(11, 91, 19, 83)(14, 138, 66, 86)(15, 131, 59, 87)(17, 99, 27, 89)(18, 134, 62, 90)(20, 132, 60, 92)(21, 137, 65, 93)(23, 123, 51, 95)(24, 128, 56, 96)(25, 143, 71, 97)(26, 126, 54, 98)(28, 104, 32, 100)(29, 129, 57, 101)(30, 122, 50, 102)(31, 105, 33, 103)(34, 108, 36, 106)(35, 133, 61, 107)(37, 111, 39, 109)(38, 130, 58, 110)(40, 114, 42, 112)(41, 121, 49, 113)(43, 117, 45, 115)(44, 124, 52, 116)(46, 120, 48, 118)(47, 127, 55, 119)(53, 135, 63, 125)(64, 140, 68, 136)(67, 141, 69, 139)(70, 144, 72, 142)
L = (1, 74)(2, 77)(3, 80)(4, 75)(5, 138)(6, 81)(7, 128)(8, 131)(9, 134)(10, 129)(11, 84)(12, 135)(13, 132)(14, 123)(15, 126)(16, 137)(17, 118)(18, 89)(19, 78)(20, 105)(21, 108)(22, 83)(23, 100)(24, 143)(25, 76)(26, 103)(27, 106)(28, 91)(29, 104)(30, 97)(31, 94)(32, 85)(33, 88)(34, 73)(35, 86)(36, 79)(37, 114)(38, 141)(39, 144)(40, 119)(41, 136)(42, 107)(43, 112)(44, 139)(45, 142)(46, 127)(47, 140)(48, 133)(49, 130)(50, 121)(51, 124)(52, 109)(53, 122)(54, 115)(55, 110)(56, 113)(57, 116)(58, 111)(59, 102)(60, 117)(61, 92)(62, 95)(63, 98)(64, 93)(65, 120)(66, 99)(67, 96)(68, 87)(69, 90)(70, 101)(71, 82)(72, 125)

MAP           : A4.652
NOTES         : type I, non-Cayley, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2) L = (1, 2)
ORBIFOLD      : O(0, {6, 4, 2})
EMBEDDING     : vertices: [ 2 ], faces: [ 4, 6 ]
UNIGROUP      : < u.1, u.2 | u.2^2, u.1^6, (u.1 * u.2)^4 >
CTG (small)   : <72, 40>
CTG (fp)      : < x.1, x.2 | x.2^2, x.1^6, (x.1 * x.2)^4, (x.2 * x.1 * x.2 * x.1^-1)^2, x.1^-2 * x.2 * x.1^-2 * x.2 * x.1^2 * x.2 * x.1^2 * x.2 >
SCHREIER VEC. : (x.1, x.1^-1)^2
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 138, 66, 73)(2, 99, 27, 74)(3, 102, 30, 75)(4, 131, 59, 76)(5, 106, 34, 77)(6, 95, 23, 78)(7, 136, 64, 79)(8, 97, 25, 80)(9, 100, 28, 81)(10, 139, 67, 82)(11, 98, 26, 83)(12, 103, 31, 84)(13, 142, 70, 85)(14, 109, 37, 86)(15, 112, 40, 87)(16, 133, 61, 88)(17, 110, 38, 89)(18, 127, 55, 90)(19, 134, 62, 91)(20, 137, 65, 92)(21, 128, 56, 93)(22, 135, 63, 94)(24, 129, 57, 96)(29, 132, 60, 101)(32, 117, 45, 104)(33, 120, 48, 105)(35, 124, 52, 107)(36, 113, 41, 108)(39, 122, 50, 111)(42, 123, 51, 114)(43, 140, 68, 115)(44, 143, 71, 116)(46, 141, 69, 118)(47, 126, 54, 119)(49, 144, 72, 121)(53, 130, 58, 125)
L = (1, 83)(2, 132)(3, 137)(4, 74)(5, 123)(6, 128)(7, 143)(8, 126)(9, 89)(10, 104)(11, 129)(12, 122)(13, 105)(14, 100)(15, 103)(16, 108)(17, 133)(18, 106)(19, 75)(20, 94)(21, 73)(22, 78)(23, 85)(24, 76)(25, 81)(26, 88)(27, 79)(28, 84)(29, 91)(30, 82)(31, 77)(32, 138)(33, 131)(34, 80)(35, 99)(36, 134)(37, 119)(38, 96)(39, 101)(40, 110)(41, 87)(42, 92)(43, 107)(44, 90)(45, 125)(46, 140)(47, 93)(48, 86)(49, 141)(50, 136)(51, 139)(52, 144)(53, 97)(54, 142)(55, 111)(56, 130)(57, 109)(58, 114)(59, 121)(60, 112)(61, 117)(62, 124)(63, 115)(64, 120)(65, 127)(66, 118)(67, 113)(68, 102)(69, 95)(70, 116)(71, 135)(72, 98)

MAP           : A4.653
NOTES         : type I, reflexible, isomorphic to Med2({6,6}), isomorphic to A4.525.
QUOTIENT      : R = (1, 2, 3, 4)(5, 6, 7, 8) L = (1, 5)(2, 3)(4, 6)(7, 8)
ORBIFOLD      : O(0, {6, 6, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 6, 6, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.1 * u.2^-1 * u.3^-1 * u.4^-1, (u.3 * u.1^-1)^3, u.2^6, u.4^6 >
CTG (small)   : <18, 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.2 * x.3^-1 * x.4 * x.3^-1, (x.3 * x.1^-1)^3, x.4^6, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3)
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 19, 37, 55)(2, 20, 38, 56)(3, 21, 39, 57)(4, 22, 40, 58)(5, 23, 41, 59)(6, 24, 42, 60)(7, 25, 43, 61)(8, 26, 44, 62)(9, 27, 45, 63)(10, 28, 46, 64)(11, 29, 47, 65)(12, 30, 48, 66)(13, 31, 49, 67)(14, 32, 50, 68)(15, 33, 51, 69)(16, 34, 52, 70)(17, 35, 53, 71)(18, 36, 54, 72)(73, 91, 109, 127)(74, 92, 110, 128)(75, 93, 111, 129)(76, 94, 112, 130)(77, 95, 113, 131)(78, 96, 114, 132)(79, 97, 115, 133)(80, 98, 116, 134)(81, 99, 117, 135)(82, 100, 118, 136)(83, 101, 119, 137)(84, 102, 120, 138)(85, 103, 121, 139)(86, 104, 122, 140)(87, 105, 123, 141)(88, 106, 124, 142)(89, 107, 125, 143)(90, 108, 126, 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, 41)(20, 37)(21, 47)(22, 49)(23, 50)(24, 40)(25, 39)(26, 38)(27, 42)(28, 43)(29, 48)(30, 53)(31, 54)(32, 52)(33, 45)(34, 44)(35, 46)(36, 51)(55, 96)(56, 99)(57, 91)(58, 101)(59, 94)(60, 93)(61, 92)(62, 105)(63, 97)(64, 98)(65, 95)(66, 104)(67, 102)(68, 103)(69, 100)(70, 108)(71, 106)(72, 107)(109, 133)(110, 136)(111, 135)(112, 127)(113, 129)(114, 128)(115, 141)(116, 143)(117, 134)(118, 144)(119, 132)(120, 130)(121, 131)(122, 137)(123, 142)(124, 138)(125, 139)(126, 140)

MAP           : A4.654
NOTES         : type I, non-biCayley, reflexible, isomorphic to Med({4,6}), isomorphic to A4.526.
QUOTIENT      : R = (1, 2)(3, 4) L = (1, 3)(2, 4)
ORBIFOLD      : O(0, {3, 2, 2, 2})
EMBEDDING     : vertices: [ 2, 2 ], faces: [ 3, 2 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1, u.3^2, u.4^2, (u.1 * u.2^-1)^3, (u.2 * u.3 * u.1^-1 * u.4)^2 >
CTG (small)   : <36, 10>
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.2 * x.4 * x.3 * x.2 * x.3, (x.1 * x.2^-1)^3, x.2 * x.3 * x.1^-1 * x.3 * x.2^-1 * x.4 * x.1^-1 * x.4, x.2^-1 * x.4 * x.2 * x.4 * x.2 * x.3 * x.2 * x.3 >
SCHREIER VEC. : (x.1, x.2)^2
LOCAL TYPE    : (4, 6, 4, 6)
#DARTS        : 144
R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 13, 49)(5, 41, 8, 44)(6, 42, 14, 50)(9, 45, 11, 47)(10, 46, 12, 48)(15, 51, 36, 72)(16, 52, 35, 71)(17, 53, 34, 70)(18, 54, 33, 69)(19, 55, 20, 56)(21, 57, 25, 61)(22, 58, 31, 67)(23, 59, 26, 62)(24, 60, 32, 68)(27, 63, 29, 65)(28, 64, 30, 66)(73, 135, 99, 109)(74, 137, 101, 110)(75, 125, 89, 111)(76, 126, 90, 112)(77, 123, 87, 113)(78, 124, 88, 114)(79, 142, 106, 115)(80, 144, 108, 116)(81, 120, 84, 117)(82, 119, 83, 118)(85, 141, 105, 121)(86, 143, 107, 122)(91, 136, 100, 127)(92, 138, 102, 128)(93, 132, 96, 129)(94, 131, 95, 130)(97, 140, 104, 133)(98, 139, 103, 134)
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, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 113)(38, 111)(39, 130)(40, 129)(41, 132)(42, 131)(43, 119)(44, 117)(45, 124)(46, 123)(47, 126)(48, 125)(49, 120)(50, 118)(51, 122)(52, 116)(53, 121)(54, 115)(55, 114)(56, 112)(57, 128)(58, 110)(59, 127)(60, 109)(61, 144)(62, 142)(63, 134)(64, 140)(65, 133)(66, 139)(67, 143)(68, 141)(69, 136)(70, 135)(71, 138)(72, 137)

MAP           : A4.655
NOTES         : type I, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)
ORBIFOLD      : O(0, {4, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.2^2, u.3^4, (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^-1 * x.2 * x.3 * x.1, x.3^4, (x.2 * x.3)^3, x.3^-2 * x.2 * x.1 * x.3^-1 * x.1, (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    : (4, 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, 28)(3, 25)(4, 27)(5, 31)(6, 29)(7, 32)(8, 30)(9, 40)(10, 39)(11, 38)(12, 37)(13, 46)(14, 48)(15, 45)(16, 47)(17, 35)(18, 33)(19, 36)(20, 34)(21, 44)(22, 43)(23, 42)(24, 41)(49, 66)(50, 68)(51, 65)(52, 67)(53, 63)(54, 61)(55, 64)(56, 62)(57, 72)(58, 71)(59, 70)(60, 69)(73, 83)(74, 81)(75, 84)(76, 82)(77, 94)(78, 96)(79, 93)(80, 95)(85, 92)(86, 91)(87, 90)(88, 89)

MAP           : A4.656
NOTES         : type I, non-Cayley, reflexible, isomorphic to {4,5}, representative.
QUOTIENT      : R = (1, 2) L = (1, 2)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 2 ], faces: [ 5, 5 ]
UNIGROUP      : < u.1, u.2 | u.2^2, u.1^5, (u.1 * u.2)^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2 | x.2^2, x.1^5, (x.1^2 * x.2)^3, (x.2 * x.1 * x.2 * x.1^-2)^2, (x.1 * x.2)^5 >
SCHREIER VEC. : (x.1, x.1^-1)^2
LOCAL TYPE    : (5, 5, 5, 5)
#DARTS        : 120
R = (1, 103, 43, 61)(2, 104, 44, 62)(3, 105, 45, 63)(4, 106, 46, 64)(5, 107, 47, 65)(6, 108, 48, 66)(7, 109, 49, 67)(8, 110, 50, 68)(9, 111, 51, 69)(10, 112, 52, 70)(11, 113, 53, 71)(12, 114, 54, 72)(13, 115, 55, 73)(14, 116, 56, 74)(15, 117, 57, 75)(16, 118, 58, 76)(17, 119, 59, 77)(18, 120, 60, 78)(19, 85, 25, 79)(20, 86, 26, 80)(21, 87, 27, 81)(22, 88, 28, 82)(23, 89, 29, 83)(24, 90, 30, 84)(31, 97, 37, 91)(32, 98, 38, 92)(33, 99, 39, 93)(34, 100, 40, 94)(35, 101, 41, 95)(36, 102, 42, 96)
L = (1, 65)(2, 78)(3, 101)(4, 62)(5, 64)(6, 94)(7, 74)(8, 77)(9, 79)(10, 73)(11, 90)(12, 89)(13, 87)(14, 63)(15, 100)(16, 99)(17, 111)(18, 61)(19, 88)(20, 85)(21, 72)(22, 114)(23, 86)(24, 116)(25, 102)(26, 112)(27, 98)(28, 113)(29, 109)(30, 75)(31, 71)(32, 96)(33, 83)(34, 68)(35, 70)(36, 76)(37, 92)(38, 95)(39, 97)(40, 91)(41, 108)(42, 107)(43, 105)(44, 69)(45, 82)(46, 81)(47, 117)(48, 67)(49, 106)(50, 103)(51, 66)(52, 120)(53, 104)(54, 110)(55, 84)(56, 118)(57, 80)(58, 119)(59, 115)(60, 93)

MAP           : A4.657
NOTES         : type I, non-Cayley, reflexible, isomorphic to {4,5}, isomorphic to A4.656.
QUOTIENT      : R = Id($) L = Id($)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 4 ], faces: [ 5 ]
UNIGROUP      : < u.1, u.2 | u.1^2, u.2^4, (u.1 * u.2)^5 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2 | x.1^2, x.2^4, (x.1 * x.2)^5, (x.1 * x.2^-1 * x.1 * x.2)^3, x.2 * x.1 * x.2^-2 * x.1 * x.2 * x.1 * x.2^-2 * x.1 * x.2^2 * x.1 * x.2 * x.1 * x.2 >
SCHREIER VEC. : (x.1)^4
LOCAL TYPE    : (5, 5, 5, 5)
#DARTS        : 120
R = (1, 14, 16, 3)(2, 13, 17, 6)(4, 26, 59, 102)(5, 25, 58, 99)(7, 15, 101, 54)(8, 18, 100, 51)(9, 28, 65, 90)(10, 108, 111, 49)(11, 105, 114, 50)(12, 29, 64, 87)(19, 48, 98, 40)(20, 45, 97, 41)(21, 78, 109, 38)(22, 43, 92, 77)(23, 44, 91, 76)(24, 75, 110, 37)(27, 56, 94, 119)(30, 55, 95, 118)(31, 93, 74, 113)(32, 96, 73, 112)(33, 106, 61, 83)(34, 72, 86, 117)(35, 69, 85, 120)(36, 107, 62, 82)(39, 60, 88, 115)(42, 57, 89, 116)(46, 104, 63, 53)(47, 103, 66, 52)(67, 80, 84, 71)(68, 79, 81, 70)
L = (1, 2)(3, 7)(4, 14)(5, 13)(6, 8)(9, 16)(10, 102)(11, 99)(12, 17)(15, 119)(18, 118)(19, 54)(20, 51)(21, 90)(22, 49)(23, 50)(24, 87)(25, 40)(26, 41)(27, 38)(28, 77)(29, 76)(30, 37)(31, 111)(32, 114)(33, 100)(34, 66)(35, 63)(36, 101)(39, 42)(43, 110)(44, 109)(45, 115)(46, 98)(47, 97)(48, 116)(52, 53)(55, 113)(56, 112)(57, 83)(58, 117)(59, 120)(60, 82)(61, 71)(62, 70)(64, 81)(65, 84)(67, 68)(69, 79)(72, 80)(73, 106)(74, 107)(75, 104)(78, 103)(85, 96)(86, 93)(88, 91)(89, 92)(94, 95)(105, 108)

MAP           : A4.658
NOTES         : type I, non-Cayley, reflexible, isomorphic to {4,5}, isomorphic to A4.656.
QUOTIENT      : R = (1, 2) L = (1, 2)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 2 ], faces: [ 5, 5 ]
UNIGROUP      : < u.1, u.2 | u.2^2, u.1^5, (u.1 * u.2)^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2 | x.2^2, x.1^5, (x.1^2 * x.2)^3, (x.2 * x.1 * x.2 * x.1^-2)^2, (x.1 * x.2)^5 >
SCHREIER VEC. : (x.1, x.1^-1)^2
LOCAL TYPE    : (5, 5, 5, 5)
#DARTS        : 120
R = (1, 67, 7, 61)(2, 68, 8, 62)(3, 69, 9, 63)(4, 70, 10, 64)(5, 71, 11, 65)(6, 72, 12, 66)(13, 91, 31, 73)(14, 92, 32, 74)(15, 93, 33, 75)(16, 94, 34, 76)(17, 95, 35, 77)(18, 96, 36, 78)(19, 97, 37, 79)(20, 98, 38, 80)(21, 99, 39, 81)(22, 100, 40, 82)(23, 101, 41, 83)(24, 102, 42, 84)(25, 103, 43, 85)(26, 104, 44, 86)(27, 105, 45, 87)(28, 106, 46, 88)(29, 107, 47, 89)(30, 108, 48, 90)(49, 115, 55, 109)(50, 116, 56, 110)(51, 117, 57, 111)(52, 118, 58, 112)(53, 119, 59, 113)(54, 120, 60, 114)
L = (1, 62)(2, 65)(3, 67)(4, 61)(5, 78)(6, 77)(7, 101)(8, 66)(9, 113)(10, 98)(11, 100)(12, 106)(13, 95)(14, 108)(15, 71)(16, 92)(17, 94)(18, 64)(19, 104)(20, 107)(21, 109)(22, 103)(23, 120)(24, 119)(25, 117)(26, 93)(27, 70)(28, 69)(29, 81)(30, 91)(31, 75)(32, 99)(33, 112)(34, 111)(35, 87)(36, 97)(37, 76)(38, 73)(39, 96)(40, 90)(41, 74)(42, 80)(43, 114)(44, 88)(45, 110)(46, 89)(47, 85)(48, 63)(49, 72)(50, 82)(51, 68)(52, 83)(53, 79)(54, 105)(55, 118)(56, 115)(57, 102)(58, 84)(59, 116)(60, 86)

MAP           : A4.659
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)   : <72, 42>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.3^2 * x.1 * x.3^-4 * x.2^-1 * x.3, x.2 * x.3^-1 * x.2 * x.3 * x.1 * x.3^-1 * x.2^-1 * x.1 * x.3^-1, 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        : 360
R = (1, 73, 145, 217, 289)(2, 74, 146, 218, 290)(3, 75, 147, 219, 291)(4, 76, 148, 220, 292)(5, 77, 149, 221, 293)(6, 78, 150, 222, 294)(7, 79, 151, 223, 295)(8, 80, 152, 224, 296)(9, 81, 153, 225, 297)(10, 82, 154, 226, 298)(11, 83, 155, 227, 299)(12, 84, 156, 228, 300)(13, 85, 157, 229, 301)(14, 86, 158, 230, 302)(15, 87, 159, 231, 303)(16, 88, 160, 232, 304)(17, 89, 161, 233, 305)(18, 90, 162, 234, 306)(19, 91, 163, 235, 307)(20, 92, 164, 236, 308)(21, 93, 165, 237, 309)(22, 94, 166, 238, 310)(23, 95, 167, 239, 311)(24, 96, 168, 240, 312)(25, 97, 169, 241, 313)(26, 98, 170, 242, 314)(27, 99, 171, 243, 315)(28, 100, 172, 244, 316)(29, 101, 173, 245, 317)(30, 102, 174, 246, 318)(31, 103, 175, 247, 319)(32, 104, 176, 248, 320)(33, 105, 177, 249, 321)(34, 106, 178, 250, 322)(35, 107, 179, 251, 323)(36, 108, 180, 252, 324)(37, 109, 181, 253, 325)(38, 110, 182, 254, 326)(39, 111, 183, 255, 327)(40, 112, 184, 256, 328)(41, 113, 185, 257, 329)(42, 114, 186, 258, 330)(43, 115, 187, 259, 331)(44, 116, 188, 260, 332)(45, 117, 189, 261, 333)(46, 118, 190, 262, 334)(47, 119, 191, 263, 335)(48, 120, 192, 264, 336)(49, 121, 193, 265, 337)(50, 122, 194, 266, 338)(51, 123, 195, 267, 339)(52, 124, 196, 268, 340)(53, 125, 197, 269, 341)(54, 126, 198, 270, 342)(55, 127, 199, 271, 343)(56, 128, 200, 272, 344)(57, 129, 201, 273, 345)(58, 130, 202, 274, 346)(59, 131, 203, 275, 347)(60, 132, 204, 276, 348)(61, 133, 205, 277, 349)(62, 134, 206, 278, 350)(63, 135, 207, 279, 351)(64, 136, 208, 280, 352)(65, 137, 209, 281, 353)(66, 138, 210, 282, 354)(67, 139, 211, 283, 355)(68, 140, 212, 284, 356)(69, 141, 213, 285, 357)(70, 142, 214, 286, 358)(71, 143, 215, 287, 359)(72, 144, 216, 288, 360)
L = (1, 4)(2, 6)(3, 43)(5, 67)(7, 11)(8, 52)(9, 38)(10, 50)(12, 40)(13, 24)(14, 33)(15, 23)(16, 36)(17, 59)(18, 21)(19, 27)(20, 60)(22, 57)(25, 28)(26, 30)(29, 55)(31, 35)(32, 64)(34, 62)(37, 48)(39, 47)(41, 71)(42, 45)(44, 72)(46, 69)(49, 56)(51, 53)(54, 58)(61, 68)(63, 65)(66, 70)(73, 147)(74, 152)(75, 150)(76, 149)(77, 153)(78, 145)(79, 202)(80, 155)(81, 148)(82, 156)(83, 146)(84, 187)(85, 159)(86, 164)(87, 162)(88, 161)(89, 165)(90, 157)(91, 190)(92, 167)(93, 160)(94, 168)(95, 158)(96, 175)(97, 183)(98, 188)(99, 186)(100, 185)(101, 189)(102, 181)(103, 166)(104, 191)(105, 184)(106, 192)(107, 182)(108, 151)(109, 195)(110, 200)(111, 198)(112, 197)(113, 201)(114, 193)(115, 154)(116, 203)(117, 196)(118, 204)(119, 194)(120, 211)(121, 171)(122, 176)(123, 174)(124, 173)(125, 177)(126, 169)(127, 214)(128, 179)(129, 172)(130, 180)(131, 170)(132, 163)(133, 207)(134, 212)(135, 210)(136, 209)(137, 213)(138, 205)(139, 178)(140, 215)(141, 208)(142, 216)(143, 206)(144, 199)(217, 290)(218, 295)(219, 292)(220, 326)(221, 289)(222, 331)(223, 304)(224, 294)(225, 355)(226, 291)(227, 340)(228, 338)(229, 309)(230, 303)(231, 312)(232, 306)(233, 324)(234, 311)(235, 308)(236, 321)(237, 347)(238, 323)(239, 348)(240, 345)(241, 346)(242, 305)(243, 344)(244, 310)(245, 296)(246, 341)(247, 301)(248, 298)(249, 339)(250, 293)(251, 337)(252, 342)(253, 314)(254, 319)(255, 316)(256, 302)(257, 313)(258, 307)(259, 328)(260, 318)(261, 343)(262, 315)(263, 352)(264, 350)(265, 333)(266, 327)(267, 336)(268, 330)(269, 300)(270, 335)(271, 332)(272, 297)(273, 359)(274, 299)(275, 360)(276, 357)(277, 358)(278, 329)(279, 356)(280, 334)(281, 320)(282, 353)(283, 325)(284, 322)(285, 351)(286, 317)(287, 349)(288, 354)

MAP           : A4.660
NOTES         : type I, chiral, isomorphic to Snub({3,12}), isomorphic to A4.659.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^3, x.2^2 * x.3 * x.2^-3 * x.1 * x.2^2, x.2^2 * x.3 * x.1 * x.2 * x.3 * x.1 * x.2 * x.3^-1, 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        : 360
R = (1, 73, 145, 217, 289)(2, 74, 146, 218, 290)(3, 75, 147, 219, 291)(4, 76, 148, 220, 292)(5, 77, 149, 221, 293)(6, 78, 150, 222, 294)(7, 79, 151, 223, 295)(8, 80, 152, 224, 296)(9, 81, 153, 225, 297)(10, 82, 154, 226, 298)(11, 83, 155, 227, 299)(12, 84, 156, 228, 300)(13, 85, 157, 229, 301)(14, 86, 158, 230, 302)(15, 87, 159, 231, 303)(16, 88, 160, 232, 304)(17, 89, 161, 233, 305)(18, 90, 162, 234, 306)(19, 91, 163, 235, 307)(20, 92, 164, 236, 308)(21, 93, 165, 237, 309)(22, 94, 166, 238, 310)(23, 95, 167, 239, 311)(24, 96, 168, 240, 312)(25, 97, 169, 241, 313)(26, 98, 170, 242, 314)(27, 99, 171, 243, 315)(28, 100, 172, 244, 316)(29, 101, 173, 245, 317)(30, 102, 174, 246, 318)(31, 103, 175, 247, 319)(32, 104, 176, 248, 320)(33, 105, 177, 249, 321)(34, 106, 178, 250, 322)(35, 107, 179, 251, 323)(36, 108, 180, 252, 324)(37, 109, 181, 253, 325)(38, 110, 182, 254, 326)(39, 111, 183, 255, 327)(40, 112, 184, 256, 328)(41, 113, 185, 257, 329)(42, 114, 186, 258, 330)(43, 115, 187, 259, 331)(44, 116, 188, 260, 332)(45, 117, 189, 261, 333)(46, 118, 190, 262, 334)(47, 119, 191, 263, 335)(48, 120, 192, 264, 336)(49, 121, 193, 265, 337)(50, 122, 194, 266, 338)(51, 123, 195, 267, 339)(52, 124, 196, 268, 340)(53, 125, 197, 269, 341)(54, 126, 198, 270, 342)(55, 127, 199, 271, 343)(56, 128, 200, 272, 344)(57, 129, 201, 273, 345)(58, 130, 202, 274, 346)(59, 131, 203, 275, 347)(60, 132, 204, 276, 348)(61, 133, 205, 277, 349)(62, 134, 206, 278, 350)(63, 135, 207, 279, 351)(64, 136, 208, 280, 352)(65, 137, 209, 281, 353)(66, 138, 210, 282, 354)(67, 139, 211, 283, 355)(68, 140, 212, 284, 356)(69, 141, 213, 285, 357)(70, 142, 214, 286, 358)(71, 143, 215, 287, 359)(72, 144, 216, 288, 360)
L = (1, 4)(2, 6)(3, 43)(5, 67)(7, 11)(8, 52)(9, 38)(10, 50)(12, 40)(13, 24)(14, 33)(15, 23)(16, 36)(17, 59)(18, 21)(19, 27)(20, 60)(22, 57)(25, 28)(26, 30)(29, 55)(31, 35)(32, 64)(34, 62)(37, 48)(39, 47)(41, 71)(42, 45)(44, 72)(46, 69)(49, 56)(51, 53)(54, 58)(61, 68)(63, 65)(66, 70)(73, 146)(74, 151)(75, 148)(76, 182)(77, 145)(78, 187)(79, 160)(80, 150)(81, 211)(82, 147)(83, 196)(84, 194)(85, 165)(86, 159)(87, 168)(88, 162)(89, 180)(90, 167)(91, 164)(92, 177)(93, 203)(94, 179)(95, 204)(96, 201)(97, 202)(98, 161)(99, 200)(100, 166)(101, 152)(102, 197)(103, 157)(104, 154)(105, 195)(106, 149)(107, 193)(108, 198)(109, 170)(110, 175)(111, 172)(112, 158)(113, 169)(114, 163)(115, 184)(116, 174)(117, 199)(118, 171)(119, 208)(120, 206)(121, 189)(122, 183)(123, 192)(124, 186)(125, 156)(126, 191)(127, 188)(128, 153)(129, 215)(130, 155)(131, 216)(132, 213)(133, 214)(134, 185)(135, 212)(136, 190)(137, 176)(138, 209)(139, 181)(140, 178)(141, 207)(142, 173)(143, 205)(144, 210)(217, 355)(218, 292)(219, 338)(220, 331)(221, 350)(222, 340)(223, 294)(224, 343)(225, 337)(226, 352)(227, 342)(228, 339)(229, 323)(230, 300)(231, 321)(232, 299)(233, 318)(234, 324)(235, 333)(236, 315)(237, 312)(238, 313)(239, 309)(240, 311)(241, 359)(242, 336)(243, 357)(244, 335)(245, 354)(246, 360)(247, 297)(248, 351)(249, 348)(250, 349)(251, 345)(252, 347)(253, 293)(254, 289)(255, 298)(256, 291)(257, 322)(258, 296)(259, 290)(260, 317)(261, 344)(262, 320)(263, 346)(264, 341)(265, 319)(266, 328)(267, 302)(268, 295)(269, 314)(270, 304)(271, 330)(272, 307)(273, 301)(274, 316)(275, 306)(276, 303)(277, 329)(278, 325)(279, 334)(280, 327)(281, 358)(282, 332)(283, 326)(284, 353)(285, 308)(286, 356)(287, 310)(288, 305)

MAP           : A4.661
NOTES         : type I, chiral, isomorphic to Snub({3,12}), isomorphic to A4.659.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^3, x.3^2 * x.1 * x.3^-4 * x.2^-1 * x.3, x.2 * x.3^-1 * x.2 * x.3 * x.1 * x.3^-1 * x.2^-1 * x.1 * x.3^-1, 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        : 360
R = (1, 73, 145, 217, 289)(2, 74, 146, 218, 290)(3, 75, 147, 219, 291)(4, 76, 148, 220, 292)(5, 77, 149, 221, 293)(6, 78, 150, 222, 294)(7, 79, 151, 223, 295)(8, 80, 152, 224, 296)(9, 81, 153, 225, 297)(10, 82, 154, 226, 298)(11, 83, 155, 227, 299)(12, 84, 156, 228, 300)(13, 85, 157, 229, 301)(14, 86, 158, 230, 302)(15, 87, 159, 231, 303)(16, 88, 160, 232, 304)(17, 89, 161, 233, 305)(18, 90, 162, 234, 306)(19, 91, 163, 235, 307)(20, 92, 164, 236, 308)(21, 93, 165, 237, 309)(22, 94, 166, 238, 310)(23, 95, 167, 239, 311)(24, 96, 168, 240, 312)(25, 97, 169, 241, 313)(26, 98, 170, 242, 314)(27, 99, 171, 243, 315)(28, 100, 172, 244, 316)(29, 101, 173, 245, 317)(30, 102, 174, 246, 318)(31, 103, 175, 247, 319)(32, 104, 176, 248, 320)(33, 105, 177, 249, 321)(34, 106, 178, 250, 322)(35, 107, 179, 251, 323)(36, 108, 180, 252, 324)(37, 109, 181, 253, 325)(38, 110, 182, 254, 326)(39, 111, 183, 255, 327)(40, 112, 184, 256, 328)(41, 113, 185, 257, 329)(42, 114, 186, 258, 330)(43, 115, 187, 259, 331)(44, 116, 188, 260, 332)(45, 117, 189, 261, 333)(46, 118, 190, 262, 334)(47, 119, 191, 263, 335)(48, 120, 192, 264, 336)(49, 121, 193, 265, 337)(50, 122, 194, 266, 338)(51, 123, 195, 267, 339)(52, 124, 196, 268, 340)(53, 125, 197, 269, 341)(54, 126, 198, 270, 342)(55, 127, 199, 271, 343)(56, 128, 200, 272, 344)(57, 129, 201, 273, 345)(58, 130, 202, 274, 346)(59, 131, 203, 275, 347)(60, 132, 204, 276, 348)(61, 133, 205, 277, 349)(62, 134, 206, 278, 350)(63, 135, 207, 279, 351)(64, 136, 208, 280, 352)(65, 137, 209, 281, 353)(66, 138, 210, 282, 354)(67, 139, 211, 283, 355)(68, 140, 212, 284, 356)(69, 141, 213, 285, 357)(70, 142, 214, 286, 358)(71, 143, 215, 287, 359)(72, 144, 216, 288, 360)
L = (1, 4)(2, 6)(3, 43)(5, 67)(7, 11)(8, 52)(9, 38)(10, 50)(12, 40)(13, 24)(14, 33)(15, 23)(16, 36)(17, 59)(18, 21)(19, 27)(20, 60)(22, 57)(25, 28)(26, 30)(29, 55)(31, 35)(32, 64)(34, 62)(37, 48)(39, 47)(41, 71)(42, 45)(44, 72)(46, 69)(49, 56)(51, 53)(54, 58)(61, 68)(63, 65)(66, 70)(73, 150)(74, 155)(75, 145)(76, 153)(77, 148)(78, 147)(79, 180)(80, 146)(81, 149)(82, 187)(83, 152)(84, 154)(85, 162)(86, 167)(87, 157)(88, 165)(89, 160)(90, 159)(91, 204)(92, 158)(93, 161)(94, 175)(95, 164)(96, 166)(97, 198)(98, 203)(99, 193)(100, 201)(101, 196)(102, 195)(103, 168)(104, 194)(105, 197)(106, 211)(107, 200)(108, 202)(109, 174)(110, 179)(111, 169)(112, 177)(113, 172)(114, 171)(115, 156)(116, 170)(117, 173)(118, 163)(119, 176)(120, 178)(121, 186)(122, 191)(123, 181)(124, 189)(125, 184)(126, 183)(127, 216)(128, 182)(129, 185)(130, 151)(131, 188)(132, 190)(133, 210)(134, 215)(135, 205)(136, 213)(137, 208)(138, 207)(139, 192)(140, 206)(141, 209)(142, 199)(143, 212)(144, 214)(217, 331)(218, 340)(219, 290)(220, 355)(221, 326)(222, 292)(223, 342)(224, 295)(225, 289)(226, 328)(227, 294)(228, 291)(229, 311)(230, 348)(231, 309)(232, 347)(233, 306)(234, 312)(235, 357)(236, 303)(237, 324)(238, 301)(239, 321)(240, 323)(241, 335)(242, 360)(243, 333)(244, 359)(245, 330)(246, 336)(247, 345)(248, 327)(249, 300)(250, 325)(251, 297)(252, 299)(253, 341)(254, 337)(255, 346)(256, 339)(257, 310)(258, 344)(259, 338)(260, 305)(261, 296)(262, 308)(263, 298)(264, 293)(265, 307)(266, 352)(267, 314)(268, 343)(269, 302)(270, 316)(271, 354)(272, 319)(273, 313)(274, 304)(275, 318)(276, 315)(277, 353)(278, 349)(279, 358)(280, 351)(281, 334)(282, 356)(283, 350)(284, 329)(285, 320)(286, 332)(287, 322)(288, 317)

MAP           : A4.662
NOTES         : type I, chiral, isomorphic to Snub({3,12}), isomorphic to A4.659.
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)   : <72, 42>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^3, x.2^2 * x.3 * x.2^-3 * x.1 * x.2^2, x.2^2 * x.3 * x.1 * x.2 * x.3 * x.1 * x.2 * x.3^-1, 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        : 360
R = (1, 73, 145, 217, 289)(2, 74, 146, 218, 290)(3, 75, 147, 219, 291)(4, 76, 148, 220, 292)(5, 77, 149, 221, 293)(6, 78, 150, 222, 294)(7, 79, 151, 223, 295)(8, 80, 152, 224, 296)(9, 81, 153, 225, 297)(10, 82, 154, 226, 298)(11, 83, 155, 227, 299)(12, 84, 156, 228, 300)(13, 85, 157, 229, 301)(14, 86, 158, 230, 302)(15, 87, 159, 231, 303)(16, 88, 160, 232, 304)(17, 89, 161, 233, 305)(18, 90, 162, 234, 306)(19, 91, 163, 235, 307)(20, 92, 164, 236, 308)(21, 93, 165, 237, 309)(22, 94, 166, 238, 310)(23, 95, 167, 239, 311)(24, 96, 168, 240, 312)(25, 97, 169, 241, 313)(26, 98, 170, 242, 314)(27, 99, 171, 243, 315)(28, 100, 172, 244, 316)(29, 101, 173, 245, 317)(30, 102, 174, 246, 318)(31, 103, 175, 247, 319)(32, 104, 176, 248, 320)(33, 105, 177, 249, 321)(34, 106, 178, 250, 322)(35, 107, 179, 251, 323)(36, 108, 180, 252, 324)(37, 109, 181, 253, 325)(38, 110, 182, 254, 326)(39, 111, 183, 255, 327)(40, 112, 184, 256, 328)(41, 113, 185, 257, 329)(42, 114, 186, 258, 330)(43, 115, 187, 259, 331)(44, 116, 188, 260, 332)(45, 117, 189, 261, 333)(46, 118, 190, 262, 334)(47, 119, 191, 263, 335)(48, 120, 192, 264, 336)(49, 121, 193, 265, 337)(50, 122, 194, 266, 338)(51, 123, 195, 267, 339)(52, 124, 196, 268, 340)(53, 125, 197, 269, 341)(54, 126, 198, 270, 342)(55, 127, 199, 271, 343)(56, 128, 200, 272, 344)(57, 129, 201, 273, 345)(58, 130, 202, 274, 346)(59, 131, 203, 275, 347)(60, 132, 204, 276, 348)(61, 133, 205, 277, 349)(62, 134, 206, 278, 350)(63, 135, 207, 279, 351)(64, 136, 208, 280, 352)(65, 137, 209, 281, 353)(66, 138, 210, 282, 354)(67, 139, 211, 283, 355)(68, 140, 212, 284, 356)(69, 141, 213, 285, 357)(70, 142, 214, 286, 358)(71, 143, 215, 287, 359)(72, 144, 216, 288, 360)
L = (1, 4)(2, 6)(3, 43)(5, 67)(7, 11)(8, 52)(9, 38)(10, 50)(12, 40)(13, 24)(14, 33)(15, 23)(16, 36)(17, 59)(18, 21)(19, 27)(20, 60)(22, 57)(25, 28)(26, 30)(29, 55)(31, 35)(32, 64)(34, 62)(37, 48)(39, 47)(41, 71)(42, 45)(44, 72)(46, 69)(49, 56)(51, 53)(54, 58)(61, 68)(63, 65)(66, 70)(73, 167)(74, 204)(75, 165)(76, 203)(77, 162)(78, 168)(79, 213)(80, 159)(81, 180)(82, 157)(83, 177)(84, 179)(85, 209)(86, 205)(87, 214)(88, 207)(89, 190)(90, 212)(91, 206)(92, 185)(93, 176)(94, 188)(95, 178)(96, 173)(97, 163)(98, 208)(99, 170)(100, 199)(101, 158)(102, 172)(103, 210)(104, 175)(105, 169)(106, 160)(107, 174)(108, 171)(109, 191)(110, 216)(111, 189)(112, 215)(113, 186)(114, 192)(115, 201)(116, 183)(117, 156)(118, 181)(119, 153)(120, 155)(121, 197)(122, 193)(123, 202)(124, 195)(125, 166)(126, 200)(127, 194)(128, 161)(129, 152)(130, 164)(131, 154)(132, 149)(133, 187)(134, 196)(135, 146)(136, 211)(137, 182)(138, 148)(139, 198)(140, 151)(141, 145)(142, 184)(143, 150)(144, 147)(217, 334)(218, 353)(219, 332)(220, 358)(221, 308)(222, 329)(223, 349)(224, 310)(225, 327)(226, 305)(227, 325)(228, 330)(229, 338)(230, 343)(231, 340)(232, 350)(233, 337)(234, 355)(235, 316)(236, 342)(237, 331)(238, 339)(239, 292)(240, 290)(241, 302)(242, 307)(243, 304)(244, 314)(245, 301)(246, 319)(247, 352)(248, 306)(249, 295)(250, 303)(251, 328)(252, 326)(253, 357)(254, 351)(255, 360)(256, 354)(257, 348)(258, 359)(259, 356)(260, 345)(261, 335)(262, 347)(263, 336)(264, 333)(265, 298)(266, 317)(267, 296)(268, 322)(269, 344)(270, 293)(271, 313)(272, 346)(273, 291)(274, 341)(275, 289)(276, 294)(277, 321)(278, 315)(279, 324)(280, 318)(281, 312)(282, 323)(283, 320)(284, 309)(285, 299)(286, 311)(287, 300)(288, 297)

MAP           : A4.663
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)   : <36, 10>
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 * x.3)^3, x.4^6, x.3 * x.1 * x.4^-1 * x.3 * x.4 * x.1 >
SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 6, 6)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 12)(2, 10)(3, 14)(4, 8)(5, 13)(6, 7)(9, 20)(11, 19)(15, 22)(16, 21)(17, 24)(18, 23)(25, 35)(26, 33)(27, 28)(29, 30)(31, 36)(32, 34)(37, 69)(38, 71)(39, 41)(40, 42)(43, 64)(44, 66)(45, 60)(46, 59)(47, 58)(48, 57)(49, 63)(50, 65)(51, 53)(52, 54)(55, 70)(56, 72)(61, 62)(67, 68)(73, 170)(74, 169)(75, 157)(76, 151)(77, 158)(78, 152)(79, 171)(80, 173)(81, 161)(82, 162)(83, 159)(84, 160)(85, 172)(86, 174)(87, 168)(88, 167)(89, 166)(90, 165)(91, 176)(92, 175)(93, 145)(94, 163)(95, 146)(96, 164)(97, 177)(98, 179)(99, 149)(100, 150)(101, 147)(102, 148)(103, 178)(104, 180)(105, 156)(106, 155)(107, 154)(108, 153)(109, 135)(110, 137)(111, 125)(112, 126)(113, 123)(114, 124)(115, 142)(116, 144)(117, 120)(118, 119)(121, 141)(122, 143)(127, 136)(128, 138)(129, 132)(130, 131)(133, 140)(134, 139)

MAP           : A4.664
NOTES         : type I, chiral, isomorphic to A4.663.
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)   : <36, 10>
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 * x.3)^3, x.4^6, x.3 * x.1 * x.4^-1 * x.3 * x.4 * x.1 >
SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 6, 6)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 6)(2, 4)(3, 20)(5, 19)(7, 36)(8, 34)(9, 26)(10, 32)(11, 25)(12, 31)(13, 35)(14, 33)(15, 28)(16, 27)(17, 30)(18, 29)(21, 22)(23, 24)(37, 56)(38, 55)(39, 61)(40, 67)(41, 62)(42, 68)(43, 57)(44, 59)(45, 65)(46, 66)(47, 63)(48, 64)(49, 58)(50, 60)(51, 54)(52, 53)(69, 72)(70, 71)(73, 147)(74, 149)(75, 155)(76, 156)(77, 153)(78, 154)(79, 166)(80, 168)(81, 162)(82, 161)(83, 160)(84, 159)(85, 165)(86, 167)(87, 173)(88, 174)(89, 171)(90, 172)(91, 148)(92, 150)(93, 180)(94, 179)(95, 178)(96, 177)(97, 164)(98, 163)(99, 169)(100, 175)(101, 170)(102, 176)(103, 146)(104, 145)(105, 151)(106, 157)(107, 152)(108, 158)(109, 110)(111, 115)(112, 121)(113, 116)(114, 122)(117, 119)(118, 120)(123, 144)(124, 143)(125, 142)(126, 141)(127, 128)(129, 133)(130, 139)(131, 134)(132, 140)(135, 137)(136, 138)

MAP           : A4.665
NOTES         : type I, chiral, isomorphic to A4.663.
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)   : <36, 10>
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 * x.3)^3, x.4^-2 * x.3 * x.4^2 * x.3, (x.4 * x.3 * x.2)^2, x.4^6 >
SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 6, 6)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 2)(3, 7)(4, 13)(5, 8)(6, 14)(9, 11)(10, 12)(15, 36)(16, 35)(17, 34)(18, 33)(19, 20)(21, 25)(22, 31)(23, 26)(24, 32)(27, 29)(28, 30)(37, 59)(38, 57)(39, 40)(41, 42)(43, 65)(44, 63)(45, 70)(46, 69)(47, 72)(48, 71)(49, 66)(50, 64)(51, 68)(52, 62)(53, 67)(54, 61)(55, 60)(56, 58)(73, 170)(74, 169)(75, 157)(76, 151)(77, 158)(78, 152)(79, 171)(80, 173)(81, 161)(82, 162)(83, 159)(84, 160)(85, 172)(86, 174)(87, 168)(88, 167)(89, 166)(90, 165)(91, 176)(92, 175)(93, 145)(94, 163)(95, 146)(96, 164)(97, 177)(98, 179)(99, 149)(100, 150)(101, 147)(102, 148)(103, 178)(104, 180)(105, 156)(106, 155)(107, 154)(108, 153)(109, 135)(110, 137)(111, 125)(112, 126)(113, 123)(114, 124)(115, 142)(116, 144)(117, 120)(118, 119)(121, 141)(122, 143)(127, 136)(128, 138)(129, 132)(130, 131)(133, 140)(134, 139)

MAP           : A4.666
NOTES         : type I, chiral, isomorphic to A4.663.
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)   : <36, 10>
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 * x.3)^3, x.4^-2 * x.3 * x.4^2 * x.3, (x.4 * x.3 * x.2)^2, x.4^6 >
SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 6, 6)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 27)(2, 29)(3, 17)(4, 18)(5, 15)(6, 16)(7, 34)(8, 36)(9, 12)(10, 11)(13, 33)(14, 35)(19, 28)(20, 30)(21, 24)(22, 23)(25, 32)(26, 31)(37, 53)(38, 51)(39, 46)(40, 45)(41, 48)(42, 47)(43, 59)(44, 57)(49, 60)(50, 58)(52, 56)(54, 55)(61, 66)(62, 64)(63, 68)(65, 67)(69, 70)(71, 72)(73, 147)(74, 149)(75, 155)(76, 156)(77, 153)(78, 154)(79, 166)(80, 168)(81, 162)(82, 161)(83, 160)(84, 159)(85, 165)(86, 167)(87, 173)(88, 174)(89, 171)(90, 172)(91, 148)(92, 150)(93, 180)(94, 179)(95, 178)(96, 177)(97, 164)(98, 163)(99, 169)(100, 175)(101, 170)(102, 176)(103, 146)(104, 145)(105, 151)(106, 157)(107, 152)(108, 158)(109, 110)(111, 115)(112, 121)(113, 116)(114, 122)(117, 119)(118, 120)(123, 144)(124, 143)(125, 142)(126, 141)(127, 128)(129, 133)(130, 139)(131, 134)(132, 140)(135, 137)(136, 138)

MAP           : A4.667
NOTES         : type I, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (3, 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.1 * u.2 * u.4^-1, (u.4 * u.3)^4 >
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.3 * x.2)^3, (x.3 * x.1)^3, (x.2 * x.1 * x.3 * x.1)^2 >
SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 8, 8)
#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, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(49, 105)(50, 106)(51, 107)(52, 108)(53, 117)(54, 118)(55, 119)(56, 120)(57, 113)(58, 114)(59, 115)(60, 116)(61, 101)(62, 102)(63, 103)(64, 104)(65, 97)(66, 98)(67, 99)(68, 100)(69, 109)(70, 110)(71, 111)(72, 112)(73, 90)(74, 92)(75, 89)(76, 91)(77, 87)(78, 85)(79, 88)(80, 86)(81, 96)(82, 95)(83, 94)(84, 93)

MAP           : A4.668
NOTES         : type I, chiral, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (3, 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.1 * u.2 * u.4^-1, (u.4 * u.3)^4 >
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.3 * x.2)^3, (x.4 * x.3)^4 >
SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 8, 8)
#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, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(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, 105)(50, 106)(51, 107)(52, 108)(53, 117)(54, 118)(55, 119)(56, 120)(57, 113)(58, 114)(59, 115)(60, 116)(61, 101)(62, 102)(63, 103)(64, 104)(65, 97)(66, 98)(67, 99)(68, 100)(69, 109)(70, 110)(71, 111)(72, 112)(73, 90)(74, 92)(75, 89)(76, 91)(77, 87)(78, 85)(79, 88)(80, 86)(81, 96)(82, 95)(83, 94)(84, 93)

MAP           : A4.669
NOTES         : type I, chiral, isomorphic to A4.668.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (3, 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.1 * u.2 * u.4^-1, (u.4 * u.3)^4 >
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.3 * x.4 * x.3 * x.4^-1 * x.3 * x.1 >
SCHREIER VEC. : (x.1, x.2, x.4, x.3, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 8, 8)
#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, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)(49, 105)(50, 106)(51, 107)(52, 108)(53, 117)(54, 118)(55, 119)(56, 120)(57, 113)(58, 114)(59, 115)(60, 116)(61, 101)(62, 102)(63, 103)(64, 104)(65, 97)(66, 98)(67, 99)(68, 100)(69, 109)(70, 110)(71, 111)(72, 112)(73, 90)(74, 92)(75, 89)(76, 91)(77, 87)(78, 85)(79, 88)(80, 86)(81, 96)(82, 95)(83, 94)(84, 93)

MAP           : A4.670
NOTES         : type I, chiral, isomorphic to Snub({4,5}), representative.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 5, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^5 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.3 * x.2, x.2^4, x.3^5, x.1 * x.2 * x.3 * x.1 * x.2 * x.3 * x.1 * x.3^-1 * x.2^-1, x.3^2 * x.2^-1 * x.3 * x.1 * x.3^-2 * 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, 4, 3, 5)
#DARTS        : 600
R = (1, 121, 241, 361, 481)(2, 122, 242, 362, 482)(3, 123, 243, 363, 483)(4, 124, 244, 364, 484)(5, 125, 245, 365, 485)(6, 126, 246, 366, 486)(7, 127, 247, 367, 487)(8, 128, 248, 368, 488)(9, 129, 249, 369, 489)(10, 130, 250, 370, 490)(11, 131, 251, 371, 491)(12, 132, 252, 372, 492)(13, 133, 253, 373, 493)(14, 134, 254, 374, 494)(15, 135, 255, 375, 495)(16, 136, 256, 376, 496)(17, 137, 257, 377, 497)(18, 138, 258, 378, 498)(19, 139, 259, 379, 499)(20, 140, 260, 380, 500)(21, 141, 261, 381, 501)(22, 142, 262, 382, 502)(23, 143, 263, 383, 503)(24, 144, 264, 384, 504)(25, 145, 265, 385, 505)(26, 146, 266, 386, 506)(27, 147, 267, 387, 507)(28, 148, 268, 388, 508)(29, 149, 269, 389, 509)(30, 150, 270, 390, 510)(31, 151, 271, 391, 511)(32, 152, 272, 392, 512)(33, 153, 273, 393, 513)(34, 154, 274, 394, 514)(35, 155, 275, 395, 515)(36, 156, 276, 396, 516)(37, 157, 277, 397, 517)(38, 158, 278, 398, 518)(39, 159, 279, 399, 519)(40, 160, 280, 400, 520)(41, 161, 281, 401, 521)(42, 162, 282, 402, 522)(43, 163, 283, 403, 523)(44, 164, 284, 404, 524)(45, 165, 285, 405, 525)(46, 166, 286, 406, 526)(47, 167, 287, 407, 527)(48, 168, 288, 408, 528)(49, 169, 289, 409, 529)(50, 170, 290, 410, 530)(51, 171, 291, 411, 531)(52, 172, 292, 412, 532)(53, 173, 293, 413, 533)(54, 174, 294, 414, 534)(55, 175, 295, 415, 535)(56, 176, 296, 416, 536)(57, 177, 297, 417, 537)(58, 178, 298, 418, 538)(59, 179, 299, 419, 539)(60, 180, 300, 420, 540)(61, 181, 301, 421, 541)(62, 182, 302, 422, 542)(63, 183, 303, 423, 543)(64, 184, 304, 424, 544)(65, 185, 305, 425, 545)(66, 186, 306, 426, 546)(67, 187, 307, 427, 547)(68, 188, 308, 428, 548)(69, 189, 309, 429, 549)(70, 190, 310, 430, 550)(71, 191, 311, 431, 551)(72, 192, 312, 432, 552)(73, 193, 313, 433, 553)(74, 194, 314, 434, 554)(75, 195, 315, 435, 555)(76, 196, 316, 436, 556)(77, 197, 317, 437, 557)(78, 198, 318, 438, 558)(79, 199, 319, 439, 559)(80, 200, 320, 440, 560)(81, 201, 321, 441, 561)(82, 202, 322, 442, 562)(83, 203, 323, 443, 563)(84, 204, 324, 444, 564)(85, 205, 325, 445, 565)(86, 206, 326, 446, 566)(87, 207, 327, 447, 567)(88, 208, 328, 448, 568)(89, 209, 329, 449, 569)(90, 210, 330, 450, 570)(91, 211, 331, 451, 571)(92, 212, 332, 452, 572)(93, 213, 333, 453, 573)(94, 214, 334, 454, 574)(95, 215, 335, 455, 575)(96, 216, 336, 456, 576)(97, 217, 337, 457, 577)(98, 218, 338, 458, 578)(99, 219, 339, 459, 579)(100, 220, 340, 460, 580)(101, 221, 341, 461, 581)(102, 222, 342, 462, 582)(103, 223, 343, 463, 583)(104, 224, 344, 464, 584)(105, 225, 345, 465, 585)(106, 226, 346, 466, 586)(107, 227, 347, 467, 587)(108, 228, 348, 468, 588)(109, 229, 349, 469, 589)(110, 230, 350, 470, 590)(111, 231, 351, 471, 591)(112, 232, 352, 472, 592)(113, 233, 353, 473, 593)(114, 234, 354, 474, 594)(115, 235, 355, 475, 595)(116, 236, 356, 476, 596)(117, 237, 357, 477, 597)(118, 238, 358, 478, 598)(119, 239, 359, 479, 599)(120, 240, 360, 480, 600)
L = (1, 2)(3, 7)(4, 14)(5, 13)(6, 8)(9, 16)(10, 102)(11, 99)(12, 17)(15, 119)(18, 118)(19, 54)(20, 51)(21, 90)(22, 49)(23, 50)(24, 87)(25, 40)(26, 41)(27, 38)(28, 77)(29, 76)(30, 37)(31, 111)(32, 114)(33, 100)(34, 66)(35, 63)(36, 101)(39, 42)(43, 110)(44, 109)(45, 115)(46, 98)(47, 97)(48, 116)(52, 53)(55, 113)(56, 112)(57, 83)(58, 117)(59, 120)(60, 82)(61, 71)(62, 70)(64, 81)(65, 84)(67, 68)(69, 79)(72, 80)(73, 106)(74, 107)(75, 104)(78, 103)(85, 96)(86, 93)(88, 91)(89, 92)(94, 95)(105, 108)(121, 243)(122, 246)(123, 256)(124, 342)(125, 339)(126, 257)(127, 294)(128, 291)(129, 330)(130, 289)(131, 290)(132, 327)(133, 242)(134, 241)(135, 247)(136, 254)(137, 253)(138, 248)(139, 280)(140, 281)(141, 278)(142, 317)(143, 316)(144, 277)(145, 245)(146, 244)(147, 359)(148, 249)(149, 252)(150, 358)(151, 353)(152, 352)(153, 323)(154, 357)(155, 360)(156, 322)(157, 350)(158, 349)(159, 355)(160, 338)(161, 337)(162, 356)(163, 262)(164, 263)(165, 260)(166, 293)(167, 292)(168, 259)(169, 351)(170, 354)(171, 340)(172, 306)(173, 303)(174, 341)(175, 270)(176, 267)(177, 282)(178, 265)(179, 266)(180, 279)(181, 346)(182, 347)(183, 344)(184, 269)(185, 268)(186, 343)(187, 311)(188, 310)(189, 275)(190, 321)(191, 324)(192, 274)(193, 336)(194, 333)(195, 264)(196, 331)(197, 332)(198, 261)(199, 308)(200, 307)(201, 319)(202, 302)(203, 301)(204, 320)(205, 309)(206, 312)(207, 304)(208, 300)(209, 297)(210, 305)(211, 284)(212, 283)(213, 271)(214, 296)(215, 295)(216, 272)(217, 285)(218, 288)(219, 298)(220, 258)(221, 255)(222, 299)(223, 287)(224, 286)(225, 251)(226, 273)(227, 276)(228, 250)(229, 318)(230, 315)(231, 348)(232, 313)(233, 314)(234, 345)(235, 328)(236, 329)(237, 326)(238, 335)(239, 334)(240, 325)(361, 484)(362, 485)(363, 482)(364, 521)(365, 520)(366, 481)(367, 599)(368, 598)(369, 557)(370, 585)(371, 588)(372, 556)(373, 492)(374, 489)(375, 516)(376, 487)(377, 488)(378, 513)(379, 596)(380, 595)(381, 583)(382, 590)(383, 589)(384, 584)(385, 597)(386, 600)(387, 592)(388, 564)(389, 561)(390, 593)(391, 566)(392, 565)(393, 553)(394, 560)(395, 559)(396, 554)(397, 567)(398, 570)(399, 562)(400, 534)(401, 531)(402, 563)(403, 569)(404, 568)(405, 527)(406, 555)(407, 558)(408, 526)(409, 582)(410, 579)(411, 486)(412, 577)(413, 578)(414, 483)(415, 574)(416, 575)(417, 572)(418, 491)(419, 490)(420, 571)(421, 537)(422, 540)(423, 532)(424, 504)(425, 501)(426, 533)(427, 552)(428, 549)(429, 576)(430, 547)(431, 548)(432, 573)(433, 536)(434, 535)(435, 523)(436, 530)(437, 529)(438, 524)(439, 544)(440, 545)(441, 542)(442, 581)(443, 580)(444, 541)(445, 539)(446, 538)(447, 497)(448, 525)(449, 528)(450, 496)(451, 509)(452, 508)(453, 587)(454, 495)(455, 498)(456, 586)(457, 506)(458, 505)(459, 493)(460, 500)(461, 499)(462, 494)(463, 514)(464, 515)(465, 512)(466, 551)(467, 550)(468, 511)(469, 507)(470, 510)(471, 502)(472, 594)(473, 591)(474, 503)(475, 522)(476, 519)(477, 546)(478, 517)(479, 518)(480, 543)

MAP           : A4.671
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)   : <72, 40>
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.2^-1 * x.1 * x.2 * x.3 * x.1 * x.3^-1 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 4, 3, 6)
#DARTS        : 360
R = (1, 73, 145, 217, 289)(2, 74, 146, 218, 290)(3, 75, 147, 219, 291)(4, 76, 148, 220, 292)(5, 77, 149, 221, 293)(6, 78, 150, 222, 294)(7, 79, 151, 223, 295)(8, 80, 152, 224, 296)(9, 81, 153, 225, 297)(10, 82, 154, 226, 298)(11, 83, 155, 227, 299)(12, 84, 156, 228, 300)(13, 85, 157, 229, 301)(14, 86, 158, 230, 302)(15, 87, 159, 231, 303)(16, 88, 160, 232, 304)(17, 89, 161, 233, 305)(18, 90, 162, 234, 306)(19, 91, 163, 235, 307)(20, 92, 164, 236, 308)(21, 93, 165, 237, 309)(22, 94, 166, 238, 310)(23, 95, 167, 239, 311)(24, 96, 168, 240, 312)(25, 97, 169, 241, 313)(26, 98, 170, 242, 314)(27, 99, 171, 243, 315)(28, 100, 172, 244, 316)(29, 101, 173, 245, 317)(30, 102, 174, 246, 318)(31, 103, 175, 247, 319)(32, 104, 176, 248, 320)(33, 105, 177, 249, 321)(34, 106, 178, 250, 322)(35, 107, 179, 251, 323)(36, 108, 180, 252, 324)(37, 109, 181, 253, 325)(38, 110, 182, 254, 326)(39, 111, 183, 255, 327)(40, 112, 184, 256, 328)(41, 113, 185, 257, 329)(42, 114, 186, 258, 330)(43, 115, 187, 259, 331)(44, 116, 188, 260, 332)(45, 117, 189, 261, 333)(46, 118, 190, 262, 334)(47, 119, 191, 263, 335)(48, 120, 192, 264, 336)(49, 121, 193, 265, 337)(50, 122, 194, 266, 338)(51, 123, 195, 267, 339)(52, 124, 196, 268, 340)(53, 125, 197, 269, 341)(54, 126, 198, 270, 342)(55, 127, 199, 271, 343)(56, 128, 200, 272, 344)(57, 129, 201, 273, 345)(58, 130, 202, 274, 346)(59, 131, 203, 275, 347)(60, 132, 204, 276, 348)(61, 133, 205, 277, 349)(62, 134, 206, 278, 350)(63, 135, 207, 279, 351)(64, 136, 208, 280, 352)(65, 137, 209, 281, 353)(66, 138, 210, 282, 354)(67, 139, 211, 283, 355)(68, 140, 212, 284, 356)(69, 141, 213, 285, 357)(70, 142, 214, 286, 358)(71, 143, 215, 287, 359)(72, 144, 216, 288, 360)
L = (1, 66)(2, 27)(3, 30)(4, 59)(5, 34)(6, 23)(7, 64)(8, 25)(9, 28)(10, 67)(11, 26)(12, 31)(13, 70)(14, 37)(15, 40)(16, 61)(17, 38)(18, 55)(19, 62)(20, 65)(21, 56)(22, 63)(24, 57)(29, 60)(32, 45)(33, 48)(35, 52)(36, 41)(39, 50)(42, 51)(43, 68)(44, 71)(46, 69)(47, 54)(49, 72)(53, 58)(73, 148)(74, 175)(75, 178)(76, 163)(77, 176)(78, 169)(79, 150)(80, 177)(81, 180)(82, 155)(83, 172)(84, 215)(85, 146)(86, 149)(87, 152)(88, 147)(89, 210)(90, 153)(91, 166)(92, 157)(93, 160)(94, 145)(95, 158)(96, 151)(97, 168)(98, 159)(99, 162)(100, 173)(101, 154)(102, 197)(103, 164)(104, 167)(105, 170)(106, 165)(107, 192)(108, 171)(109, 202)(110, 193)(111, 196)(112, 181)(113, 194)(114, 187)(115, 204)(116, 195)(117, 198)(118, 209)(119, 190)(120, 161)(121, 200)(122, 203)(123, 206)(124, 201)(125, 156)(126, 207)(127, 184)(128, 211)(129, 214)(130, 199)(131, 212)(132, 205)(133, 186)(134, 213)(135, 216)(136, 191)(137, 208)(138, 179)(139, 182)(140, 185)(141, 188)(142, 183)(143, 174)(144, 189)(217, 351)(218, 358)(219, 349)(220, 354)(221, 325)(222, 352)(223, 345)(224, 328)(225, 343)(226, 348)(227, 355)(228, 346)(229, 353)(230, 294)(231, 299)(232, 344)(233, 321)(234, 290)(235, 347)(236, 300)(237, 293)(238, 350)(239, 333)(240, 296)(241, 311)(242, 336)(243, 329)(244, 314)(245, 297)(246, 332)(247, 315)(248, 322)(249, 313)(250, 318)(251, 289)(252, 316)(253, 303)(254, 298)(255, 301)(256, 306)(257, 331)(258, 304)(259, 339)(260, 334)(261, 337)(262, 342)(263, 295)(264, 340)(265, 305)(266, 324)(267, 359)(268, 338)(269, 291)(270, 320)(271, 341)(272, 360)(273, 323)(274, 302)(275, 327)(276, 356)(277, 317)(278, 330)(279, 335)(280, 308)(281, 357)(282, 326)(283, 309)(284, 292)(285, 307)(286, 312)(287, 319)(288, 310)

MAP           : A4.672
NOTES         : type I, chiral, isomorphic to Snub({4,6}), isomorphic to A4.671.
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)   : <72, 40>
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.2^-1 * x.1 * x.2 * x.3 * x.1 * x.3^-1 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 4, 3, 6)
#DARTS        : 360
R = (1, 73, 145, 217, 289)(2, 74, 146, 218, 290)(3, 75, 147, 219, 291)(4, 76, 148, 220, 292)(5, 77, 149, 221, 293)(6, 78, 150, 222, 294)(7, 79, 151, 223, 295)(8, 80, 152, 224, 296)(9, 81, 153, 225, 297)(10, 82, 154, 226, 298)(11, 83, 155, 227, 299)(12, 84, 156, 228, 300)(13, 85, 157, 229, 301)(14, 86, 158, 230, 302)(15, 87, 159, 231, 303)(16, 88, 160, 232, 304)(17, 89, 161, 233, 305)(18, 90, 162, 234, 306)(19, 91, 163, 235, 307)(20, 92, 164, 236, 308)(21, 93, 165, 237, 309)(22, 94, 166, 238, 310)(23, 95, 167, 239, 311)(24, 96, 168, 240, 312)(25, 97, 169, 241, 313)(26, 98, 170, 242, 314)(27, 99, 171, 243, 315)(28, 100, 172, 244, 316)(29, 101, 173, 245, 317)(30, 102, 174, 246, 318)(31, 103, 175, 247, 319)(32, 104, 176, 248, 320)(33, 105, 177, 249, 321)(34, 106, 178, 250, 322)(35, 107, 179, 251, 323)(36, 108, 180, 252, 324)(37, 109, 181, 253, 325)(38, 110, 182, 254, 326)(39, 111, 183, 255, 327)(40, 112, 184, 256, 328)(41, 113, 185, 257, 329)(42, 114, 186, 258, 330)(43, 115, 187, 259, 331)(44, 116, 188, 260, 332)(45, 117, 189, 261, 333)(46, 118, 190, 262, 334)(47, 119, 191, 263, 335)(48, 120, 192, 264, 336)(49, 121, 193, 265, 337)(50, 122, 194, 266, 338)(51, 123, 195, 267, 339)(52, 124, 196, 268, 340)(53, 125, 197, 269, 341)(54, 126, 198, 270, 342)(55, 127, 199, 271, 343)(56, 128, 200, 272, 344)(57, 129, 201, 273, 345)(58, 130, 202, 274, 346)(59, 131, 203, 275, 347)(60, 132, 204, 276, 348)(61, 133, 205, 277, 349)(62, 134, 206, 278, 350)(63, 135, 207, 279, 351)(64, 136, 208, 280, 352)(65, 137, 209, 281, 353)(66, 138, 210, 282, 354)(67, 139, 211, 283, 355)(68, 140, 212, 284, 356)(69, 141, 213, 285, 357)(70, 142, 214, 286, 358)(71, 143, 215, 287, 359)(72, 144, 216, 288, 360)
L = (1, 3)(2, 22)(4, 6)(5, 13)(7, 9)(8, 16)(10, 12)(11, 19)(14, 66)(15, 59)(17, 27)(18, 62)(20, 60)(21, 65)(23, 51)(24, 56)(25, 71)(26, 54)(28, 32)(29, 57)(30, 50)(31, 33)(34, 36)(35, 61)(37, 39)(38, 58)(40, 42)(41, 49)(43, 45)(44, 52)(46, 48)(47, 55)(53, 63)(64, 68)(67, 69)(70, 72)(73, 148)(74, 175)(75, 178)(76, 163)(77, 176)(78, 169)(79, 150)(80, 177)(81, 180)(82, 155)(83, 172)(84, 215)(85, 146)(86, 149)(87, 152)(88, 147)(89, 210)(90, 153)(91, 166)(92, 157)(93, 160)(94, 145)(95, 158)(96, 151)(97, 168)(98, 159)(99, 162)(100, 173)(101, 154)(102, 197)(103, 164)(104, 167)(105, 170)(106, 165)(107, 192)(108, 171)(109, 202)(110, 193)(111, 196)(112, 181)(113, 194)(114, 187)(115, 204)(116, 195)(117, 198)(118, 209)(119, 190)(120, 161)(121, 200)(122, 203)(123, 206)(124, 201)(125, 156)(126, 207)(127, 184)(128, 211)(129, 214)(130, 199)(131, 212)(132, 205)(133, 186)(134, 213)(135, 216)(136, 191)(137, 208)(138, 179)(139, 182)(140, 185)(141, 188)(142, 183)(143, 174)(144, 189)(217, 290)(218, 293)(219, 296)(220, 291)(221, 354)(222, 297)(223, 344)(224, 347)(225, 350)(226, 345)(227, 300)(228, 351)(229, 348)(230, 339)(231, 342)(232, 353)(233, 334)(234, 305)(235, 294)(236, 321)(237, 324)(238, 299)(239, 316)(240, 359)(241, 292)(242, 319)(243, 322)(244, 307)(245, 320)(246, 313)(247, 310)(248, 301)(249, 304)(250, 289)(251, 302)(252, 295)(253, 330)(254, 357)(255, 360)(256, 335)(257, 352)(258, 323)(259, 328)(260, 355)(261, 358)(262, 343)(263, 356)(264, 349)(265, 346)(266, 337)(267, 340)(268, 325)(269, 338)(270, 331)(271, 326)(272, 329)(273, 332)(274, 327)(275, 318)(276, 333)(277, 308)(278, 311)(279, 314)(280, 309)(281, 336)(282, 315)(283, 312)(284, 303)(285, 306)(286, 317)(287, 298)(288, 341)

MAP           : A4.673
NOTES         : type I, chiral, isomorphic to Snub({4,10}), representative.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 10, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^10 >
CTG (small)   : <40, 8>
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.3^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 4, 3, 10)
#DARTS        : 200
R = (1, 41, 81, 121, 161)(2, 42, 82, 122, 162)(3, 43, 83, 123, 163)(4, 44, 84, 124, 164)(5, 45, 85, 125, 165)(6, 46, 86, 126, 166)(7, 47, 87, 127, 167)(8, 48, 88, 128, 168)(9, 49, 89, 129, 169)(10, 50, 90, 130, 170)(11, 51, 91, 131, 171)(12, 52, 92, 132, 172)(13, 53, 93, 133, 173)(14, 54, 94, 134, 174)(15, 55, 95, 135, 175)(16, 56, 96, 136, 176)(17, 57, 97, 137, 177)(18, 58, 98, 138, 178)(19, 59, 99, 139, 179)(20, 60, 100, 140, 180)(21, 61, 101, 141, 181)(22, 62, 102, 142, 182)(23, 63, 103, 143, 183)(24, 64, 104, 144, 184)(25, 65, 105, 145, 185)(26, 66, 106, 146, 186)(27, 67, 107, 147, 187)(28, 68, 108, 148, 188)(29, 69, 109, 149, 189)(30, 70, 110, 150, 190)(31, 71, 111, 151, 191)(32, 72, 112, 152, 192)(33, 73, 113, 153, 193)(34, 74, 114, 154, 194)(35, 75, 115, 155, 195)(36, 76, 116, 156, 196)(37, 77, 117, 157, 197)(38, 78, 118, 158, 198)(39, 79, 119, 159, 199)(40, 80, 120, 160, 200)
L = (1, 7)(2, 3)(4, 6)(5, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 27)(22, 23)(24, 26)(25, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 83)(42, 88)(43, 107)(44, 87)(45, 92)(46, 111)(47, 106)(48, 103)(49, 86)(50, 96)(51, 115)(52, 108)(53, 91)(54, 100)(55, 119)(56, 112)(57, 95)(58, 99)(59, 120)(60, 116)(61, 84)(62, 81)(63, 105)(64, 89)(65, 82)(66, 101)(67, 102)(68, 110)(69, 93)(70, 85)(71, 104)(72, 114)(73, 97)(74, 90)(75, 109)(76, 118)(77, 98)(78, 94)(79, 113)(80, 117)(121, 183)(122, 188)(123, 167)(124, 187)(125, 192)(126, 171)(127, 166)(128, 163)(129, 186)(130, 196)(131, 175)(132, 168)(133, 191)(134, 200)(135, 179)(136, 172)(137, 195)(138, 199)(139, 180)(140, 176)(141, 184)(142, 181)(143, 165)(144, 189)(145, 182)(146, 161)(147, 162)(148, 170)(149, 193)(150, 185)(151, 164)(152, 174)(153, 197)(154, 190)(155, 169)(156, 178)(157, 198)(158, 194)(159, 173)(160, 177)

MAP           : A4.674
NOTES         : type I, chiral, isomorphic to Snub({4,10}), isomorphic to A4.673.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 10, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^10 >
CTG (small)   : <40, 8>
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.3^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 4, 3, 10)
#DARTS        : 200
R = (1, 41, 81, 121, 161)(2, 42, 82, 122, 162)(3, 43, 83, 123, 163)(4, 44, 84, 124, 164)(5, 45, 85, 125, 165)(6, 46, 86, 126, 166)(7, 47, 87, 127, 167)(8, 48, 88, 128, 168)(9, 49, 89, 129, 169)(10, 50, 90, 130, 170)(11, 51, 91, 131, 171)(12, 52, 92, 132, 172)(13, 53, 93, 133, 173)(14, 54, 94, 134, 174)(15, 55, 95, 135, 175)(16, 56, 96, 136, 176)(17, 57, 97, 137, 177)(18, 58, 98, 138, 178)(19, 59, 99, 139, 179)(20, 60, 100, 140, 180)(21, 61, 101, 141, 181)(22, 62, 102, 142, 182)(23, 63, 103, 143, 183)(24, 64, 104, 144, 184)(25, 65, 105, 145, 185)(26, 66, 106, 146, 186)(27, 67, 107, 147, 187)(28, 68, 108, 148, 188)(29, 69, 109, 149, 189)(30, 70, 110, 150, 190)(31, 71, 111, 151, 191)(32, 72, 112, 152, 192)(33, 73, 113, 153, 193)(34, 74, 114, 154, 194)(35, 75, 115, 155, 195)(36, 76, 116, 156, 196)(37, 77, 117, 157, 197)(38, 78, 118, 158, 198)(39, 79, 119, 159, 199)(40, 80, 120, 160, 200)
L = (1, 7)(2, 3)(4, 6)(5, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 27)(22, 23)(24, 26)(25, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 110)(42, 114)(43, 89)(44, 105)(45, 118)(46, 97)(47, 93)(48, 84)(49, 102)(50, 117)(51, 98)(52, 81)(53, 101)(54, 113)(55, 94)(56, 82)(57, 104)(58, 109)(59, 90)(60, 85)(61, 115)(62, 111)(63, 96)(64, 119)(65, 106)(66, 88)(67, 92)(68, 100)(69, 120)(70, 107)(71, 83)(72, 99)(73, 116)(74, 103)(75, 87)(76, 95)(77, 112)(78, 108)(79, 86)(80, 91)(121, 170)(122, 174)(123, 189)(124, 165)(125, 178)(126, 197)(127, 193)(128, 184)(129, 162)(130, 177)(131, 198)(132, 181)(133, 161)(134, 173)(135, 194)(136, 182)(137, 164)(138, 169)(139, 190)(140, 185)(141, 175)(142, 171)(143, 196)(144, 179)(145, 166)(146, 188)(147, 192)(148, 200)(149, 180)(150, 167)(151, 183)(152, 199)(153, 176)(154, 163)(155, 187)(156, 195)(157, 172)(158, 168)(159, 186)(160, 191)

MAP           : A4.675
NOTES         : type I, chiral, isomorphic to Snub({4,10}), isomorphic to A4.673.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 10, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^10 >
CTG (small)   : <40, 8>
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.3^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 4, 3, 10)
#DARTS        : 200
R = (1, 41, 81, 121, 161)(2, 42, 82, 122, 162)(3, 43, 83, 123, 163)(4, 44, 84, 124, 164)(5, 45, 85, 125, 165)(6, 46, 86, 126, 166)(7, 47, 87, 127, 167)(8, 48, 88, 128, 168)(9, 49, 89, 129, 169)(10, 50, 90, 130, 170)(11, 51, 91, 131, 171)(12, 52, 92, 132, 172)(13, 53, 93, 133, 173)(14, 54, 94, 134, 174)(15, 55, 95, 135, 175)(16, 56, 96, 136, 176)(17, 57, 97, 137, 177)(18, 58, 98, 138, 178)(19, 59, 99, 139, 179)(20, 60, 100, 140, 180)(21, 61, 101, 141, 181)(22, 62, 102, 142, 182)(23, 63, 103, 143, 183)(24, 64, 104, 144, 184)(25, 65, 105, 145, 185)(26, 66, 106, 146, 186)(27, 67, 107, 147, 187)(28, 68, 108, 148, 188)(29, 69, 109, 149, 189)(30, 70, 110, 150, 190)(31, 71, 111, 151, 191)(32, 72, 112, 152, 192)(33, 73, 113, 153, 193)(34, 74, 114, 154, 194)(35, 75, 115, 155, 195)(36, 76, 116, 156, 196)(37, 77, 117, 157, 197)(38, 78, 118, 158, 198)(39, 79, 119, 159, 199)(40, 80, 120, 160, 200)
L = (1, 7)(2, 3)(4, 6)(5, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 27)(22, 23)(24, 26)(25, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 92)(42, 96)(43, 111)(44, 88)(45, 100)(46, 119)(47, 115)(48, 106)(49, 83)(50, 99)(51, 120)(52, 107)(53, 87)(54, 95)(55, 116)(56, 103)(57, 86)(58, 91)(59, 112)(60, 108)(61, 93)(62, 89)(63, 114)(64, 97)(65, 84)(66, 105)(67, 110)(68, 118)(69, 98)(70, 81)(71, 102)(72, 117)(73, 94)(74, 82)(75, 101)(76, 113)(77, 90)(78, 85)(79, 104)(80, 109)(121, 192)(122, 196)(123, 171)(124, 188)(125, 200)(126, 179)(127, 175)(128, 166)(129, 183)(130, 199)(131, 180)(132, 167)(133, 187)(134, 195)(135, 176)(136, 163)(137, 186)(138, 191)(139, 172)(140, 168)(141, 193)(142, 189)(143, 174)(144, 197)(145, 184)(146, 165)(147, 170)(148, 178)(149, 198)(150, 181)(151, 162)(152, 177)(153, 194)(154, 182)(155, 161)(156, 173)(157, 190)(158, 185)(159, 164)(160, 169)

MAP           : A4.676
NOTES         : type I, chiral, isomorphic to Snub({4,10}), isomorphic to A4.673.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 10, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^4, u.3^10 >
CTG (small)   : <40, 8>
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.3^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 4, 3, 10)
#DARTS        : 200
R = (1, 41, 81, 121, 161)(2, 42, 82, 122, 162)(3, 43, 83, 123, 163)(4, 44, 84, 124, 164)(5, 45, 85, 125, 165)(6, 46, 86, 126, 166)(7, 47, 87, 127, 167)(8, 48, 88, 128, 168)(9, 49, 89, 129, 169)(10, 50, 90, 130, 170)(11, 51, 91, 131, 171)(12, 52, 92, 132, 172)(13, 53, 93, 133, 173)(14, 54, 94, 134, 174)(15, 55, 95, 135, 175)(16, 56, 96, 136, 176)(17, 57, 97, 137, 177)(18, 58, 98, 138, 178)(19, 59, 99, 139, 179)(20, 60, 100, 140, 180)(21, 61, 101, 141, 181)(22, 62, 102, 142, 182)(23, 63, 103, 143, 183)(24, 64, 104, 144, 184)(25, 65, 105, 145, 185)(26, 66, 106, 146, 186)(27, 67, 107, 147, 187)(28, 68, 108, 148, 188)(29, 69, 109, 149, 189)(30, 70, 110, 150, 190)(31, 71, 111, 151, 191)(32, 72, 112, 152, 192)(33, 73, 113, 153, 193)(34, 74, 114, 154, 194)(35, 75, 115, 155, 195)(36, 76, 116, 156, 196)(37, 77, 117, 157, 197)(38, 78, 118, 158, 198)(39, 79, 119, 159, 199)(40, 80, 120, 160, 200)
L = (1, 7)(2, 3)(4, 6)(5, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 27)(22, 23)(24, 26)(25, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 102)(42, 105)(43, 81)(44, 101)(45, 110)(46, 89)(47, 84)(48, 82)(49, 104)(50, 114)(51, 93)(52, 85)(53, 109)(54, 118)(55, 97)(56, 90)(57, 113)(58, 117)(59, 98)(60, 94)(61, 106)(62, 107)(63, 88)(64, 111)(65, 103)(66, 87)(67, 83)(68, 92)(69, 115)(70, 108)(71, 86)(72, 96)(73, 119)(74, 112)(75, 91)(76, 100)(77, 120)(78, 116)(79, 95)(80, 99)(121, 162)(122, 165)(123, 181)(124, 161)(125, 170)(126, 189)(127, 184)(128, 182)(129, 164)(130, 174)(131, 193)(132, 185)(133, 169)(134, 178)(135, 197)(136, 190)(137, 173)(138, 177)(139, 198)(140, 194)(141, 166)(142, 167)(143, 188)(144, 171)(145, 163)(146, 187)(147, 183)(148, 192)(149, 175)(150, 168)(151, 186)(152, 196)(153, 179)(154, 172)(155, 191)(156, 200)(157, 180)(158, 176)(159, 195)(160, 199)

MAP           : A4.677
NOTES         : type I, chiral, isomorphic to Snub({4,5}), isomorphic to A4.670.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 4, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^5 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^4, x.2^5, x.3 * x.1 * x.2 * x.3 * x.1 * x.3^-1 * x.2^-1 * x.1 * x.2, x.2^2 * x.3 * x.2^-1 * x.1 * x.2 * x.3^-1 * x.2^-2 * x.1 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 5, 3, 4)
#DARTS        : 600
R = (1, 121, 241, 361, 481)(2, 122, 242, 362, 482)(3, 123, 243, 363, 483)(4, 124, 244, 364, 484)(5, 125, 245, 365, 485)(6, 126, 246, 366, 486)(7, 127, 247, 367, 487)(8, 128, 248, 368, 488)(9, 129, 249, 369, 489)(10, 130, 250, 370, 490)(11, 131, 251, 371, 491)(12, 132, 252, 372, 492)(13, 133, 253, 373, 493)(14, 134, 254, 374, 494)(15, 135, 255, 375, 495)(16, 136, 256, 376, 496)(17, 137, 257, 377, 497)(18, 138, 258, 378, 498)(19, 139, 259, 379, 499)(20, 140, 260, 380, 500)(21, 141, 261, 381, 501)(22, 142, 262, 382, 502)(23, 143, 263, 383, 503)(24, 144, 264, 384, 504)(25, 145, 265, 385, 505)(26, 146, 266, 386, 506)(27, 147, 267, 387, 507)(28, 148, 268, 388, 508)(29, 149, 269, 389, 509)(30, 150, 270, 390, 510)(31, 151, 271, 391, 511)(32, 152, 272, 392, 512)(33, 153, 273, 393, 513)(34, 154, 274, 394, 514)(35, 155, 275, 395, 515)(36, 156, 276, 396, 516)(37, 157, 277, 397, 517)(38, 158, 278, 398, 518)(39, 159, 279, 399, 519)(40, 160, 280, 400, 520)(41, 161, 281, 401, 521)(42, 162, 282, 402, 522)(43, 163, 283, 403, 523)(44, 164, 284, 404, 524)(45, 165, 285, 405, 525)(46, 166, 286, 406, 526)(47, 167, 287, 407, 527)(48, 168, 288, 408, 528)(49, 169, 289, 409, 529)(50, 170, 290, 410, 530)(51, 171, 291, 411, 531)(52, 172, 292, 412, 532)(53, 173, 293, 413, 533)(54, 174, 294, 414, 534)(55, 175, 295, 415, 535)(56, 176, 296, 416, 536)(57, 177, 297, 417, 537)(58, 178, 298, 418, 538)(59, 179, 299, 419, 539)(60, 180, 300, 420, 540)(61, 181, 301, 421, 541)(62, 182, 302, 422, 542)(63, 183, 303, 423, 543)(64, 184, 304, 424, 544)(65, 185, 305, 425, 545)(66, 186, 306, 426, 546)(67, 187, 307, 427, 547)(68, 188, 308, 428, 548)(69, 189, 309, 429, 549)(70, 190, 310, 430, 550)(71, 191, 311, 431, 551)(72, 192, 312, 432, 552)(73, 193, 313, 433, 553)(74, 194, 314, 434, 554)(75, 195, 315, 435, 555)(76, 196, 316, 436, 556)(77, 197, 317, 437, 557)(78, 198, 318, 438, 558)(79, 199, 319, 439, 559)(80, 200, 320, 440, 560)(81, 201, 321, 441, 561)(82, 202, 322, 442, 562)(83, 203, 323, 443, 563)(84, 204, 324, 444, 564)(85, 205, 325, 445, 565)(86, 206, 326, 446, 566)(87, 207, 327, 447, 567)(88, 208, 328, 448, 568)(89, 209, 329, 449, 569)(90, 210, 330, 450, 570)(91, 211, 331, 451, 571)(92, 212, 332, 452, 572)(93, 213, 333, 453, 573)(94, 214, 334, 454, 574)(95, 215, 335, 455, 575)(96, 216, 336, 456, 576)(97, 217, 337, 457, 577)(98, 218, 338, 458, 578)(99, 219, 339, 459, 579)(100, 220, 340, 460, 580)(101, 221, 341, 461, 581)(102, 222, 342, 462, 582)(103, 223, 343, 463, 583)(104, 224, 344, 464, 584)(105, 225, 345, 465, 585)(106, 226, 346, 466, 586)(107, 227, 347, 467, 587)(108, 228, 348, 468, 588)(109, 229, 349, 469, 589)(110, 230, 350, 470, 590)(111, 231, 351, 471, 591)(112, 232, 352, 472, 592)(113, 233, 353, 473, 593)(114, 234, 354, 474, 594)(115, 235, 355, 475, 595)(116, 236, 356, 476, 596)(117, 237, 357, 477, 597)(118, 238, 358, 478, 598)(119, 239, 359, 479, 599)(120, 240, 360, 480, 600)
L = (1, 2)(3, 7)(4, 14)(5, 13)(6, 8)(9, 16)(10, 102)(11, 99)(12, 17)(15, 119)(18, 118)(19, 54)(20, 51)(21, 90)(22, 49)(23, 50)(24, 87)(25, 40)(26, 41)(27, 38)(28, 77)(29, 76)(30, 37)(31, 111)(32, 114)(33, 100)(34, 66)(35, 63)(36, 101)(39, 42)(43, 110)(44, 109)(45, 115)(46, 98)(47, 97)(48, 116)(52, 53)(55, 113)(56, 112)(57, 83)(58, 117)(59, 120)(60, 82)(61, 71)(62, 70)(64, 81)(65, 84)(67, 68)(69, 79)(72, 80)(73, 106)(74, 107)(75, 104)(78, 103)(85, 96)(86, 93)(88, 91)(89, 92)(94, 95)(105, 108)(121, 244)(122, 245)(123, 242)(124, 281)(125, 280)(126, 241)(127, 359)(128, 358)(129, 317)(130, 345)(131, 348)(132, 316)(133, 252)(134, 249)(135, 276)(136, 247)(137, 248)(138, 273)(139, 356)(140, 355)(141, 343)(142, 350)(143, 349)(144, 344)(145, 357)(146, 360)(147, 352)(148, 324)(149, 321)(150, 353)(151, 326)(152, 325)(153, 313)(154, 320)(155, 319)(156, 314)(157, 327)(158, 330)(159, 322)(160, 294)(161, 291)(162, 323)(163, 329)(164, 328)(165, 287)(166, 315)(167, 318)(168, 286)(169, 342)(170, 339)(171, 246)(172, 337)(173, 338)(174, 243)(175, 334)(176, 335)(177, 332)(178, 251)(179, 250)(180, 331)(181, 297)(182, 300)(183, 292)(184, 264)(185, 261)(186, 293)(187, 312)(188, 309)(189, 336)(190, 307)(191, 308)(192, 333)(193, 296)(194, 295)(195, 283)(196, 290)(197, 289)(198, 284)(199, 304)(200, 305)(201, 302)(202, 341)(203, 340)(204, 301)(205, 299)(206, 298)(207, 257)(208, 285)(209, 288)(210, 256)(211, 269)(212, 268)(213, 347)(214, 255)(215, 258)(216, 346)(217, 266)(218, 265)(219, 253)(220, 260)(221, 259)(222, 254)(223, 274)(224, 275)(225, 272)(226, 311)(227, 310)(228, 271)(229, 267)(230, 270)(231, 262)(232, 354)(233, 351)(234, 263)(235, 282)(236, 279)(237, 306)(238, 277)(239, 278)(240, 303)(361, 488)(362, 487)(363, 499)(364, 482)(365, 481)(366, 500)(367, 489)(368, 492)(369, 484)(370, 600)(371, 597)(372, 485)(373, 491)(374, 490)(375, 575)(376, 501)(377, 504)(378, 574)(379, 516)(380, 513)(381, 564)(382, 511)(383, 512)(384, 561)(385, 526)(386, 527)(387, 524)(388, 569)(389, 568)(390, 523)(391, 585)(392, 588)(393, 598)(394, 558)(395, 555)(396, 599)(397, 498)(398, 495)(399, 528)(400, 493)(401, 494)(402, 525)(403, 584)(404, 583)(405, 571)(406, 596)(407, 595)(408, 572)(409, 508)(410, 509)(411, 506)(412, 515)(413, 514)(414, 505)(415, 587)(416, 586)(417, 551)(418, 573)(419, 576)(420, 550)(421, 545)(422, 544)(423, 539)(424, 549)(425, 552)(426, 538)(427, 542)(428, 541)(429, 547)(430, 554)(431, 553)(432, 548)(433, 580)(434, 581)(435, 578)(436, 497)(437, 496)(438, 577)(439, 543)(440, 546)(441, 556)(442, 522)(443, 519)(444, 557)(445, 594)(446, 591)(447, 510)(448, 589)(449, 590)(450, 507)(451, 562)(452, 563)(453, 560)(454, 593)(455, 592)(456, 559)(457, 533)(458, 532)(459, 503)(460, 537)(461, 540)(462, 502)(463, 570)(464, 567)(465, 582)(466, 565)(467, 566)(468, 579)(469, 530)(470, 529)(471, 535)(472, 518)(473, 517)(474, 536)(475, 531)(476, 534)(477, 520)(478, 486)(479, 483)(480, 521)

MAP           : A4.678
NOTES         : type I, reflexible, isomorphic to Snub({5,5}), representative.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 5, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^5, u.3^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^5, x.3^5, (x.3 * x.2^-1)^3, x.2^-1 * x.1 * x.2 * x.3 * x.2^-1 * x.1 * x.3^-1 * x.2^-1, x.2 * x.3^2 * x.1 * x.3^-1 * x.2^-1 * x.3 * x.1 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 5, 3, 5)
#DARTS        : 300
R = (1, 61, 121, 181, 241)(2, 62, 122, 182, 242)(3, 63, 123, 183, 243)(4, 64, 124, 184, 244)(5, 65, 125, 185, 245)(6, 66, 126, 186, 246)(7, 67, 127, 187, 247)(8, 68, 128, 188, 248)(9, 69, 129, 189, 249)(10, 70, 130, 190, 250)(11, 71, 131, 191, 251)(12, 72, 132, 192, 252)(13, 73, 133, 193, 253)(14, 74, 134, 194, 254)(15, 75, 135, 195, 255)(16, 76, 136, 196, 256)(17, 77, 137, 197, 257)(18, 78, 138, 198, 258)(19, 79, 139, 199, 259)(20, 80, 140, 200, 260)(21, 81, 141, 201, 261)(22, 82, 142, 202, 262)(23, 83, 143, 203, 263)(24, 84, 144, 204, 264)(25, 85, 145, 205, 265)(26, 86, 146, 206, 266)(27, 87, 147, 207, 267)(28, 88, 148, 208, 268)(29, 89, 149, 209, 269)(30, 90, 150, 210, 270)(31, 91, 151, 211, 271)(32, 92, 152, 212, 272)(33, 93, 153, 213, 273)(34, 94, 154, 214, 274)(35, 95, 155, 215, 275)(36, 96, 156, 216, 276)(37, 97, 157, 217, 277)(38, 98, 158, 218, 278)(39, 99, 159, 219, 279)(40, 100, 160, 220, 280)(41, 101, 161, 221, 281)(42, 102, 162, 222, 282)(43, 103, 163, 223, 283)(44, 104, 164, 224, 284)(45, 105, 165, 225, 285)(46, 106, 166, 226, 286)(47, 107, 167, 227, 287)(48, 108, 168, 228, 288)(49, 109, 169, 229, 289)(50, 110, 170, 230, 290)(51, 111, 171, 231, 291)(52, 112, 172, 232, 292)(53, 113, 173, 233, 293)(54, 114, 174, 234, 294)(55, 115, 175, 235, 295)(56, 116, 176, 236, 296)(57, 117, 177, 237, 297)(58, 118, 178, 238, 298)(59, 119, 179, 239, 299)(60, 120, 180, 240, 300)
L = (1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)(19, 37)(20, 38)(21, 39)(22, 40)(23, 41)(24, 42)(25, 43)(26, 44)(27, 45)(28, 46)(29, 47)(30, 48)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(61, 122)(62, 125)(63, 127)(64, 121)(65, 138)(66, 137)(67, 161)(68, 126)(69, 173)(70, 158)(71, 160)(72, 166)(73, 155)(74, 168)(75, 131)(76, 152)(77, 154)(78, 124)(79, 164)(80, 167)(81, 169)(82, 163)(83, 180)(84, 179)(85, 177)(86, 153)(87, 130)(88, 129)(89, 141)(90, 151)(91, 135)(92, 159)(93, 172)(94, 171)(95, 147)(96, 157)(97, 136)(98, 133)(99, 156)(100, 150)(101, 134)(102, 140)(103, 174)(104, 148)(105, 170)(106, 149)(107, 145)(108, 123)(109, 132)(110, 142)(111, 128)(112, 143)(113, 139)(114, 165)(115, 178)(116, 175)(117, 162)(118, 144)(119, 176)(120, 146)(181, 250)(182, 247)(183, 270)(184, 276)(185, 248)(186, 242)(187, 249)(188, 297)(189, 286)(190, 285)(191, 273)(192, 295)(193, 260)(194, 263)(195, 253)(196, 259)(197, 252)(198, 251)(199, 299)(200, 264)(201, 287)(202, 296)(203, 298)(204, 292)(205, 269)(206, 294)(207, 257)(208, 266)(209, 268)(210, 262)(211, 288)(212, 274)(213, 284)(214, 275)(215, 271)(216, 261)(217, 258)(218, 244)(219, 254)(220, 245)(221, 241)(222, 291)(223, 280)(224, 277)(225, 300)(226, 246)(227, 278)(228, 272)(229, 279)(230, 267)(231, 256)(232, 255)(233, 243)(234, 265)(235, 290)(236, 293)(237, 283)(238, 289)(239, 282)(240, 281)

MAP           : A4.679
NOTES         : type I, reflexible, isomorphic to Snub({5,5}), isomorphic to A4.678.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 5, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^5, u.3^5 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.2^5, x.3^5, (x.3 * x.2^-1)^3, x.2^-1 * x.1 * x.2 * x.3 * x.2^-1 * x.1 * x.3^-1 * x.2^-1, x.2 * x.3^2 * x.1 * x.3^-1 * x.2^-1 * x.3 * x.1 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 5, 3, 5)
#DARTS        : 300
R = (1, 61, 121, 181, 241)(2, 62, 122, 182, 242)(3, 63, 123, 183, 243)(4, 64, 124, 184, 244)(5, 65, 125, 185, 245)(6, 66, 126, 186, 246)(7, 67, 127, 187, 247)(8, 68, 128, 188, 248)(9, 69, 129, 189, 249)(10, 70, 130, 190, 250)(11, 71, 131, 191, 251)(12, 72, 132, 192, 252)(13, 73, 133, 193, 253)(14, 74, 134, 194, 254)(15, 75, 135, 195, 255)(16, 76, 136, 196, 256)(17, 77, 137, 197, 257)(18, 78, 138, 198, 258)(19, 79, 139, 199, 259)(20, 80, 140, 200, 260)(21, 81, 141, 201, 261)(22, 82, 142, 202, 262)(23, 83, 143, 203, 263)(24, 84, 144, 204, 264)(25, 85, 145, 205, 265)(26, 86, 146, 206, 266)(27, 87, 147, 207, 267)(28, 88, 148, 208, 268)(29, 89, 149, 209, 269)(30, 90, 150, 210, 270)(31, 91, 151, 211, 271)(32, 92, 152, 212, 272)(33, 93, 153, 213, 273)(34, 94, 154, 214, 274)(35, 95, 155, 215, 275)(36, 96, 156, 216, 276)(37, 97, 157, 217, 277)(38, 98, 158, 218, 278)(39, 99, 159, 219, 279)(40, 100, 160, 220, 280)(41, 101, 161, 221, 281)(42, 102, 162, 222, 282)(43, 103, 163, 223, 283)(44, 104, 164, 224, 284)(45, 105, 165, 225, 285)(46, 106, 166, 226, 286)(47, 107, 167, 227, 287)(48, 108, 168, 228, 288)(49, 109, 169, 229, 289)(50, 110, 170, 230, 290)(51, 111, 171, 231, 291)(52, 112, 172, 232, 292)(53, 113, 173, 233, 293)(54, 114, 174, 234, 294)(55, 115, 175, 235, 295)(56, 116, 176, 236, 296)(57, 117, 177, 237, 297)(58, 118, 178, 238, 298)(59, 119, 179, 239, 299)(60, 120, 180, 240, 300)
L = (1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)(19, 37)(20, 38)(21, 39)(22, 40)(23, 41)(24, 42)(25, 43)(26, 44)(27, 45)(28, 46)(29, 47)(30, 48)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(61, 161)(62, 126)(63, 173)(64, 158)(65, 160)(66, 166)(67, 122)(68, 125)(69, 127)(70, 121)(71, 138)(72, 137)(73, 135)(74, 159)(75, 172)(76, 171)(77, 147)(78, 157)(79, 136)(80, 133)(81, 156)(82, 150)(83, 134)(84, 140)(85, 174)(86, 148)(87, 170)(88, 149)(89, 145)(90, 123)(91, 155)(92, 168)(93, 131)(94, 152)(95, 154)(96, 124)(97, 164)(98, 167)(99, 169)(100, 163)(101, 180)(102, 179)(103, 177)(104, 153)(105, 130)(106, 129)(107, 141)(108, 151)(109, 178)(110, 175)(111, 162)(112, 144)(113, 176)(114, 146)(115, 132)(116, 142)(117, 128)(118, 143)(119, 139)(120, 165)(181, 244)(182, 241)(183, 288)(184, 258)(185, 242)(186, 248)(187, 243)(188, 291)(189, 268)(190, 267)(191, 255)(192, 289)(193, 278)(194, 281)(195, 271)(196, 277)(197, 246)(198, 245)(199, 293)(200, 282)(201, 269)(202, 290)(203, 292)(204, 298)(205, 287)(206, 300)(207, 275)(208, 284)(209, 286)(210, 280)(211, 270)(212, 256)(213, 266)(214, 257)(215, 253)(216, 279)(217, 276)(218, 250)(219, 272)(220, 251)(221, 247)(222, 297)(223, 262)(224, 259)(225, 294)(226, 252)(227, 260)(228, 254)(229, 261)(230, 285)(231, 274)(232, 273)(233, 249)(234, 283)(235, 296)(236, 299)(237, 265)(238, 295)(239, 264)(240, 263)

MAP           : A4.680
NOTES         : type I, chiral, isomorphic to Snub({4,6}), isomorphic to A4.671.
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)   : <72, 40>
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.1 * x.2 * x.3 * x.1 * x.3^-1 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 6, 3, 4)
#DARTS        : 360
R = (1, 73, 145, 217, 289)(2, 74, 146, 218, 290)(3, 75, 147, 219, 291)(4, 76, 148, 220, 292)(5, 77, 149, 221, 293)(6, 78, 150, 222, 294)(7, 79, 151, 223, 295)(8, 80, 152, 224, 296)(9, 81, 153, 225, 297)(10, 82, 154, 226, 298)(11, 83, 155, 227, 299)(12, 84, 156, 228, 300)(13, 85, 157, 229, 301)(14, 86, 158, 230, 302)(15, 87, 159, 231, 303)(16, 88, 160, 232, 304)(17, 89, 161, 233, 305)(18, 90, 162, 234, 306)(19, 91, 163, 235, 307)(20, 92, 164, 236, 308)(21, 93, 165, 237, 309)(22, 94, 166, 238, 310)(23, 95, 167, 239, 311)(24, 96, 168, 240, 312)(25, 97, 169, 241, 313)(26, 98, 170, 242, 314)(27, 99, 171, 243, 315)(28, 100, 172, 244, 316)(29, 101, 173, 245, 317)(30, 102, 174, 246, 318)(31, 103, 175, 247, 319)(32, 104, 176, 248, 320)(33, 105, 177, 249, 321)(34, 106, 178, 250, 322)(35, 107, 179, 251, 323)(36, 108, 180, 252, 324)(37, 109, 181, 253, 325)(38, 110, 182, 254, 326)(39, 111, 183, 255, 327)(40, 112, 184, 256, 328)(41, 113, 185, 257, 329)(42, 114, 186, 258, 330)(43, 115, 187, 259, 331)(44, 116, 188, 260, 332)(45, 117, 189, 261, 333)(46, 118, 190, 262, 334)(47, 119, 191, 263, 335)(48, 120, 192, 264, 336)(49, 121, 193, 265, 337)(50, 122, 194, 266, 338)(51, 123, 195, 267, 339)(52, 124, 196, 268, 340)(53, 125, 197, 269, 341)(54, 126, 198, 270, 342)(55, 127, 199, 271, 343)(56, 128, 200, 272, 344)(57, 129, 201, 273, 345)(58, 130, 202, 274, 346)(59, 131, 203, 275, 347)(60, 132, 204, 276, 348)(61, 133, 205, 277, 349)(62, 134, 206, 278, 350)(63, 135, 207, 279, 351)(64, 136, 208, 280, 352)(65, 137, 209, 281, 353)(66, 138, 210, 282, 354)(67, 139, 211, 283, 355)(68, 140, 212, 284, 356)(69, 141, 213, 285, 357)(70, 142, 214, 286, 358)(71, 143, 215, 287, 359)(72, 144, 216, 288, 360)
L = (1, 3)(2, 22)(4, 6)(5, 13)(7, 9)(8, 16)(10, 12)(11, 19)(14, 66)(15, 59)(17, 27)(18, 62)(20, 60)(21, 65)(23, 51)(24, 56)(25, 71)(26, 54)(28, 32)(29, 57)(30, 50)(31, 33)(34, 36)(35, 61)(37, 39)(38, 58)(40, 42)(41, 49)(43, 45)(44, 52)(46, 48)(47, 55)(53, 63)(64, 68)(67, 69)(70, 72)(73, 146)(74, 149)(75, 152)(76, 147)(77, 210)(78, 153)(79, 200)(80, 203)(81, 206)(82, 201)(83, 156)(84, 207)(85, 204)(86, 195)(87, 198)(88, 209)(89, 190)(90, 161)(91, 150)(92, 177)(93, 180)(94, 155)(95, 172)(96, 215)(97, 148)(98, 175)(99, 178)(100, 163)(101, 176)(102, 169)(103, 166)(104, 157)(105, 160)(106, 145)(107, 158)(108, 151)(109, 186)(110, 213)(111, 216)(112, 191)(113, 208)(114, 179)(115, 184)(116, 211)(117, 214)(118, 199)(119, 212)(120, 205)(121, 202)(122, 193)(123, 196)(124, 181)(125, 194)(126, 187)(127, 182)(128, 185)(129, 188)(130, 183)(131, 174)(132, 189)(133, 164)(134, 167)(135, 170)(136, 165)(137, 192)(138, 171)(139, 168)(140, 159)(141, 162)(142, 173)(143, 154)(144, 197)(217, 324)(218, 291)(219, 294)(220, 359)(221, 310)(222, 299)(223, 322)(224, 289)(225, 292)(226, 313)(227, 290)(228, 307)(229, 316)(230, 349)(231, 352)(232, 319)(233, 350)(234, 355)(235, 320)(236, 323)(237, 356)(238, 321)(239, 306)(240, 357)(241, 338)(242, 341)(243, 302)(244, 339)(245, 360)(246, 303)(247, 342)(248, 345)(249, 348)(250, 305)(251, 328)(252, 353)(253, 332)(254, 335)(255, 326)(256, 333)(257, 312)(258, 327)(259, 314)(260, 317)(261, 308)(262, 315)(263, 330)(264, 309)(265, 318)(266, 351)(267, 354)(268, 311)(269, 358)(270, 347)(271, 336)(272, 297)(273, 300)(274, 329)(275, 304)(276, 293)(277, 334)(278, 295)(279, 298)(280, 337)(281, 296)(282, 301)(283, 340)(284, 343)(285, 346)(286, 331)(287, 344)(288, 325)

MAP           : A4.681
NOTES         : type I, chiral, isomorphic to Snub({4,6}), isomorphic to A4.671.
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)   : <72, 40>
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.1 * x.2 * x.3 * x.1 * x.3^-1 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 6, 3, 4)
#DARTS        : 360
R = (1, 73, 145, 217, 289)(2, 74, 146, 218, 290)(3, 75, 147, 219, 291)(4, 76, 148, 220, 292)(5, 77, 149, 221, 293)(6, 78, 150, 222, 294)(7, 79, 151, 223, 295)(8, 80, 152, 224, 296)(9, 81, 153, 225, 297)(10, 82, 154, 226, 298)(11, 83, 155, 227, 299)(12, 84, 156, 228, 300)(13, 85, 157, 229, 301)(14, 86, 158, 230, 302)(15, 87, 159, 231, 303)(16, 88, 160, 232, 304)(17, 89, 161, 233, 305)(18, 90, 162, 234, 306)(19, 91, 163, 235, 307)(20, 92, 164, 236, 308)(21, 93, 165, 237, 309)(22, 94, 166, 238, 310)(23, 95, 167, 239, 311)(24, 96, 168, 240, 312)(25, 97, 169, 241, 313)(26, 98, 170, 242, 314)(27, 99, 171, 243, 315)(28, 100, 172, 244, 316)(29, 101, 173, 245, 317)(30, 102, 174, 246, 318)(31, 103, 175, 247, 319)(32, 104, 176, 248, 320)(33, 105, 177, 249, 321)(34, 106, 178, 250, 322)(35, 107, 179, 251, 323)(36, 108, 180, 252, 324)(37, 109, 181, 253, 325)(38, 110, 182, 254, 326)(39, 111, 183, 255, 327)(40, 112, 184, 256, 328)(41, 113, 185, 257, 329)(42, 114, 186, 258, 330)(43, 115, 187, 259, 331)(44, 116, 188, 260, 332)(45, 117, 189, 261, 333)(46, 118, 190, 262, 334)(47, 119, 191, 263, 335)(48, 120, 192, 264, 336)(49, 121, 193, 265, 337)(50, 122, 194, 266, 338)(51, 123, 195, 267, 339)(52, 124, 196, 268, 340)(53, 125, 197, 269, 341)(54, 126, 198, 270, 342)(55, 127, 199, 271, 343)(56, 128, 200, 272, 344)(57, 129, 201, 273, 345)(58, 130, 202, 274, 346)(59, 131, 203, 275, 347)(60, 132, 204, 276, 348)(61, 133, 205, 277, 349)(62, 134, 206, 278, 350)(63, 135, 207, 279, 351)(64, 136, 208, 280, 352)(65, 137, 209, 281, 353)(66, 138, 210, 282, 354)(67, 139, 211, 283, 355)(68, 140, 212, 284, 356)(69, 141, 213, 285, 357)(70, 142, 214, 286, 358)(71, 143, 215, 287, 359)(72, 144, 216, 288, 360)
L = (1, 66)(2, 27)(3, 30)(4, 59)(5, 34)(6, 23)(7, 64)(8, 25)(9, 28)(10, 67)(11, 26)(12, 31)(13, 70)(14, 37)(15, 40)(16, 61)(17, 38)(18, 55)(19, 62)(20, 65)(21, 56)(22, 63)(24, 57)(29, 60)(32, 45)(33, 48)(35, 52)(36, 41)(39, 50)(42, 51)(43, 68)(44, 71)(46, 69)(47, 54)(49, 72)(53, 58)(73, 155)(74, 204)(75, 209)(76, 146)(77, 195)(78, 200)(79, 215)(80, 198)(81, 161)(82, 176)(83, 201)(84, 194)(85, 177)(86, 172)(87, 175)(88, 180)(89, 205)(90, 178)(91, 147)(92, 166)(93, 145)(94, 150)(95, 157)(96, 148)(97, 153)(98, 160)(99, 151)(100, 156)(101, 163)(102, 154)(103, 149)(104, 210)(105, 203)(106, 152)(107, 171)(108, 206)(109, 191)(110, 168)(111, 173)(112, 182)(113, 159)(114, 164)(115, 179)(116, 162)(117, 197)(118, 212)(119, 165)(120, 158)(121, 213)(122, 208)(123, 211)(124, 216)(125, 169)(126, 214)(127, 183)(128, 202)(129, 181)(130, 186)(131, 193)(132, 184)(133, 189)(134, 196)(135, 187)(136, 192)(137, 199)(138, 190)(139, 185)(140, 174)(141, 167)(142, 188)(143, 207)(144, 170)(217, 344)(218, 347)(219, 350)(220, 345)(221, 300)(222, 351)(223, 290)(224, 293)(225, 296)(226, 291)(227, 354)(228, 297)(229, 294)(230, 321)(231, 324)(232, 299)(233, 316)(234, 359)(235, 348)(236, 339)(237, 342)(238, 353)(239, 334)(240, 305)(241, 346)(242, 337)(243, 340)(244, 325)(245, 338)(246, 331)(247, 328)(248, 355)(249, 358)(250, 343)(251, 356)(252, 349)(253, 312)(254, 303)(255, 306)(256, 317)(257, 298)(258, 341)(259, 310)(260, 301)(261, 304)(262, 289)(263, 302)(264, 295)(265, 292)(266, 319)(267, 322)(268, 307)(269, 320)(270, 313)(271, 308)(272, 311)(273, 314)(274, 309)(275, 336)(276, 315)(277, 326)(278, 329)(279, 332)(280, 327)(281, 318)(282, 333)(283, 330)(284, 357)(285, 360)(286, 335)(287, 352)(288, 323)

MAP           : A4.682
NOTES         : type I, chiral, isomorphic to Snub({6,6}), representative.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^6, u.3^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^-1 * x.2 * x.3^2 * x.1, (x.2^-1 * x.3 * x.2^-1)^2, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 2)(3, 5)(4, 6)(7, 27)(8, 12)(9, 10)(11, 16)(13, 34)(14, 33)(15, 28)(17, 30)(18, 19)(20, 25)(21, 32)(22, 36)(23, 31)(24, 26)(29, 35)(37, 75)(38, 88)(39, 85)(40, 74)(41, 80)(42, 93)(43, 94)(44, 89)(45, 78)(46, 79)(47, 84)(48, 95)(49, 87)(50, 100)(51, 97)(52, 86)(53, 92)(54, 105)(55, 106)(56, 101)(57, 90)(58, 91)(59, 96)(60, 107)(61, 99)(62, 76)(63, 73)(64, 98)(65, 104)(66, 81)(67, 82)(68, 77)(69, 102)(70, 103)(71, 108)(72, 83)(109, 151)(110, 150)(111, 146)(112, 168)(113, 165)(114, 154)(115, 153)(116, 147)(117, 161)(118, 167)(119, 166)(120, 160)(121, 149)(122, 155)(123, 178)(124, 145)(125, 156)(126, 176)(127, 180)(128, 174)(129, 148)(130, 171)(131, 152)(132, 175)(133, 172)(134, 159)(135, 164)(136, 177)(137, 169)(138, 158)(139, 157)(140, 179)(141, 163)(142, 162)(143, 170)(144, 173)

MAP           : A4.683
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), representative.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 107)(56, 99)(57, 98)(58, 97)(59, 103)(60, 101)(61, 94)(62, 93)(63, 92)(64, 102)(65, 96)(66, 100)(67, 95)(68, 106)(69, 108)(70, 104)(71, 91)(72, 105)(73, 148)(74, 152)(75, 153)(76, 150)(77, 162)(78, 145)(79, 161)(80, 160)(81, 158)(82, 159)(83, 151)(84, 149)(85, 154)(86, 147)(87, 157)(88, 146)(89, 155)(90, 156)(163, 173)(164, 176)(165, 178)(166, 179)(167, 172)(168, 169)(170, 171)(174, 177)(175, 180)

MAP           : A4.684
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 101)(56, 104)(57, 106)(58, 107)(59, 100)(60, 97)(61, 96)(62, 99)(63, 98)(64, 95)(65, 91)(66, 105)(67, 108)(68, 92)(69, 102)(70, 93)(71, 94)(72, 103)(73, 148)(74, 152)(75, 153)(76, 150)(77, 162)(78, 145)(79, 161)(80, 160)(81, 158)(82, 159)(83, 151)(84, 149)(85, 154)(86, 147)(87, 157)(88, 146)(89, 155)(90, 156)(163, 169)(164, 165)(166, 173)(167, 177)(168, 179)(170, 176)(171, 178)(172, 180)(174, 175)

MAP           : A4.685
NOTES         : type I, chiral, isomorphic to Snub({6,6}), isomorphic to A4.682.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^6, u.3^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3 * x.2^-1 * x.1 * x.2^2, x.3 * x.2^-3 * x.3 * x.2^-1, x.3^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 31)(2, 30)(3, 26)(4, 12)(5, 9)(6, 34)(7, 33)(8, 27)(10, 11)(13, 29)(14, 35)(15, 22)(16, 25)(17, 36)(18, 20)(19, 24)(21, 28)(23, 32)(37, 82)(38, 81)(39, 76)(40, 95)(41, 78)(42, 103)(43, 102)(44, 73)(45, 80)(46, 84)(47, 79)(48, 74)(49, 104)(50, 108)(51, 91)(52, 99)(53, 83)(54, 101)(55, 107)(56, 105)(57, 98)(58, 97)(59, 77)(60, 106)(61, 86)(62, 85)(63, 89)(64, 90)(65, 87)(66, 88)(67, 75)(68, 96)(69, 94)(70, 93)(71, 100)(72, 92)(109, 171)(110, 148)(111, 145)(112, 170)(113, 176)(114, 153)(115, 154)(116, 149)(117, 174)(118, 175)(119, 180)(120, 155)(121, 147)(122, 160)(123, 157)(124, 146)(125, 152)(126, 165)(127, 166)(128, 161)(129, 150)(130, 151)(131, 156)(132, 167)(133, 159)(134, 172)(135, 169)(136, 158)(137, 164)(138, 177)(139, 178)(140, 173)(141, 162)(142, 163)(143, 168)(144, 179)

MAP           : A4.686
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 107)(56, 99)(57, 98)(58, 97)(59, 103)(60, 101)(61, 94)(62, 93)(63, 92)(64, 102)(65, 96)(66, 100)(67, 95)(68, 106)(69, 108)(70, 104)(71, 91)(72, 105)(73, 162)(74, 148)(75, 157)(76, 156)(77, 152)(78, 149)(79, 153)(80, 150)(81, 154)(82, 151)(83, 147)(84, 146)(85, 155)(86, 159)(87, 161)(88, 145)(89, 158)(90, 160)(163, 176)(164, 172)(165, 168)(166, 171)(167, 173)(169, 174)(170, 175)(177, 178)(179, 180)

MAP           : A4.687
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^6, u.3^6 >
CTG (small)   : <36, 10>
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.2^6, x.3^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 3)(2, 23)(4, 5)(6, 19)(7, 30)(8, 34)(9, 36)(10, 32)(11, 26)(12, 33)(13, 27)(14, 35)(15, 25)(16, 29)(17, 28)(18, 31)(20, 22)(21, 24)(37, 74)(38, 78)(39, 80)(40, 79)(41, 73)(42, 94)(43, 92)(44, 96)(45, 98)(46, 97)(47, 91)(48, 76)(49, 106)(50, 105)(51, 95)(52, 75)(53, 102)(54, 101)(55, 88)(56, 87)(57, 77)(58, 93)(59, 84)(60, 83)(61, 89)(62, 85)(63, 100)(64, 108)(65, 81)(66, 86)(67, 107)(68, 103)(69, 82)(70, 90)(71, 99)(72, 104)(109, 148)(110, 147)(111, 173)(112, 177)(113, 168)(114, 167)(115, 149)(116, 145)(117, 160)(118, 156)(119, 165)(120, 146)(121, 155)(122, 151)(123, 166)(124, 150)(125, 159)(126, 152)(127, 170)(128, 174)(129, 164)(130, 163)(131, 169)(132, 178)(133, 176)(134, 180)(135, 158)(136, 157)(137, 175)(138, 172)(139, 154)(140, 153)(141, 179)(142, 171)(143, 162)(144, 161)

MAP           : A4.688
NOTES         : type I, chiral, isomorphic to Snub({6,6}), isomorphic to A4.682.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^6, u.3^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3 * x.2^-1 * x.1 * x.2^2, x.3 * x.2^-3 * x.3 * x.2^-1, x.3^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 31)(2, 30)(3, 26)(4, 12)(5, 9)(6, 34)(7, 33)(8, 27)(10, 11)(13, 29)(14, 35)(15, 22)(16, 25)(17, 36)(18, 20)(19, 24)(21, 28)(23, 32)(37, 80)(38, 84)(39, 103)(40, 75)(41, 95)(42, 77)(43, 83)(44, 81)(45, 74)(46, 73)(47, 89)(48, 82)(49, 98)(50, 97)(51, 101)(52, 102)(53, 99)(54, 100)(55, 87)(56, 108)(57, 106)(58, 105)(59, 76)(60, 104)(61, 94)(62, 93)(63, 88)(64, 107)(65, 90)(66, 79)(67, 78)(68, 85)(69, 92)(70, 96)(71, 91)(72, 86)(109, 155)(110, 149)(111, 156)(112, 176)(113, 178)(114, 145)(115, 146)(116, 175)(117, 171)(118, 148)(119, 177)(120, 174)(121, 167)(122, 161)(123, 168)(124, 152)(125, 154)(126, 157)(127, 158)(128, 151)(129, 147)(130, 160)(131, 153)(132, 150)(133, 179)(134, 173)(135, 180)(136, 164)(137, 166)(138, 169)(139, 170)(140, 163)(141, 159)(142, 172)(143, 165)(144, 162)

MAP           : A4.689
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 97)(56, 93)(57, 92)(58, 101)(59, 105)(60, 107)(61, 91)(62, 104)(63, 106)(64, 108)(65, 94)(66, 103)(67, 102)(68, 98)(69, 95)(70, 99)(71, 96)(72, 100)(73, 150)(74, 160)(75, 158)(76, 145)(77, 156)(78, 148)(79, 155)(80, 146)(81, 147)(82, 157)(83, 161)(84, 162)(85, 159)(86, 153)(87, 154)(88, 152)(89, 151)(90, 149)(163, 173)(164, 176)(165, 178)(166, 179)(167, 172)(168, 169)(170, 171)(174, 177)(175, 180)

MAP           : A4.690
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 97)(56, 93)(57, 92)(58, 101)(59, 105)(60, 107)(61, 91)(62, 104)(63, 106)(64, 108)(65, 94)(66, 103)(67, 102)(68, 98)(69, 95)(70, 99)(71, 96)(72, 100)(73, 152)(74, 162)(75, 161)(76, 160)(77, 148)(78, 146)(79, 157)(80, 156)(81, 155)(82, 147)(83, 159)(84, 145)(85, 158)(86, 151)(87, 153)(88, 149)(89, 154)(90, 150)(163, 175)(164, 179)(165, 180)(166, 177)(167, 171)(168, 172)(169, 170)(173, 178)(174, 176)

MAP           : A4.691
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 97)(56, 93)(57, 92)(58, 101)(59, 105)(60, 107)(61, 91)(62, 104)(63, 106)(64, 108)(65, 94)(66, 103)(67, 102)(68, 98)(69, 95)(70, 99)(71, 96)(72, 100)(73, 148)(74, 152)(75, 153)(76, 150)(77, 162)(78, 145)(79, 161)(80, 160)(81, 158)(82, 159)(83, 151)(84, 149)(85, 154)(86, 147)(87, 157)(88, 146)(89, 155)(90, 156)(163, 179)(164, 171)(165, 170)(166, 169)(167, 175)(168, 173)(172, 174)(176, 178)(177, 180)

MAP           : A4.692
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 107)(56, 99)(57, 98)(58, 97)(59, 103)(60, 101)(61, 94)(62, 93)(63, 92)(64, 102)(65, 96)(66, 100)(67, 95)(68, 106)(69, 108)(70, 104)(71, 91)(72, 105)(73, 146)(74, 149)(75, 151)(76, 152)(77, 145)(78, 160)(79, 159)(80, 162)(81, 161)(82, 158)(83, 154)(84, 150)(85, 153)(86, 155)(87, 147)(88, 156)(89, 157)(90, 148)(163, 175)(164, 179)(165, 180)(166, 177)(167, 171)(168, 172)(169, 170)(173, 178)(174, 176)

MAP           : A4.693
NOTES         : type I, chiral, isomorphic to Snub({6,6}), isomorphic to A4.682.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^6, u.3^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^-1 * x.2 * x.3^2 * x.1, (x.2^-1 * x.3 * x.2^-1)^2, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 2)(3, 5)(4, 6)(7, 27)(8, 12)(9, 10)(11, 16)(13, 34)(14, 33)(15, 28)(17, 30)(18, 19)(20, 25)(21, 32)(22, 36)(23, 31)(24, 26)(29, 35)(37, 99)(38, 76)(39, 73)(40, 98)(41, 104)(42, 81)(43, 82)(44, 77)(45, 102)(46, 103)(47, 108)(48, 83)(49, 75)(50, 88)(51, 85)(52, 74)(53, 80)(54, 93)(55, 94)(56, 89)(57, 78)(58, 79)(59, 84)(60, 95)(61, 87)(62, 100)(63, 97)(64, 86)(65, 92)(66, 105)(67, 106)(68, 101)(69, 90)(70, 91)(71, 96)(72, 107)(109, 149)(110, 155)(111, 178)(112, 145)(113, 156)(114, 176)(115, 180)(116, 174)(117, 148)(118, 171)(119, 152)(120, 175)(121, 172)(122, 159)(123, 164)(124, 177)(125, 169)(126, 158)(127, 157)(128, 179)(129, 163)(130, 162)(131, 170)(132, 173)(133, 151)(134, 150)(135, 146)(136, 168)(137, 165)(138, 154)(139, 153)(140, 147)(141, 161)(142, 167)(143, 166)(144, 160)

MAP           : A4.694
NOTES         : type I, chiral, isomorphic to Snub({6,6}), isomorphic to A4.682.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^6, u.3^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3 * x.2^-1 * x.1 * x.2^2, x.3 * x.2^-3 * x.3 * x.2^-1, x.3^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 2)(3, 5)(4, 6)(7, 27)(8, 12)(9, 10)(11, 16)(13, 34)(14, 33)(15, 28)(17, 30)(18, 19)(20, 25)(21, 32)(22, 36)(23, 31)(24, 26)(29, 35)(37, 76)(38, 99)(39, 104)(40, 81)(41, 73)(42, 98)(43, 97)(44, 83)(45, 103)(46, 102)(47, 74)(48, 77)(49, 91)(50, 90)(51, 86)(52, 108)(53, 105)(54, 94)(55, 93)(56, 87)(57, 101)(58, 107)(59, 106)(60, 100)(61, 89)(62, 95)(63, 82)(64, 85)(65, 96)(66, 80)(67, 84)(68, 78)(69, 88)(70, 75)(71, 92)(72, 79)(109, 147)(110, 160)(111, 157)(112, 146)(113, 152)(114, 165)(115, 166)(116, 161)(117, 150)(118, 151)(119, 156)(120, 167)(121, 159)(122, 172)(123, 169)(124, 158)(125, 164)(126, 177)(127, 178)(128, 173)(129, 162)(130, 163)(131, 168)(132, 179)(133, 171)(134, 148)(135, 145)(136, 170)(137, 176)(138, 153)(139, 154)(140, 149)(141, 174)(142, 175)(143, 180)(144, 155)

MAP           : A4.695
NOTES         : type I, chiral, isomorphic to Snub({6,6}), isomorphic to A4.682.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^6, u.3^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3 * x.2^-1 * x.1 * x.2^2, x.3 * x.2^-3 * x.3 * x.2^-1, x.3^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 2)(3, 5)(4, 6)(7, 27)(8, 12)(9, 10)(11, 16)(13, 34)(14, 33)(15, 28)(17, 30)(18, 19)(20, 25)(21, 32)(22, 36)(23, 31)(24, 26)(29, 35)(37, 77)(38, 83)(39, 106)(40, 73)(41, 84)(42, 104)(43, 108)(44, 102)(45, 76)(46, 99)(47, 80)(48, 103)(49, 100)(50, 87)(51, 92)(52, 105)(53, 97)(54, 86)(55, 85)(56, 107)(57, 91)(58, 90)(59, 98)(60, 101)(61, 79)(62, 78)(63, 74)(64, 96)(65, 93)(66, 82)(67, 81)(68, 75)(69, 89)(70, 95)(71, 94)(72, 88)(109, 150)(110, 151)(111, 165)(112, 154)(113, 146)(114, 168)(115, 164)(116, 160)(117, 167)(118, 161)(119, 145)(120, 147)(121, 162)(122, 163)(123, 177)(124, 166)(125, 158)(126, 180)(127, 176)(128, 172)(129, 179)(130, 173)(131, 157)(132, 159)(133, 174)(134, 175)(135, 153)(136, 178)(137, 170)(138, 156)(139, 152)(140, 148)(141, 155)(142, 149)(143, 169)(144, 171)

MAP           : A4.696
NOTES         : type I, chiral, isomorphic to Snub({6,6}), isomorphic to A4.682.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^6, u.3^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^-1 * x.2 * x.3^2 * x.1, (x.2^-1 * x.3 * x.2^-1)^2, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 31)(2, 30)(3, 26)(4, 12)(5, 9)(6, 34)(7, 33)(8, 27)(10, 11)(13, 29)(14, 35)(15, 22)(16, 25)(17, 36)(18, 20)(19, 24)(21, 28)(23, 32)(37, 75)(38, 88)(39, 85)(40, 74)(41, 80)(42, 93)(43, 94)(44, 89)(45, 78)(46, 79)(47, 84)(48, 95)(49, 87)(50, 100)(51, 97)(52, 86)(53, 92)(54, 105)(55, 106)(56, 101)(57, 90)(58, 91)(59, 96)(60, 107)(61, 99)(62, 76)(63, 73)(64, 98)(65, 104)(66, 81)(67, 82)(68, 77)(69, 102)(70, 103)(71, 108)(72, 83)(109, 152)(110, 156)(111, 175)(112, 147)(113, 167)(114, 149)(115, 155)(116, 153)(117, 146)(118, 145)(119, 161)(120, 154)(121, 170)(122, 169)(123, 173)(124, 174)(125, 171)(126, 172)(127, 159)(128, 180)(129, 178)(130, 177)(131, 148)(132, 176)(133, 166)(134, 165)(135, 160)(136, 179)(137, 162)(138, 151)(139, 150)(140, 157)(141, 164)(142, 168)(143, 163)(144, 158)

MAP           : A4.697
NOTES         : type I, chiral, isomorphic to Snub({6,6}), isomorphic to A4.682.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^6, u.3^6 >
CTG (small)   : <36, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, x.3^-1 * x.2 * x.3^2 * x.1, (x.2^-1 * x.3 * x.2^-1)^2, x.2^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 31)(2, 30)(3, 26)(4, 12)(5, 9)(6, 34)(7, 33)(8, 27)(10, 11)(13, 29)(14, 35)(15, 22)(16, 25)(17, 36)(18, 20)(19, 24)(21, 28)(23, 32)(37, 99)(38, 76)(39, 73)(40, 98)(41, 104)(42, 81)(43, 82)(44, 77)(45, 102)(46, 103)(47, 108)(48, 83)(49, 75)(50, 88)(51, 85)(52, 74)(53, 80)(54, 93)(55, 94)(56, 89)(57, 78)(58, 79)(59, 84)(60, 95)(61, 87)(62, 100)(63, 97)(64, 86)(65, 92)(66, 105)(67, 106)(68, 101)(69, 90)(70, 91)(71, 96)(72, 107)(109, 170)(110, 169)(111, 173)(112, 174)(113, 171)(114, 172)(115, 159)(116, 180)(117, 178)(118, 177)(119, 148)(120, 176)(121, 166)(122, 165)(123, 160)(124, 179)(125, 162)(126, 151)(127, 150)(128, 157)(129, 164)(130, 168)(131, 163)(132, 158)(133, 152)(134, 156)(135, 175)(136, 147)(137, 167)(138, 149)(139, 155)(140, 153)(141, 146)(142, 145)(143, 161)(144, 154)

MAP           : A4.698
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 107)(56, 99)(57, 98)(58, 97)(59, 103)(60, 101)(61, 94)(62, 93)(63, 92)(64, 102)(65, 96)(66, 100)(67, 95)(68, 106)(69, 108)(70, 104)(71, 91)(72, 105)(73, 150)(74, 160)(75, 158)(76, 145)(77, 156)(78, 148)(79, 155)(80, 146)(81, 147)(82, 157)(83, 161)(84, 162)(85, 159)(86, 153)(87, 154)(88, 152)(89, 151)(90, 149)(163, 169)(164, 165)(166, 173)(167, 177)(168, 179)(170, 176)(171, 178)(172, 180)(174, 175)

MAP           : A4.699
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 97)(56, 93)(57, 92)(58, 101)(59, 105)(60, 107)(61, 91)(62, 104)(63, 106)(64, 108)(65, 94)(66, 103)(67, 102)(68, 98)(69, 95)(70, 99)(71, 96)(72, 100)(73, 162)(74, 148)(75, 157)(76, 156)(77, 152)(78, 149)(79, 153)(80, 150)(81, 154)(82, 151)(83, 147)(84, 146)(85, 155)(86, 159)(87, 161)(88, 145)(89, 158)(90, 160)(163, 171)(164, 175)(165, 166)(167, 179)(168, 176)(169, 180)(170, 177)(172, 178)(173, 174)

MAP           : A4.700
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 107)(56, 99)(57, 98)(58, 97)(59, 103)(60, 101)(61, 94)(62, 93)(63, 92)(64, 102)(65, 96)(66, 100)(67, 95)(68, 106)(69, 108)(70, 104)(71, 91)(72, 105)(73, 160)(74, 156)(75, 155)(76, 146)(77, 150)(78, 152)(79, 154)(80, 149)(81, 151)(82, 153)(83, 157)(84, 148)(85, 147)(86, 161)(87, 158)(88, 162)(89, 159)(90, 145)(163, 177)(164, 169)(165, 167)(166, 172)(168, 175)(170, 173)(171, 174)(176, 180)(178, 179)

MAP           : A4.701
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 97)(56, 93)(57, 92)(58, 101)(59, 105)(60, 107)(61, 91)(62, 104)(63, 106)(64, 108)(65, 94)(66, 103)(67, 102)(68, 98)(69, 95)(70, 99)(71, 96)(72, 100)(73, 156)(74, 150)(75, 154)(76, 149)(77, 160)(78, 162)(79, 158)(80, 145)(81, 159)(82, 161)(83, 153)(84, 152)(85, 151)(86, 157)(87, 155)(88, 148)(89, 147)(90, 146)(163, 176)(164, 172)(165, 168)(166, 171)(167, 173)(169, 174)(170, 175)(177, 178)(179, 180)

MAP           : A4.702
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 101)(56, 104)(57, 106)(58, 107)(59, 100)(60, 97)(61, 96)(62, 99)(63, 98)(64, 95)(65, 91)(66, 105)(67, 108)(68, 92)(69, 102)(70, 93)(71, 94)(72, 103)(73, 150)(74, 160)(75, 158)(76, 145)(77, 156)(78, 148)(79, 155)(80, 146)(81, 147)(82, 157)(83, 161)(84, 162)(85, 159)(86, 153)(87, 154)(88, 152)(89, 151)(90, 149)(163, 179)(164, 171)(165, 170)(166, 169)(167, 175)(168, 173)(172, 174)(176, 178)(177, 180)

MAP           : A4.703
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 101)(56, 104)(57, 106)(58, 107)(59, 100)(60, 97)(61, 96)(62, 99)(63, 98)(64, 95)(65, 91)(66, 105)(67, 108)(68, 92)(69, 102)(70, 93)(71, 94)(72, 103)(73, 152)(74, 162)(75, 161)(76, 160)(77, 148)(78, 146)(79, 157)(80, 156)(81, 155)(82, 147)(83, 159)(84, 145)(85, 158)(86, 151)(87, 153)(88, 149)(89, 154)(90, 150)(163, 177)(164, 169)(165, 167)(166, 172)(168, 175)(170, 173)(171, 174)(176, 180)(178, 179)

MAP           : A4.704
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {6, 6, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 6, 6, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.2^6, u.3^6 >
CTG (small)   : <36, 10>
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.2^6, x.3^6 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 3)(2, 23)(4, 5)(6, 19)(7, 30)(8, 34)(9, 36)(10, 32)(11, 26)(12, 33)(13, 27)(14, 35)(15, 25)(16, 29)(17, 28)(18, 31)(20, 22)(21, 24)(37, 76)(38, 75)(39, 101)(40, 105)(41, 96)(42, 95)(43, 77)(44, 73)(45, 88)(46, 84)(47, 93)(48, 74)(49, 83)(50, 79)(51, 94)(52, 78)(53, 87)(54, 80)(55, 98)(56, 102)(57, 92)(58, 91)(59, 97)(60, 106)(61, 104)(62, 108)(63, 86)(64, 85)(65, 103)(66, 100)(67, 82)(68, 81)(69, 107)(70, 99)(71, 90)(72, 89)(109, 178)(110, 177)(111, 167)(112, 147)(113, 174)(114, 173)(115, 179)(116, 175)(117, 154)(118, 162)(119, 171)(120, 176)(121, 161)(122, 157)(123, 172)(124, 180)(125, 153)(126, 158)(127, 164)(128, 168)(129, 170)(130, 169)(131, 163)(132, 148)(133, 146)(134, 150)(135, 152)(136, 151)(137, 145)(138, 166)(139, 160)(140, 159)(141, 149)(142, 165)(143, 156)(144, 155)

MAP           : A4.705
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 99)(56, 103)(57, 94)(58, 93)(59, 107)(60, 104)(61, 108)(62, 105)(63, 91)(64, 106)(65, 102)(66, 101)(67, 92)(68, 96)(69, 98)(70, 100)(71, 95)(72, 97)(73, 146)(74, 149)(75, 151)(76, 152)(77, 145)(78, 160)(79, 159)(80, 162)(81, 161)(82, 158)(83, 154)(84, 150)(85, 153)(86, 155)(87, 147)(88, 156)(89, 157)(90, 148)(163, 179)(164, 171)(165, 170)(166, 169)(167, 175)(168, 173)(172, 174)(176, 178)(177, 180)

MAP           : A4.706
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 99)(56, 103)(57, 94)(58, 93)(59, 107)(60, 104)(61, 108)(62, 105)(63, 91)(64, 106)(65, 102)(66, 101)(67, 92)(68, 96)(69, 98)(70, 100)(71, 95)(72, 97)(73, 149)(74, 145)(75, 159)(76, 162)(77, 146)(78, 156)(79, 147)(80, 148)(81, 157)(82, 155)(83, 158)(84, 160)(85, 161)(86, 154)(87, 151)(88, 150)(89, 153)(90, 152)(163, 175)(164, 179)(165, 180)(166, 177)(167, 171)(168, 172)(169, 170)(173, 178)(174, 176)

MAP           : A4.707
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 99)(56, 103)(57, 94)(58, 93)(59, 107)(60, 104)(61, 108)(62, 105)(63, 91)(64, 106)(65, 102)(66, 101)(67, 92)(68, 96)(69, 98)(70, 100)(71, 95)(72, 97)(73, 162)(74, 148)(75, 157)(76, 156)(77, 152)(78, 149)(79, 153)(80, 150)(81, 154)(82, 151)(83, 147)(84, 146)(85, 155)(86, 159)(87, 161)(88, 145)(89, 158)(90, 160)(163, 172)(164, 173)(165, 174)(166, 175)(167, 176)(168, 177)(169, 178)(170, 179)(171, 180)

MAP           : A4.708
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 101)(56, 104)(57, 106)(58, 107)(59, 100)(60, 97)(61, 96)(62, 99)(63, 98)(64, 95)(65, 91)(66, 105)(67, 108)(68, 92)(69, 102)(70, 93)(71, 94)(72, 103)(73, 149)(74, 145)(75, 159)(76, 162)(77, 146)(78, 156)(79, 147)(80, 148)(81, 157)(82, 155)(83, 158)(84, 160)(85, 161)(86, 154)(87, 151)(88, 150)(89, 153)(90, 152)(163, 176)(164, 172)(165, 168)(166, 171)(167, 173)(169, 174)(170, 175)(177, 178)(179, 180)

MAP           : A4.709
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 101)(56, 104)(57, 106)(58, 107)(59, 100)(60, 97)(61, 96)(62, 99)(63, 98)(64, 95)(65, 91)(66, 105)(67, 108)(68, 92)(69, 102)(70, 93)(71, 94)(72, 103)(73, 146)(74, 149)(75, 151)(76, 152)(77, 145)(78, 160)(79, 159)(80, 162)(81, 161)(82, 158)(83, 154)(84, 150)(85, 153)(86, 155)(87, 147)(88, 156)(89, 157)(90, 148)(163, 172)(164, 173)(165, 174)(166, 175)(167, 176)(168, 177)(169, 178)(170, 179)(171, 180)

MAP           : A4.710
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 101)(56, 104)(57, 106)(58, 107)(59, 100)(60, 97)(61, 96)(62, 99)(63, 98)(64, 95)(65, 91)(66, 105)(67, 108)(68, 92)(69, 102)(70, 93)(71, 94)(72, 103)(73, 156)(74, 150)(75, 154)(76, 149)(77, 160)(78, 162)(79, 158)(80, 145)(81, 159)(82, 161)(83, 153)(84, 152)(85, 151)(86, 157)(87, 155)(88, 148)(89, 147)(90, 146)(163, 171)(164, 175)(165, 166)(167, 179)(168, 176)(169, 180)(170, 177)(172, 178)(173, 174)

MAP           : A4.711
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 99)(56, 103)(57, 94)(58, 93)(59, 107)(60, 104)(61, 108)(62, 105)(63, 91)(64, 106)(65, 102)(66, 101)(67, 92)(68, 96)(69, 98)(70, 100)(71, 95)(72, 97)(73, 160)(74, 156)(75, 155)(76, 146)(77, 150)(78, 152)(79, 154)(80, 149)(81, 151)(82, 153)(83, 157)(84, 148)(85, 147)(86, 161)(87, 158)(88, 162)(89, 159)(90, 145)(163, 169)(164, 165)(166, 173)(167, 177)(168, 179)(170, 176)(171, 178)(172, 180)(174, 175)

MAP           : A4.712
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 107)(56, 99)(57, 98)(58, 97)(59, 103)(60, 101)(61, 94)(62, 93)(63, 92)(64, 102)(65, 96)(66, 100)(67, 95)(68, 106)(69, 108)(70, 104)(71, 91)(72, 105)(73, 149)(74, 145)(75, 159)(76, 162)(77, 146)(78, 156)(79, 147)(80, 148)(81, 157)(82, 155)(83, 158)(84, 160)(85, 161)(86, 154)(87, 151)(88, 150)(89, 153)(90, 152)(163, 171)(164, 175)(165, 166)(167, 179)(168, 176)(169, 180)(170, 177)(172, 178)(173, 174)

MAP           : A4.713
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 99)(56, 103)(57, 94)(58, 93)(59, 107)(60, 104)(61, 108)(62, 105)(63, 91)(64, 106)(65, 102)(66, 101)(67, 92)(68, 96)(69, 98)(70, 100)(71, 95)(72, 97)(73, 156)(74, 150)(75, 154)(76, 149)(77, 160)(78, 162)(79, 158)(80, 145)(81, 159)(82, 161)(83, 153)(84, 152)(85, 151)(86, 157)(87, 155)(88, 148)(89, 147)(90, 146)(163, 177)(164, 169)(165, 167)(166, 172)(168, 175)(170, 173)(171, 174)(176, 180)(178, 179)

MAP           : A4.714
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 99)(56, 103)(57, 94)(58, 93)(59, 107)(60, 104)(61, 108)(62, 105)(63, 91)(64, 106)(65, 102)(66, 101)(67, 92)(68, 96)(69, 98)(70, 100)(71, 95)(72, 97)(73, 152)(74, 162)(75, 161)(76, 160)(77, 148)(78, 146)(79, 157)(80, 156)(81, 155)(82, 147)(83, 159)(84, 145)(85, 158)(86, 151)(87, 153)(88, 149)(89, 154)(90, 150)(163, 173)(164, 176)(165, 178)(166, 179)(167, 172)(168, 169)(170, 171)(174, 177)(175, 180)

MAP           : A4.715
NOTES         : type I, reflexible, isomorphic to Snub({6,6}), isomorphic to A4.683.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 8)(3, 7)(4, 6)(5, 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.3 * u.1 * u.4^-1, u.5 * u.6^-1 * u.2, (u.6 * u.3^-1)^3, (u.4 * u.5^-1)^3 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.2 * x.5 * x.6^-1, x.3 * x.1 * x.4^-1, (x.6 * x.1)^2, (x.4 * x.5)^3, (x.6 * x.3^-1)^3, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.3, x.1, x.4, x.5, x.6)
LOCAL TYPE    : (3, 3, 6, 3, 6)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 21)(20, 33)(22, 32)(23, 25)(24, 27)(26, 28)(29, 36)(30, 35)(31, 34)(37, 111)(38, 123)(39, 109)(40, 122)(41, 115)(42, 117)(43, 113)(44, 118)(45, 114)(46, 116)(47, 126)(48, 125)(49, 124)(50, 112)(51, 110)(52, 121)(53, 120)(54, 119)(55, 97)(56, 93)(57, 92)(58, 101)(59, 105)(60, 107)(61, 91)(62, 104)(63, 106)(64, 108)(65, 94)(66, 103)(67, 102)(68, 98)(69, 95)(70, 99)(71, 96)(72, 100)(73, 160)(74, 156)(75, 155)(76, 146)(77, 150)(78, 152)(79, 154)(80, 149)(81, 151)(82, 153)(83, 157)(84, 148)(85, 147)(86, 161)(87, 158)(88, 162)(89, 159)(90, 145)(163, 172)(164, 173)(165, 174)(166, 175)(167, 176)(168, 177)(169, 178)(170, 179)(171, 180)

MAP           : A4.716
NOTES         : type I, chiral, isomorphic to Snub({4,10}), isomorphic to A4.673.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 10, 4, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.2 * x.3^-1)^2, x.3^4, x.2^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 10, 3, 4)
#DARTS        : 200
R = (1, 41, 81, 121, 161)(2, 42, 82, 122, 162)(3, 43, 83, 123, 163)(4, 44, 84, 124, 164)(5, 45, 85, 125, 165)(6, 46, 86, 126, 166)(7, 47, 87, 127, 167)(8, 48, 88, 128, 168)(9, 49, 89, 129, 169)(10, 50, 90, 130, 170)(11, 51, 91, 131, 171)(12, 52, 92, 132, 172)(13, 53, 93, 133, 173)(14, 54, 94, 134, 174)(15, 55, 95, 135, 175)(16, 56, 96, 136, 176)(17, 57, 97, 137, 177)(18, 58, 98, 138, 178)(19, 59, 99, 139, 179)(20, 60, 100, 140, 180)(21, 61, 101, 141, 181)(22, 62, 102, 142, 182)(23, 63, 103, 143, 183)(24, 64, 104, 144, 184)(25, 65, 105, 145, 185)(26, 66, 106, 146, 186)(27, 67, 107, 147, 187)(28, 68, 108, 148, 188)(29, 69, 109, 149, 189)(30, 70, 110, 150, 190)(31, 71, 111, 151, 191)(32, 72, 112, 152, 192)(33, 73, 113, 153, 193)(34, 74, 114, 154, 194)(35, 75, 115, 155, 195)(36, 76, 116, 156, 196)(37, 77, 117, 157, 197)(38, 78, 118, 158, 198)(39, 79, 119, 159, 199)(40, 80, 120, 160, 200)
L = (1, 7)(2, 3)(4, 6)(5, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 27)(22, 23)(24, 26)(25, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 84)(42, 81)(43, 105)(44, 89)(45, 82)(46, 101)(47, 102)(48, 110)(49, 93)(50, 85)(51, 104)(52, 114)(53, 97)(54, 90)(55, 109)(56, 118)(57, 98)(58, 94)(59, 113)(60, 117)(61, 83)(62, 88)(63, 107)(64, 87)(65, 92)(66, 111)(67, 106)(68, 103)(69, 86)(70, 96)(71, 115)(72, 108)(73, 91)(74, 100)(75, 119)(76, 112)(77, 95)(78, 99)(79, 120)(80, 116)(121, 163)(122, 168)(123, 187)(124, 167)(125, 172)(126, 191)(127, 186)(128, 183)(129, 166)(130, 176)(131, 195)(132, 188)(133, 171)(134, 180)(135, 199)(136, 192)(137, 175)(138, 179)(139, 200)(140, 196)(141, 164)(142, 161)(143, 185)(144, 169)(145, 162)(146, 181)(147, 182)(148, 190)(149, 173)(150, 165)(151, 184)(152, 194)(153, 177)(154, 170)(155, 189)(156, 198)(157, 178)(158, 174)(159, 193)(160, 197)

MAP           : A4.717
NOTES         : type I, chiral, isomorphic to Snub({4,10}), isomorphic to A4.673.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 10, 4, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.2 * x.3^-1)^2, x.3^4, x.2^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 10, 3, 4)
#DARTS        : 200
R = (1, 41, 81, 121, 161)(2, 42, 82, 122, 162)(3, 43, 83, 123, 163)(4, 44, 84, 124, 164)(5, 45, 85, 125, 165)(6, 46, 86, 126, 166)(7, 47, 87, 127, 167)(8, 48, 88, 128, 168)(9, 49, 89, 129, 169)(10, 50, 90, 130, 170)(11, 51, 91, 131, 171)(12, 52, 92, 132, 172)(13, 53, 93, 133, 173)(14, 54, 94, 134, 174)(15, 55, 95, 135, 175)(16, 56, 96, 136, 176)(17, 57, 97, 137, 177)(18, 58, 98, 138, 178)(19, 59, 99, 139, 179)(20, 60, 100, 140, 180)(21, 61, 101, 141, 181)(22, 62, 102, 142, 182)(23, 63, 103, 143, 183)(24, 64, 104, 144, 184)(25, 65, 105, 145, 185)(26, 66, 106, 146, 186)(27, 67, 107, 147, 187)(28, 68, 108, 148, 188)(29, 69, 109, 149, 189)(30, 70, 110, 150, 190)(31, 71, 111, 151, 191)(32, 72, 112, 152, 192)(33, 73, 113, 153, 193)(34, 74, 114, 154, 194)(35, 75, 115, 155, 195)(36, 76, 116, 156, 196)(37, 77, 117, 157, 197)(38, 78, 118, 158, 198)(39, 79, 119, 159, 199)(40, 80, 120, 160, 200)
L = (1, 7)(2, 3)(4, 6)(5, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 27)(22, 23)(24, 26)(25, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 90)(42, 94)(43, 109)(44, 85)(45, 98)(46, 117)(47, 113)(48, 104)(49, 82)(50, 97)(51, 118)(52, 101)(53, 81)(54, 93)(55, 114)(56, 102)(57, 84)(58, 89)(59, 110)(60, 105)(61, 95)(62, 91)(63, 116)(64, 99)(65, 86)(66, 108)(67, 112)(68, 120)(69, 100)(70, 87)(71, 103)(72, 119)(73, 96)(74, 83)(75, 107)(76, 115)(77, 92)(78, 88)(79, 106)(80, 111)(121, 175)(122, 171)(123, 196)(124, 179)(125, 166)(126, 188)(127, 192)(128, 200)(129, 180)(130, 167)(131, 183)(132, 199)(133, 176)(134, 163)(135, 187)(136, 195)(137, 172)(138, 168)(139, 186)(140, 191)(141, 170)(142, 174)(143, 189)(144, 165)(145, 178)(146, 197)(147, 193)(148, 184)(149, 162)(150, 177)(151, 198)(152, 181)(153, 161)(154, 173)(155, 194)(156, 182)(157, 164)(158, 169)(159, 190)(160, 185)

MAP           : A4.718
NOTES         : type I, chiral, isomorphic to Snub({4,10}), isomorphic to A4.673.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 10, 4, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.2 * x.3^-1)^2, x.3^4, x.2^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 10, 3, 4)
#DARTS        : 200
R = (1, 41, 81, 121, 161)(2, 42, 82, 122, 162)(3, 43, 83, 123, 163)(4, 44, 84, 124, 164)(5, 45, 85, 125, 165)(6, 46, 86, 126, 166)(7, 47, 87, 127, 167)(8, 48, 88, 128, 168)(9, 49, 89, 129, 169)(10, 50, 90, 130, 170)(11, 51, 91, 131, 171)(12, 52, 92, 132, 172)(13, 53, 93, 133, 173)(14, 54, 94, 134, 174)(15, 55, 95, 135, 175)(16, 56, 96, 136, 176)(17, 57, 97, 137, 177)(18, 58, 98, 138, 178)(19, 59, 99, 139, 179)(20, 60, 100, 140, 180)(21, 61, 101, 141, 181)(22, 62, 102, 142, 182)(23, 63, 103, 143, 183)(24, 64, 104, 144, 184)(25, 65, 105, 145, 185)(26, 66, 106, 146, 186)(27, 67, 107, 147, 187)(28, 68, 108, 148, 188)(29, 69, 109, 149, 189)(30, 70, 110, 150, 190)(31, 71, 111, 151, 191)(32, 72, 112, 152, 192)(33, 73, 113, 153, 193)(34, 74, 114, 154, 194)(35, 75, 115, 155, 195)(36, 76, 116, 156, 196)(37, 77, 117, 157, 197)(38, 78, 118, 158, 198)(39, 79, 119, 159, 199)(40, 80, 120, 160, 200)
L = (1, 7)(2, 3)(4, 6)(5, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 27)(22, 23)(24, 26)(25, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 93)(42, 89)(43, 114)(44, 97)(45, 84)(46, 105)(47, 110)(48, 118)(49, 98)(50, 81)(51, 102)(52, 117)(53, 94)(54, 82)(55, 101)(56, 113)(57, 90)(58, 85)(59, 104)(60, 109)(61, 92)(62, 96)(63, 111)(64, 88)(65, 100)(66, 119)(67, 115)(68, 106)(69, 83)(70, 99)(71, 120)(72, 107)(73, 87)(74, 95)(75, 116)(76, 103)(77, 86)(78, 91)(79, 112)(80, 108)(121, 172)(122, 176)(123, 191)(124, 168)(125, 180)(126, 199)(127, 195)(128, 186)(129, 163)(130, 179)(131, 200)(132, 187)(133, 167)(134, 175)(135, 196)(136, 183)(137, 166)(138, 171)(139, 192)(140, 188)(141, 173)(142, 169)(143, 194)(144, 177)(145, 164)(146, 185)(147, 190)(148, 198)(149, 178)(150, 161)(151, 182)(152, 197)(153, 174)(154, 162)(155, 181)(156, 193)(157, 170)(158, 165)(159, 184)(160, 189)

MAP           : A4.719
NOTES         : type I, chiral, isomorphic to Snub({4,10}), isomorphic to A4.673.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (2, 3)(4, 5)
ORBIFOLD      : O(0, {10, 4, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 10, 4, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, u.1 * u.2^-1 * u.3^-1, u.3^4, u.2^10 >
CTG (small)   : <40, 8>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.1 * x.2^-1 * x.3^-1, (x.2 * x.3^-1)^2, x.3^4, x.2^10 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 3, 10, 3, 4)
#DARTS        : 200
R = (1, 41, 81, 121, 161)(2, 42, 82, 122, 162)(3, 43, 83, 123, 163)(4, 44, 84, 124, 164)(5, 45, 85, 125, 165)(6, 46, 86, 126, 166)(7, 47, 87, 127, 167)(8, 48, 88, 128, 168)(9, 49, 89, 129, 169)(10, 50, 90, 130, 170)(11, 51, 91, 131, 171)(12, 52, 92, 132, 172)(13, 53, 93, 133, 173)(14, 54, 94, 134, 174)(15, 55, 95, 135, 175)(16, 56, 96, 136, 176)(17, 57, 97, 137, 177)(18, 58, 98, 138, 178)(19, 59, 99, 139, 179)(20, 60, 100, 140, 180)(21, 61, 101, 141, 181)(22, 62, 102, 142, 182)(23, 63, 103, 143, 183)(24, 64, 104, 144, 184)(25, 65, 105, 145, 185)(26, 66, 106, 146, 186)(27, 67, 107, 147, 187)(28, 68, 108, 148, 188)(29, 69, 109, 149, 189)(30, 70, 110, 150, 190)(31, 71, 111, 151, 191)(32, 72, 112, 152, 192)(33, 73, 113, 153, 193)(34, 74, 114, 154, 194)(35, 75, 115, 155, 195)(36, 76, 116, 156, 196)(37, 77, 117, 157, 197)(38, 78, 118, 158, 198)(39, 79, 119, 159, 199)(40, 80, 120, 160, 200)
L = (1, 7)(2, 3)(4, 6)(5, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 27)(22, 23)(24, 26)(25, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 82)(42, 85)(43, 101)(44, 81)(45, 90)(46, 109)(47, 104)(48, 102)(49, 84)(50, 94)(51, 113)(52, 105)(53, 89)(54, 98)(55, 117)(56, 110)(57, 93)(58, 97)(59, 118)(60, 114)(61, 86)(62, 87)(63, 108)(64, 91)(65, 83)(66, 107)(67, 103)(68, 112)(69, 95)(70, 88)(71, 106)(72, 116)(73, 99)(74, 92)(75, 111)(76, 120)(77, 100)(78, 96)(79, 115)(80, 119)(121, 166)(122, 167)(123, 188)(124, 171)(125, 163)(126, 187)(127, 183)(128, 192)(129, 175)(130, 168)(131, 186)(132, 196)(133, 179)(134, 172)(135, 191)(136, 200)(137, 180)(138, 176)(139, 195)(140, 199)(141, 162)(142, 165)(143, 181)(144, 161)(145, 170)(146, 189)(147, 184)(148, 182)(149, 164)(150, 174)(151, 193)(152, 185)(153, 169)(154, 178)(155, 197)(156, 190)(157, 173)(158, 177)(159, 198)(160, 194)

MAP           : A4.720
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 166)(146, 170)(147, 171)(148, 168)(149, 180)(150, 163)(151, 179)(152, 178)(153, 176)(154, 177)(155, 169)(156, 167)(157, 172)(158, 165)(159, 175)(160, 164)(161, 173)(162, 174)

MAP           : A4.721
NOTES         : type I, reflexible, representative.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 9)(2, 13)(3, 4)(5, 17)(6, 14)(7, 18)(8, 15)(10, 16)(11, 12)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 56)(38, 59)(39, 61)(40, 62)(41, 55)(42, 70)(43, 69)(44, 72)(45, 71)(46, 68)(47, 64)(48, 60)(49, 63)(50, 65)(51, 57)(52, 66)(53, 67)(54, 58)(73, 169)(74, 165)(75, 164)(76, 173)(77, 177)(78, 179)(79, 163)(80, 176)(81, 178)(82, 180)(83, 166)(84, 175)(85, 174)(86, 170)(87, 167)(88, 171)(89, 168)(90, 172)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 160)(128, 156)(129, 155)(130, 146)(131, 150)(132, 152)(133, 154)(134, 149)(135, 151)(136, 153)(137, 157)(138, 148)(139, 147)(140, 161)(141, 158)(142, 162)(143, 159)(144, 145)

MAP           : A4.722
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 174)(146, 168)(147, 172)(148, 167)(149, 178)(150, 180)(151, 176)(152, 163)(153, 177)(154, 179)(155, 171)(156, 170)(157, 169)(158, 175)(159, 173)(160, 166)(161, 165)(162, 164)

MAP           : A4.723
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 44)(20, 54)(21, 53)(22, 52)(23, 40)(24, 38)(25, 49)(26, 48)(27, 47)(28, 39)(29, 51)(30, 37)(31, 50)(32, 43)(33, 45)(34, 41)(35, 46)(36, 42)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 178)(146, 174)(147, 173)(148, 164)(149, 168)(150, 170)(151, 172)(152, 167)(153, 169)(154, 171)(155, 175)(156, 166)(157, 165)(158, 179)(159, 176)(160, 180)(161, 177)(162, 163)

MAP           : A4.724
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 13)(2, 17)(3, 18)(4, 15)(5, 9)(6, 10)(7, 8)(11, 16)(12, 14)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 56)(38, 59)(39, 61)(40, 62)(41, 55)(42, 70)(43, 69)(44, 72)(45, 71)(46, 68)(47, 64)(48, 60)(49, 63)(50, 65)(51, 57)(52, 66)(53, 67)(54, 58)(73, 169)(74, 165)(75, 164)(76, 173)(77, 177)(78, 179)(79, 163)(80, 176)(81, 178)(82, 180)(83, 166)(84, 175)(85, 174)(86, 170)(87, 167)(88, 171)(89, 168)(90, 172)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 156)(128, 150)(129, 154)(130, 149)(131, 160)(132, 162)(133, 158)(134, 145)(135, 159)(136, 161)(137, 153)(138, 152)(139, 151)(140, 157)(141, 155)(142, 148)(143, 147)(144, 146)

MAP           : A4.725
NOTES         : type I, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 119)(110, 122)(111, 124)(112, 125)(113, 118)(114, 115)(116, 117)(120, 123)(121, 126)(145, 167)(146, 163)(147, 177)(148, 180)(149, 164)(150, 174)(151, 165)(152, 166)(153, 175)(154, 173)(155, 176)(156, 178)(157, 179)(158, 172)(159, 169)(160, 168)(161, 171)(162, 170)

MAP           : A4.726
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 144)(56, 130)(57, 139)(58, 138)(59, 134)(60, 131)(61, 135)(62, 132)(63, 136)(64, 133)(65, 129)(66, 128)(67, 137)(68, 141)(69, 143)(70, 127)(71, 140)(72, 142)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 121)(110, 125)(111, 126)(112, 123)(113, 117)(114, 118)(115, 116)(119, 124)(120, 122)(145, 170)(146, 180)(147, 179)(148, 178)(149, 166)(150, 164)(151, 175)(152, 174)(153, 173)(154, 165)(155, 177)(156, 163)(157, 176)(158, 169)(159, 171)(160, 167)(161, 172)(162, 168)

MAP           : A4.727
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 11)(2, 14)(3, 16)(4, 17)(5, 10)(6, 7)(8, 9)(12, 15)(13, 18)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 56)(38, 59)(39, 61)(40, 62)(41, 55)(42, 70)(43, 69)(44, 72)(45, 71)(46, 68)(47, 64)(48, 60)(49, 63)(50, 65)(51, 57)(52, 66)(53, 67)(54, 58)(73, 169)(74, 165)(75, 164)(76, 173)(77, 177)(78, 179)(79, 163)(80, 176)(81, 178)(82, 180)(83, 166)(84, 175)(85, 174)(86, 170)(87, 167)(88, 171)(89, 168)(90, 172)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 148)(128, 152)(129, 153)(130, 150)(131, 162)(132, 145)(133, 161)(134, 160)(135, 158)(136, 159)(137, 151)(138, 149)(139, 154)(140, 147)(141, 157)(142, 146)(143, 155)(144, 156)

MAP           : A4.728
NOTES         : type I, reflexible, isomorphic to A4.725.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.5 * x.2 * x.3, x.2^3, x.5^3, x.3^3, (x.4 * x.1^-1)^2, x.5^-1 * x.4 * x.2^-1 * x.4^-1, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.4 * x.5^-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)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 47)(20, 42)(21, 50)(22, 43)(23, 46)(24, 45)(25, 53)(26, 48)(27, 38)(28, 49)(29, 52)(30, 51)(31, 41)(32, 54)(33, 44)(34, 37)(35, 40)(36, 39)(55, 136)(56, 129)(57, 138)(58, 137)(59, 133)(60, 140)(61, 142)(62, 135)(63, 144)(64, 143)(65, 139)(66, 128)(67, 130)(68, 141)(69, 132)(70, 131)(71, 127)(72, 134)(73, 110)(74, 109)(75, 125)(76, 123)(77, 126)(78, 121)(79, 117)(80, 124)(81, 115)(82, 120)(83, 122)(84, 118)(85, 114)(86, 119)(87, 112)(88, 116)(89, 111)(90, 113)(145, 169)(146, 170)(147, 171)(148, 172)(149, 173)(150, 174)(151, 175)(152, 176)(153, 177)(154, 178)(155, 179)(156, 180)(157, 163)(158, 164)(159, 165)(160, 166)(161, 167)(162, 168)

MAP           : A4.729
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 44)(20, 54)(21, 53)(22, 52)(23, 40)(24, 38)(25, 49)(26, 48)(27, 47)(28, 39)(29, 51)(30, 37)(31, 50)(32, 43)(33, 45)(34, 41)(35, 46)(36, 42)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 117)(110, 121)(111, 112)(113, 125)(114, 122)(115, 126)(116, 123)(118, 124)(119, 120)(145, 180)(146, 166)(147, 175)(148, 174)(149, 170)(150, 167)(151, 171)(152, 168)(153, 172)(154, 169)(155, 165)(156, 164)(157, 173)(158, 177)(159, 179)(160, 163)(161, 176)(162, 178)

MAP           : A4.730
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 42)(20, 52)(21, 50)(22, 37)(23, 48)(24, 40)(25, 47)(26, 38)(27, 39)(28, 49)(29, 53)(30, 54)(31, 51)(32, 45)(33, 46)(34, 44)(35, 43)(36, 41)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 180)(146, 166)(147, 175)(148, 174)(149, 170)(150, 167)(151, 171)(152, 168)(153, 172)(154, 169)(155, 165)(156, 164)(157, 173)(158, 177)(159, 179)(160, 163)(161, 176)(162, 178)

MAP           : A4.731
NOTES         : type I, reflexible, isomorphic to A4.725.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.5 * x.2 * x.3, x.2^3, x.5^3, x.3^3, (x.4 * x.1^-1)^2, x.5^-1 * x.4 * x.2^-1 * x.4^-1, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.4 * x.5^-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)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(25, 49)(26, 50)(27, 51)(28, 52)(29, 53)(30, 54)(31, 37)(32, 38)(33, 39)(34, 40)(35, 41)(36, 42)(55, 136)(56, 129)(57, 138)(58, 137)(59, 133)(60, 140)(61, 142)(62, 135)(63, 144)(64, 143)(65, 139)(66, 128)(67, 130)(68, 141)(69, 132)(70, 131)(71, 127)(72, 134)(73, 110)(74, 109)(75, 125)(76, 123)(77, 126)(78, 121)(79, 117)(80, 124)(81, 115)(82, 120)(83, 122)(84, 118)(85, 114)(86, 119)(87, 112)(88, 116)(89, 111)(90, 113)(145, 173)(146, 168)(147, 176)(148, 169)(149, 172)(150, 171)(151, 179)(152, 174)(153, 164)(154, 175)(155, 178)(156, 177)(157, 167)(158, 180)(159, 170)(160, 163)(161, 166)(162, 165)

MAP           : A4.732
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 170)(146, 180)(147, 179)(148, 178)(149, 166)(150, 164)(151, 175)(152, 174)(153, 173)(154, 165)(155, 177)(156, 163)(157, 176)(158, 169)(159, 171)(160, 167)(161, 172)(162, 168)

MAP           : A4.733
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 115)(110, 111)(112, 119)(113, 123)(114, 125)(116, 122)(117, 124)(118, 126)(120, 121)(145, 170)(146, 180)(147, 179)(148, 178)(149, 166)(150, 164)(151, 175)(152, 174)(153, 173)(154, 165)(155, 177)(156, 163)(157, 176)(158, 169)(159, 171)(160, 167)(161, 172)(162, 168)

MAP           : A4.734
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <36, 10>
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.2)^2, (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        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 149)(2, 147)(3, 166)(4, 165)(5, 168)(6, 167)(7, 155)(8, 153)(9, 160)(10, 159)(11, 162)(12, 161)(13, 156)(14, 154)(15, 158)(16, 152)(17, 157)(18, 151)(19, 150)(20, 148)(21, 164)(22, 146)(23, 163)(24, 145)(25, 180)(26, 178)(27, 170)(28, 176)(29, 169)(30, 175)(31, 179)(32, 177)(33, 172)(34, 171)(35, 174)(36, 173)(37, 38)(39, 43)(40, 49)(41, 44)(42, 50)(45, 47)(46, 48)(51, 72)(52, 71)(53, 70)(54, 69)(55, 56)(57, 61)(58, 67)(59, 62)(60, 68)(63, 65)(64, 66)(73, 78)(74, 76)(75, 92)(77, 91)(79, 108)(80, 106)(81, 98)(82, 104)(83, 97)(84, 103)(85, 107)(86, 105)(87, 100)(88, 99)(89, 102)(90, 101)(93, 94)(95, 96)(109, 118)(110, 120)(111, 114)(112, 113)(115, 122)(116, 121)(117, 127)(119, 128)(123, 139)(124, 133)(125, 140)(126, 134)(129, 143)(130, 144)(131, 141)(132, 142)(135, 138)(136, 137)

MAP           : A4.735
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <36, 10>
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.2)^2, (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        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 151)(2, 152)(3, 153)(4, 154)(5, 155)(6, 156)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 157)(20, 158)(21, 159)(22, 160)(23, 161)(24, 162)(25, 163)(26, 164)(27, 165)(28, 166)(29, 167)(30, 168)(31, 145)(32, 146)(33, 147)(34, 148)(35, 149)(36, 150)(37, 63)(38, 65)(39, 53)(40, 54)(41, 51)(42, 52)(43, 70)(44, 72)(45, 48)(46, 47)(49, 69)(50, 71)(55, 64)(56, 66)(57, 60)(58, 59)(61, 68)(62, 67)(73, 84)(74, 82)(75, 86)(76, 80)(77, 85)(78, 79)(81, 92)(83, 91)(87, 94)(88, 93)(89, 96)(90, 95)(97, 107)(98, 105)(99, 100)(101, 102)(103, 108)(104, 106)(109, 141)(110, 143)(111, 113)(112, 114)(115, 136)(116, 138)(117, 132)(118, 131)(119, 130)(120, 129)(121, 135)(122, 137)(123, 125)(124, 126)(127, 142)(128, 144)(133, 134)(139, 140)

MAP           : A4.736
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 125)(110, 117)(111, 116)(112, 115)(113, 121)(114, 119)(118, 120)(122, 124)(123, 126)(145, 180)(146, 166)(147, 175)(148, 174)(149, 170)(150, 167)(151, 171)(152, 168)(153, 172)(154, 169)(155, 165)(156, 164)(157, 173)(158, 177)(159, 179)(160, 163)(161, 176)(162, 178)

MAP           : A4.737
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 138)(56, 132)(57, 136)(58, 131)(59, 142)(60, 144)(61, 140)(62, 127)(63, 141)(64, 143)(65, 135)(66, 134)(67, 133)(68, 139)(69, 137)(70, 130)(71, 129)(72, 128)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 118)(110, 119)(111, 120)(112, 121)(113, 122)(114, 123)(115, 124)(116, 125)(117, 126)(145, 164)(146, 167)(147, 169)(148, 170)(149, 163)(150, 178)(151, 177)(152, 180)(153, 179)(154, 176)(155, 172)(156, 168)(157, 171)(158, 173)(159, 165)(160, 174)(161, 175)(162, 166)

MAP           : A4.738
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 164)(146, 167)(147, 169)(148, 170)(149, 163)(150, 178)(151, 177)(152, 180)(153, 179)(154, 176)(155, 172)(156, 168)(157, 171)(158, 173)(159, 165)(160, 174)(161, 175)(162, 166)

MAP           : A4.739
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 56)(38, 59)(39, 61)(40, 62)(41, 55)(42, 70)(43, 69)(44, 72)(45, 71)(46, 68)(47, 64)(48, 60)(49, 63)(50, 65)(51, 57)(52, 66)(53, 67)(54, 58)(73, 169)(74, 165)(75, 164)(76, 173)(77, 177)(78, 179)(79, 163)(80, 176)(81, 178)(82, 180)(83, 166)(84, 175)(85, 174)(86, 170)(87, 167)(88, 171)(89, 168)(90, 172)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 162)(128, 148)(129, 157)(130, 156)(131, 152)(132, 149)(133, 153)(134, 150)(135, 154)(136, 151)(137, 147)(138, 146)(139, 155)(140, 159)(141, 161)(142, 145)(143, 158)(144, 160)

MAP           : A4.740
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.3^3, (x.2 * x.1)^2, (x.2 * x.3^-1)^2, x.2^-2 * x.3 * x.1 * x.3^-1 * x.1, x.2^3 * x.3^-1 * x.2^-1 * x.3^-1, (x.3 * x.2 * x.3)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 112)(2, 114)(3, 144)(4, 143)(5, 142)(6, 141)(7, 128)(8, 127)(9, 133)(10, 139)(11, 134)(12, 140)(13, 110)(14, 109)(15, 115)(16, 121)(17, 116)(18, 122)(19, 111)(20, 113)(21, 119)(22, 120)(23, 117)(24, 118)(25, 130)(26, 132)(27, 126)(28, 125)(29, 124)(30, 123)(31, 129)(32, 131)(33, 137)(34, 138)(35, 135)(36, 136)(37, 77)(38, 75)(39, 94)(40, 93)(41, 96)(42, 95)(43, 83)(44, 81)(45, 88)(46, 87)(47, 90)(48, 89)(49, 84)(50, 82)(51, 86)(52, 80)(53, 85)(54, 79)(55, 78)(56, 76)(57, 92)(58, 74)(59, 91)(60, 73)(61, 108)(62, 106)(63, 98)(64, 104)(65, 97)(66, 103)(67, 107)(68, 105)(69, 100)(70, 99)(71, 102)(72, 101)(145, 146)(147, 151)(148, 157)(149, 152)(150, 158)(153, 155)(154, 156)(159, 180)(160, 179)(161, 178)(162, 177)(163, 164)(165, 169)(166, 175)(167, 170)(168, 176)(171, 173)(172, 174)

MAP           : A4.741
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.3^3, (x.2 * x.1)^2, (x.2 * x.3^-1)^2, x.2^-2 * x.3 * x.1 * x.3^-1 * x.1, x.2^3 * x.3^-1 * x.2^-1 * x.3^-1, (x.3 * x.2 * x.3)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 111)(2, 113)(3, 119)(4, 120)(5, 117)(6, 118)(7, 130)(8, 132)(9, 126)(10, 125)(11, 124)(12, 123)(13, 129)(14, 131)(15, 137)(16, 138)(17, 135)(18, 136)(19, 112)(20, 114)(21, 144)(22, 143)(23, 142)(24, 141)(25, 128)(26, 127)(27, 133)(28, 139)(29, 134)(30, 140)(31, 110)(32, 109)(33, 115)(34, 121)(35, 116)(36, 122)(37, 77)(38, 75)(39, 94)(40, 93)(41, 96)(42, 95)(43, 83)(44, 81)(45, 88)(46, 87)(47, 90)(48, 89)(49, 84)(50, 82)(51, 86)(52, 80)(53, 85)(54, 79)(55, 78)(56, 76)(57, 92)(58, 74)(59, 91)(60, 73)(61, 108)(62, 106)(63, 98)(64, 104)(65, 97)(66, 103)(67, 107)(68, 105)(69, 100)(70, 99)(71, 102)(72, 101)(145, 171)(146, 173)(147, 161)(148, 162)(149, 159)(150, 160)(151, 178)(152, 180)(153, 156)(154, 155)(157, 177)(158, 179)(163, 172)(164, 174)(165, 168)(166, 167)(169, 176)(170, 175)

MAP           : A4.742
NOTES         : type I, reflexible, isomorphic to A4.725.
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)   : <36, 10>
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^-2 * x.3 * x.2 * x.3 * x.2^-1, x.3 * x.2 * x.3 * x.2^3 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 111)(2, 113)(3, 119)(4, 120)(5, 117)(6, 118)(7, 130)(8, 132)(9, 126)(10, 125)(11, 124)(12, 123)(13, 129)(14, 131)(15, 137)(16, 138)(17, 135)(18, 136)(19, 112)(20, 114)(21, 144)(22, 143)(23, 142)(24, 141)(25, 128)(26, 127)(27, 133)(28, 139)(29, 134)(30, 140)(31, 110)(32, 109)(33, 115)(34, 121)(35, 116)(36, 122)(37, 77)(38, 75)(39, 94)(40, 93)(41, 96)(42, 95)(43, 83)(44, 81)(45, 88)(46, 87)(47, 90)(48, 89)(49, 84)(50, 82)(51, 86)(52, 80)(53, 85)(54, 79)(55, 78)(56, 76)(57, 92)(58, 74)(59, 91)(60, 73)(61, 108)(62, 106)(63, 98)(64, 104)(65, 97)(66, 103)(67, 107)(68, 105)(69, 100)(70, 99)(71, 102)(72, 101)(145, 150)(146, 148)(147, 164)(149, 163)(151, 180)(152, 178)(153, 170)(154, 176)(155, 169)(156, 175)(157, 179)(158, 177)(159, 172)(160, 171)(161, 174)(162, 173)(165, 166)(167, 168)

MAP           : A4.743
NOTES         : type I, reflexible, isomorphic to A4.725.
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)   : <36, 10>
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^-2 * x.3 * x.2 * x.3 * x.2^-1, x.3 * x.2 * x.3 * x.2^3 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 37, 73, 109, 145)(2, 38, 74, 110, 146)(3, 39, 75, 111, 147)(4, 40, 76, 112, 148)(5, 41, 77, 113, 149)(6, 42, 78, 114, 150)(7, 43, 79, 115, 151)(8, 44, 80, 116, 152)(9, 45, 81, 117, 153)(10, 46, 82, 118, 154)(11, 47, 83, 119, 155)(12, 48, 84, 120, 156)(13, 49, 85, 121, 157)(14, 50, 86, 122, 158)(15, 51, 87, 123, 159)(16, 52, 88, 124, 160)(17, 53, 89, 125, 161)(18, 54, 90, 126, 162)(19, 55, 91, 127, 163)(20, 56, 92, 128, 164)(21, 57, 93, 129, 165)(22, 58, 94, 130, 166)(23, 59, 95, 131, 167)(24, 60, 96, 132, 168)(25, 61, 97, 133, 169)(26, 62, 98, 134, 170)(27, 63, 99, 135, 171)(28, 64, 100, 136, 172)(29, 65, 101, 137, 173)(30, 66, 102, 138, 174)(31, 67, 103, 139, 175)(32, 68, 104, 140, 176)(33, 69, 105, 141, 177)(34, 70, 106, 142, 178)(35, 71, 107, 143, 179)(36, 72, 108, 144, 180)
L = (1, 112)(2, 114)(3, 144)(4, 143)(5, 142)(6, 141)(7, 128)(8, 127)(9, 133)(10, 139)(11, 134)(12, 140)(13, 110)(14, 109)(15, 115)(16, 121)(17, 116)(18, 122)(19, 111)(20, 113)(21, 119)(22, 120)(23, 117)(24, 118)(25, 130)(26, 132)(27, 126)(28, 125)(29, 124)(30, 123)(31, 129)(32, 131)(33, 137)(34, 138)(35, 135)(36, 136)(37, 77)(38, 75)(39, 94)(40, 93)(41, 96)(42, 95)(43, 83)(44, 81)(45, 88)(46, 87)(47, 90)(48, 89)(49, 84)(50, 82)(51, 86)(52, 80)(53, 85)(54, 79)(55, 78)(56, 76)(57, 92)(58, 74)(59, 91)(60, 73)(61, 108)(62, 106)(63, 98)(64, 104)(65, 97)(66, 103)(67, 107)(68, 105)(69, 100)(70, 99)(71, 102)(72, 101)(145, 150)(146, 148)(147, 164)(149, 163)(151, 180)(152, 178)(153, 170)(154, 176)(155, 169)(156, 175)(157, 179)(158, 177)(159, 172)(160, 171)(161, 174)(162, 173)(165, 166)(167, 168)

MAP           : A4.744
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 44)(20, 54)(21, 53)(22, 52)(23, 40)(24, 38)(25, 49)(26, 48)(27, 47)(28, 39)(29, 51)(30, 37)(31, 50)(32, 43)(33, 45)(34, 41)(35, 46)(36, 42)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 119)(110, 122)(111, 124)(112, 125)(113, 118)(114, 115)(116, 117)(120, 123)(121, 126)(145, 164)(146, 167)(147, 169)(148, 170)(149, 163)(150, 178)(151, 177)(152, 180)(153, 179)(154, 176)(155, 172)(156, 168)(157, 171)(158, 173)(159, 165)(160, 174)(161, 175)(162, 166)

MAP           : A4.745
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 44)(20, 54)(21, 53)(22, 52)(23, 40)(24, 38)(25, 49)(26, 48)(27, 47)(28, 39)(29, 51)(30, 37)(31, 50)(32, 43)(33, 45)(34, 41)(35, 46)(36, 42)(55, 144)(56, 130)(57, 139)(58, 138)(59, 134)(60, 131)(61, 135)(62, 132)(63, 136)(64, 133)(65, 129)(66, 128)(67, 137)(68, 141)(69, 143)(70, 127)(71, 140)(72, 142)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 121)(110, 125)(111, 126)(112, 123)(113, 117)(114, 118)(115, 116)(119, 124)(120, 122)(145, 166)(146, 170)(147, 171)(148, 168)(149, 180)(150, 163)(151, 179)(152, 178)(153, 176)(154, 177)(155, 169)(156, 167)(157, 172)(158, 165)(159, 175)(160, 164)(161, 173)(162, 174)

MAP           : A4.746
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 54)(20, 40)(21, 49)(22, 48)(23, 44)(24, 41)(25, 45)(26, 42)(27, 46)(28, 43)(29, 39)(30, 38)(31, 47)(32, 51)(33, 53)(34, 37)(35, 50)(36, 52)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 166)(146, 170)(147, 171)(148, 168)(149, 180)(150, 163)(151, 179)(152, 178)(153, 176)(154, 177)(155, 169)(156, 167)(157, 172)(158, 165)(159, 175)(160, 164)(161, 173)(162, 174)

MAP           : A4.747
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 54)(20, 40)(21, 49)(22, 48)(23, 44)(24, 41)(25, 45)(26, 42)(27, 46)(28, 43)(29, 39)(30, 38)(31, 47)(32, 51)(33, 53)(34, 37)(35, 50)(36, 52)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 168)(146, 178)(147, 176)(148, 163)(149, 174)(150, 166)(151, 173)(152, 164)(153, 165)(154, 175)(155, 179)(156, 180)(157, 177)(158, 171)(159, 172)(160, 170)(161, 169)(162, 167)

MAP           : A4.748
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 174)(146, 168)(147, 172)(148, 167)(149, 178)(150, 180)(151, 176)(152, 163)(153, 177)(154, 179)(155, 171)(156, 170)(157, 169)(158, 175)(159, 173)(160, 166)(161, 165)(162, 164)

MAP           : A4.749
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 178)(146, 174)(147, 173)(148, 164)(149, 168)(150, 170)(151, 172)(152, 167)(153, 169)(154, 171)(155, 175)(156, 166)(157, 165)(158, 179)(159, 176)(160, 180)(161, 177)(162, 163)

MAP           : A4.750
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 44)(20, 54)(21, 53)(22, 52)(23, 40)(24, 38)(25, 49)(26, 48)(27, 47)(28, 39)(29, 51)(30, 37)(31, 50)(32, 43)(33, 45)(34, 41)(35, 46)(36, 42)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 180)(146, 166)(147, 175)(148, 174)(149, 170)(150, 167)(151, 171)(152, 168)(153, 172)(154, 169)(155, 165)(156, 164)(157, 173)(158, 177)(159, 179)(160, 163)(161, 176)(162, 178)

MAP           : A4.751
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 13)(2, 17)(3, 18)(4, 15)(5, 9)(6, 10)(7, 8)(11, 16)(12, 14)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 62)(38, 72)(39, 71)(40, 70)(41, 58)(42, 56)(43, 67)(44, 66)(45, 65)(46, 57)(47, 69)(48, 55)(49, 68)(50, 61)(51, 63)(52, 59)(53, 64)(54, 60)(73, 179)(74, 171)(75, 170)(76, 169)(77, 175)(78, 173)(79, 166)(80, 165)(81, 164)(82, 174)(83, 168)(84, 172)(85, 167)(86, 178)(87, 180)(88, 176)(89, 163)(90, 177)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 149)(128, 145)(129, 159)(130, 162)(131, 146)(132, 156)(133, 147)(134, 148)(135, 157)(136, 155)(137, 158)(138, 160)(139, 161)(140, 154)(141, 151)(142, 150)(143, 153)(144, 152)

MAP           : A4.752
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 7)(2, 3)(4, 11)(5, 15)(6, 17)(8, 14)(9, 16)(10, 18)(12, 13)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 70)(38, 66)(39, 65)(40, 56)(41, 60)(42, 62)(43, 64)(44, 59)(45, 61)(46, 63)(47, 67)(48, 58)(49, 57)(50, 71)(51, 68)(52, 72)(53, 69)(54, 55)(73, 173)(74, 176)(75, 178)(76, 179)(77, 172)(78, 169)(79, 168)(80, 171)(81, 170)(82, 167)(83, 163)(84, 177)(85, 180)(86, 164)(87, 174)(88, 165)(89, 166)(90, 175)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 150)(128, 160)(129, 158)(130, 145)(131, 156)(132, 148)(133, 155)(134, 146)(135, 147)(136, 157)(137, 161)(138, 162)(139, 159)(140, 153)(141, 154)(142, 152)(143, 151)(144, 149)

MAP           : A4.753
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 9)(2, 13)(3, 4)(5, 17)(6, 14)(7, 18)(8, 15)(10, 16)(11, 12)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 70)(38, 66)(39, 65)(40, 56)(41, 60)(42, 62)(43, 64)(44, 59)(45, 61)(46, 63)(47, 67)(48, 58)(49, 57)(50, 71)(51, 68)(52, 72)(53, 69)(54, 55)(73, 173)(74, 176)(75, 178)(76, 179)(77, 172)(78, 169)(79, 168)(80, 171)(81, 170)(82, 167)(83, 163)(84, 177)(85, 180)(86, 164)(87, 174)(88, 165)(89, 166)(90, 175)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 152)(128, 162)(129, 161)(130, 160)(131, 148)(132, 146)(133, 157)(134, 156)(135, 155)(136, 147)(137, 159)(138, 145)(139, 158)(140, 151)(141, 153)(142, 149)(143, 154)(144, 150)

MAP           : A4.754
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 17)(2, 9)(3, 8)(4, 7)(5, 13)(6, 11)(10, 12)(14, 16)(15, 18)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 70)(38, 66)(39, 65)(40, 56)(41, 60)(42, 62)(43, 64)(44, 59)(45, 61)(46, 63)(47, 67)(48, 58)(49, 57)(50, 71)(51, 68)(52, 72)(53, 69)(54, 55)(73, 173)(74, 176)(75, 178)(76, 179)(77, 172)(78, 169)(79, 168)(80, 171)(81, 170)(82, 167)(83, 163)(84, 177)(85, 180)(86, 164)(87, 174)(88, 165)(89, 166)(90, 175)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 148)(128, 152)(129, 153)(130, 150)(131, 162)(132, 145)(133, 161)(134, 160)(135, 158)(136, 159)(137, 151)(138, 149)(139, 154)(140, 147)(141, 157)(142, 146)(143, 155)(144, 156)

MAP           : A4.755
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 15)(2, 7)(3, 5)(4, 10)(6, 13)(8, 11)(9, 12)(14, 18)(16, 17)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 70)(38, 66)(39, 65)(40, 56)(41, 60)(42, 62)(43, 64)(44, 59)(45, 61)(46, 63)(47, 67)(48, 58)(49, 57)(50, 71)(51, 68)(52, 72)(53, 69)(54, 55)(73, 173)(74, 176)(75, 178)(76, 179)(77, 172)(78, 169)(79, 168)(80, 171)(81, 170)(82, 167)(83, 163)(84, 177)(85, 180)(86, 164)(87, 174)(88, 165)(89, 166)(90, 175)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 156)(128, 150)(129, 154)(130, 149)(131, 160)(132, 162)(133, 158)(134, 145)(135, 159)(136, 161)(137, 153)(138, 152)(139, 151)(140, 157)(141, 155)(142, 148)(143, 147)(144, 146)

MAP           : A4.756
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 14)(2, 10)(3, 6)(4, 9)(5, 11)(7, 12)(8, 13)(15, 16)(17, 18)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 70)(38, 66)(39, 65)(40, 56)(41, 60)(42, 62)(43, 64)(44, 59)(45, 61)(46, 63)(47, 67)(48, 58)(49, 57)(50, 71)(51, 68)(52, 72)(53, 69)(54, 55)(73, 173)(74, 176)(75, 178)(76, 179)(77, 172)(78, 169)(79, 168)(80, 171)(81, 170)(82, 167)(83, 163)(84, 177)(85, 180)(86, 164)(87, 174)(88, 165)(89, 166)(90, 175)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 146)(128, 149)(129, 151)(130, 152)(131, 145)(132, 160)(133, 159)(134, 162)(135, 161)(136, 158)(137, 154)(138, 150)(139, 153)(140, 155)(141, 147)(142, 156)(143, 157)(144, 148)

MAP           : A4.757
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 70)(38, 66)(39, 65)(40, 56)(41, 60)(42, 62)(43, 64)(44, 59)(45, 61)(46, 63)(47, 67)(48, 58)(49, 57)(50, 71)(51, 68)(52, 72)(53, 69)(54, 55)(73, 173)(74, 176)(75, 178)(76, 179)(77, 172)(78, 169)(79, 168)(80, 171)(81, 170)(82, 167)(83, 163)(84, 177)(85, 180)(86, 164)(87, 174)(88, 165)(89, 166)(90, 175)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 149)(128, 145)(129, 159)(130, 162)(131, 146)(132, 156)(133, 147)(134, 148)(135, 157)(136, 155)(137, 158)(138, 160)(139, 161)(140, 154)(141, 151)(142, 150)(143, 153)(144, 152)

MAP           : A4.758
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 138)(56, 132)(57, 136)(58, 131)(59, 142)(60, 144)(61, 140)(62, 127)(63, 141)(64, 143)(65, 135)(66, 134)(67, 133)(68, 139)(69, 137)(70, 130)(71, 129)(72, 128)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 118)(110, 119)(111, 120)(112, 121)(113, 122)(114, 123)(115, 124)(116, 125)(117, 126)(145, 166)(146, 170)(147, 171)(148, 168)(149, 180)(150, 163)(151, 179)(152, 178)(153, 176)(154, 177)(155, 169)(156, 167)(157, 172)(158, 165)(159, 175)(160, 164)(161, 173)(162, 174)

MAP           : A4.759
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 119)(110, 122)(111, 124)(112, 125)(113, 118)(114, 115)(116, 117)(120, 123)(121, 126)(145, 170)(146, 180)(147, 179)(148, 178)(149, 166)(150, 164)(151, 175)(152, 174)(153, 173)(154, 165)(155, 177)(156, 163)(157, 176)(158, 169)(159, 171)(160, 167)(161, 172)(162, 168)

MAP           : A4.760
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 144)(56, 130)(57, 139)(58, 138)(59, 134)(60, 131)(61, 135)(62, 132)(63, 136)(64, 133)(65, 129)(66, 128)(67, 137)(68, 141)(69, 143)(70, 127)(71, 140)(72, 142)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 121)(110, 125)(111, 126)(112, 123)(113, 117)(114, 118)(115, 116)(119, 124)(120, 122)(145, 168)(146, 178)(147, 176)(148, 163)(149, 174)(150, 166)(151, 173)(152, 164)(153, 165)(154, 175)(155, 179)(156, 180)(157, 177)(158, 171)(159, 172)(160, 170)(161, 169)(162, 167)

MAP           : A4.761
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 115)(110, 111)(112, 119)(113, 123)(114, 125)(116, 122)(117, 124)(118, 126)(120, 121)(145, 174)(146, 168)(147, 172)(148, 167)(149, 178)(150, 180)(151, 176)(152, 163)(153, 177)(154, 179)(155, 171)(156, 170)(157, 169)(158, 175)(159, 173)(160, 166)(161, 165)(162, 164)

MAP           : A4.762
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 131)(56, 127)(57, 141)(58, 144)(59, 128)(60, 138)(61, 129)(62, 130)(63, 139)(64, 137)(65, 140)(66, 142)(67, 143)(68, 136)(69, 133)(70, 132)(71, 135)(72, 134)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 123)(110, 115)(111, 113)(112, 118)(114, 121)(116, 119)(117, 120)(122, 126)(124, 125)(145, 178)(146, 174)(147, 173)(148, 164)(149, 168)(150, 170)(151, 172)(152, 167)(153, 169)(154, 171)(155, 175)(156, 166)(157, 165)(158, 179)(159, 176)(160, 180)(161, 177)(162, 163)

MAP           : A4.763
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 132)(56, 142)(57, 140)(58, 127)(59, 138)(60, 130)(61, 137)(62, 128)(63, 129)(64, 139)(65, 143)(66, 144)(67, 141)(68, 135)(69, 136)(70, 134)(71, 133)(72, 131)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 122)(110, 118)(111, 114)(112, 117)(113, 119)(115, 120)(116, 121)(123, 124)(125, 126)(145, 174)(146, 168)(147, 172)(148, 167)(149, 178)(150, 180)(151, 176)(152, 163)(153, 177)(154, 179)(155, 171)(156, 170)(157, 169)(158, 175)(159, 173)(160, 166)(161, 165)(162, 164)

MAP           : A4.764
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 125)(110, 117)(111, 116)(112, 115)(113, 121)(114, 119)(118, 120)(122, 124)(123, 126)(145, 164)(146, 167)(147, 169)(148, 170)(149, 163)(150, 178)(151, 177)(152, 180)(153, 179)(154, 176)(155, 172)(156, 168)(157, 171)(158, 173)(159, 165)(160, 174)(161, 175)(162, 166)

MAP           : A4.765
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 138)(56, 132)(57, 136)(58, 131)(59, 142)(60, 144)(61, 140)(62, 127)(63, 141)(64, 143)(65, 135)(66, 134)(67, 133)(68, 139)(69, 137)(70, 130)(71, 129)(72, 128)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 118)(110, 119)(111, 120)(112, 121)(113, 122)(114, 123)(115, 124)(116, 125)(117, 126)(145, 168)(146, 178)(147, 176)(148, 163)(149, 174)(150, 166)(151, 173)(152, 164)(153, 165)(154, 175)(155, 179)(156, 180)(157, 177)(158, 171)(159, 172)(160, 170)(161, 169)(162, 167)

MAP           : A4.766
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 167)(146, 163)(147, 177)(148, 180)(149, 164)(150, 174)(151, 165)(152, 166)(153, 175)(154, 173)(155, 176)(156, 178)(157, 179)(158, 172)(159, 169)(160, 168)(161, 171)(162, 170)

MAP           : A4.767
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 44)(20, 54)(21, 53)(22, 52)(23, 40)(24, 38)(25, 49)(26, 48)(27, 47)(28, 39)(29, 51)(30, 37)(31, 50)(32, 43)(33, 45)(34, 41)(35, 46)(36, 42)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 115)(110, 111)(112, 119)(113, 123)(114, 125)(116, 122)(117, 124)(118, 126)(120, 121)(145, 178)(146, 174)(147, 173)(148, 164)(149, 168)(150, 170)(151, 172)(152, 167)(153, 169)(154, 171)(155, 175)(156, 166)(157, 165)(158, 179)(159, 176)(160, 180)(161, 177)(162, 163)

MAP           : A4.768
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 44)(20, 54)(21, 53)(22, 52)(23, 40)(24, 38)(25, 49)(26, 48)(27, 47)(28, 39)(29, 51)(30, 37)(31, 50)(32, 43)(33, 45)(34, 41)(35, 46)(36, 42)(55, 131)(56, 127)(57, 141)(58, 144)(59, 128)(60, 138)(61, 129)(62, 130)(63, 139)(64, 137)(65, 140)(66, 142)(67, 143)(68, 136)(69, 133)(70, 132)(71, 135)(72, 134)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 123)(110, 115)(111, 113)(112, 118)(114, 121)(116, 119)(117, 120)(122, 126)(124, 125)(145, 168)(146, 178)(147, 176)(148, 163)(149, 174)(150, 166)(151, 173)(152, 164)(153, 165)(154, 175)(155, 179)(156, 180)(157, 177)(158, 171)(159, 172)(160, 170)(161, 169)(162, 167)

MAP           : A4.769
NOTES         : type I, reflexible, isomorphic to A4.725.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.5^-1 * x.3^-1, x.5^3, x.3^3, x.1 * x.2^-1 * x.1^-1 * x.4^-1, (x.2 * x.3^-1)^2, (x.4 * x.5^-1)^2, x.3 * x.2^2 * x.3^-1 * x.2^-2, x.4^3 * x.3^-1 * x.2^-1 * x.3^-1, x.4^2 * x.3 * x.4^-1 * x.5^-1 * x.2^-1, x.4 * x.3 * x.2 * x.5^-1 * x.2^-2 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.2^-1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 80)(20, 79)(21, 77)(22, 75)(23, 78)(24, 73)(25, 87)(26, 76)(27, 85)(28, 90)(29, 74)(30, 88)(31, 84)(32, 89)(33, 82)(34, 86)(35, 81)(36, 83)(37, 61)(38, 62)(39, 63)(40, 64)(41, 65)(42, 66)(43, 67)(44, 68)(45, 69)(46, 70)(47, 71)(48, 72)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(109, 168)(110, 173)(111, 166)(112, 170)(113, 165)(114, 167)(115, 164)(116, 163)(117, 179)(118, 177)(119, 180)(120, 175)(121, 171)(122, 178)(123, 169)(124, 174)(125, 176)(126, 172)(127, 157)(128, 158)(129, 159)(130, 160)(131, 161)(132, 162)(133, 145)(134, 146)(135, 147)(136, 148)(137, 149)(138, 150)(139, 151)(140, 152)(141, 153)(142, 154)(143, 155)(144, 156)

MAP           : A4.770
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 44)(20, 54)(21, 53)(22, 52)(23, 40)(24, 38)(25, 49)(26, 48)(27, 47)(28, 39)(29, 51)(30, 37)(31, 50)(32, 43)(33, 45)(34, 41)(35, 46)(36, 42)(55, 132)(56, 142)(57, 140)(58, 127)(59, 138)(60, 130)(61, 137)(62, 128)(63, 129)(64, 139)(65, 143)(66, 144)(67, 141)(68, 135)(69, 136)(70, 134)(71, 133)(72, 131)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 122)(110, 118)(111, 114)(112, 117)(113, 119)(115, 120)(116, 121)(123, 124)(125, 126)(145, 167)(146, 163)(147, 177)(148, 180)(149, 164)(150, 174)(151, 165)(152, 166)(153, 175)(154, 173)(155, 176)(156, 178)(157, 179)(158, 172)(159, 169)(160, 168)(161, 171)(162, 170)

MAP           : A4.771
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 42)(20, 52)(21, 50)(22, 37)(23, 48)(24, 40)(25, 47)(26, 38)(27, 39)(28, 49)(29, 53)(30, 54)(31, 51)(32, 45)(33, 46)(34, 44)(35, 43)(36, 41)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 167)(146, 163)(147, 177)(148, 180)(149, 164)(150, 174)(151, 165)(152, 166)(153, 175)(154, 173)(155, 176)(156, 178)(157, 179)(158, 172)(159, 169)(160, 168)(161, 171)(162, 170)

MAP           : A4.772
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 164)(146, 167)(147, 169)(148, 170)(149, 163)(150, 178)(151, 177)(152, 180)(153, 179)(154, 176)(155, 172)(156, 168)(157, 171)(158, 173)(159, 165)(160, 174)(161, 175)(162, 166)

MAP           : A4.773
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 58)(38, 62)(39, 63)(40, 60)(41, 72)(42, 55)(43, 71)(44, 70)(45, 68)(46, 69)(47, 61)(48, 59)(49, 64)(50, 57)(51, 67)(52, 56)(53, 65)(54, 66)(73, 171)(74, 175)(75, 166)(76, 165)(77, 179)(78, 176)(79, 180)(80, 177)(81, 163)(82, 178)(83, 174)(84, 173)(85, 164)(86, 168)(87, 170)(88, 172)(89, 167)(90, 169)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 160)(128, 156)(129, 155)(130, 146)(131, 150)(132, 152)(133, 154)(134, 149)(135, 151)(136, 153)(137, 157)(138, 148)(139, 147)(140, 161)(141, 158)(142, 162)(143, 159)(144, 145)

MAP           : A4.774
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 131)(56, 127)(57, 141)(58, 144)(59, 128)(60, 138)(61, 129)(62, 130)(63, 139)(64, 137)(65, 140)(66, 142)(67, 143)(68, 136)(69, 133)(70, 132)(71, 135)(72, 134)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 123)(110, 115)(111, 113)(112, 118)(114, 121)(116, 119)(117, 120)(122, 126)(124, 125)(145, 166)(146, 170)(147, 171)(148, 168)(149, 180)(150, 163)(151, 179)(152, 178)(153, 176)(154, 177)(155, 169)(156, 167)(157, 172)(158, 165)(159, 175)(160, 164)(161, 173)(162, 174)

MAP           : A4.775
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 117)(110, 121)(111, 112)(113, 125)(114, 122)(115, 126)(116, 123)(118, 124)(119, 120)(145, 167)(146, 163)(147, 177)(148, 180)(149, 164)(150, 174)(151, 165)(152, 166)(153, 175)(154, 173)(155, 176)(156, 178)(157, 179)(158, 172)(159, 169)(160, 168)(161, 171)(162, 170)

MAP           : A4.776
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 167)(146, 163)(147, 177)(148, 180)(149, 164)(150, 174)(151, 165)(152, 166)(153, 175)(154, 173)(155, 176)(156, 178)(157, 179)(158, 172)(159, 169)(160, 168)(161, 171)(162, 170)

MAP           : A4.777
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 42)(20, 52)(21, 50)(22, 37)(23, 48)(24, 40)(25, 47)(26, 38)(27, 39)(28, 49)(29, 53)(30, 54)(31, 51)(32, 45)(33, 46)(34, 44)(35, 43)(36, 41)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 174)(146, 168)(147, 172)(148, 167)(149, 178)(150, 180)(151, 176)(152, 163)(153, 177)(154, 179)(155, 171)(156, 170)(157, 169)(158, 175)(159, 173)(160, 166)(161, 165)(162, 164)

MAP           : A4.778
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 44)(20, 54)(21, 53)(22, 52)(23, 40)(24, 38)(25, 49)(26, 48)(27, 47)(28, 39)(29, 51)(30, 37)(31, 50)(32, 43)(33, 45)(34, 41)(35, 46)(36, 42)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 164)(146, 167)(147, 169)(148, 170)(149, 163)(150, 178)(151, 177)(152, 180)(153, 179)(154, 176)(155, 172)(156, 168)(157, 171)(158, 173)(159, 165)(160, 174)(161, 175)(162, 166)

MAP           : A4.779
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 168)(146, 178)(147, 176)(148, 163)(149, 174)(150, 166)(151, 173)(152, 164)(153, 165)(154, 175)(155, 179)(156, 180)(157, 177)(158, 171)(159, 172)(160, 170)(161, 169)(162, 167)

MAP           : A4.780
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 54)(20, 40)(21, 49)(22, 48)(23, 44)(24, 41)(25, 45)(26, 42)(27, 46)(28, 43)(29, 39)(30, 38)(31, 47)(32, 51)(33, 53)(34, 37)(35, 50)(36, 52)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 170)(146, 180)(147, 179)(148, 178)(149, 166)(150, 164)(151, 175)(152, 174)(153, 173)(154, 165)(155, 177)(156, 163)(157, 176)(158, 169)(159, 171)(160, 167)(161, 172)(162, 168)

MAP           : A4.781
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 178)(146, 174)(147, 173)(148, 164)(149, 168)(150, 170)(151, 172)(152, 167)(153, 169)(154, 171)(155, 175)(156, 166)(157, 165)(158, 179)(159, 176)(160, 180)(161, 177)(162, 163)

MAP           : A4.782
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 168)(146, 178)(147, 176)(148, 163)(149, 174)(150, 166)(151, 173)(152, 164)(153, 165)(154, 175)(155, 179)(156, 180)(157, 177)(158, 171)(159, 172)(160, 170)(161, 169)(162, 167)

MAP           : A4.783
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 180)(146, 166)(147, 175)(148, 174)(149, 170)(150, 167)(151, 171)(152, 168)(153, 172)(154, 169)(155, 165)(156, 164)(157, 173)(158, 177)(159, 179)(160, 163)(161, 176)(162, 178)

MAP           : A4.784
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 125)(110, 117)(111, 116)(112, 115)(113, 121)(114, 119)(118, 120)(122, 124)(123, 126)(145, 178)(146, 174)(147, 173)(148, 164)(149, 168)(150, 170)(151, 172)(152, 167)(153, 169)(154, 171)(155, 175)(156, 166)(157, 165)(158, 179)(159, 176)(160, 180)(161, 177)(162, 163)

MAP           : A4.785
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 11)(2, 14)(3, 16)(4, 17)(5, 10)(6, 7)(8, 9)(12, 15)(13, 18)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 58)(38, 62)(39, 63)(40, 60)(41, 72)(42, 55)(43, 71)(44, 70)(45, 68)(46, 69)(47, 61)(48, 59)(49, 64)(50, 57)(51, 67)(52, 56)(53, 65)(54, 66)(73, 171)(74, 175)(75, 166)(76, 165)(77, 179)(78, 176)(79, 180)(80, 177)(81, 163)(82, 178)(83, 174)(84, 173)(85, 164)(86, 168)(87, 170)(88, 172)(89, 167)(90, 169)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 156)(128, 150)(129, 154)(130, 149)(131, 160)(132, 162)(133, 158)(134, 145)(135, 159)(136, 161)(137, 153)(138, 152)(139, 151)(140, 157)(141, 155)(142, 148)(143, 147)(144, 146)

MAP           : A4.786
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 13)(2, 17)(3, 18)(4, 15)(5, 9)(6, 10)(7, 8)(11, 16)(12, 14)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 58)(38, 62)(39, 63)(40, 60)(41, 72)(42, 55)(43, 71)(44, 70)(45, 68)(46, 69)(47, 61)(48, 59)(49, 64)(50, 57)(51, 67)(52, 56)(53, 65)(54, 66)(73, 171)(74, 175)(75, 166)(76, 165)(77, 179)(78, 176)(79, 180)(80, 177)(81, 163)(82, 178)(83, 174)(84, 173)(85, 164)(86, 168)(87, 170)(88, 172)(89, 167)(90, 169)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 146)(128, 149)(129, 151)(130, 152)(131, 145)(132, 160)(133, 159)(134, 162)(135, 161)(136, 158)(137, 154)(138, 150)(139, 153)(140, 155)(141, 147)(142, 156)(143, 157)(144, 148)

MAP           : A4.787
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 170)(146, 180)(147, 179)(148, 178)(149, 166)(150, 164)(151, 175)(152, 174)(153, 173)(154, 165)(155, 177)(156, 163)(157, 176)(158, 169)(159, 171)(160, 167)(161, 172)(162, 168)

MAP           : A4.788
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.3^3, x.5 * x.2 * x.3, x.2^3, x.5^3, x.2 * x.4 * x.2 * x.4^-1, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1, x.5 * x.4 * x.5 * x.4^-1, (x.3 * x.4^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(145, 166)(146, 170)(147, 171)(148, 168)(149, 180)(150, 163)(151, 179)(152, 178)(153, 176)(154, 177)(155, 169)(156, 167)(157, 172)(158, 165)(159, 175)(160, 164)(161, 173)(162, 174)

MAP           : A4.789
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 9)(2, 13)(3, 4)(5, 17)(6, 14)(7, 18)(8, 15)(10, 16)(11, 12)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 62)(38, 72)(39, 71)(40, 70)(41, 58)(42, 56)(43, 67)(44, 66)(45, 65)(46, 57)(47, 69)(48, 55)(49, 68)(50, 61)(51, 63)(52, 59)(53, 64)(54, 60)(73, 179)(74, 171)(75, 170)(76, 169)(77, 175)(78, 173)(79, 166)(80, 165)(81, 164)(82, 174)(83, 168)(84, 172)(85, 167)(86, 178)(87, 180)(88, 176)(89, 163)(90, 177)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 146)(128, 149)(129, 151)(130, 152)(131, 145)(132, 160)(133, 159)(134, 162)(135, 161)(136, 158)(137, 154)(138, 150)(139, 153)(140, 155)(141, 147)(142, 156)(143, 157)(144, 148)

MAP           : A4.790
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 17)(2, 9)(3, 8)(4, 7)(5, 13)(6, 11)(10, 12)(14, 16)(15, 18)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 56)(38, 59)(39, 61)(40, 62)(41, 55)(42, 70)(43, 69)(44, 72)(45, 71)(46, 68)(47, 64)(48, 60)(49, 63)(50, 65)(51, 57)(52, 66)(53, 67)(54, 58)(73, 169)(74, 165)(75, 164)(76, 173)(77, 177)(78, 179)(79, 163)(80, 176)(81, 178)(82, 180)(83, 166)(84, 175)(85, 174)(86, 170)(87, 167)(88, 171)(89, 168)(90, 172)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 150)(128, 160)(129, 158)(130, 145)(131, 156)(132, 148)(133, 155)(134, 146)(135, 147)(136, 157)(137, 161)(138, 162)(139, 159)(140, 153)(141, 154)(142, 152)(143, 151)(144, 149)

MAP           : A4.791
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 14)(2, 10)(3, 6)(4, 9)(5, 11)(7, 12)(8, 13)(15, 16)(17, 18)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 56)(38, 59)(39, 61)(40, 62)(41, 55)(42, 70)(43, 69)(44, 72)(45, 71)(46, 68)(47, 64)(48, 60)(49, 63)(50, 65)(51, 57)(52, 66)(53, 67)(54, 58)(73, 169)(74, 165)(75, 164)(76, 173)(77, 177)(78, 179)(79, 163)(80, 176)(81, 178)(82, 180)(83, 166)(84, 175)(85, 174)(86, 170)(87, 167)(88, 171)(89, 168)(90, 172)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 152)(128, 162)(129, 161)(130, 160)(131, 148)(132, 146)(133, 157)(134, 156)(135, 155)(136, 147)(137, 159)(138, 145)(139, 158)(140, 151)(141, 153)(142, 149)(143, 154)(144, 150)

MAP           : A4.792
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 11)(2, 14)(3, 16)(4, 17)(5, 10)(6, 7)(8, 9)(12, 15)(13, 18)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 62)(38, 72)(39, 71)(40, 70)(41, 58)(42, 56)(43, 67)(44, 66)(45, 65)(46, 57)(47, 69)(48, 55)(49, 68)(50, 61)(51, 63)(52, 59)(53, 64)(54, 60)(73, 179)(74, 171)(75, 170)(76, 169)(77, 175)(78, 173)(79, 166)(80, 165)(81, 164)(82, 174)(83, 168)(84, 172)(85, 167)(86, 178)(87, 180)(88, 176)(89, 163)(90, 177)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 150)(128, 160)(129, 158)(130, 145)(131, 156)(132, 148)(133, 155)(134, 146)(135, 147)(136, 157)(137, 161)(138, 162)(139, 159)(140, 153)(141, 154)(142, 152)(143, 151)(144, 149)

MAP           : A4.793
NOTES         : type I, reflexible, isomorphic to A4.720.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 3>
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.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, x.4 * x.1 * x.6 * x.1, x.3 * x.4^-1 * x.5^-1 * x.6^-1 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(25, 49)(26, 50)(27, 51)(28, 52)(29, 53)(30, 54)(31, 37)(32, 38)(33, 39)(34, 40)(35, 41)(36, 42)(55, 136)(56, 129)(57, 138)(58, 137)(59, 133)(60, 140)(61, 142)(62, 135)(63, 144)(64, 143)(65, 139)(66, 128)(67, 130)(68, 141)(69, 132)(70, 131)(71, 127)(72, 134)(73, 74)(75, 89)(76, 87)(77, 90)(78, 85)(79, 81)(80, 88)(82, 84)(83, 86)(109, 111)(110, 118)(112, 114)(113, 116)(115, 126)(117, 124)(119, 123)(120, 125)(121, 122)(145, 173)(146, 168)(147, 176)(148, 169)(149, 172)(150, 171)(151, 179)(152, 174)(153, 164)(154, 175)(155, 178)(156, 177)(157, 167)(158, 180)(159, 170)(160, 163)(161, 166)(162, 165)

MAP           : A4.794
NOTES         : type I, reflexible, isomorphic to A4.720.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 3>
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.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, x.4 * x.1 * x.6 * x.1, x.3 * x.4^-1 * x.5^-1 * x.6^-1 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)(55, 143)(56, 138)(57, 128)(58, 139)(59, 142)(60, 141)(61, 131)(62, 144)(63, 134)(64, 127)(65, 130)(66, 129)(67, 137)(68, 132)(69, 140)(70, 133)(71, 136)(72, 135)(73, 74)(75, 89)(76, 87)(77, 90)(78, 85)(79, 81)(80, 88)(82, 84)(83, 86)(109, 120)(110, 125)(111, 118)(112, 122)(113, 117)(114, 119)(115, 116)(121, 123)(124, 126)(145, 178)(146, 171)(147, 180)(148, 179)(149, 175)(150, 164)(151, 166)(152, 177)(153, 168)(154, 167)(155, 163)(156, 170)(157, 172)(158, 165)(159, 174)(160, 173)(161, 169)(162, 176)

MAP           : A4.795
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 117)(110, 121)(111, 112)(113, 125)(114, 122)(115, 126)(116, 123)(118, 124)(119, 120)(145, 174)(146, 168)(147, 172)(148, 167)(149, 178)(150, 180)(151, 176)(152, 163)(153, 177)(154, 179)(155, 171)(156, 170)(157, 169)(158, 175)(159, 173)(160, 166)(161, 165)(162, 164)

MAP           : A4.796
NOTES         : type I, reflexible, isomorphic to A4.725.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 6)(2, 3)(4, 8)(9, 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.3, u.1^2, u.2^2, u.4^3, u.6^3, u.5 * u.1 * u.3^-1 * u.2, u.3 * u.4^-1 * u.5^-1 * u.6^-1 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.6 * x.5 * x.4, x.5^3, x.2 * x.5 * x.1, x.4^3, x.6^3, x.6 * x.4 * x.5, (x.4 * x.1)^2, (x.6 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 132)(56, 142)(57, 140)(58, 127)(59, 138)(60, 130)(61, 137)(62, 128)(63, 129)(64, 139)(65, 143)(66, 144)(67, 141)(68, 135)(69, 136)(70, 134)(71, 133)(72, 131)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)(109, 122)(110, 118)(111, 114)(112, 117)(113, 119)(115, 120)(116, 121)(123, 124)(125, 126)(145, 180)(146, 166)(147, 175)(148, 174)(149, 170)(150, 167)(151, 171)(152, 168)(153, 172)(154, 169)(155, 165)(156, 164)(157, 173)(158, 177)(159, 179)(160, 163)(161, 176)(162, 178)

MAP           : A4.797
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.2^-1 * x.4^-1, x.3^3, x.5^3, x.5 * x.4^-1 * x.3 * x.2^-1, x.2^2 * x.5 * x.3^-1, (x.5^-1, x.3^-1), x.4^2 * x.2^2, x.1 * x.2^-1 * x.1^-1 * x.4^-1, x.5 * x.4^-1 * x.2 * x.3^-1, x.3 * x.2^-1 * x.4 * 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        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 80)(20, 79)(21, 77)(22, 75)(23, 78)(24, 73)(25, 87)(26, 76)(27, 85)(28, 90)(29, 74)(30, 88)(31, 84)(32, 89)(33, 82)(34, 86)(35, 81)(36, 83)(37, 61)(38, 62)(39, 63)(40, 64)(41, 65)(42, 66)(43, 67)(44, 68)(45, 69)(46, 70)(47, 71)(48, 72)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(109, 168)(110, 173)(111, 166)(112, 170)(113, 165)(114, 167)(115, 164)(116, 163)(117, 179)(118, 177)(119, 180)(120, 175)(121, 171)(122, 178)(123, 169)(124, 174)(125, 176)(126, 172)(127, 155)(128, 150)(129, 158)(130, 151)(131, 154)(132, 153)(133, 161)(134, 156)(135, 146)(136, 157)(137, 160)(138, 159)(139, 149)(140, 162)(141, 152)(142, 145)(143, 148)(144, 147)

MAP           : A4.798
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 15)(2, 7)(3, 5)(4, 10)(6, 13)(8, 11)(9, 12)(14, 18)(16, 17)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 58)(38, 62)(39, 63)(40, 60)(41, 72)(42, 55)(43, 71)(44, 70)(45, 68)(46, 69)(47, 61)(48, 59)(49, 64)(50, 57)(51, 67)(52, 56)(53, 65)(54, 66)(73, 171)(74, 175)(75, 166)(76, 165)(77, 179)(78, 176)(79, 180)(80, 177)(81, 163)(82, 178)(83, 174)(84, 173)(85, 164)(86, 168)(87, 170)(88, 172)(89, 167)(90, 169)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 152)(128, 162)(129, 161)(130, 160)(131, 148)(132, 146)(133, 157)(134, 156)(135, 155)(136, 147)(137, 159)(138, 145)(139, 158)(140, 151)(141, 153)(142, 149)(143, 154)(144, 150)

MAP           : A4.799
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 15)(2, 7)(3, 5)(4, 10)(6, 13)(8, 11)(9, 12)(14, 18)(16, 17)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 62)(38, 72)(39, 71)(40, 70)(41, 58)(42, 56)(43, 67)(44, 66)(45, 65)(46, 57)(47, 69)(48, 55)(49, 68)(50, 61)(51, 63)(52, 59)(53, 64)(54, 60)(73, 179)(74, 171)(75, 170)(76, 169)(77, 175)(78, 173)(79, 166)(80, 165)(81, 164)(82, 174)(83, 168)(84, 172)(85, 167)(86, 178)(87, 180)(88, 176)(89, 163)(90, 177)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 162)(128, 148)(129, 157)(130, 156)(131, 152)(132, 149)(133, 153)(134, 150)(135, 154)(136, 151)(137, 147)(138, 146)(139, 155)(140, 159)(141, 161)(142, 145)(143, 158)(144, 160)

MAP           : A4.800
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 14)(2, 10)(3, 6)(4, 9)(5, 11)(7, 12)(8, 13)(15, 16)(17, 18)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 62)(38, 72)(39, 71)(40, 70)(41, 58)(42, 56)(43, 67)(44, 66)(45, 65)(46, 57)(47, 69)(48, 55)(49, 68)(50, 61)(51, 63)(52, 59)(53, 64)(54, 60)(73, 179)(74, 171)(75, 170)(76, 169)(77, 175)(78, 173)(79, 166)(80, 165)(81, 164)(82, 174)(83, 168)(84, 172)(85, 167)(86, 178)(87, 180)(88, 176)(89, 163)(90, 177)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 160)(128, 156)(129, 155)(130, 146)(131, 150)(132, 152)(133, 154)(134, 149)(135, 151)(136, 153)(137, 157)(138, 148)(139, 147)(140, 161)(141, 158)(142, 162)(143, 159)(144, 145)

MAP           : A4.801
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 7)(2, 3)(4, 11)(5, 15)(6, 17)(8, 14)(9, 16)(10, 18)(12, 13)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 62)(38, 72)(39, 71)(40, 70)(41, 58)(42, 56)(43, 67)(44, 66)(45, 65)(46, 57)(47, 69)(48, 55)(49, 68)(50, 61)(51, 63)(52, 59)(53, 64)(54, 60)(73, 179)(74, 171)(75, 170)(76, 169)(77, 175)(78, 173)(79, 166)(80, 165)(81, 164)(82, 174)(83, 168)(84, 172)(85, 167)(86, 178)(87, 180)(88, 176)(89, 163)(90, 177)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 148)(128, 152)(129, 153)(130, 150)(131, 162)(132, 145)(133, 161)(134, 160)(135, 158)(136, 159)(137, 151)(138, 149)(139, 154)(140, 147)(141, 157)(142, 146)(143, 155)(144, 156)

MAP           : A4.802
NOTES         : type I, reflexible, isomorphic to A4.725.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.5^-1 * x.3^-1, x.5^3, x.3^3, x.1 * x.2^-1 * x.1^-1 * x.4^-1, (x.2 * x.3^-1)^2, (x.4 * x.5^-1)^2, x.3 * x.2^2 * x.3^-1 * x.2^-2, x.4^3 * x.3^-1 * x.2^-1 * x.3^-1, x.4^2 * x.3 * x.4^-1 * x.5^-1 * x.2^-1, x.4 * x.3 * x.2 * x.5^-1 * x.2^-2 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.2^-1)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 78)(20, 83)(21, 76)(22, 80)(23, 75)(24, 77)(25, 74)(26, 73)(27, 89)(28, 87)(29, 90)(30, 85)(31, 81)(32, 88)(33, 79)(34, 84)(35, 86)(36, 82)(37, 67)(38, 68)(39, 69)(40, 70)(41, 71)(42, 72)(43, 55)(44, 56)(45, 57)(46, 58)(47, 59)(48, 60)(49, 61)(50, 62)(51, 63)(52, 64)(53, 65)(54, 66)(109, 170)(110, 169)(111, 167)(112, 165)(113, 168)(114, 163)(115, 177)(116, 166)(117, 175)(118, 180)(119, 164)(120, 178)(121, 174)(122, 179)(123, 172)(124, 176)(125, 171)(126, 173)(127, 151)(128, 152)(129, 153)(130, 154)(131, 155)(132, 156)(133, 157)(134, 158)(135, 159)(136, 160)(137, 161)(138, 162)(139, 145)(140, 146)(141, 147)(142, 148)(143, 149)(144, 150)

MAP           : A4.803
NOTES         : type I, reflexible, isomorphic to A4.720.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.2^-1 * x.4^-1, x.3^3, x.5^3, x.5 * x.4^-1 * x.3 * x.2^-1, x.2^2 * x.5 * x.3^-1, (x.5^-1, x.3^-1), x.4^2 * x.2^2, x.1 * x.2^-1 * x.1^-1 * x.4^-1, x.5 * x.4^-1 * x.2 * x.3^-1, x.3 * x.2^-1 * x.4 * 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        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 101)(12, 102)(13, 103)(14, 104)(15, 105)(16, 106)(17, 107)(18, 108)(19, 78)(20, 83)(21, 76)(22, 80)(23, 75)(24, 77)(25, 74)(26, 73)(27, 89)(28, 87)(29, 90)(30, 85)(31, 81)(32, 88)(33, 79)(34, 84)(35, 86)(36, 82)(37, 67)(38, 68)(39, 69)(40, 70)(41, 71)(42, 72)(43, 55)(44, 56)(45, 57)(46, 58)(47, 59)(48, 60)(49, 61)(50, 62)(51, 63)(52, 64)(53, 65)(54, 66)(109, 170)(110, 169)(111, 167)(112, 165)(113, 168)(114, 163)(115, 177)(116, 166)(117, 175)(118, 180)(119, 164)(120, 178)(121, 174)(122, 179)(123, 172)(124, 176)(125, 171)(126, 173)(127, 160)(128, 153)(129, 162)(130, 161)(131, 157)(132, 146)(133, 148)(134, 159)(135, 150)(136, 149)(137, 145)(138, 152)(139, 154)(140, 147)(141, 156)(142, 155)(143, 151)(144, 158)

MAP           : A4.804
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 17)(2, 9)(3, 8)(4, 7)(5, 13)(6, 11)(10, 12)(14, 16)(15, 18)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 58)(38, 62)(39, 63)(40, 60)(41, 72)(42, 55)(43, 71)(44, 70)(45, 68)(46, 69)(47, 61)(48, 59)(49, 64)(50, 57)(51, 67)(52, 56)(53, 65)(54, 66)(73, 171)(74, 175)(75, 166)(76, 165)(77, 179)(78, 176)(79, 180)(80, 177)(81, 163)(82, 178)(83, 174)(84, 173)(85, 164)(86, 168)(87, 170)(88, 172)(89, 167)(90, 169)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 149)(128, 145)(129, 159)(130, 162)(131, 146)(132, 156)(133, 147)(134, 148)(135, 157)(136, 155)(137, 158)(138, 160)(139, 161)(140, 154)(141, 151)(142, 150)(143, 153)(144, 152)

MAP           : A4.805
NOTES         : type I, reflexible, isomorphic to A4.721.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.1 * x.5 * x.6, x.6^3, x.2 * x.5 * x.4, x.4^3, (x.6^-1, x.4^-1), (x.6 * x.2)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (3, 4, 4, 4, 4)
#DARTS        : 180
R = (1, 19, 37, 55, 73)(2, 20, 38, 56, 74)(3, 21, 39, 57, 75)(4, 22, 40, 58, 76)(5, 23, 41, 59, 77)(6, 24, 42, 60, 78)(7, 25, 43, 61, 79)(8, 26, 44, 62, 80)(9, 27, 45, 63, 81)(10, 28, 46, 64, 82)(11, 29, 47, 65, 83)(12, 30, 48, 66, 84)(13, 31, 49, 67, 85)(14, 32, 50, 68, 86)(15, 33, 51, 69, 87)(16, 34, 52, 70, 88)(17, 35, 53, 71, 89)(18, 36, 54, 72, 90)(91, 109, 127, 145, 163)(92, 110, 128, 146, 164)(93, 111, 129, 147, 165)(94, 112, 130, 148, 166)(95, 113, 131, 149, 167)(96, 114, 132, 150, 168)(97, 115, 133, 151, 169)(98, 116, 134, 152, 170)(99, 117, 135, 153, 171)(100, 118, 136, 154, 172)(101, 119, 137, 155, 173)(102, 120, 138, 156, 174)(103, 121, 139, 157, 175)(104, 122, 140, 158, 176)(105, 123, 141, 159, 177)(106, 124, 142, 160, 178)(107, 125, 143, 161, 179)(108, 126, 144, 162, 180)
L = (1, 7)(2, 3)(4, 11)(5, 15)(6, 17)(8, 14)(9, 16)(10, 18)(12, 13)(19, 109)(20, 110)(21, 111)(22, 112)(23, 113)(24, 114)(25, 115)(26, 116)(27, 117)(28, 118)(29, 119)(30, 120)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 58)(38, 62)(39, 63)(40, 60)(41, 72)(42, 55)(43, 71)(44, 70)(45, 68)(46, 69)(47, 61)(48, 59)(49, 64)(50, 57)(51, 67)(52, 56)(53, 65)(54, 66)(73, 171)(74, 175)(75, 166)(76, 165)(77, 179)(78, 176)(79, 180)(80, 177)(81, 163)(82, 178)(83, 174)(84, 173)(85, 164)(86, 168)(87, 170)(88, 172)(89, 167)(90, 169)(91, 93)(92, 105)(94, 104)(95, 97)(96, 99)(98, 100)(101, 108)(102, 107)(103, 106)(127, 162)(128, 148)(129, 157)(130, 156)(131, 152)(132, 149)(133, 153)(134, 150)(135, 154)(136, 151)(137, 147)(138, 146)(139, 155)(140, 159)(141, 161)(142, 145)(143, 158)(144, 160)

MAP           : A4.806
NOTES         : type II, 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, 3, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5 | u.1, u.2^3, u.5^3, (u.3 * u.4^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.5^-1, (u.4 * u.1^-1)^3 >
CTG (small)   : <12, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.2 * x.4 * x.5, x.3^3, x.2^3, x.5^3, x.3 * x.5 * x.4, x.2 * x.3 * x.4, x.2 * x.5^-1 * x.4 * x.3^-1, (x.5 * x.2^-1)^2, x.2 * x.5^-1 * x.3 * x.4^-1, x.3 * x.5^-1 * x.4 * x.2^-1, x.1 * x.2^-1 * x.3^-1 * x.5^-1, (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 6, 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, 30)(14, 36)(15, 32)(16, 34)(17, 27)(18, 31)(19, 25)(20, 29)(21, 28)(22, 33)(23, 26)(24, 35)(37, 92)(38, 85)(39, 90)(40, 87)(41, 94)(42, 88)(43, 96)(44, 86)(45, 91)(46, 95)(47, 89)(48, 93)(49, 81)(50, 82)(51, 83)(52, 84)(53, 73)(54, 74)(55, 75)(56, 76)(57, 77)(58, 78)(59, 79)(60, 80)(97, 119)(98, 111)(99, 117)(100, 109)(101, 120)(102, 113)(103, 118)(104, 115)(105, 110)(106, 116)(107, 112)(108, 114)

MAP           : A4.807
NOTES         : type II, reflexible, isomorphic to A4.806.
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, 3, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 2, 3, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5 | u.1, u.2^3, u.5^3, (u.3 * u.4^-1)^2, u.1 * u.2^-1 * u.3^-1 * u.5^-1, (u.4 * u.1^-1)^3 >
CTG (small)   : <12, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.2 * x.4 * x.5, x.3^3, x.2^3, x.5^3, x.3 * x.5 * x.4, x.2 * x.3 * x.4, x.2 * x.5^-1 * x.4 * x.3^-1, (x.5 * x.2^-1)^2, x.2 * x.5^-1 * x.3 * x.4^-1, x.3 * x.5^-1 * x.4 * x.2^-1, x.1 * x.2^-1 * x.3^-1 * x.5^-1, (x.4 * x.1^-1)^3 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 4, 6, 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, 28)(14, 33)(15, 26)(16, 35)(17, 30)(18, 36)(19, 32)(20, 34)(21, 27)(22, 31)(23, 25)(24, 29)(37, 86)(38, 92)(39, 88)(40, 90)(41, 95)(42, 87)(43, 93)(44, 85)(45, 96)(46, 89)(47, 94)(48, 91)(49, 77)(50, 78)(51, 79)(52, 80)(53, 81)(54, 82)(55, 83)(56, 84)(57, 73)(58, 74)(59, 75)(60, 76)(97, 115)(98, 119)(99, 113)(100, 117)(101, 116)(102, 109)(103, 114)(104, 111)(105, 118)(106, 112)(107, 120)(108, 110)

MAP           : A4.808
NOTES         : type II, reflexible, isomorphic to A4.806.
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, 3, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 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.1 * u.2^-1 * u.3^-1 * u.5^-1, (u.3 * u.4^-1)^3 >
CTG (small)   : <12, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.4^2, x.4 * x.3 * x.5^-1, x.2^3, x.5^3, x.3^3, x.4 * x.3^-1 * x.2, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 6, 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, 29)(14, 30)(15, 31)(16, 32)(17, 33)(18, 34)(19, 35)(20, 36)(21, 25)(22, 26)(23, 27)(24, 28)(37, 86)(38, 92)(39, 88)(40, 90)(41, 95)(42, 87)(43, 93)(44, 85)(45, 96)(46, 89)(47, 94)(48, 91)(49, 82)(50, 76)(51, 84)(52, 74)(53, 79)(54, 83)(55, 77)(56, 81)(57, 80)(58, 73)(59, 78)(60, 75)(97, 112)(98, 117)(99, 110)(100, 119)(101, 114)(102, 120)(103, 116)(104, 118)(105, 111)(106, 115)(107, 109)(108, 113)

MAP           : A4.809
NOTES         : type II, reflexible, isomorphic to A4.806.
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, 3, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 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.1 * u.2^-1 * u.3^-1 * u.5^-1, (u.3 * u.4^-1)^3 >
CTG (small)   : <12, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1, x.4^2, x.4 * x.3 * x.5^-1, x.2^3, x.5^3, x.3^3, x.4 * x.3^-1 * x.2, (x.4 * x.1^-1)^2, x.1 * x.2^-1 * x.3^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4)
LOCAL TYPE    : (3, 4, 6, 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, 35)(14, 27)(15, 33)(16, 25)(17, 36)(18, 29)(19, 34)(20, 31)(21, 26)(22, 32)(23, 28)(24, 30)(37, 92)(38, 85)(39, 90)(40, 87)(41, 94)(42, 88)(43, 96)(44, 86)(45, 91)(46, 95)(47, 89)(48, 93)(49, 82)(50, 76)(51, 84)(52, 74)(53, 79)(54, 83)(55, 77)(56, 81)(57, 80)(58, 73)(59, 78)(60, 75)(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           : A4.810
NOTES         : type I, non-biCayley, reflexible, isomorphic to Dual({4,5}), representative.
QUOTIENT      : R = Id($) L = (1, 2)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 5, 5 ], faces: [ 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, u.2^5, u.3^5, (u.1 * u.2 * u.1^-1 * u.3)^2 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.2^-1 * x.3^-1)^2, x.2^5, x.3^5, (x.3 * x.2^-1)^3, (x.1 * x.2 * x.1^-1 * x.3)^2, (x.3^2 * x.2^-2)^2 >
SCHREIER VEC. : (x.1)^5
LOCAL TYPE    : (4, 4, 4, 4, 4)
#DARTS        : 120
R = (1, 18, 2, 4, 5)(3, 14, 7, 48, 41)(6, 51, 17, 8, 34)(9, 44, 53, 28, 19)(10, 35, 38, 27, 13)(11, 31, 40, 15, 30)(12, 21, 46, 49, 29)(16, 36, 32, 37, 39)(20, 57, 47, 42, 25)(22, 45, 43, 50, 54)(23, 33, 60, 52, 26)(24, 55, 59, 58, 56)(61, 83, 92, 90, 69)(62, 72, 95, 76, 117)(63, 119, 97, 86, 106)(64, 80, 91, 77, 105)(65, 82, 108, 73, 93)(66, 88, 107, 99, 115)(67, 68, 71, 96, 70)(74, 81, 78, 79, 94)(75, 118, 101, 114, 104)(84, 98, 89, 103, 111)(85, 120, 87, 116, 100)(102, 113, 110, 109, 112)
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, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(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, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)

MAP           : A4.811
NOTES         : type I, reflexible, isomorphic to Dual({4,5}), isomorphic to A4.810.
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)   : <24, 12>
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.4 * x.2, x.4 * x.1 * x.2 * x.3, x.4 * x.3 * x.4^-1 * x.2, x.4^4, (x.3 * x.1)^2, (x.2 * x.1)^3 >
SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1)
LOCAL TYPE    : (4, 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, 98)(2, 100)(3, 97)(4, 99)(5, 103)(6, 101)(7, 104)(8, 102)(9, 112)(10, 111)(11, 110)(12, 109)(13, 118)(14, 120)(15, 117)(16, 119)(17, 107)(18, 105)(19, 108)(20, 106)(21, 116)(22, 115)(23, 114)(24, 113)(25, 42)(26, 44)(27, 41)(28, 43)(29, 39)(30, 37)(31, 40)(32, 38)(33, 48)(34, 47)(35, 46)(36, 45)(49, 69)(50, 70)(51, 71)(52, 72)(53, 57)(54, 58)(55, 59)(56, 60)(61, 65)(62, 66)(63, 67)(64, 68)(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           : A4.812
NOTES         : type I, chiral, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3)
ORBIFOLD      : O(0, {4, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 2, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, (u.2 * u.3^-1)^2, u.3^4, (u.2^-1 * u.1)^2 >
CTG (small)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.2^3, (x.2^-1 * x.1)^2, (x.2 * x.3^-1)^2, x.3^4, x.1 * x.3 * x.1 * x.3^-1 * x.2^-1, x.3 * x.2^-1 * x.3^-1 * x.1 * x.3 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1)
LOCAL TYPE    : (4, 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, 88)(3, 85)(4, 87)(5, 91)(6, 89)(7, 92)(8, 90)(9, 76)(10, 75)(11, 74)(12, 73)(13, 82)(14, 84)(15, 81)(16, 83)(17, 95)(18, 93)(19, 96)(20, 94)(21, 80)(22, 79)(23, 78)(24, 77)(25, 58)(26, 60)(27, 57)(28, 59)(29, 71)(30, 69)(31, 72)(32, 70)(33, 56)(34, 55)(35, 54)(36, 53)(37, 62)(38, 64)(39, 61)(40, 63)(41, 67)(42, 65)(43, 68)(44, 66)(45, 52)(46, 51)(47, 50)(48, 49)(97, 114)(98, 116)(99, 113)(100, 115)(101, 111)(102, 109)(103, 112)(104, 110)(105, 120)(106, 119)(107, 118)(108, 117)

MAP           : A4.813
NOTES         : type II, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 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.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.1 * x.4 * x.5^-1, x.4 * x.2 * x.5^-1, x.5^2 * x.6, x.2 * x.4 * x.5, x.4 * x.1 * x.5, x.1 * x.3^-1 * x.2 * x.6, (x.3 * x.4^-1)^2, x.2 * x.6^-2 * x.1, (x.5 * x.6^-1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6)
LOCAL TYPE    : (4, 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, 6)(3, 11)(4, 5)(7, 10)(8, 9)(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, 98)(26, 97)(27, 100)(28, 99)(29, 103)(30, 105)(31, 101)(32, 107)(33, 102)(34, 108)(35, 104)(36, 106)(37, 90)(38, 96)(39, 89)(40, 95)(41, 94)(42, 92)(43, 88)(44, 87)(45, 86)(46, 85)(47, 93)(48, 91)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 69)(62, 70)(63, 67)(64, 68)(65, 72)(66, 71)

MAP           : A4.814
NOTES         : type II, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 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.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.1 * x.6 * x.4^-1, x.2 * x.4 * x.6, x.5 * x.1 * x.5 * x.2, (x.4 * x.5)^2, x.1 * x.3^-1 * x.2 * x.6, (x.3 * x.4^-1)^2, (x.5 * x.6^-1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6)
LOCAL TYPE    : (4, 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, 6)(3, 11)(4, 5)(7, 10)(8, 9)(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, 100)(26, 99)(27, 98)(28, 97)(29, 105)(30, 103)(31, 102)(32, 108)(33, 101)(34, 107)(35, 106)(36, 104)(37, 86)(38, 85)(39, 88)(40, 87)(41, 91)(42, 93)(43, 89)(44, 95)(45, 90)(46, 96)(47, 92)(48, 94)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 69)(62, 70)(63, 67)(64, 68)(65, 72)(66, 71)

MAP           : A4.815
NOTES         : type II, reflexible, isomorphic to A4.813.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 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.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.1 * x.4 * x.5^-1, x.4 * x.2 * x.5^-1, x.5^2 * x.6, x.2 * x.4 * x.5, x.4 * x.1 * x.5, x.1 * x.3^-1 * x.2 * x.6, (x.3 * x.4^-1)^2, x.2 * x.6^-2 * x.1, (x.5 * x.6^-1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6)
LOCAL TYPE    : (4, 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, 5)(3, 12)(4, 6)(7, 8)(9, 10)(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, 100)(26, 99)(27, 98)(28, 97)(29, 105)(30, 103)(31, 102)(32, 108)(33, 101)(34, 107)(35, 106)(36, 104)(37, 90)(38, 96)(39, 89)(40, 95)(41, 94)(42, 92)(43, 88)(44, 87)(45, 86)(46, 85)(47, 93)(48, 91)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 67)(62, 68)(63, 69)(64, 70)(65, 71)(66, 72)

MAP           : A4.816
NOTES         : type II, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 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.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 >
CTG (small)   : <12, 4>
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.2 * x.6 * x.1, x.5^-2 * x.6^-1, x.2 * x.4 * x.6, x.1 * x.6 * x.4^-1, (x.3 * x.4^-1)^2, (x.4 * x.5^-1)^2, (x.5 * x.6^-1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6)
LOCAL TYPE    : (4, 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, 6)(3, 11)(4, 5)(7, 10)(8, 9)(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, 100)(26, 99)(27, 98)(28, 97)(29, 105)(30, 103)(31, 102)(32, 108)(33, 101)(34, 107)(35, 106)(36, 104)(37, 90)(38, 96)(39, 89)(40, 95)(41, 94)(42, 92)(43, 88)(44, 87)(45, 86)(46, 85)(47, 93)(48, 91)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 69)(62, 70)(63, 67)(64, 68)(65, 72)(66, 71)

MAP           : A4.817
NOTES         : type II, reflexible, isomorphic to A4.814.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 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.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.1 * x.5 * x.6^-1, x.2 * x.5 * x.6, (x.4 * x.5)^2, x.1 * x.3^-1 * x.2 * x.6, x.4 * x.1 * x.4^-1 * x.2, (x.3 * x.4^-1)^2, x.6^-1 * x.4 * x.6^-1 * x.4^-1, x.4 * x.2 * x.4^-1 * x.1 >
SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6)
LOCAL TYPE    : (4, 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, 5)(3, 12)(4, 6)(7, 8)(9, 10)(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, 100)(26, 99)(27, 98)(28, 97)(29, 105)(30, 103)(31, 102)(32, 108)(33, 101)(34, 107)(35, 106)(36, 104)(37, 86)(38, 85)(39, 88)(40, 87)(41, 91)(42, 93)(43, 89)(44, 95)(45, 90)(46, 96)(47, 92)(48, 94)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 67)(62, 68)(63, 69)(64, 70)(65, 71)(66, 72)

MAP           : A4.818
NOTES         : type I, chiral, isomorphic to A4.812.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3)
ORBIFOLD      : O(0, {4, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 2, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, (u.2 * u.3^-1)^2, u.3^4, (u.2^-1 * u.1)^2 >
CTG (small)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.2^3, (x.1 * x.2^-1)^2, (x.2 * x.3^-1)^2, x.3^4, x.1 * x.3^2 * x.2 * x.3, x.1 * x.3 * x.1 * x.2^-1 * x.3^-1 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1)
LOCAL TYPE    : (4, 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, 88)(3, 85)(4, 87)(5, 91)(6, 89)(7, 92)(8, 90)(9, 76)(10, 75)(11, 74)(12, 73)(13, 82)(14, 84)(15, 81)(16, 83)(17, 95)(18, 93)(19, 96)(20, 94)(21, 80)(22, 79)(23, 78)(24, 77)(25, 50)(26, 52)(27, 49)(28, 51)(29, 55)(30, 53)(31, 56)(32, 54)(33, 64)(34, 63)(35, 62)(36, 61)(37, 70)(38, 72)(39, 69)(40, 71)(41, 59)(42, 57)(43, 60)(44, 58)(45, 68)(46, 67)(47, 66)(48, 65)(97, 114)(98, 116)(99, 113)(100, 115)(101, 111)(102, 109)(103, 112)(104, 110)(105, 120)(106, 119)(107, 118)(108, 117)

MAP           : A4.819
NOTES         : type II, reflexible, isomorphic to A4.816.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 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.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.1 * x.5 * x.6^-1, x.2 * x.5 * x.6, (x.4 * x.5)^2, x.1 * x.3^-1 * x.2 * x.6, x.4 * x.1 * x.4^-1 * x.1, x.4 * x.2 * x.4^-1 * x.2, (x.3 * x.4^-1)^2, (x.6, x.4^-1) >
SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6)
LOCAL TYPE    : (4, 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, 5)(3, 12)(4, 6)(7, 8)(9, 10)(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, 99)(26, 100)(27, 97)(28, 98)(29, 102)(30, 101)(31, 105)(32, 106)(33, 103)(34, 104)(35, 108)(36, 107)(37, 86)(38, 85)(39, 88)(40, 87)(41, 91)(42, 93)(43, 89)(44, 95)(45, 90)(46, 96)(47, 92)(48, 94)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 67)(62, 68)(63, 69)(64, 70)(65, 71)(66, 72)

MAP           : A4.820
NOTES         : type I, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5) L = (1, 4)(2, 3)
ORBIFOLD      : O(0, {4, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 2, 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^2, (u.2 * u.3^-1)^2, u.3^4, (u.2^-1 * u.1)^2 >
CTG (small)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3 | x.1^2, x.2^3, (x.2 * x.3^-1)^2, x.3^4, (x.2^-1 * x.1)^2, (x.3^-1 * x.1)^2, x.2 * x.3^-2 * x.2^-1 * x.3^-1 * x.1 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.2^-1, x.1)
LOCAL TYPE    : (4, 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, 88)(3, 85)(4, 87)(5, 91)(6, 89)(7, 92)(8, 90)(9, 76)(10, 75)(11, 74)(12, 73)(13, 82)(14, 84)(15, 81)(16, 83)(17, 95)(18, 93)(19, 96)(20, 94)(21, 80)(22, 79)(23, 78)(24, 77)(25, 67)(26, 65)(27, 68)(28, 66)(29, 62)(30, 64)(31, 61)(32, 63)(33, 58)(34, 60)(35, 57)(36, 59)(37, 52)(38, 51)(39, 50)(40, 49)(41, 56)(42, 55)(43, 54)(44, 53)(45, 71)(46, 69)(47, 72)(48, 70)(97, 114)(98, 116)(99, 113)(100, 115)(101, 111)(102, 109)(103, 112)(104, 110)(105, 120)(106, 119)(107, 118)(108, 117)

MAP           : A4.821
NOTES         : type II, reflexible, isomorphic to A4.816.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 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.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 >
CTG (small)   : <12, 4>
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.2 * x.6 * x.1, x.5^-2 * x.6^-1, x.2 * x.4 * x.6, x.1 * x.6 * x.4^-1, (x.3 * x.4^-1)^2, (x.4 * x.5^-1)^2, (x.5 * x.6^-1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6)
LOCAL TYPE    : (4, 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, 5)(3, 12)(4, 6)(7, 8)(9, 10)(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, 98)(26, 97)(27, 100)(28, 99)(29, 103)(30, 105)(31, 101)(32, 107)(33, 102)(34, 108)(35, 104)(36, 106)(37, 90)(38, 96)(39, 89)(40, 95)(41, 94)(42, 92)(43, 88)(44, 87)(45, 86)(46, 85)(47, 93)(48, 91)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 67)(62, 68)(63, 69)(64, 70)(65, 71)(66, 72)

MAP           : A4.822
NOTES         : type I, non-Cayley, reflexible, isomorphic to Dual({4,5}), isomorphic to A4.810.
QUOTIENT      : R = Id($) L = Id($)
ORBIFOLD      : O(0, {5, 4, 2})
EMBEDDING     : vertices: [ 5 ], faces: [ 4 ]
UNIGROUP      : < u.1, u.2 | u.1^2, u.2^5, (u.1 * u.2)^4 >
CTG (small)   : <120, 34>
CTG (fp)      : < x.1, x.2 | x.1^2, x.2^5, (x.1 * x.2)^4, (x.2^-1 * x.1 * x.2^2 * x.1 * x.2^-1)^2, (x.2 * x.1 * x.2^-1 * x.1)^3 >
SCHREIER VEC. : (x.1)^5
LOCAL TYPE    : (4, 4, 4, 4, 4)
#DARTS        : 120
R = (1, 6, 51, 41, 4)(2, 3, 54, 40, 5)(7, 16, 90, 38, 119)(8, 17, 87, 37, 118)(9, 14, 102, 49, 77)(10, 59, 85, 32, 105)(11, 58, 86, 31, 108)(12, 13, 99, 50, 76)(15, 94, 55, 74, 36)(18, 95, 56, 73, 33)(19, 101, 82, 39, 116)(20, 100, 83, 42, 115)(21, 65, 80, 34, 103)(22, 111, 113, 30, 110)(23, 114, 112, 27, 109)(24, 64, 79, 35, 104)(25, 98, 53, 66, 117)(26, 97, 52, 63, 120)(28, 92, 57, 61, 84)(29, 91, 60, 62, 81)(43, 75, 46, 48, 89)(44, 78, 47, 45, 88)(67, 70, 107, 93, 72)(68, 71, 106, 96, 69)
L = (1, 2)(3, 7)(4, 14)(5, 13)(6, 8)(9, 16)(10, 102)(11, 99)(12, 17)(15, 119)(18, 118)(19, 54)(20, 51)(21, 90)(22, 49)(23, 50)(24, 87)(25, 40)(26, 41)(27, 38)(28, 77)(29, 76)(30, 37)(31, 111)(32, 114)(33, 100)(34, 66)(35, 63)(36, 101)(39, 42)(43, 110)(44, 109)(45, 115)(46, 98)(47, 97)(48, 116)(52, 53)(55, 113)(56, 112)(57, 83)(58, 117)(59, 120)(60, 82)(61, 71)(62, 70)(64, 81)(65, 84)(67, 68)(69, 79)(72, 80)(73, 106)(74, 107)(75, 104)(78, 103)(85, 96)(86, 93)(88, 91)(89, 92)(94, 95)(105, 108)

MAP           : A4.823
NOTES         : type I, non-biCayley, reflexible, isomorphic to Dual({4,5}), isomorphic to A4.810.
QUOTIENT      : R = Id($) L = (1, 2)
ORBIFOLD      : O(0, {5, 5, 2})
EMBEDDING     : vertices: [ 5, 5 ], faces: [ 2 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1, u.2^5, u.3^5, (u.1 * u.2 * u.1^-1 * u.3)^2 >
CTG (small)   : <60, 5>
CTG (fp)      : < x.1, x.2, x.3 | x.1, (x.2^-1 * x.3^-1)^2, x.2^5, x.3^5, (x.3 * x.2^-1)^3, (x.1 * x.2 * x.1^-1 * x.3)^2, (x.3^2 * x.2^-2)^2 >
SCHREIER VEC. : (x.1)^5
LOCAL TYPE    : (4, 4, 4, 4, 4)
#DARTS        : 120
R = (1, 4, 18, 5, 2)(3, 48, 14, 41, 7)(6, 8, 51, 34, 17)(9, 28, 44, 19, 53)(10, 27, 35, 13, 38)(11, 15, 31, 30, 40)(12, 49, 21, 29, 46)(16, 37, 36, 39, 32)(20, 42, 57, 25, 47)(22, 50, 45, 54, 43)(23, 52, 33, 26, 60)(24, 58, 55, 56, 59)(61, 92, 69, 83, 90)(62, 95, 117, 72, 76)(63, 97, 106, 119, 86)(64, 91, 105, 80, 77)(65, 108, 93, 82, 73)(66, 107, 115, 88, 99)(67, 71, 70, 68, 96)(74, 78, 94, 81, 79)(75, 101, 104, 118, 114)(84, 89, 111, 98, 103)(85, 87, 100, 120, 116)(102, 110, 112, 113, 109)
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, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(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, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)

MAP           : A4.824
NOTES         : type II, reflexible, isomorphic to A4.814.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 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.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.1 * x.5 * x.6^-1, x.2 * x.5 * x.6, (x.4 * x.5)^2, x.1 * x.3^-1 * x.2 * x.6, x.4 * x.1 * x.4^-1 * x.2, (x.3 * x.4^-1)^2, x.6^-1 * x.4 * x.6^-1 * x.4^-1, x.4 * x.2 * x.4^-1 * x.1 >
SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6)
LOCAL TYPE    : (4, 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, 6)(3, 11)(4, 5)(7, 10)(8, 9)(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, 98)(26, 97)(27, 100)(28, 99)(29, 103)(30, 105)(31, 101)(32, 107)(33, 102)(34, 108)(35, 104)(36, 106)(37, 88)(38, 87)(39, 86)(40, 85)(41, 93)(42, 91)(43, 90)(44, 96)(45, 89)(46, 95)(47, 94)(48, 92)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 69)(62, 70)(63, 67)(64, 68)(65, 72)(66, 71)

MAP           : A4.825
NOTES         : type II, reflexible, isomorphic to A4.813.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 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.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.4^2, x.5 * x.4 * x.6^-1 * x.1, (x.4 * x.5)^2, x.5 * x.1 * x.5 * x.2, (x.3 * x.4)^2, x.6^-1 * x.1 * x.6 * x.2, (x.4 * x.1)^2, x.1 * x.3^-1 * x.2 * x.6 >
SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6)
LOCAL TYPE    : (4, 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, 6)(3, 11)(4, 5)(7, 10)(8, 9)(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, 99)(26, 100)(27, 97)(28, 98)(29, 102)(30, 101)(31, 105)(32, 106)(33, 103)(34, 104)(35, 108)(36, 107)(37, 86)(38, 85)(39, 88)(40, 87)(41, 91)(42, 93)(43, 89)(44, 95)(45, 90)(46, 96)(47, 92)(48, 94)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 69)(62, 70)(63, 67)(64, 68)(65, 72)(66, 71)

MAP           : A4.826
NOTES         : type II, reflexible, isomorphic to A4.813.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 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.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.4^2, x.5 * x.4 * x.6^-1 * x.1, (x.4 * x.5)^2, x.5 * x.1 * x.5 * x.2, (x.3 * x.4)^2, x.6^-1 * x.1 * x.6 * x.2, (x.4 * x.1)^2, x.1 * x.3^-1 * x.2 * x.6 >
SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6)
LOCAL TYPE    : (4, 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, 5)(3, 12)(4, 6)(7, 8)(9, 10)(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, 99)(26, 100)(27, 97)(28, 98)(29, 102)(30, 101)(31, 105)(32, 106)(33, 103)(34, 104)(35, 108)(36, 107)(37, 88)(38, 87)(39, 86)(40, 85)(41, 93)(42, 91)(43, 90)(44, 96)(45, 89)(46, 95)(47, 94)(48, 92)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 67)(62, 68)(63, 69)(64, 70)(65, 71)(66, 72)

MAP           : A4.827
NOTES         : type II, reflexible, isomorphic to A4.816.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 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.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.1 * x.5 * x.6^-1, x.2 * x.5 * x.6, (x.4 * x.5)^2, x.1 * x.3^-1 * x.2 * x.6, x.4 * x.1 * x.4^-1 * x.1, x.4 * x.2 * x.4^-1 * x.2, (x.3 * x.4^-1)^2, (x.6, x.4^-1) >
SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6)
LOCAL TYPE    : (4, 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, 6)(3, 11)(4, 5)(7, 10)(8, 9)(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, 99)(26, 100)(27, 97)(28, 98)(29, 102)(30, 101)(31, 105)(32, 106)(33, 103)(34, 104)(35, 108)(36, 107)(37, 88)(38, 87)(39, 86)(40, 85)(41, 93)(42, 91)(43, 90)(44, 96)(45, 89)(46, 95)(47, 94)(48, 92)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 69)(62, 70)(63, 67)(64, 68)(65, 72)(66, 71)

MAP           : A4.828
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)   : <24, 12>
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.4 * x.3, x.4 * x.1 * x.2 * x.3, (x.4 * x.2)^2, x.4^4, (x.2 * x.1)^3, (x.4^-1 * x.1)^3 >
SCHREIER VEC. : (x.4, x.1, x.2, x.3, x.4^-1)
LOCAL TYPE    : (4, 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, 106)(2, 108)(3, 105)(4, 107)(5, 119)(6, 117)(7, 120)(8, 118)(9, 104)(10, 103)(11, 102)(12, 101)(13, 110)(14, 112)(15, 109)(16, 111)(17, 115)(18, 113)(19, 116)(20, 114)(21, 100)(22, 99)(23, 98)(24, 97)(25, 42)(26, 44)(27, 41)(28, 43)(29, 39)(30, 37)(31, 40)(32, 38)(33, 48)(34, 47)(35, 46)(36, 45)(49, 69)(50, 70)(51, 71)(52, 72)(53, 57)(54, 58)(55, 59)(56, 60)(61, 65)(62, 66)(63, 67)(64, 68)(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           : A4.829
NOTES         : type II, reflexible, isomorphic to A4.814.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 10)(3, 9)(4, 8)(5, 7)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 2, 2, 2, 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.2 * u.6, (u.3 * u.4^-1)^2, (u.4 * u.5^-1)^2, (u.5 * u.6^-1)^2 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.5^2, x.1^2, x.2^2, x.1 * x.6 * x.4^-1, x.2 * x.4 * x.6, x.5 * x.1 * x.5 * x.2, (x.4 * x.5)^2, x.1 * x.3^-1 * x.2 * x.6, (x.3 * x.4^-1)^2, (x.5 * x.6^-1)^2 >
SCHREIER VEC. : (x.1, x.3, x.4, x.5, x.6)
LOCAL TYPE    : (4, 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, 5)(3, 12)(4, 6)(7, 8)(9, 10)(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, 98)(26, 97)(27, 100)(28, 99)(29, 103)(30, 105)(31, 101)(32, 107)(33, 102)(34, 108)(35, 104)(36, 106)(37, 88)(38, 87)(39, 86)(40, 85)(41, 93)(42, 91)(43, 90)(44, 96)(45, 89)(46, 95)(47, 94)(48, 92)(49, 77)(50, 83)(51, 78)(52, 84)(53, 80)(54, 82)(55, 74)(56, 73)(57, 76)(58, 75)(59, 79)(60, 81)(61, 67)(62, 68)(63, 69)(64, 70)(65, 71)(66, 72)

MAP           : A4.830
NOTES         : type II, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9)
ORBIFOLD      : O(0, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3 * u.4^-1 * u.5^-1 * u.2, u.4^5, u.6^5 >
CTG (small)   : <10, 1>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.5^2, x.2^2, x.1^2, x.6 * x.4^-2, x.6^-2 * x.4^-1, x.1 * x.5 * x.6, x.2 * x.1 * x.4^-1, x.1 * x.2 * x.4, x.3 * x.4^-1 * x.5 * x.2, x.4 * x.5 * x.6^-1 * x.1 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (4, 4, 4, 4, 5)
#DARTS        : 100
R = (1, 11, 21, 31, 41)(2, 12, 22, 32, 42)(3, 13, 23, 33, 43)(4, 14, 24, 34, 44)(5, 15, 25, 35, 45)(6, 16, 26, 36, 46)(7, 17, 27, 37, 47)(8, 18, 28, 38, 48)(9, 19, 29, 39, 49)(10, 20, 30, 40, 50)(51, 61, 71, 81, 91)(52, 62, 72, 82, 92)(53, 63, 73, 83, 93)(54, 64, 74, 84, 94)(55, 65, 75, 85, 95)(56, 66, 76, 86, 96)(57, 67, 77, 87, 97)(58, 68, 78, 88, 98)(59, 69, 79, 89, 99)(60, 70, 80, 90, 100)
L = (1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 35)(22, 38)(23, 37)(24, 32)(25, 34)(26, 33)(27, 39)(28, 31)(29, 40)(30, 36)(41, 97)(42, 100)(43, 95)(44, 96)(45, 93)(46, 94)(47, 91)(48, 99)(49, 98)(50, 92)(51, 53)(52, 59)(54, 60)(55, 56)(57, 58)(71, 84)(72, 81)(73, 89)(74, 88)(75, 82)(76, 87)(77, 90)(78, 85)(79, 86)(80, 83)

MAP           : A4.831
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3 * u.4^-1 * u.2 * u.6^-1, u.5^5, u.6^5 >
CTG (small)   : <10, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.5^-1 * x.6^-1, x.2 * x.1, x.4^-1 * x.1 * x.6^-1, x.4 * x.2 * x.5^-1, x.1 * x.6 * x.4, x.4 * x.5^-1 * x.1 * x.3^-1, x.3 * x.4^-1 * x.2 * x.6^-1, x.6^5, x.5^5 >
SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1)
LOCAL TYPE    : (4, 4, 4, 4, 5)
#DARTS        : 100
R = (1, 11, 21, 31, 41)(2, 12, 22, 32, 42)(3, 13, 23, 33, 43)(4, 14, 24, 34, 44)(5, 15, 25, 35, 45)(6, 16, 26, 36, 46)(7, 17, 27, 37, 47)(8, 18, 28, 38, 48)(9, 19, 29, 39, 49)(10, 20, 30, 40, 50)(51, 61, 71, 81, 91)(52, 62, 72, 82, 92)(53, 63, 73, 83, 93)(54, 64, 74, 84, 94)(55, 65, 75, 85, 95)(56, 66, 76, 86, 96)(57, 67, 77, 87, 97)(58, 68, 78, 88, 98)(59, 69, 79, 89, 99)(60, 70, 80, 90, 100)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 60)(12, 58)(13, 59)(14, 57)(15, 54)(16, 53)(17, 56)(18, 55)(19, 51)(20, 52)(21, 37)(22, 33)(23, 35)(24, 40)(25, 31)(26, 38)(27, 32)(28, 39)(29, 34)(30, 36)(41, 44)(42, 46)(43, 48)(45, 49)(47, 50)(61, 64)(62, 66)(63, 68)(65, 69)(67, 70)(71, 85)(72, 87)(73, 82)(74, 89)(75, 83)(76, 90)(77, 81)(78, 86)(79, 88)(80, 84)

MAP           : A4.832
NOTES         : type II, reflexible, isomorphic to A4.830.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9)
ORBIFOLD      : O(0, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3 * u.4^-1 * u.5^-1 * u.2, u.4^5, u.6^5 >
CTG (small)   : <10, 1>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.6 * x.4^-1 * x.6, x.1 * x.6 * x.2, x.2 * x.5 * x.4, x.4^2 * x.6, x.1 * x.2 * x.6^-1, x.1 * x.5 * x.6 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (4, 4, 4, 4, 5)
#DARTS        : 100
R = (1, 11, 21, 31, 41)(2, 12, 22, 32, 42)(3, 13, 23, 33, 43)(4, 14, 24, 34, 44)(5, 15, 25, 35, 45)(6, 16, 26, 36, 46)(7, 17, 27, 37, 47)(8, 18, 28, 38, 48)(9, 19, 29, 39, 49)(10, 20, 30, 40, 50)(51, 61, 71, 81, 91)(52, 62, 72, 82, 92)(53, 63, 73, 83, 93)(54, 64, 74, 84, 94)(55, 65, 75, 85, 95)(56, 66, 76, 86, 96)(57, 67, 77, 87, 97)(58, 68, 78, 88, 98)(59, 69, 79, 89, 99)(60, 70, 80, 90, 100)
L = (1, 10)(2, 3)(4, 7)(5, 9)(6, 8)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 35)(22, 38)(23, 37)(24, 32)(25, 34)(26, 33)(27, 39)(28, 31)(29, 40)(30, 36)(41, 97)(42, 100)(43, 95)(44, 96)(45, 93)(46, 94)(47, 91)(48, 99)(49, 98)(50, 92)(51, 53)(52, 59)(54, 60)(55, 56)(57, 58)(71, 82)(72, 85)(73, 90)(74, 81)(75, 88)(76, 89)(77, 86)(78, 84)(79, 83)(80, 87)

MAP           : A4.833
NOTES         : type II, reflexible, isomorphic to A4.831.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9)
ORBIFOLD      : O(0, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3 * u.4^-1 * u.2 * u.6^-1, u.5^5, u.6^5 >
CTG (small)   : <10, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.5^-1 * x.6^-1, x.2 * x.1, x.4^-1 * x.1 * x.6^-1, x.4 * x.2 * x.5^-1, x.1 * x.6 * x.4, x.4 * x.5^-1 * x.1 * x.3^-1, x.3 * x.4^-1 * x.2 * x.6^-1, x.6^5, x.5^5 >
SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1)
LOCAL TYPE    : (4, 4, 4, 4, 5)
#DARTS        : 100
R = (1, 11, 21, 31, 41)(2, 12, 22, 32, 42)(3, 13, 23, 33, 43)(4, 14, 24, 34, 44)(5, 15, 25, 35, 45)(6, 16, 26, 36, 46)(7, 17, 27, 37, 47)(8, 18, 28, 38, 48)(9, 19, 29, 39, 49)(10, 20, 30, 40, 50)(51, 61, 71, 81, 91)(52, 62, 72, 82, 92)(53, 63, 73, 83, 93)(54, 64, 74, 84, 94)(55, 65, 75, 85, 95)(56, 66, 76, 86, 96)(57, 67, 77, 87, 97)(58, 68, 78, 88, 98)(59, 69, 79, 89, 99)(60, 70, 80, 90, 100)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 56)(12, 59)(13, 54)(14, 52)(15, 60)(16, 55)(17, 58)(18, 51)(19, 57)(20, 53)(21, 32)(22, 35)(23, 31)(24, 36)(25, 37)(26, 39)(27, 33)(28, 34)(29, 40)(30, 38)(41, 44)(42, 46)(43, 48)(45, 49)(47, 50)(61, 64)(62, 66)(63, 68)(65, 69)(67, 70)(71, 83)(72, 81)(73, 87)(74, 88)(75, 82)(76, 84)(77, 85)(78, 90)(79, 86)(80, 89)

MAP           : A4.834
NOTES         : type II, reflexible, isomorphic to A4.830.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9)
ORBIFOLD      : O(0, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3 * u.4^-1 * u.5^-1 * u.2, u.4^5, u.6^5 >
CTG (small)   : <10, 1>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.5^2, x.2^2, x.1^2, x.6 * x.4^-2, x.6^-2 * x.4^-1, x.1 * x.5 * x.6, x.2 * x.1 * x.4^-1, x.1 * x.2 * x.4, x.3 * x.4^-1 * x.5 * x.2, x.4 * x.5 * x.6^-1 * x.1 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (4, 4, 4, 4, 5)
#DARTS        : 100
R = (1, 11, 21, 31, 41)(2, 12, 22, 32, 42)(3, 13, 23, 33, 43)(4, 14, 24, 34, 44)(5, 15, 25, 35, 45)(6, 16, 26, 36, 46)(7, 17, 27, 37, 47)(8, 18, 28, 38, 48)(9, 19, 29, 39, 49)(10, 20, 30, 40, 50)(51, 61, 71, 81, 91)(52, 62, 72, 82, 92)(53, 63, 73, 83, 93)(54, 64, 74, 84, 94)(55, 65, 75, 85, 95)(56, 66, 76, 86, 96)(57, 67, 77, 87, 97)(58, 68, 78, 88, 98)(59, 69, 79, 89, 99)(60, 70, 80, 90, 100)
L = (1, 9)(2, 6)(3, 4)(5, 7)(8, 10)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 32)(22, 35)(23, 40)(24, 31)(25, 38)(26, 39)(27, 36)(28, 34)(29, 33)(30, 37)(41, 100)(42, 93)(43, 92)(44, 97)(45, 99)(46, 98)(47, 94)(48, 96)(49, 95)(50, 91)(51, 53)(52, 59)(54, 60)(55, 56)(57, 58)(71, 85)(72, 88)(73, 87)(74, 82)(75, 84)(76, 83)(77, 89)(78, 81)(79, 90)(80, 86)

MAP           : A4.835
NOTES         : type II, reflexible, isomorphic to A4.831.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9)
ORBIFOLD      : O(0, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3 * u.4^-1 * u.2 * u.6^-1, u.5^5, u.6^5 >
CTG (small)   : <10, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.5^-1 * x.6^-1, x.2 * x.1, x.4^-1 * x.1 * x.6^-1, x.4 * x.2 * x.5^-1, x.1 * x.6 * x.4, x.4 * x.5^-1 * x.1 * x.3^-1, x.3 * x.4^-1 * x.2 * x.6^-1, x.6^5, x.5^5 >
SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1)
LOCAL TYPE    : (4, 4, 4, 4, 5)
#DARTS        : 100
R = (1, 11, 21, 31, 41)(2, 12, 22, 32, 42)(3, 13, 23, 33, 43)(4, 14, 24, 34, 44)(5, 15, 25, 35, 45)(6, 16, 26, 36, 46)(7, 17, 27, 37, 47)(8, 18, 28, 38, 48)(9, 19, 29, 39, 49)(10, 20, 30, 40, 50)(51, 61, 71, 81, 91)(52, 62, 72, 82, 92)(53, 63, 73, 83, 93)(54, 64, 74, 84, 94)(55, 65, 75, 85, 95)(56, 66, 76, 86, 96)(57, 67, 77, 87, 97)(58, 68, 78, 88, 98)(59, 69, 79, 89, 99)(60, 70, 80, 90, 100)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 59)(12, 60)(13, 56)(14, 55)(15, 58)(16, 57)(17, 54)(18, 52)(19, 53)(20, 51)(21, 35)(22, 37)(23, 32)(24, 39)(25, 33)(26, 40)(27, 31)(28, 36)(29, 38)(30, 34)(41, 44)(42, 46)(43, 48)(45, 49)(47, 50)(61, 64)(62, 66)(63, 68)(65, 69)(67, 70)(71, 87)(72, 83)(73, 85)(74, 90)(75, 81)(76, 88)(77, 82)(78, 89)(79, 84)(80, 86)

MAP           : A4.836
NOTES         : type II, reflexible, isomorphic to A4.831.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (1, 10)(2, 6)(3, 4)(8, 9)
ORBIFOLD      : O(0, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3 * u.4^-1 * u.2 * u.6^-1, u.5^5, u.6^5 >
CTG (small)   : <10, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.1^2, x.2^2, x.5^-1 * x.6^-1, x.2 * x.1, x.4^-1 * x.1 * x.6^-1, x.4 * x.2 * x.5^-1, x.1 * x.6 * x.4, x.4 * x.5^-1 * x.1 * x.3^-1, x.3 * x.4^-1 * x.2 * x.6^-1, x.6^5, x.5^5 >
SCHREIER VEC. : (x.3, x.4, x.5, x.5^-1, x.1)
LOCAL TYPE    : (4, 4, 4, 4, 5)
#DARTS        : 100
R = (1, 11, 21, 31, 41)(2, 12, 22, 32, 42)(3, 13, 23, 33, 43)(4, 14, 24, 34, 44)(5, 15, 25, 35, 45)(6, 16, 26, 36, 46)(7, 17, 27, 37, 47)(8, 18, 28, 38, 48)(9, 19, 29, 39, 49)(10, 20, 30, 40, 50)(51, 61, 71, 81, 91)(52, 62, 72, 82, 92)(53, 63, 73, 83, 93)(54, 64, 74, 84, 94)(55, 65, 75, 85, 95)(56, 66, 76, 86, 96)(57, 67, 77, 87, 97)(58, 68, 78, 88, 98)(59, 69, 79, 89, 99)(60, 70, 80, 90, 100)
L = (1, 91)(2, 92)(3, 93)(4, 94)(5, 95)(6, 96)(7, 97)(8, 98)(9, 99)(10, 100)(11, 58)(12, 54)(13, 60)(14, 53)(15, 56)(16, 51)(17, 59)(18, 57)(19, 52)(20, 55)(21, 33)(22, 31)(23, 37)(24, 38)(25, 32)(26, 34)(27, 35)(28, 40)(29, 36)(30, 39)(41, 44)(42, 46)(43, 48)(45, 49)(47, 50)(61, 64)(62, 66)(63, 68)(65, 69)(67, 70)(71, 82)(72, 85)(73, 81)(74, 86)(75, 87)(76, 89)(77, 83)(78, 84)(79, 90)(80, 88)

MAP           : A4.837
NOTES         : type II, reflexible, isomorphic to A4.830.
QUOTIENT      : R = (1, 2, 3, 4, 5)(6, 7, 8, 9, 10) L = (2, 7)(3, 4)(5, 10)(8, 9)
ORBIFOLD      : O(0, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3 * u.4^-1 * u.5^-1 * u.2, u.4^5, u.6^5 >
CTG (small)   : <10, 1>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.6 * x.4^-1 * x.6, x.1 * x.6 * x.2, x.2 * x.5 * x.4, x.4^2 * x.6, x.1 * x.2 * x.6^-1, x.1 * x.5 * x.6 >
SCHREIER VEC. : (x.1, x.3, x.4, x.4^-1, x.5)
LOCAL TYPE    : (4, 4, 4, 4, 5)
#DARTS        : 100
R = (1, 11, 21, 31, 41)(2, 12, 22, 32, 42)(3, 13, 23, 33, 43)(4, 14, 24, 34, 44)(5, 15, 25, 35, 45)(6, 16, 26, 36, 46)(7, 17, 27, 37, 47)(8, 18, 28, 38, 48)(9, 19, 29, 39, 49)(10, 20, 30, 40, 50)(51, 61, 71, 81, 91)(52, 62, 72, 82, 92)(53, 63, 73, 83, 93)(54, 64, 74, 84, 94)(55, 65, 75, 85, 95)(56, 66, 76, 86, 96)(57, 67, 77, 87, 97)(58, 68, 78, 88, 98)(59, 69, 79, 89, 99)(60, 70, 80, 90, 100)
L = (1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 32)(22, 35)(23, 40)(24, 31)(25, 38)(26, 39)(27, 36)(28, 34)(29, 33)(30, 37)(41, 100)(42, 93)(43, 92)(44, 97)(45, 99)(46, 98)(47, 94)(48, 96)(49, 95)(50, 91)(51, 53)(52, 59)(54, 60)(55, 56)(57, 58)(71, 88)(72, 84)(73, 86)(74, 85)(75, 81)(76, 90)(77, 83)(78, 82)(79, 87)(80, 89)

MAP           : A4.838
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)   : <36, 11>
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 * x.1 * x.3^-1 * x.2 * x.3, x.3^6, x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 47)(2, 66)(3, 40)(4, 46)(5, 62)(6, 65)(7, 64)(8, 37)(9, 42)(10, 39)(11, 44)(12, 61)(13, 60)(14, 53)(15, 43)(16, 55)(17, 54)(18, 50)(19, 70)(20, 48)(21, 38)(22, 67)(23, 72)(24, 71)(25, 56)(26, 69)(27, 58)(28, 51)(29, 45)(30, 57)(31, 63)(32, 59)(33, 41)(34, 52)(35, 49)(36, 68)(73, 110)(74, 112)(75, 133)(76, 109)(77, 118)(78, 111)(79, 119)(80, 134)(81, 135)(82, 121)(83, 122)(84, 138)(85, 113)(86, 115)(87, 143)(88, 120)(89, 127)(90, 139)(91, 132)(92, 126)(93, 136)(94, 116)(95, 129)(96, 125)(97, 114)(98, 130)(99, 140)(100, 131)(101, 123)(102, 124)(103, 128)(104, 117)(105, 142)(106, 144)(107, 137)(108, 141)(145, 183)(146, 188)(147, 189)(148, 201)(149, 215)(150, 192)(151, 198)(152, 207)(153, 216)(154, 213)(155, 195)(156, 214)(157, 184)(158, 181)(159, 186)(160, 182)(161, 193)(162, 205)(163, 194)(164, 202)(165, 212)(166, 185)(167, 187)(168, 196)(169, 190)(170, 191)(171, 209)(172, 210)(173, 204)(174, 200)(175, 197)(176, 211)(177, 203)(178, 206)(179, 208)(180, 199)

MAP           : A4.839
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.1^-1 * x.3 * x.1^2, x.1^6, x.3 * x.1 * x.3^-1 * x.1 * 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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 39)(2, 44)(3, 45)(4, 57)(5, 71)(6, 48)(7, 54)(8, 63)(9, 72)(10, 69)(11, 51)(12, 70)(13, 40)(14, 37)(15, 42)(16, 38)(17, 49)(18, 61)(19, 50)(20, 58)(21, 68)(22, 41)(23, 43)(24, 52)(25, 46)(26, 47)(27, 65)(28, 66)(29, 60)(30, 56)(31, 53)(32, 67)(33, 59)(34, 62)(35, 64)(36, 55)(73, 119)(74, 138)(75, 112)(76, 118)(77, 134)(78, 137)(79, 136)(80, 109)(81, 114)(82, 111)(83, 116)(84, 133)(85, 132)(86, 125)(87, 115)(88, 127)(89, 126)(90, 122)(91, 142)(92, 120)(93, 110)(94, 139)(95, 144)(96, 143)(97, 128)(98, 141)(99, 130)(100, 123)(101, 117)(102, 129)(103, 135)(104, 131)(105, 113)(106, 124)(107, 121)(108, 140)(145, 182)(146, 184)(147, 205)(148, 181)(149, 190)(150, 183)(151, 191)(152, 206)(153, 207)(154, 193)(155, 194)(156, 210)(157, 185)(158, 187)(159, 215)(160, 192)(161, 199)(162, 211)(163, 204)(164, 198)(165, 208)(166, 188)(167, 201)(168, 197)(169, 186)(170, 202)(171, 212)(172, 203)(173, 195)(174, 196)(175, 200)(176, 189)(177, 214)(178, 216)(179, 209)(180, 213)

MAP           : A4.840
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.1^-1 * x.3 * x.1^2, x.1^6, x.3 * x.1 * x.3^-1 * x.1 * 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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 50)(2, 52)(3, 37)(4, 49)(5, 58)(6, 51)(7, 59)(8, 38)(9, 39)(10, 61)(11, 62)(12, 42)(13, 53)(14, 55)(15, 47)(16, 60)(17, 67)(18, 43)(19, 72)(20, 66)(21, 40)(22, 56)(23, 69)(24, 65)(25, 54)(26, 70)(27, 44)(28, 71)(29, 63)(30, 64)(31, 68)(32, 57)(33, 46)(34, 48)(35, 41)(36, 45)(73, 110)(74, 112)(75, 133)(76, 109)(77, 118)(78, 111)(79, 119)(80, 134)(81, 135)(82, 121)(83, 122)(84, 138)(85, 113)(86, 115)(87, 143)(88, 120)(89, 127)(90, 139)(91, 132)(92, 126)(93, 136)(94, 116)(95, 129)(96, 125)(97, 114)(98, 130)(99, 140)(100, 131)(101, 123)(102, 124)(103, 128)(104, 117)(105, 142)(106, 144)(107, 137)(108, 141)(145, 201)(146, 183)(147, 192)(148, 188)(149, 184)(150, 190)(151, 181)(152, 185)(153, 211)(154, 215)(155, 198)(156, 182)(157, 213)(158, 195)(159, 204)(160, 200)(161, 196)(162, 202)(163, 193)(164, 197)(165, 187)(166, 191)(167, 210)(168, 194)(169, 189)(170, 207)(171, 216)(172, 212)(173, 208)(174, 214)(175, 205)(176, 209)(177, 199)(178, 203)(179, 186)(180, 206)

MAP           : A4.841
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.1^-1 * x.3 * x.1^2, x.1^6, x.3 * x.1 * x.3^-1 * x.1 * 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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 50)(2, 52)(3, 37)(4, 49)(5, 58)(6, 51)(7, 59)(8, 38)(9, 39)(10, 61)(11, 62)(12, 42)(13, 53)(14, 55)(15, 47)(16, 60)(17, 67)(18, 43)(19, 72)(20, 66)(21, 40)(22, 56)(23, 69)(24, 65)(25, 54)(26, 70)(27, 44)(28, 71)(29, 63)(30, 64)(31, 68)(32, 57)(33, 46)(34, 48)(35, 41)(36, 45)(73, 112)(74, 109)(75, 114)(76, 110)(77, 121)(78, 133)(79, 122)(80, 130)(81, 140)(82, 113)(83, 115)(84, 124)(85, 118)(86, 119)(87, 137)(88, 138)(89, 132)(90, 128)(91, 125)(92, 139)(93, 131)(94, 134)(95, 136)(96, 127)(97, 111)(98, 116)(99, 117)(100, 129)(101, 143)(102, 120)(103, 126)(104, 135)(105, 144)(106, 141)(107, 123)(108, 142)(145, 188)(146, 201)(147, 190)(148, 183)(149, 213)(150, 189)(151, 195)(152, 191)(153, 209)(154, 184)(155, 181)(156, 200)(157, 215)(158, 198)(159, 208)(160, 214)(161, 194)(162, 197)(163, 196)(164, 205)(165, 210)(166, 207)(167, 212)(168, 193)(169, 192)(170, 185)(171, 211)(172, 187)(173, 186)(174, 182)(175, 202)(176, 216)(177, 206)(178, 199)(179, 204)(180, 203)

MAP           : A4.842
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.1^-1 * x.3 * x.1^2, x.1^6, x.3 * x.1 * x.3^-1 * x.1 * 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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 50)(2, 52)(3, 37)(4, 49)(5, 58)(6, 51)(7, 59)(8, 38)(9, 39)(10, 61)(11, 62)(12, 42)(13, 53)(14, 55)(15, 47)(16, 60)(17, 67)(18, 43)(19, 72)(20, 66)(21, 40)(22, 56)(23, 69)(24, 65)(25, 54)(26, 70)(27, 44)(28, 71)(29, 63)(30, 64)(31, 68)(32, 57)(33, 46)(34, 48)(35, 41)(36, 45)(73, 114)(74, 130)(75, 140)(76, 131)(77, 123)(78, 124)(79, 128)(80, 117)(81, 142)(82, 144)(83, 137)(84, 141)(85, 110)(86, 112)(87, 133)(88, 109)(89, 118)(90, 111)(91, 119)(92, 134)(93, 135)(94, 121)(95, 122)(96, 138)(97, 113)(98, 115)(99, 143)(100, 120)(101, 127)(102, 139)(103, 132)(104, 126)(105, 136)(106, 116)(107, 129)(108, 125)(145, 182)(146, 184)(147, 205)(148, 181)(149, 190)(150, 183)(151, 191)(152, 206)(153, 207)(154, 193)(155, 194)(156, 210)(157, 185)(158, 187)(159, 215)(160, 192)(161, 199)(162, 211)(163, 204)(164, 198)(165, 208)(166, 188)(167, 201)(168, 197)(169, 186)(170, 202)(171, 212)(172, 203)(173, 195)(174, 196)(175, 200)(176, 189)(177, 214)(178, 216)(179, 209)(180, 213)

MAP           : A4.843
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.1^-1 * x.3 * x.1^2, x.1^6, x.3 * x.1 * x.3^-1 * x.1 * 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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 50)(2, 52)(3, 37)(4, 49)(5, 58)(6, 51)(7, 59)(8, 38)(9, 39)(10, 61)(11, 62)(12, 42)(13, 53)(14, 55)(15, 47)(16, 60)(17, 67)(18, 43)(19, 72)(20, 66)(21, 40)(22, 56)(23, 69)(24, 65)(25, 54)(26, 70)(27, 44)(28, 71)(29, 63)(30, 64)(31, 68)(32, 57)(33, 46)(34, 48)(35, 41)(36, 45)(73, 124)(74, 121)(75, 126)(76, 122)(77, 133)(78, 109)(79, 134)(80, 142)(81, 116)(82, 125)(83, 127)(84, 136)(85, 130)(86, 131)(87, 113)(88, 114)(89, 144)(90, 140)(91, 137)(92, 115)(93, 143)(94, 110)(95, 112)(96, 139)(97, 123)(98, 128)(99, 129)(100, 141)(101, 119)(102, 132)(103, 138)(104, 111)(105, 120)(106, 117)(107, 135)(108, 118)(145, 192)(146, 185)(147, 211)(148, 187)(149, 186)(150, 182)(151, 202)(152, 216)(153, 206)(154, 199)(155, 204)(156, 203)(157, 188)(158, 201)(159, 190)(160, 183)(161, 213)(162, 189)(163, 195)(164, 191)(165, 209)(166, 184)(167, 181)(168, 200)(169, 215)(170, 198)(171, 208)(172, 214)(173, 194)(174, 197)(175, 196)(176, 205)(177, 210)(178, 207)(179, 212)(180, 193)

MAP           : A4.844
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.1^-1 * x.3 * x.1^2, x.1^6, x.3 * x.1 * x.3^-1 * x.1 * 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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 50)(2, 52)(3, 37)(4, 49)(5, 58)(6, 51)(7, 59)(8, 38)(9, 39)(10, 61)(11, 62)(12, 42)(13, 53)(14, 55)(15, 47)(16, 60)(17, 67)(18, 43)(19, 72)(20, 66)(21, 40)(22, 56)(23, 69)(24, 65)(25, 54)(26, 70)(27, 44)(28, 71)(29, 63)(30, 64)(31, 68)(32, 57)(33, 46)(34, 48)(35, 41)(36, 45)(73, 116)(74, 129)(75, 118)(76, 111)(77, 141)(78, 117)(79, 123)(80, 119)(81, 137)(82, 112)(83, 109)(84, 128)(85, 143)(86, 126)(87, 136)(88, 142)(89, 122)(90, 125)(91, 124)(92, 133)(93, 138)(94, 135)(95, 140)(96, 121)(97, 120)(98, 113)(99, 139)(100, 115)(101, 114)(102, 110)(103, 130)(104, 144)(105, 134)(106, 127)(107, 132)(108, 131)(145, 195)(146, 200)(147, 201)(148, 213)(149, 191)(150, 204)(151, 210)(152, 183)(153, 192)(154, 189)(155, 207)(156, 190)(157, 196)(158, 193)(159, 198)(160, 194)(161, 205)(162, 181)(163, 206)(164, 214)(165, 188)(166, 197)(167, 199)(168, 208)(169, 202)(170, 203)(171, 185)(172, 186)(173, 216)(174, 212)(175, 209)(176, 187)(177, 215)(178, 182)(179, 184)(180, 211)

MAP           : A4.845
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.1^-1 * x.3 * x.1^2, x.1^6, x.3 * x.1 * x.3^-1 * x.1 * 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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 50)(2, 52)(3, 37)(4, 49)(5, 58)(6, 51)(7, 59)(8, 38)(9, 39)(10, 61)(11, 62)(12, 42)(13, 53)(14, 55)(15, 47)(16, 60)(17, 67)(18, 43)(19, 72)(20, 66)(21, 40)(22, 56)(23, 69)(24, 65)(25, 54)(26, 70)(27, 44)(28, 71)(29, 63)(30, 64)(31, 68)(32, 57)(33, 46)(34, 48)(35, 41)(36, 45)(73, 119)(74, 138)(75, 112)(76, 118)(77, 134)(78, 137)(79, 136)(80, 109)(81, 114)(82, 111)(83, 116)(84, 133)(85, 132)(86, 125)(87, 115)(88, 127)(89, 126)(90, 122)(91, 142)(92, 120)(93, 110)(94, 139)(95, 144)(96, 143)(97, 128)(98, 141)(99, 130)(100, 123)(101, 117)(102, 129)(103, 135)(104, 131)(105, 113)(106, 124)(107, 121)(108, 140)(145, 207)(146, 212)(147, 213)(148, 189)(149, 203)(150, 216)(151, 186)(152, 195)(153, 204)(154, 201)(155, 183)(156, 202)(157, 208)(158, 205)(159, 210)(160, 206)(161, 181)(162, 193)(163, 182)(164, 190)(165, 200)(166, 209)(167, 211)(168, 184)(169, 214)(170, 215)(171, 197)(172, 198)(173, 192)(174, 188)(175, 185)(176, 199)(177, 191)(178, 194)(179, 196)(180, 187)

MAP           : A4.846
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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^-1, x.2^6, (x.1^-1 * x.3^-1 * x.2^-1)^2, x.3 * x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 38)(2, 40)(3, 61)(4, 37)(5, 46)(6, 39)(7, 47)(8, 62)(9, 63)(10, 49)(11, 50)(12, 66)(13, 41)(14, 43)(15, 71)(16, 48)(17, 55)(18, 67)(19, 60)(20, 54)(21, 64)(22, 44)(23, 57)(24, 53)(25, 42)(26, 58)(27, 68)(28, 59)(29, 51)(30, 52)(31, 56)(32, 45)(33, 70)(34, 72)(35, 65)(36, 69)(73, 111)(74, 116)(75, 117)(76, 129)(77, 143)(78, 120)(79, 126)(80, 135)(81, 144)(82, 141)(83, 123)(84, 142)(85, 112)(86, 109)(87, 114)(88, 110)(89, 121)(90, 133)(91, 122)(92, 130)(93, 140)(94, 113)(95, 115)(96, 124)(97, 118)(98, 119)(99, 137)(100, 138)(101, 132)(102, 128)(103, 125)(104, 139)(105, 131)(106, 134)(107, 136)(108, 127)(145, 191)(146, 210)(147, 184)(148, 190)(149, 206)(150, 209)(151, 208)(152, 181)(153, 186)(154, 183)(155, 188)(156, 205)(157, 204)(158, 197)(159, 187)(160, 199)(161, 198)(162, 194)(163, 214)(164, 192)(165, 182)(166, 211)(167, 216)(168, 215)(169, 200)(170, 213)(171, 202)(172, 195)(173, 189)(174, 201)(175, 207)(176, 203)(177, 185)(178, 196)(179, 193)(180, 212)

MAP           : A4.847
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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^-1, x.2^6, (x.1^-1 * x.3^-1 * x.2^-1)^2, x.3 * x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 38)(2, 40)(3, 61)(4, 37)(5, 46)(6, 39)(7, 47)(8, 62)(9, 63)(10, 49)(11, 50)(12, 66)(13, 41)(14, 43)(15, 71)(16, 48)(17, 55)(18, 67)(19, 60)(20, 54)(21, 64)(22, 44)(23, 57)(24, 53)(25, 42)(26, 58)(27, 68)(28, 59)(29, 51)(30, 52)(31, 56)(32, 45)(33, 70)(34, 72)(35, 65)(36, 69)(73, 122)(74, 124)(75, 109)(76, 121)(77, 130)(78, 123)(79, 131)(80, 110)(81, 111)(82, 133)(83, 134)(84, 114)(85, 125)(86, 127)(87, 119)(88, 132)(89, 139)(90, 115)(91, 144)(92, 138)(93, 112)(94, 128)(95, 141)(96, 137)(97, 126)(98, 142)(99, 116)(100, 143)(101, 135)(102, 136)(103, 140)(104, 129)(105, 118)(106, 120)(107, 113)(108, 117)(145, 186)(146, 202)(147, 212)(148, 203)(149, 195)(150, 196)(151, 200)(152, 189)(153, 214)(154, 216)(155, 209)(156, 213)(157, 182)(158, 184)(159, 205)(160, 181)(161, 190)(162, 183)(163, 191)(164, 206)(165, 207)(166, 193)(167, 194)(168, 210)(169, 185)(170, 187)(171, 215)(172, 192)(173, 199)(174, 211)(175, 204)(176, 198)(177, 208)(178, 188)(179, 201)(180, 197)

MAP           : A4.848
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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^-1, x.2^6, (x.1^-1 * x.3^-1 * x.2^-1)^2, x.3 * x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 40)(2, 37)(3, 42)(4, 38)(5, 49)(6, 61)(7, 50)(8, 58)(9, 68)(10, 41)(11, 43)(12, 52)(13, 46)(14, 47)(15, 65)(16, 66)(17, 60)(18, 56)(19, 53)(20, 67)(21, 59)(22, 62)(23, 64)(24, 55)(25, 39)(26, 44)(27, 45)(28, 57)(29, 71)(30, 48)(31, 54)(32, 63)(33, 72)(34, 69)(35, 51)(36, 70)(73, 111)(74, 116)(75, 117)(76, 129)(77, 143)(78, 120)(79, 126)(80, 135)(81, 144)(82, 141)(83, 123)(84, 142)(85, 112)(86, 109)(87, 114)(88, 110)(89, 121)(90, 133)(91, 122)(92, 130)(93, 140)(94, 113)(95, 115)(96, 124)(97, 118)(98, 119)(99, 137)(100, 138)(101, 132)(102, 128)(103, 125)(104, 139)(105, 131)(106, 134)(107, 136)(108, 127)(145, 187)(146, 192)(147, 182)(148, 185)(149, 188)(150, 215)(151, 201)(152, 184)(153, 205)(154, 186)(155, 202)(156, 183)(157, 199)(158, 204)(159, 194)(160, 197)(161, 200)(162, 191)(163, 213)(164, 196)(165, 181)(166, 198)(167, 214)(168, 195)(169, 211)(170, 216)(171, 206)(172, 209)(173, 212)(174, 203)(175, 189)(176, 208)(177, 193)(178, 210)(179, 190)(180, 207)

MAP           : A4.849
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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^-1, x.2^6, (x.1^-1 * x.3^-1 * x.2^-1)^2, x.3 * x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 40)(2, 37)(3, 42)(4, 38)(5, 49)(6, 61)(7, 50)(8, 58)(9, 68)(10, 41)(11, 43)(12, 52)(13, 46)(14, 47)(15, 65)(16, 66)(17, 60)(18, 56)(19, 53)(20, 67)(21, 59)(22, 62)(23, 64)(24, 55)(25, 39)(26, 44)(27, 45)(28, 57)(29, 71)(30, 48)(31, 54)(32, 63)(33, 72)(34, 69)(35, 51)(36, 70)(73, 122)(74, 124)(75, 109)(76, 121)(77, 130)(78, 123)(79, 131)(80, 110)(81, 111)(82, 133)(83, 134)(84, 114)(85, 125)(86, 127)(87, 119)(88, 132)(89, 139)(90, 115)(91, 144)(92, 138)(93, 112)(94, 128)(95, 141)(96, 137)(97, 126)(98, 142)(99, 116)(100, 143)(101, 135)(102, 136)(103, 140)(104, 129)(105, 118)(106, 120)(107, 113)(108, 117)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 181)(158, 182)(159, 183)(160, 184)(161, 185)(162, 186)(163, 187)(164, 188)(165, 189)(166, 190)(167, 191)(168, 192)(169, 193)(170, 194)(171, 195)(172, 196)(173, 197)(174, 198)(175, 199)(176, 200)(177, 201)(178, 202)(179, 203)(180, 204)

MAP           : A4.850
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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^-1, x.2^6, (x.1^-1 * x.3^-1 * x.2^-1)^2, x.3 * x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 42)(2, 58)(3, 68)(4, 59)(5, 51)(6, 52)(7, 56)(8, 45)(9, 70)(10, 72)(11, 65)(12, 69)(13, 38)(14, 40)(15, 61)(16, 37)(17, 46)(18, 39)(19, 47)(20, 62)(21, 63)(22, 49)(23, 50)(24, 66)(25, 41)(26, 43)(27, 71)(28, 48)(29, 55)(30, 67)(31, 60)(32, 54)(33, 64)(34, 44)(35, 57)(36, 53)(73, 111)(74, 116)(75, 117)(76, 129)(77, 143)(78, 120)(79, 126)(80, 135)(81, 144)(82, 141)(83, 123)(84, 142)(85, 112)(86, 109)(87, 114)(88, 110)(89, 121)(90, 133)(91, 122)(92, 130)(93, 140)(94, 113)(95, 115)(96, 124)(97, 118)(98, 119)(99, 137)(100, 138)(101, 132)(102, 128)(103, 125)(104, 139)(105, 131)(106, 134)(107, 136)(108, 127)(145, 203)(146, 186)(147, 196)(148, 202)(149, 182)(150, 185)(151, 184)(152, 193)(153, 198)(154, 195)(155, 200)(156, 181)(157, 216)(158, 209)(159, 199)(160, 211)(161, 210)(162, 206)(163, 190)(164, 204)(165, 194)(166, 187)(167, 192)(168, 191)(169, 212)(170, 189)(171, 214)(172, 207)(173, 201)(174, 213)(175, 183)(176, 215)(177, 197)(178, 208)(179, 205)(180, 188)

MAP           : A4.851
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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^-1, x.2^6, (x.1^-1 * x.3^-1 * x.2^-1)^2, x.3 * x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 42)(2, 58)(3, 68)(4, 59)(5, 51)(6, 52)(7, 56)(8, 45)(9, 70)(10, 72)(11, 65)(12, 69)(13, 38)(14, 40)(15, 61)(16, 37)(17, 46)(18, 39)(19, 47)(20, 62)(21, 63)(22, 49)(23, 50)(24, 66)(25, 41)(26, 43)(27, 71)(28, 48)(29, 55)(30, 67)(31, 60)(32, 54)(33, 64)(34, 44)(35, 57)(36, 53)(73, 122)(74, 124)(75, 109)(76, 121)(77, 130)(78, 123)(79, 131)(80, 110)(81, 111)(82, 133)(83, 134)(84, 114)(85, 125)(86, 127)(87, 119)(88, 132)(89, 139)(90, 115)(91, 144)(92, 138)(93, 112)(94, 128)(95, 141)(96, 137)(97, 126)(98, 142)(99, 116)(100, 143)(101, 135)(102, 136)(103, 140)(104, 129)(105, 118)(106, 120)(107, 113)(108, 117)(145, 198)(146, 214)(147, 188)(148, 215)(149, 207)(150, 208)(151, 212)(152, 201)(153, 190)(154, 192)(155, 185)(156, 189)(157, 194)(158, 196)(159, 181)(160, 193)(161, 202)(162, 195)(163, 203)(164, 182)(165, 183)(166, 205)(167, 206)(168, 186)(169, 197)(170, 199)(171, 191)(172, 204)(173, 211)(174, 187)(175, 216)(176, 210)(177, 184)(178, 200)(179, 213)(180, 209)

MAP           : A4.852
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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^-1, x.2^6, (x.1^-1 * x.3^-1 * x.2^-1)^2, x.3 * x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 52)(2, 49)(3, 54)(4, 50)(5, 61)(6, 37)(7, 62)(8, 70)(9, 44)(10, 53)(11, 55)(12, 64)(13, 58)(14, 59)(15, 41)(16, 42)(17, 72)(18, 68)(19, 65)(20, 43)(21, 71)(22, 38)(23, 40)(24, 67)(25, 51)(26, 56)(27, 57)(28, 69)(29, 47)(30, 60)(31, 66)(32, 39)(33, 48)(34, 45)(35, 63)(36, 46)(73, 111)(74, 116)(75, 117)(76, 129)(77, 143)(78, 120)(79, 126)(80, 135)(81, 144)(82, 141)(83, 123)(84, 142)(85, 112)(86, 109)(87, 114)(88, 110)(89, 121)(90, 133)(91, 122)(92, 130)(93, 140)(94, 113)(95, 115)(96, 124)(97, 118)(98, 119)(99, 137)(100, 138)(101, 132)(102, 128)(103, 125)(104, 139)(105, 131)(106, 134)(107, 136)(108, 127)(145, 184)(146, 181)(147, 186)(148, 182)(149, 193)(150, 205)(151, 194)(152, 202)(153, 212)(154, 185)(155, 187)(156, 196)(157, 190)(158, 191)(159, 209)(160, 210)(161, 204)(162, 200)(163, 197)(164, 211)(165, 203)(166, 206)(167, 208)(168, 199)(169, 183)(170, 188)(171, 189)(172, 201)(173, 215)(174, 192)(175, 198)(176, 207)(177, 216)(178, 213)(179, 195)(180, 214)

MAP           : A4.853
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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^-1, x.2^6, (x.1^-1 * x.3^-1 * x.2^-1)^2, x.3 * x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 52)(2, 49)(3, 54)(4, 50)(5, 61)(6, 37)(7, 62)(8, 70)(9, 44)(10, 53)(11, 55)(12, 64)(13, 58)(14, 59)(15, 41)(16, 42)(17, 72)(18, 68)(19, 65)(20, 43)(21, 71)(22, 38)(23, 40)(24, 67)(25, 51)(26, 56)(27, 57)(28, 69)(29, 47)(30, 60)(31, 66)(32, 39)(33, 48)(34, 45)(35, 63)(36, 46)(73, 122)(74, 124)(75, 109)(76, 121)(77, 130)(78, 123)(79, 131)(80, 110)(81, 111)(82, 133)(83, 134)(84, 114)(85, 125)(86, 127)(87, 119)(88, 132)(89, 139)(90, 115)(91, 144)(92, 138)(93, 112)(94, 128)(95, 141)(96, 137)(97, 126)(98, 142)(99, 116)(100, 143)(101, 135)(102, 136)(103, 140)(104, 129)(105, 118)(106, 120)(107, 113)(108, 117)(145, 212)(146, 189)(147, 214)(148, 207)(149, 201)(150, 213)(151, 183)(152, 215)(153, 197)(154, 208)(155, 205)(156, 188)(157, 203)(158, 186)(159, 196)(160, 202)(161, 182)(162, 185)(163, 184)(164, 193)(165, 198)(166, 195)(167, 200)(168, 181)(169, 216)(170, 209)(171, 199)(172, 211)(173, 210)(174, 206)(175, 190)(176, 204)(177, 194)(178, 187)(179, 192)(180, 191)

MAP           : A4.854
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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^-1, x.2^6, (x.1^-1 * x.3^-1 * x.2^-1)^2, x.3 * x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 44)(2, 57)(3, 46)(4, 39)(5, 69)(6, 45)(7, 51)(8, 47)(9, 65)(10, 40)(11, 37)(12, 56)(13, 71)(14, 54)(15, 64)(16, 70)(17, 50)(18, 53)(19, 52)(20, 61)(21, 66)(22, 63)(23, 68)(24, 49)(25, 48)(26, 41)(27, 67)(28, 43)(29, 42)(30, 38)(31, 58)(32, 72)(33, 62)(34, 55)(35, 60)(36, 59)(73, 111)(74, 116)(75, 117)(76, 129)(77, 143)(78, 120)(79, 126)(80, 135)(81, 144)(82, 141)(83, 123)(84, 142)(85, 112)(86, 109)(87, 114)(88, 110)(89, 121)(90, 133)(91, 122)(92, 130)(93, 140)(94, 113)(95, 115)(96, 124)(97, 118)(98, 119)(99, 137)(100, 138)(101, 132)(102, 128)(103, 125)(104, 139)(105, 131)(106, 134)(107, 136)(108, 127)(145, 197)(146, 199)(147, 191)(148, 204)(149, 211)(150, 187)(151, 216)(152, 210)(153, 184)(154, 200)(155, 213)(156, 209)(157, 198)(158, 214)(159, 188)(160, 215)(161, 207)(162, 208)(163, 212)(164, 201)(165, 190)(166, 192)(167, 185)(168, 189)(169, 194)(170, 196)(171, 181)(172, 193)(173, 202)(174, 195)(175, 203)(176, 182)(177, 183)(178, 205)(179, 206)(180, 186)

MAP           : A4.855
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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^-1, x.2^6, (x.1^-1 * x.3^-1 * x.2^-1)^2, x.3 * x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 44)(2, 57)(3, 46)(4, 39)(5, 69)(6, 45)(7, 51)(8, 47)(9, 65)(10, 40)(11, 37)(12, 56)(13, 71)(14, 54)(15, 64)(16, 70)(17, 50)(18, 53)(19, 52)(20, 61)(21, 66)(22, 63)(23, 68)(24, 49)(25, 48)(26, 41)(27, 67)(28, 43)(29, 42)(30, 38)(31, 58)(32, 72)(33, 62)(34, 55)(35, 60)(36, 59)(73, 122)(74, 124)(75, 109)(76, 121)(77, 130)(78, 123)(79, 131)(80, 110)(81, 111)(82, 133)(83, 134)(84, 114)(85, 125)(86, 127)(87, 119)(88, 132)(89, 139)(90, 115)(91, 144)(92, 138)(93, 112)(94, 128)(95, 141)(96, 137)(97, 126)(98, 142)(99, 116)(100, 143)(101, 135)(102, 136)(103, 140)(104, 129)(105, 118)(106, 120)(107, 113)(108, 117)(145, 184)(146, 181)(147, 186)(148, 182)(149, 193)(150, 205)(151, 194)(152, 202)(153, 212)(154, 185)(155, 187)(156, 196)(157, 190)(158, 191)(159, 209)(160, 210)(161, 204)(162, 200)(163, 197)(164, 211)(165, 203)(166, 206)(167, 208)(168, 199)(169, 183)(170, 188)(171, 189)(172, 201)(173, 215)(174, 192)(175, 198)(176, 207)(177, 216)(178, 213)(179, 195)(180, 214)

MAP           : A4.856
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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^-1, x.2^6, (x.1^-1 * x.3^-1 * x.2^-1)^2, x.3 * x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 47)(2, 66)(3, 40)(4, 46)(5, 62)(6, 65)(7, 64)(8, 37)(9, 42)(10, 39)(11, 44)(12, 61)(13, 60)(14, 53)(15, 43)(16, 55)(17, 54)(18, 50)(19, 70)(20, 48)(21, 38)(22, 67)(23, 72)(24, 71)(25, 56)(26, 69)(27, 58)(28, 51)(29, 45)(30, 57)(31, 63)(32, 59)(33, 41)(34, 52)(35, 49)(36, 68)(73, 111)(74, 116)(75, 117)(76, 129)(77, 143)(78, 120)(79, 126)(80, 135)(81, 144)(82, 141)(83, 123)(84, 142)(85, 112)(86, 109)(87, 114)(88, 110)(89, 121)(90, 133)(91, 122)(92, 130)(93, 140)(94, 113)(95, 115)(96, 124)(97, 118)(98, 119)(99, 137)(100, 138)(101, 132)(102, 128)(103, 125)(104, 139)(105, 131)(106, 134)(107, 136)(108, 127)(145, 198)(146, 214)(147, 188)(148, 215)(149, 207)(150, 208)(151, 212)(152, 201)(153, 190)(154, 192)(155, 185)(156, 189)(157, 194)(158, 196)(159, 181)(160, 193)(161, 202)(162, 195)(163, 203)(164, 182)(165, 183)(166, 205)(167, 206)(168, 186)(169, 197)(170, 199)(171, 191)(172, 204)(173, 211)(174, 187)(175, 216)(176, 210)(177, 184)(178, 200)(179, 213)(180, 209)

MAP           : A4.857
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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^-1, x.2^6, (x.1^-1 * x.3^-1 * x.2^-1)^2, x.3 * x.1 * x.2^-1 * x.1 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 47)(2, 66)(3, 40)(4, 46)(5, 62)(6, 65)(7, 64)(8, 37)(9, 42)(10, 39)(11, 44)(12, 61)(13, 60)(14, 53)(15, 43)(16, 55)(17, 54)(18, 50)(19, 70)(20, 48)(21, 38)(22, 67)(23, 72)(24, 71)(25, 56)(26, 69)(27, 58)(28, 51)(29, 45)(30, 57)(31, 63)(32, 59)(33, 41)(34, 52)(35, 49)(36, 68)(73, 122)(74, 124)(75, 109)(76, 121)(77, 130)(78, 123)(79, 131)(80, 110)(81, 111)(82, 133)(83, 134)(84, 114)(85, 125)(86, 127)(87, 119)(88, 132)(89, 139)(90, 115)(91, 144)(92, 138)(93, 112)(94, 128)(95, 141)(96, 137)(97, 126)(98, 142)(99, 116)(100, 143)(101, 135)(102, 136)(103, 140)(104, 129)(105, 118)(106, 120)(107, 113)(108, 117)(145, 190)(146, 191)(147, 209)(148, 210)(149, 204)(150, 200)(151, 197)(152, 211)(153, 203)(154, 206)(155, 208)(156, 199)(157, 183)(158, 188)(159, 189)(160, 201)(161, 215)(162, 192)(163, 198)(164, 207)(165, 216)(166, 213)(167, 195)(168, 214)(169, 184)(170, 181)(171, 186)(172, 182)(173, 193)(174, 205)(175, 194)(176, 202)(177, 212)(178, 185)(179, 187)(180, 196)

MAP           : A4.858
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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 * x.1 * x.3^-1 * x.2 * x.3, x.3^6, x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 38)(2, 40)(3, 61)(4, 37)(5, 46)(6, 39)(7, 47)(8, 62)(9, 63)(10, 49)(11, 50)(12, 66)(13, 41)(14, 43)(15, 71)(16, 48)(17, 55)(18, 67)(19, 60)(20, 54)(21, 64)(22, 44)(23, 57)(24, 53)(25, 42)(26, 58)(27, 68)(28, 59)(29, 51)(30, 52)(31, 56)(32, 45)(33, 70)(34, 72)(35, 65)(36, 69)(73, 114)(74, 130)(75, 140)(76, 131)(77, 123)(78, 124)(79, 128)(80, 117)(81, 142)(82, 144)(83, 137)(84, 141)(85, 110)(86, 112)(87, 133)(88, 109)(89, 118)(90, 111)(91, 119)(92, 134)(93, 135)(94, 121)(95, 122)(96, 138)(97, 113)(98, 115)(99, 143)(100, 120)(101, 127)(102, 139)(103, 132)(104, 126)(105, 136)(106, 116)(107, 129)(108, 125)(145, 210)(146, 190)(147, 200)(148, 191)(149, 183)(150, 184)(151, 188)(152, 213)(153, 202)(154, 204)(155, 197)(156, 201)(157, 206)(158, 208)(159, 193)(160, 205)(161, 214)(162, 207)(163, 215)(164, 194)(165, 195)(166, 181)(167, 182)(168, 198)(169, 209)(170, 211)(171, 203)(172, 216)(173, 187)(174, 199)(175, 192)(176, 186)(177, 196)(178, 212)(179, 189)(180, 185)

MAP           : A4.859
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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 * x.1 * x.3^-1 * x.2 * x.3, x.3^6, x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 38)(2, 40)(3, 61)(4, 37)(5, 46)(6, 39)(7, 47)(8, 62)(9, 63)(10, 49)(11, 50)(12, 66)(13, 41)(14, 43)(15, 71)(16, 48)(17, 55)(18, 67)(19, 60)(20, 54)(21, 64)(22, 44)(23, 57)(24, 53)(25, 42)(26, 58)(27, 68)(28, 59)(29, 51)(30, 52)(31, 56)(32, 45)(33, 70)(34, 72)(35, 65)(36, 69)(73, 119)(74, 138)(75, 112)(76, 118)(77, 134)(78, 137)(79, 136)(80, 109)(81, 114)(82, 111)(83, 116)(84, 133)(85, 132)(86, 125)(87, 115)(88, 127)(89, 126)(90, 122)(91, 142)(92, 120)(93, 110)(94, 139)(95, 144)(96, 143)(97, 128)(98, 141)(99, 130)(100, 123)(101, 117)(102, 129)(103, 135)(104, 131)(105, 113)(106, 124)(107, 121)(108, 140)(145, 202)(146, 203)(147, 185)(148, 186)(149, 216)(150, 212)(151, 209)(152, 187)(153, 215)(154, 182)(155, 184)(156, 211)(157, 195)(158, 200)(159, 201)(160, 213)(161, 191)(162, 204)(163, 210)(164, 183)(165, 192)(166, 189)(167, 207)(168, 190)(169, 196)(170, 193)(171, 198)(172, 194)(173, 205)(174, 181)(175, 206)(176, 214)(177, 188)(178, 197)(179, 199)(180, 208)

MAP           : A4.860
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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 * x.1 * x.3^-1 * x.2 * x.3, x.3^6, x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 40)(2, 37)(3, 42)(4, 38)(5, 49)(6, 61)(7, 50)(8, 58)(9, 68)(10, 41)(11, 43)(12, 52)(13, 46)(14, 47)(15, 65)(16, 66)(17, 60)(18, 56)(19, 53)(20, 67)(21, 59)(22, 62)(23, 64)(24, 55)(25, 39)(26, 44)(27, 45)(28, 57)(29, 71)(30, 48)(31, 54)(32, 63)(33, 72)(34, 69)(35, 51)(36, 70)(73, 124)(74, 121)(75, 126)(76, 122)(77, 133)(78, 109)(79, 134)(80, 142)(81, 116)(82, 125)(83, 127)(84, 136)(85, 130)(86, 131)(87, 113)(88, 114)(89, 144)(90, 140)(91, 137)(92, 115)(93, 143)(94, 110)(95, 112)(96, 139)(97, 123)(98, 128)(99, 129)(100, 141)(101, 119)(102, 132)(103, 138)(104, 111)(105, 120)(106, 117)(107, 135)(108, 118)(145, 183)(146, 188)(147, 189)(148, 201)(149, 215)(150, 192)(151, 198)(152, 207)(153, 216)(154, 213)(155, 195)(156, 214)(157, 184)(158, 181)(159, 186)(160, 182)(161, 193)(162, 205)(163, 194)(164, 202)(165, 212)(166, 185)(167, 187)(168, 196)(169, 190)(170, 191)(171, 209)(172, 210)(173, 204)(174, 200)(175, 197)(176, 211)(177, 203)(178, 206)(179, 208)(180, 199)

MAP           : A4.861
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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 * x.1 * x.3^-1 * x.2 * x.3, x.3^6, x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 40)(2, 37)(3, 42)(4, 38)(5, 49)(6, 61)(7, 50)(8, 58)(9, 68)(10, 41)(11, 43)(12, 52)(13, 46)(14, 47)(15, 65)(16, 66)(17, 60)(18, 56)(19, 53)(20, 67)(21, 59)(22, 62)(23, 64)(24, 55)(25, 39)(26, 44)(27, 45)(28, 57)(29, 71)(30, 48)(31, 54)(32, 63)(33, 72)(34, 69)(35, 51)(36, 70)(73, 116)(74, 129)(75, 118)(76, 111)(77, 141)(78, 117)(79, 123)(80, 119)(81, 137)(82, 112)(83, 109)(84, 128)(85, 143)(86, 126)(87, 136)(88, 142)(89, 122)(90, 125)(91, 124)(92, 133)(93, 138)(94, 135)(95, 140)(96, 121)(97, 120)(98, 113)(99, 139)(100, 115)(101, 114)(102, 110)(103, 130)(104, 144)(105, 134)(106, 127)(107, 132)(108, 131)(145, 194)(146, 196)(147, 181)(148, 193)(149, 202)(150, 195)(151, 203)(152, 182)(153, 183)(154, 205)(155, 206)(156, 186)(157, 197)(158, 199)(159, 191)(160, 204)(161, 211)(162, 187)(163, 216)(164, 210)(165, 184)(166, 200)(167, 213)(168, 209)(169, 198)(170, 214)(171, 188)(172, 215)(173, 207)(174, 208)(175, 212)(176, 201)(177, 190)(178, 192)(179, 185)(180, 189)

MAP           : A4.862
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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 * x.1 * x.3^-1 * x.2 * x.3, x.3^6, x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 42)(2, 58)(3, 68)(4, 59)(5, 51)(6, 52)(7, 56)(8, 45)(9, 70)(10, 72)(11, 65)(12, 69)(13, 38)(14, 40)(15, 61)(16, 37)(17, 46)(18, 39)(19, 47)(20, 62)(21, 63)(22, 49)(23, 50)(24, 66)(25, 41)(26, 43)(27, 71)(28, 48)(29, 55)(30, 67)(31, 60)(32, 54)(33, 64)(34, 44)(35, 57)(36, 53)(73, 110)(74, 112)(75, 133)(76, 109)(77, 118)(78, 111)(79, 119)(80, 134)(81, 135)(82, 121)(83, 122)(84, 138)(85, 113)(86, 115)(87, 143)(88, 120)(89, 127)(90, 139)(91, 132)(92, 126)(93, 136)(94, 116)(95, 129)(96, 125)(97, 114)(98, 130)(99, 140)(100, 131)(101, 123)(102, 124)(103, 128)(104, 117)(105, 142)(106, 144)(107, 137)(108, 141)(145, 194)(146, 196)(147, 181)(148, 193)(149, 202)(150, 195)(151, 203)(152, 182)(153, 183)(154, 205)(155, 206)(156, 186)(157, 197)(158, 199)(159, 191)(160, 204)(161, 211)(162, 187)(163, 216)(164, 210)(165, 184)(166, 200)(167, 213)(168, 209)(169, 198)(170, 214)(171, 188)(172, 215)(173, 207)(174, 208)(175, 212)(176, 201)(177, 190)(178, 192)(179, 185)(180, 189)

MAP           : A4.863
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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 * x.1 * x.3^-1 * x.2 * x.3, x.3^6, x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 42)(2, 58)(3, 68)(4, 59)(5, 51)(6, 52)(7, 56)(8, 45)(9, 70)(10, 72)(11, 65)(12, 69)(13, 38)(14, 40)(15, 61)(16, 37)(17, 46)(18, 39)(19, 47)(20, 62)(21, 63)(22, 49)(23, 50)(24, 66)(25, 41)(26, 43)(27, 71)(28, 48)(29, 55)(30, 67)(31, 60)(32, 54)(33, 64)(34, 44)(35, 57)(36, 53)(73, 131)(74, 114)(75, 124)(76, 130)(77, 110)(78, 113)(79, 112)(80, 121)(81, 126)(82, 123)(83, 128)(84, 109)(85, 144)(86, 137)(87, 127)(88, 139)(89, 138)(90, 134)(91, 118)(92, 132)(93, 122)(94, 115)(95, 120)(96, 119)(97, 140)(98, 117)(99, 142)(100, 135)(101, 129)(102, 141)(103, 111)(104, 143)(105, 125)(106, 136)(107, 133)(108, 116)(145, 208)(146, 205)(147, 210)(148, 206)(149, 181)(150, 193)(151, 182)(152, 190)(153, 200)(154, 209)(155, 211)(156, 184)(157, 214)(158, 215)(159, 197)(160, 198)(161, 192)(162, 188)(163, 185)(164, 199)(165, 191)(166, 194)(167, 196)(168, 187)(169, 207)(170, 212)(171, 213)(172, 189)(173, 203)(174, 216)(175, 186)(176, 195)(177, 204)(178, 201)(179, 183)(180, 202)

MAP           : A4.864
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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 * x.1 * x.3^-1 * x.2 * x.3, x.3^6, x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 52)(2, 49)(3, 54)(4, 50)(5, 61)(6, 37)(7, 62)(8, 70)(9, 44)(10, 53)(11, 55)(12, 64)(13, 58)(14, 59)(15, 41)(16, 42)(17, 72)(18, 68)(19, 65)(20, 43)(21, 71)(22, 38)(23, 40)(24, 67)(25, 51)(26, 56)(27, 57)(28, 69)(29, 47)(30, 60)(31, 66)(32, 39)(33, 48)(34, 45)(35, 63)(36, 46)(73, 112)(74, 109)(75, 114)(76, 110)(77, 121)(78, 133)(79, 122)(80, 130)(81, 140)(82, 113)(83, 115)(84, 124)(85, 118)(86, 119)(87, 137)(88, 138)(89, 132)(90, 128)(91, 125)(92, 139)(93, 131)(94, 134)(95, 136)(96, 127)(97, 111)(98, 116)(99, 117)(100, 129)(101, 143)(102, 120)(103, 126)(104, 135)(105, 144)(106, 141)(107, 123)(108, 142)(145, 202)(146, 203)(147, 185)(148, 186)(149, 216)(150, 212)(151, 209)(152, 187)(153, 215)(154, 182)(155, 184)(156, 211)(157, 195)(158, 200)(159, 201)(160, 213)(161, 191)(162, 204)(163, 210)(164, 183)(165, 192)(166, 189)(167, 207)(168, 190)(169, 196)(170, 193)(171, 198)(172, 194)(173, 205)(174, 181)(175, 206)(176, 214)(177, 188)(178, 197)(179, 199)(180, 208)

MAP           : A4.865
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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 * x.1 * x.3^-1 * x.2 * x.3, x.3^6, x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 52)(2, 49)(3, 54)(4, 50)(5, 61)(6, 37)(7, 62)(8, 70)(9, 44)(10, 53)(11, 55)(12, 64)(13, 58)(14, 59)(15, 41)(16, 42)(17, 72)(18, 68)(19, 65)(20, 43)(21, 71)(22, 38)(23, 40)(24, 67)(25, 51)(26, 56)(27, 57)(28, 69)(29, 47)(30, 60)(31, 66)(32, 39)(33, 48)(34, 45)(35, 63)(36, 46)(73, 120)(74, 113)(75, 139)(76, 115)(77, 114)(78, 110)(79, 130)(80, 144)(81, 134)(82, 127)(83, 132)(84, 131)(85, 116)(86, 129)(87, 118)(88, 111)(89, 141)(90, 117)(91, 123)(92, 119)(93, 137)(94, 112)(95, 109)(96, 128)(97, 143)(98, 126)(99, 136)(100, 142)(101, 122)(102, 125)(103, 124)(104, 133)(105, 138)(106, 135)(107, 140)(108, 121)(145, 194)(146, 196)(147, 181)(148, 193)(149, 202)(150, 195)(151, 203)(152, 182)(153, 183)(154, 205)(155, 206)(156, 186)(157, 197)(158, 199)(159, 191)(160, 204)(161, 211)(162, 187)(163, 216)(164, 210)(165, 184)(166, 200)(167, 213)(168, 209)(169, 198)(170, 214)(171, 188)(172, 215)(173, 207)(174, 208)(175, 212)(176, 201)(177, 190)(178, 192)(179, 185)(180, 189)

MAP           : A4.866
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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 * x.1 * x.3^-1 * x.2 * x.3, x.3^6, x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 44)(2, 57)(3, 46)(4, 39)(5, 69)(6, 45)(7, 51)(8, 47)(9, 65)(10, 40)(11, 37)(12, 56)(13, 71)(14, 54)(15, 64)(16, 70)(17, 50)(18, 53)(19, 52)(20, 61)(21, 66)(22, 63)(23, 68)(24, 49)(25, 48)(26, 41)(27, 67)(28, 43)(29, 42)(30, 38)(31, 58)(32, 72)(33, 62)(34, 55)(35, 60)(36, 59)(73, 112)(74, 109)(75, 114)(76, 110)(77, 121)(78, 133)(79, 122)(80, 130)(81, 140)(82, 113)(83, 115)(84, 124)(85, 118)(86, 119)(87, 137)(88, 138)(89, 132)(90, 128)(91, 125)(92, 139)(93, 131)(94, 134)(95, 136)(96, 127)(97, 111)(98, 116)(99, 117)(100, 129)(101, 143)(102, 120)(103, 126)(104, 135)(105, 144)(106, 141)(107, 123)(108, 142)(145, 210)(146, 190)(147, 200)(148, 191)(149, 183)(150, 184)(151, 188)(152, 213)(153, 202)(154, 204)(155, 197)(156, 201)(157, 206)(158, 208)(159, 193)(160, 205)(161, 214)(162, 207)(163, 215)(164, 194)(165, 195)(166, 181)(167, 182)(168, 198)(169, 209)(170, 211)(171, 203)(172, 216)(173, 187)(174, 199)(175, 192)(176, 186)(177, 196)(178, 212)(179, 189)(180, 185)

MAP           : A4.867
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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 * x.1 * x.3^-1 * x.2 * x.3, x.3^6, x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 44)(2, 57)(3, 46)(4, 39)(5, 69)(6, 45)(7, 51)(8, 47)(9, 65)(10, 40)(11, 37)(12, 56)(13, 71)(14, 54)(15, 64)(16, 70)(17, 50)(18, 53)(19, 52)(20, 61)(21, 66)(22, 63)(23, 68)(24, 49)(25, 48)(26, 41)(27, 67)(28, 43)(29, 42)(30, 38)(31, 58)(32, 72)(33, 62)(34, 55)(35, 60)(36, 59)(73, 134)(74, 136)(75, 121)(76, 133)(77, 142)(78, 135)(79, 143)(80, 122)(81, 123)(82, 109)(83, 110)(84, 126)(85, 137)(86, 139)(87, 131)(88, 144)(89, 115)(90, 127)(91, 120)(92, 114)(93, 124)(94, 140)(95, 117)(96, 113)(97, 138)(98, 118)(99, 128)(100, 119)(101, 111)(102, 112)(103, 116)(104, 141)(105, 130)(106, 132)(107, 125)(108, 129)(145, 183)(146, 188)(147, 189)(148, 201)(149, 215)(150, 192)(151, 198)(152, 207)(153, 216)(154, 213)(155, 195)(156, 214)(157, 184)(158, 181)(159, 186)(160, 182)(161, 193)(162, 205)(163, 194)(164, 202)(165, 212)(166, 185)(167, 187)(168, 196)(169, 190)(170, 191)(171, 209)(172, 210)(173, 204)(174, 200)(175, 197)(176, 211)(177, 203)(178, 206)(179, 208)(180, 199)

MAP           : A4.868
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.1^-1 * x.3 * x.1^2, x.1^6, x.3 * x.1 * x.3^-1 * x.1 * 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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 39)(2, 44)(3, 45)(4, 57)(5, 71)(6, 48)(7, 54)(8, 63)(9, 72)(10, 69)(11, 51)(12, 70)(13, 40)(14, 37)(15, 42)(16, 38)(17, 49)(18, 61)(19, 50)(20, 58)(21, 68)(22, 41)(23, 43)(24, 52)(25, 46)(26, 47)(27, 65)(28, 66)(29, 60)(30, 56)(31, 53)(32, 67)(33, 59)(34, 62)(35, 64)(36, 55)(73, 114)(74, 130)(75, 140)(76, 131)(77, 123)(78, 124)(79, 128)(80, 117)(81, 142)(82, 144)(83, 137)(84, 141)(85, 110)(86, 112)(87, 133)(88, 109)(89, 118)(90, 111)(91, 119)(92, 134)(93, 135)(94, 121)(95, 122)(96, 138)(97, 113)(98, 115)(99, 143)(100, 120)(101, 127)(102, 139)(103, 132)(104, 126)(105, 136)(106, 116)(107, 129)(108, 125)(145, 204)(146, 197)(147, 187)(148, 199)(149, 198)(150, 194)(151, 214)(152, 192)(153, 182)(154, 211)(155, 216)(156, 215)(157, 200)(158, 213)(159, 202)(160, 195)(161, 189)(162, 201)(163, 207)(164, 203)(165, 185)(166, 196)(167, 193)(168, 212)(169, 191)(170, 210)(171, 184)(172, 190)(173, 206)(174, 209)(175, 208)(176, 181)(177, 186)(178, 183)(179, 188)(180, 205)

MAP           : A4.869
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
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 * x.1 * x.3^-1 * x.2 * x.3, x.3^6, x.2 * x.3 * x.2^-1 * x.3 * x.2^-1 * x.1^-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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 47)(2, 66)(3, 40)(4, 46)(5, 62)(6, 65)(7, 64)(8, 37)(9, 42)(10, 39)(11, 44)(12, 61)(13, 60)(14, 53)(15, 43)(16, 55)(17, 54)(18, 50)(19, 70)(20, 48)(21, 38)(22, 67)(23, 72)(24, 71)(25, 56)(26, 69)(27, 58)(28, 51)(29, 45)(30, 57)(31, 63)(32, 59)(33, 41)(34, 52)(35, 49)(36, 68)(73, 118)(74, 119)(75, 137)(76, 138)(77, 132)(78, 128)(79, 125)(80, 139)(81, 131)(82, 134)(83, 136)(84, 127)(85, 111)(86, 116)(87, 117)(88, 129)(89, 143)(90, 120)(91, 126)(92, 135)(93, 144)(94, 141)(95, 123)(96, 142)(97, 112)(98, 109)(99, 114)(100, 110)(101, 121)(102, 133)(103, 122)(104, 130)(105, 140)(106, 113)(107, 115)(108, 124)(145, 185)(146, 187)(147, 215)(148, 192)(149, 199)(150, 211)(151, 204)(152, 198)(153, 208)(154, 188)(155, 201)(156, 197)(157, 186)(158, 202)(159, 212)(160, 203)(161, 195)(162, 196)(163, 200)(164, 189)(165, 214)(166, 216)(167, 209)(168, 213)(169, 182)(170, 184)(171, 205)(172, 181)(173, 190)(174, 183)(175, 191)(176, 206)(177, 207)(178, 193)(179, 194)(180, 210)

MAP           : A4.870
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.1^-1 * x.3 * x.1^2, x.1^6, x.3 * x.1 * x.3^-1 * x.1 * 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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 39)(2, 44)(3, 45)(4, 57)(5, 71)(6, 48)(7, 54)(8, 63)(9, 72)(10, 69)(11, 51)(12, 70)(13, 40)(14, 37)(15, 42)(16, 38)(17, 49)(18, 61)(19, 50)(20, 58)(21, 68)(22, 41)(23, 43)(24, 52)(25, 46)(26, 47)(27, 65)(28, 66)(29, 60)(30, 56)(31, 53)(32, 67)(33, 59)(34, 62)(35, 64)(36, 55)(73, 110)(74, 112)(75, 133)(76, 109)(77, 118)(78, 111)(79, 119)(80, 134)(81, 135)(82, 121)(83, 122)(84, 138)(85, 113)(86, 115)(87, 143)(88, 120)(89, 127)(90, 139)(91, 132)(92, 126)(93, 136)(94, 116)(95, 129)(96, 125)(97, 114)(98, 130)(99, 140)(100, 131)(101, 123)(102, 124)(103, 128)(104, 117)(105, 142)(106, 144)(107, 137)(108, 141)(145, 193)(146, 194)(147, 195)(148, 196)(149, 197)(150, 198)(151, 199)(152, 200)(153, 201)(154, 202)(155, 203)(156, 204)(157, 205)(158, 206)(159, 207)(160, 208)(161, 209)(162, 210)(163, 211)(164, 212)(165, 213)(166, 214)(167, 215)(168, 216)(169, 181)(170, 182)(171, 183)(172, 184)(173, 185)(174, 186)(175, 187)(176, 188)(177, 189)(178, 190)(179, 191)(180, 192)

MAP           : A4.871
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.1^-1 * x.3 * x.1^2, x.1^6, x.3 * x.1 * x.3^-1 * x.1 * 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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 39)(2, 44)(3, 45)(4, 57)(5, 71)(6, 48)(7, 54)(8, 63)(9, 72)(10, 69)(11, 51)(12, 70)(13, 40)(14, 37)(15, 42)(16, 38)(17, 49)(18, 61)(19, 50)(20, 58)(21, 68)(22, 41)(23, 43)(24, 52)(25, 46)(26, 47)(27, 65)(28, 66)(29, 60)(30, 56)(31, 53)(32, 67)(33, 59)(34, 62)(35, 64)(36, 55)(73, 112)(74, 109)(75, 114)(76, 110)(77, 121)(78, 133)(79, 122)(80, 130)(81, 140)(82, 113)(83, 115)(84, 124)(85, 118)(86, 119)(87, 137)(88, 138)(89, 132)(90, 128)(91, 125)(92, 139)(93, 131)(94, 134)(95, 136)(96, 127)(97, 111)(98, 116)(99, 117)(100, 129)(101, 143)(102, 120)(103, 126)(104, 135)(105, 144)(106, 141)(107, 123)(108, 142)(145, 196)(146, 193)(147, 198)(148, 194)(149, 205)(150, 181)(151, 206)(152, 214)(153, 188)(154, 197)(155, 199)(156, 208)(157, 202)(158, 203)(159, 185)(160, 186)(161, 216)(162, 212)(163, 209)(164, 187)(165, 215)(166, 182)(167, 184)(168, 211)(169, 195)(170, 200)(171, 201)(172, 213)(173, 191)(174, 204)(175, 210)(176, 183)(177, 192)(178, 189)(179, 207)(180, 190)

MAP           : A4.872
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.1^-1 * x.3 * x.1^2, x.1^6, x.3 * x.1 * x.3^-1 * x.1 * 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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 39)(2, 44)(3, 45)(4, 57)(5, 71)(6, 48)(7, 54)(8, 63)(9, 72)(10, 69)(11, 51)(12, 70)(13, 40)(14, 37)(15, 42)(16, 38)(17, 49)(18, 61)(19, 50)(20, 58)(21, 68)(22, 41)(23, 43)(24, 52)(25, 46)(26, 47)(27, 65)(28, 66)(29, 60)(30, 56)(31, 53)(32, 67)(33, 59)(34, 62)(35, 64)(36, 55)(73, 124)(74, 121)(75, 126)(76, 122)(77, 133)(78, 109)(79, 134)(80, 142)(81, 116)(82, 125)(83, 127)(84, 136)(85, 130)(86, 131)(87, 113)(88, 114)(89, 144)(90, 140)(91, 137)(92, 115)(93, 143)(94, 110)(95, 112)(96, 139)(97, 123)(98, 128)(99, 129)(100, 141)(101, 119)(102, 132)(103, 138)(104, 111)(105, 120)(106, 117)(107, 135)(108, 118)(145, 195)(146, 200)(147, 201)(148, 213)(149, 191)(150, 204)(151, 210)(152, 183)(153, 192)(154, 189)(155, 207)(156, 190)(157, 196)(158, 193)(159, 198)(160, 194)(161, 205)(162, 181)(163, 206)(164, 214)(165, 188)(166, 197)(167, 199)(168, 208)(169, 202)(170, 203)(171, 185)(172, 186)(173, 216)(174, 212)(175, 209)(176, 187)(177, 215)(178, 182)(179, 184)(180, 211)

MAP           : A4.873
NOTES         : type I, reflexible, isomorphic to A4.838.
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)   : <36, 11>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.3^3, x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.1^-1 * x.3 * x.1^2, x.1^6, x.3 * x.1 * x.3^-1 * x.1 * 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, 6)
#DARTS        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 39)(2, 44)(3, 45)(4, 57)(5, 71)(6, 48)(7, 54)(8, 63)(9, 72)(10, 69)(11, 51)(12, 70)(13, 40)(14, 37)(15, 42)(16, 38)(17, 49)(18, 61)(19, 50)(20, 58)(21, 68)(22, 41)(23, 43)(24, 52)(25, 46)(26, 47)(27, 65)(28, 66)(29, 60)(30, 56)(31, 53)(32, 67)(33, 59)(34, 62)(35, 64)(36, 55)(73, 116)(74, 129)(75, 118)(76, 111)(77, 141)(78, 117)(79, 123)(80, 119)(81, 137)(82, 112)(83, 109)(84, 128)(85, 143)(86, 126)(87, 136)(88, 142)(89, 122)(90, 125)(91, 124)(92, 133)(93, 138)(94, 135)(95, 140)(96, 121)(97, 120)(98, 113)(99, 139)(100, 115)(101, 114)(102, 110)(103, 130)(104, 144)(105, 134)(106, 127)(107, 132)(108, 131)(145, 206)(146, 208)(147, 193)(148, 205)(149, 214)(150, 207)(151, 215)(152, 194)(153, 195)(154, 181)(155, 182)(156, 198)(157, 209)(158, 211)(159, 203)(160, 216)(161, 187)(162, 199)(163, 192)(164, 186)(165, 196)(166, 212)(167, 189)(168, 185)(169, 210)(170, 190)(171, 200)(172, 191)(173, 183)(174, 184)(175, 188)(176, 213)(177, 202)(178, 204)(179, 197)(180, 201)

MAP           : A4.874
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)   : <36, 10>
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.3^-1)^2, (x.4 * x.2)^2, x.1 * x.4^-1 * x.3 * x.4^2 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 2)(3, 7)(4, 13)(5, 8)(6, 14)(9, 11)(10, 12)(15, 36)(16, 35)(17, 34)(18, 33)(19, 20)(21, 25)(22, 31)(23, 26)(24, 32)(27, 29)(28, 30)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 73)(44, 74)(45, 75)(46, 76)(47, 77)(48, 78)(49, 91)(50, 92)(51, 93)(52, 94)(53, 95)(54, 96)(55, 97)(56, 98)(57, 99)(58, 100)(59, 101)(60, 102)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67, 79)(68, 80)(69, 81)(70, 82)(71, 83)(72, 84)(109, 183)(110, 185)(111, 191)(112, 192)(113, 189)(114, 190)(115, 202)(116, 204)(117, 198)(118, 197)(119, 196)(120, 195)(121, 201)(122, 203)(123, 209)(124, 210)(125, 207)(126, 208)(127, 184)(128, 186)(129, 216)(130, 215)(131, 214)(132, 213)(133, 200)(134, 199)(135, 205)(136, 211)(137, 206)(138, 212)(139, 182)(140, 181)(141, 187)(142, 193)(143, 188)(144, 194)(145, 150)(146, 148)(147, 164)(149, 163)(151, 180)(152, 178)(153, 170)(154, 176)(155, 169)(156, 175)(157, 179)(158, 177)(159, 172)(160, 171)(161, 174)(162, 173)(165, 166)(167, 168)

MAP           : A4.875
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)   : <36, 10>
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.1)^2, (x.2 * x.4^-1)^2, x.1 * x.4^-1 * x.3 * x.4^2 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 10)(2, 12)(3, 6)(4, 5)(7, 14)(8, 13)(9, 19)(11, 20)(15, 31)(16, 25)(17, 32)(18, 26)(21, 35)(22, 36)(23, 33)(24, 34)(27, 30)(28, 29)(37, 96)(38, 94)(39, 74)(40, 92)(41, 73)(42, 91)(43, 90)(44, 88)(45, 80)(46, 86)(47, 79)(48, 85)(49, 89)(50, 87)(51, 82)(52, 81)(53, 84)(54, 83)(55, 95)(56, 93)(57, 76)(58, 75)(59, 78)(60, 77)(61, 101)(62, 99)(63, 106)(64, 105)(65, 108)(66, 107)(67, 102)(68, 100)(69, 104)(70, 98)(71, 103)(72, 97)(109, 184)(110, 186)(111, 216)(112, 215)(113, 214)(114, 213)(115, 200)(116, 199)(117, 205)(118, 211)(119, 206)(120, 212)(121, 182)(122, 181)(123, 187)(124, 193)(125, 188)(126, 194)(127, 183)(128, 185)(129, 191)(130, 192)(131, 189)(132, 190)(133, 202)(134, 204)(135, 198)(136, 197)(137, 196)(138, 195)(139, 201)(140, 203)(141, 209)(142, 210)(143, 207)(144, 208)(145, 146)(147, 151)(148, 157)(149, 152)(150, 158)(153, 155)(154, 156)(159, 180)(160, 179)(161, 178)(162, 177)(163, 164)(165, 169)(166, 175)(167, 170)(168, 176)(171, 173)(172, 174)

MAP           : A4.876
NOTES         : type I, chiral, isomorphic to A4.875.
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)   : <36, 10>
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.1)^2, (x.2 * x.4^-1)^2, x.1 * x.4^-1 * x.3 * x.4^2 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 2)(3, 7)(4, 13)(5, 8)(6, 14)(9, 11)(10, 12)(15, 36)(16, 35)(17, 34)(18, 33)(19, 20)(21, 25)(22, 31)(23, 26)(24, 32)(27, 29)(28, 30)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 73)(44, 74)(45, 75)(46, 76)(47, 77)(48, 78)(49, 91)(50, 92)(51, 93)(52, 94)(53, 95)(54, 96)(55, 97)(56, 98)(57, 99)(58, 100)(59, 101)(60, 102)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67, 79)(68, 80)(69, 81)(70, 82)(71, 83)(72, 84)(109, 183)(110, 185)(111, 191)(112, 192)(113, 189)(114, 190)(115, 202)(116, 204)(117, 198)(118, 197)(119, 196)(120, 195)(121, 201)(122, 203)(123, 209)(124, 210)(125, 207)(126, 208)(127, 184)(128, 186)(129, 216)(130, 215)(131, 214)(132, 213)(133, 200)(134, 199)(135, 205)(136, 211)(137, 206)(138, 212)(139, 182)(140, 181)(141, 187)(142, 193)(143, 188)(144, 194)(145, 171)(146, 173)(147, 161)(148, 162)(149, 159)(150, 160)(151, 178)(152, 180)(153, 156)(154, 155)(157, 177)(158, 179)(163, 172)(164, 174)(165, 168)(166, 167)(169, 176)(170, 175)

MAP           : A4.877
NOTES         : type I, chiral, isomorphic to A4.875.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.4 * x.3^-1 * x.1, x.4^3, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, x.3 * x.1 * x.3^-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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 147)(2, 149)(3, 155)(4, 156)(5, 153)(6, 154)(7, 166)(8, 168)(9, 162)(10, 161)(11, 160)(12, 159)(13, 165)(14, 167)(15, 173)(16, 174)(17, 171)(18, 172)(19, 148)(20, 150)(21, 180)(22, 179)(23, 178)(24, 177)(25, 164)(26, 163)(27, 169)(28, 175)(29, 170)(30, 176)(31, 146)(32, 145)(33, 151)(34, 157)(35, 152)(36, 158)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 97)(50, 98)(51, 99)(52, 100)(53, 101)(54, 102)(55, 85)(56, 86)(57, 87)(58, 88)(59, 89)(60, 90)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 73)(68, 74)(69, 75)(70, 76)(71, 77)(72, 78)(109, 110)(111, 115)(112, 121)(113, 116)(114, 122)(117, 119)(118, 120)(123, 144)(124, 143)(125, 142)(126, 141)(127, 128)(129, 133)(130, 139)(131, 134)(132, 140)(135, 137)(136, 138)(181, 207)(182, 209)(183, 197)(184, 198)(185, 195)(186, 196)(187, 214)(188, 216)(189, 192)(190, 191)(193, 213)(194, 215)(199, 208)(200, 210)(201, 204)(202, 203)(205, 212)(206, 211)

MAP           : A4.878
NOTES         : type I, chiral, isomorphic to A4.874.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.4 * x.3^-1 * x.1, x.4^3, (x.2 * x.4)^2, (x.3^-1 * x.2)^2, x.3^2 * x.1 * x.3^-1 * x.4^-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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 148)(2, 150)(3, 180)(4, 179)(5, 178)(6, 177)(7, 164)(8, 163)(9, 169)(10, 175)(11, 170)(12, 176)(13, 146)(14, 145)(15, 151)(16, 157)(17, 152)(18, 158)(19, 147)(20, 149)(21, 155)(22, 156)(23, 153)(24, 154)(25, 166)(26, 168)(27, 162)(28, 161)(29, 160)(30, 159)(31, 165)(32, 167)(33, 173)(34, 174)(35, 171)(36, 172)(37, 77)(38, 75)(39, 94)(40, 93)(41, 96)(42, 95)(43, 83)(44, 81)(45, 88)(46, 87)(47, 90)(48, 89)(49, 84)(50, 82)(51, 86)(52, 80)(53, 85)(54, 79)(55, 78)(56, 76)(57, 92)(58, 74)(59, 91)(60, 73)(61, 108)(62, 106)(63, 98)(64, 104)(65, 97)(66, 103)(67, 107)(68, 105)(69, 100)(70, 99)(71, 102)(72, 101)(109, 118)(110, 120)(111, 114)(112, 113)(115, 122)(116, 121)(117, 127)(119, 128)(123, 139)(124, 133)(125, 140)(126, 134)(129, 143)(130, 144)(131, 141)(132, 142)(135, 138)(136, 137)(181, 186)(182, 184)(183, 200)(185, 199)(187, 216)(188, 214)(189, 206)(190, 212)(191, 205)(192, 211)(193, 215)(194, 213)(195, 208)(196, 207)(197, 210)(198, 209)(201, 202)(203, 204)

MAP           : A4.879
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)   : <18, 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.4 * x.7, x.3^-1 * x.4^-1 * x.1, x.3^3, x.2 * x.3 * x.7^-1, x.6^3, x.1 * x.6 * x.7^-1, x.6 * x.2 * x.7^-1, (x.6^-1, x.3^-1), x.4 * x.5^-1 * x.7 * x.5, x.3 * x.7 * x.6 * 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        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(37, 78)(38, 83)(39, 76)(40, 80)(41, 75)(42, 77)(43, 74)(44, 73)(45, 89)(46, 87)(47, 90)(48, 85)(49, 81)(50, 88)(51, 79)(52, 84)(53, 86)(54, 82)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)(109, 214)(110, 207)(111, 216)(112, 215)(113, 211)(114, 200)(115, 202)(116, 213)(117, 204)(118, 203)(119, 199)(120, 206)(121, 208)(122, 201)(123, 210)(124, 209)(125, 205)(126, 212)(127, 138)(128, 143)(129, 136)(130, 140)(131, 135)(132, 137)(133, 134)(139, 141)(142, 144)(145, 188)(146, 187)(147, 185)(148, 183)(149, 186)(150, 181)(151, 195)(152, 184)(153, 193)(154, 198)(155, 182)(156, 196)(157, 192)(158, 197)(159, 190)(160, 194)(161, 189)(162, 191)

MAP           : A4.880
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)   : <18, 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.6^3, x.3^3, 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.4^2 * x.1 * x.4^-1 * x.3, x.1 * x.7 * x.3 * x.7^-2, x.3 * x.7^2 * 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        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(13, 25)(14, 26)(15, 27)(16, 28)(17, 29)(18, 30)(37, 81)(38, 88)(39, 79)(40, 84)(41, 86)(42, 82)(43, 78)(44, 83)(45, 76)(46, 80)(47, 75)(48, 77)(49, 74)(50, 73)(51, 89)(52, 87)(53, 90)(54, 85)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)(109, 211)(110, 212)(111, 213)(112, 214)(113, 215)(114, 216)(115, 199)(116, 200)(117, 201)(118, 202)(119, 203)(120, 204)(121, 205)(122, 206)(123, 207)(124, 208)(125, 209)(126, 210)(127, 128)(129, 143)(130, 141)(131, 144)(132, 139)(133, 135)(134, 142)(136, 138)(137, 140)(145, 194)(146, 193)(147, 191)(148, 189)(149, 192)(150, 187)(151, 183)(152, 190)(153, 181)(154, 186)(155, 188)(156, 184)(157, 198)(158, 185)(159, 196)(160, 182)(161, 195)(162, 197)

MAP           : A4.881
NOTES         : type II, reflexible, isomorphic to A4.879.
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)   : <18, 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.4 * x.7, x.3^-1 * x.4^-1 * x.1, x.3^3, x.2 * x.3 * x.7^-1, x.6^3, x.1 * x.6 * x.7^-1, x.6 * x.2 * x.7^-1, (x.6^-1, x.3^-1), x.4 * x.5^-1 * x.7 * x.5, x.3 * x.7 * x.6 * 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        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(13, 25)(14, 26)(15, 27)(16, 28)(17, 29)(18, 30)(37, 81)(38, 88)(39, 79)(40, 84)(41, 86)(42, 82)(43, 78)(44, 83)(45, 76)(46, 80)(47, 75)(48, 77)(49, 74)(50, 73)(51, 89)(52, 87)(53, 90)(54, 85)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)(109, 209)(110, 204)(111, 212)(112, 205)(113, 208)(114, 207)(115, 215)(116, 210)(117, 200)(118, 211)(119, 214)(120, 213)(121, 203)(122, 216)(123, 206)(124, 199)(125, 202)(126, 201)(127, 129)(128, 136)(130, 132)(131, 134)(133, 144)(135, 142)(137, 141)(138, 143)(139, 140)(145, 194)(146, 193)(147, 191)(148, 189)(149, 192)(150, 187)(151, 183)(152, 190)(153, 181)(154, 186)(155, 188)(156, 184)(157, 198)(158, 185)(159, 196)(160, 182)(161, 195)(162, 197)

MAP           : A4.882
NOTES         : type I, chiral, isomorphic to A4.874.
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)   : <36, 10>
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.3^-1)^2, (x.4 * x.2)^2, x.1 * x.4^-1 * x.3 * x.4^2 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 10)(2, 12)(3, 6)(4, 5)(7, 14)(8, 13)(9, 19)(11, 20)(15, 31)(16, 25)(17, 32)(18, 26)(21, 35)(22, 36)(23, 33)(24, 34)(27, 30)(28, 29)(37, 96)(38, 94)(39, 74)(40, 92)(41, 73)(42, 91)(43, 90)(44, 88)(45, 80)(46, 86)(47, 79)(48, 85)(49, 89)(50, 87)(51, 82)(52, 81)(53, 84)(54, 83)(55, 95)(56, 93)(57, 76)(58, 75)(59, 78)(60, 77)(61, 101)(62, 99)(63, 106)(64, 105)(65, 108)(66, 107)(67, 102)(68, 100)(69, 104)(70, 98)(71, 103)(72, 97)(109, 184)(110, 186)(111, 216)(112, 215)(113, 214)(114, 213)(115, 200)(116, 199)(117, 205)(118, 211)(119, 206)(120, 212)(121, 182)(122, 181)(123, 187)(124, 193)(125, 188)(126, 194)(127, 183)(128, 185)(129, 191)(130, 192)(131, 189)(132, 190)(133, 202)(134, 204)(135, 198)(136, 197)(137, 196)(138, 195)(139, 201)(140, 203)(141, 209)(142, 210)(143, 207)(144, 208)(145, 150)(146, 148)(147, 164)(149, 163)(151, 180)(152, 178)(153, 170)(154, 176)(155, 169)(156, 175)(157, 179)(158, 177)(159, 172)(160, 171)(161, 174)(162, 173)(165, 166)(167, 168)

MAP           : A4.883
NOTES         : type I, chiral, isomorphic to A4.874.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.4 * x.3^-1 * x.1, x.4^3, (x.2 * x.4)^2, (x.3^-1 * x.2)^2, x.3^2 * x.1 * x.3^-1 * x.4^-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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 147)(2, 149)(3, 155)(4, 156)(5, 153)(6, 154)(7, 166)(8, 168)(9, 162)(10, 161)(11, 160)(12, 159)(13, 165)(14, 167)(15, 173)(16, 174)(17, 171)(18, 172)(19, 148)(20, 150)(21, 180)(22, 179)(23, 178)(24, 177)(25, 164)(26, 163)(27, 169)(28, 175)(29, 170)(30, 176)(31, 146)(32, 145)(33, 151)(34, 157)(35, 152)(36, 158)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 97)(50, 98)(51, 99)(52, 100)(53, 101)(54, 102)(55, 85)(56, 86)(57, 87)(58, 88)(59, 89)(60, 90)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 73)(68, 74)(69, 75)(70, 76)(71, 77)(72, 78)(109, 110)(111, 115)(112, 121)(113, 116)(114, 122)(117, 119)(118, 120)(123, 144)(124, 143)(125, 142)(126, 141)(127, 128)(129, 133)(130, 139)(131, 134)(132, 140)(135, 137)(136, 138)(181, 186)(182, 184)(183, 200)(185, 199)(187, 216)(188, 214)(189, 206)(190, 212)(191, 205)(192, 211)(193, 215)(194, 213)(195, 208)(196, 207)(197, 210)(198, 209)(201, 202)(203, 204)

MAP           : A4.884
NOTES         : type II, reflexible, isomorphic to A4.880.
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)   : <18, 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.6^3, x.3^3, 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.4^2 * x.1 * x.4^-1 * x.3, x.1 * x.7 * x.3 * x.7^-2, x.3 * x.7^2 * 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        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(37, 78)(38, 83)(39, 76)(40, 80)(41, 75)(42, 77)(43, 74)(44, 73)(45, 89)(46, 87)(47, 90)(48, 85)(49, 81)(50, 88)(51, 79)(52, 84)(53, 86)(54, 82)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)(109, 205)(110, 206)(111, 207)(112, 208)(113, 209)(114, 210)(115, 211)(116, 212)(117, 213)(118, 214)(119, 215)(120, 216)(121, 199)(122, 200)(123, 201)(124, 202)(125, 203)(126, 204)(127, 128)(129, 143)(130, 141)(131, 144)(132, 139)(133, 135)(134, 142)(136, 138)(137, 140)(145, 188)(146, 187)(147, 185)(148, 183)(149, 186)(150, 181)(151, 195)(152, 184)(153, 193)(154, 198)(155, 182)(156, 196)(157, 192)(158, 197)(159, 190)(160, 194)(161, 189)(162, 191)

MAP           : A4.885
NOTES         : type I, chiral, isomorphic to A4.875.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.4 * x.3^-1 * x.1, x.4^3, (x.2 * x.1)^2, (x.3^-1 * x.2)^2, x.3 * x.1 * x.3^-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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 148)(2, 150)(3, 180)(4, 179)(5, 178)(6, 177)(7, 164)(8, 163)(9, 169)(10, 175)(11, 170)(12, 176)(13, 146)(14, 145)(15, 151)(16, 157)(17, 152)(18, 158)(19, 147)(20, 149)(21, 155)(22, 156)(23, 153)(24, 154)(25, 166)(26, 168)(27, 162)(28, 161)(29, 160)(30, 159)(31, 165)(32, 167)(33, 173)(34, 174)(35, 171)(36, 172)(37, 77)(38, 75)(39, 94)(40, 93)(41, 96)(42, 95)(43, 83)(44, 81)(45, 88)(46, 87)(47, 90)(48, 89)(49, 84)(50, 82)(51, 86)(52, 80)(53, 85)(54, 79)(55, 78)(56, 76)(57, 92)(58, 74)(59, 91)(60, 73)(61, 108)(62, 106)(63, 98)(64, 104)(65, 97)(66, 103)(67, 107)(68, 105)(69, 100)(70, 99)(71, 102)(72, 101)(109, 118)(110, 120)(111, 114)(112, 113)(115, 122)(116, 121)(117, 127)(119, 128)(123, 139)(124, 133)(125, 140)(126, 134)(129, 143)(130, 144)(131, 141)(132, 142)(135, 138)(136, 137)(181, 182)(183, 187)(184, 193)(185, 188)(186, 194)(189, 191)(190, 192)(195, 216)(196, 215)(197, 214)(198, 213)(199, 200)(201, 205)(202, 211)(203, 206)(204, 212)(207, 209)(208, 210)

MAP           : A4.886
NOTES         : type I, chiral, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3)
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 * u.4^-1 * u.1, u.4^3, (u.3^-1 * u.2)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.1 * x.4^-1 * x.3, x.4^3, x.4 * x.2 * x.4^-1 * x.2, (x.3^-1 * x.2)^3, (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, 6, 6)
#DARTS        : 108
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)
L = (1, 80)(2, 79)(3, 77)(4, 75)(5, 78)(6, 73)(7, 87)(8, 76)(9, 85)(10, 90)(11, 74)(12, 88)(13, 84)(14, 89)(15, 82)(16, 86)(17, 81)(18, 83)(19, 41)(20, 54)(21, 44)(22, 37)(23, 40)(24, 39)(25, 47)(26, 42)(27, 50)(28, 43)(29, 46)(30, 45)(31, 53)(32, 48)(33, 38)(34, 49)(35, 52)(36, 51)(55, 57)(56, 64)(58, 60)(59, 62)(61, 72)(63, 70)(65, 69)(66, 71)(67, 68)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)

MAP           : A4.887
NOTES         : type I, chiral, isomorphic to A4.886.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6)
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.1 * u.3^-1 * u.4^-1, u.3^3, (u.4 * u.2)^3 >
CTG (small)   : <18, 3>
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 * x.4^-2, x.1 * x.3 * x.4, x.3^3, x.2 * x.3 * x.2 * x.3^-1, (x.2 * x.1)^3, (x.4 * x.2)^3 >
SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 6, 6)
#DARTS        : 108
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)
L = (1, 3)(2, 10)(4, 6)(5, 8)(7, 18)(9, 16)(11, 15)(12, 17)(13, 14)(19, 40)(20, 51)(21, 42)(22, 41)(23, 37)(24, 44)(25, 46)(26, 39)(27, 48)(28, 47)(29, 43)(30, 50)(31, 52)(32, 45)(33, 54)(34, 53)(35, 49)(36, 38)(55, 98)(56, 97)(57, 95)(58, 93)(59, 96)(60, 91)(61, 105)(62, 94)(63, 103)(64, 108)(65, 92)(66, 106)(67, 102)(68, 107)(69, 100)(70, 104)(71, 99)(72, 101)(73, 74)(75, 89)(76, 87)(77, 90)(78, 85)(79, 81)(80, 88)(82, 84)(83, 86)

MAP           : A4.888
NOTES         : type I, chiral, isomorphic to A4.886.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3)
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 * u.4^-1 * u.1, u.4^3, (u.3^-1 * u.2)^3 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.4^-1 * x.1, x.1 * x.4^-1 * x.3, x.4^3, x.4 * x.2 * x.4^-1 * x.2, (x.3^-1 * x.2)^3, (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, 6, 6)
#DARTS        : 108
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)
L = (1, 78)(2, 83)(3, 76)(4, 80)(5, 75)(6, 77)(7, 74)(8, 73)(9, 89)(10, 87)(11, 90)(12, 85)(13, 81)(14, 88)(15, 79)(16, 84)(17, 86)(18, 82)(19, 40)(20, 51)(21, 42)(22, 41)(23, 37)(24, 44)(25, 46)(26, 39)(27, 48)(28, 47)(29, 43)(30, 50)(31, 52)(32, 45)(33, 54)(34, 53)(35, 49)(36, 38)(55, 57)(56, 64)(58, 60)(59, 62)(61, 72)(63, 70)(65, 69)(66, 71)(67, 68)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)

MAP           : A4.889
NOTES         : type I, chiral, isomorphic to A4.886.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6)
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.1 * u.3^-1 * u.4^-1, u.3^3, (u.4 * u.2)^3 >
CTG (small)   : <18, 3>
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 * x.4^-2, x.1 * x.3 * x.4, x.3^3, x.2 * x.3 * x.2 * x.3^-1, (x.2 * x.1)^3, (x.4 * x.2)^3 >
SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 6, 6)
#DARTS        : 108
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)
L = (1, 3)(2, 10)(4, 6)(5, 8)(7, 18)(9, 16)(11, 15)(12, 17)(13, 14)(19, 41)(20, 54)(21, 44)(22, 37)(23, 40)(24, 39)(25, 47)(26, 42)(27, 50)(28, 43)(29, 46)(30, 45)(31, 53)(32, 48)(33, 38)(34, 49)(35, 52)(36, 51)(55, 96)(56, 101)(57, 94)(58, 98)(59, 93)(60, 95)(61, 92)(62, 91)(63, 107)(64, 105)(65, 108)(66, 103)(67, 99)(68, 106)(69, 97)(70, 102)(71, 104)(72, 100)(73, 74)(75, 89)(76, 87)(77, 90)(78, 85)(79, 81)(80, 88)(82, 84)(83, 86)

MAP           : A4.890
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: [ 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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1 * x.3 * x.2, x.1^3, x.3^4, x.2^4, (x.3^-1 * x.2)^2 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 55)(32, 56)(33, 57)(34, 58)(35, 59)(36, 60)(73, 117)(74, 124)(75, 109)(76, 131)(77, 138)(78, 140)(79, 111)(80, 130)(81, 115)(82, 125)(83, 144)(84, 134)(85, 126)(86, 129)(87, 122)(88, 116)(89, 112)(90, 127)(91, 132)(92, 123)(93, 128)(94, 110)(95, 118)(96, 121)(97, 136)(98, 114)(99, 137)(100, 139)(101, 141)(102, 119)(103, 142)(104, 120)(105, 143)(106, 133)(107, 135)(108, 113)(145, 207)(146, 214)(147, 199)(148, 185)(149, 192)(150, 194)(151, 201)(152, 184)(153, 205)(154, 215)(155, 198)(156, 188)(157, 216)(158, 183)(159, 212)(160, 206)(161, 202)(162, 181)(163, 186)(164, 213)(165, 182)(166, 200)(167, 208)(168, 211)(169, 190)(170, 204)(171, 191)(172, 193)(173, 195)(174, 209)(175, 196)(176, 210)(177, 197)(178, 187)(179, 189)(180, 203)

MAP           : A4.891
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1 * x.3 * x.2, x.1^3, x.3^4, x.2^4, (x.3^-1 * x.2)^2 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 55)(32, 56)(33, 57)(34, 58)(35, 59)(36, 60)(73, 111)(74, 130)(75, 115)(76, 125)(77, 144)(78, 134)(79, 117)(80, 124)(81, 109)(82, 131)(83, 138)(84, 140)(85, 132)(86, 123)(87, 128)(88, 110)(89, 118)(90, 121)(91, 126)(92, 129)(93, 122)(94, 116)(95, 112)(96, 127)(97, 142)(98, 120)(99, 143)(100, 133)(101, 135)(102, 113)(103, 136)(104, 114)(105, 137)(106, 139)(107, 141)(108, 119)(145, 201)(146, 184)(147, 205)(148, 215)(149, 198)(150, 188)(151, 207)(152, 214)(153, 199)(154, 185)(155, 192)(156, 194)(157, 186)(158, 213)(159, 182)(160, 200)(161, 208)(162, 211)(163, 216)(164, 183)(165, 212)(166, 206)(167, 202)(168, 181)(169, 196)(170, 210)(171, 197)(172, 187)(173, 189)(174, 203)(175, 190)(176, 204)(177, 191)(178, 193)(179, 195)(180, 209)

MAP           : A4.892
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 179)(92, 171)(93, 170)(94, 169)(95, 175)(96, 173)(97, 166)(98, 165)(99, 164)(100, 174)(101, 168)(102, 172)(103, 167)(104, 178)(105, 180)(106, 176)(107, 163)(108, 177)(181, 210)(182, 204)(183, 208)(184, 203)(185, 214)(186, 216)(187, 212)(188, 199)(189, 213)(190, 215)(191, 207)(192, 206)(193, 205)(194, 211)(195, 209)(196, 202)(197, 201)(198, 200)

MAP           : A4.893
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.3 * x.2 * x.1, x.3^3, x.2^4, x.1^4, (x.2 * x.1^-1)^2 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 39)(2, 58)(3, 43)(4, 53)(5, 72)(6, 62)(7, 45)(8, 52)(9, 37)(10, 59)(11, 66)(12, 68)(13, 60)(14, 51)(15, 56)(16, 38)(17, 46)(18, 49)(19, 54)(20, 57)(21, 50)(22, 44)(23, 40)(24, 55)(25, 70)(26, 48)(27, 71)(28, 61)(29, 63)(30, 41)(31, 64)(32, 42)(33, 65)(34, 67)(35, 69)(36, 47)(73, 126)(74, 129)(75, 122)(76, 116)(77, 112)(78, 127)(79, 142)(80, 120)(81, 143)(82, 133)(83, 135)(84, 113)(85, 136)(86, 114)(87, 137)(88, 139)(89, 141)(90, 119)(91, 111)(92, 130)(93, 115)(94, 125)(95, 144)(96, 134)(97, 117)(98, 124)(99, 109)(100, 131)(101, 138)(102, 140)(103, 132)(104, 123)(105, 128)(106, 110)(107, 118)(108, 121)(145, 209)(146, 205)(147, 204)(148, 210)(149, 206)(150, 201)(151, 200)(152, 203)(153, 208)(154, 207)(155, 199)(156, 202)(157, 185)(158, 181)(159, 192)(160, 186)(161, 182)(162, 189)(163, 212)(164, 215)(165, 196)(166, 195)(167, 211)(168, 214)(169, 197)(170, 193)(171, 216)(172, 198)(173, 194)(174, 213)(175, 188)(176, 191)(177, 184)(178, 183)(179, 187)(180, 190)

MAP           : A4.894
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 169)(92, 165)(93, 164)(94, 173)(95, 177)(96, 179)(97, 163)(98, 176)(99, 178)(100, 180)(101, 166)(102, 175)(103, 174)(104, 170)(105, 167)(106, 171)(107, 168)(108, 172)(181, 203)(182, 199)(183, 213)(184, 216)(185, 200)(186, 210)(187, 201)(188, 202)(189, 211)(190, 209)(191, 212)(192, 214)(193, 215)(194, 208)(195, 205)(196, 204)(197, 207)(198, 206)

MAP           : A4.895
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 171)(92, 175)(93, 166)(94, 165)(95, 179)(96, 176)(97, 180)(98, 177)(99, 163)(100, 178)(101, 174)(102, 173)(103, 164)(104, 168)(105, 170)(106, 172)(107, 167)(108, 169)(181, 204)(182, 214)(183, 212)(184, 199)(185, 210)(186, 202)(187, 209)(188, 200)(189, 201)(190, 211)(191, 215)(192, 216)(193, 213)(194, 207)(195, 208)(196, 206)(197, 205)(198, 203)

MAP           : A4.896
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1 * x.3 * x.2, x.1^3, x.3^4, x.2^4, (x.3^-1 * x.2)^2 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 38)(2, 41)(3, 46)(4, 45)(5, 37)(6, 40)(7, 47)(8, 43)(9, 42)(10, 48)(11, 44)(12, 39)(13, 50)(14, 53)(15, 70)(16, 69)(17, 49)(18, 52)(19, 59)(20, 55)(21, 66)(22, 60)(23, 56)(24, 63)(25, 62)(26, 65)(27, 58)(28, 57)(29, 61)(30, 64)(31, 71)(32, 67)(33, 54)(34, 72)(35, 68)(36, 51)(73, 111)(74, 130)(75, 115)(76, 125)(77, 144)(78, 134)(79, 117)(80, 124)(81, 109)(82, 131)(83, 138)(84, 140)(85, 132)(86, 123)(87, 128)(88, 110)(89, 118)(90, 121)(91, 126)(92, 129)(93, 122)(94, 116)(95, 112)(96, 127)(97, 142)(98, 120)(99, 143)(100, 133)(101, 135)(102, 113)(103, 136)(104, 114)(105, 137)(106, 139)(107, 141)(108, 119)(145, 184)(146, 198)(147, 185)(148, 199)(149, 201)(150, 215)(151, 192)(152, 207)(153, 188)(154, 194)(155, 214)(156, 205)(157, 213)(158, 208)(159, 193)(160, 191)(161, 186)(162, 200)(163, 202)(164, 216)(165, 203)(166, 181)(167, 183)(168, 197)(169, 210)(170, 189)(171, 206)(172, 212)(173, 196)(174, 187)(175, 195)(176, 190)(177, 211)(178, 209)(179, 204)(180, 182)

MAP           : A4.897
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.1 * x.3 * x.2, x.1^3, x.3^4, x.2^4, (x.3^-1 * x.2)^2 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 38)(2, 41)(3, 46)(4, 45)(5, 37)(6, 40)(7, 47)(8, 43)(9, 42)(10, 48)(11, 44)(12, 39)(13, 50)(14, 53)(15, 70)(16, 69)(17, 49)(18, 52)(19, 59)(20, 55)(21, 66)(22, 60)(23, 56)(24, 63)(25, 62)(26, 65)(27, 58)(28, 57)(29, 61)(30, 64)(31, 71)(32, 67)(33, 54)(34, 72)(35, 68)(36, 51)(73, 117)(74, 124)(75, 109)(76, 131)(77, 138)(78, 140)(79, 111)(80, 130)(81, 115)(82, 125)(83, 144)(84, 134)(85, 126)(86, 129)(87, 122)(88, 116)(89, 112)(90, 127)(91, 132)(92, 123)(93, 128)(94, 110)(95, 118)(96, 121)(97, 136)(98, 114)(99, 137)(100, 139)(101, 141)(102, 119)(103, 142)(104, 120)(105, 143)(106, 133)(107, 135)(108, 113)(145, 192)(146, 207)(147, 188)(148, 194)(149, 214)(150, 205)(151, 184)(152, 198)(153, 185)(154, 199)(155, 201)(156, 215)(157, 202)(158, 216)(159, 203)(160, 181)(161, 183)(162, 197)(163, 213)(164, 208)(165, 193)(166, 191)(167, 186)(168, 200)(169, 195)(170, 190)(171, 211)(172, 209)(173, 204)(174, 182)(175, 210)(176, 189)(177, 206)(178, 212)(179, 196)(180, 187)

MAP           : A4.898
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.1^-1 * x.2^-1 * x.3^-1, (x.3^-1 * x.1)^2, x.1^4, x.3^4, x.2 * x.3^-2 * x.2^-1 * x.3 * x.1^-1 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 45)(2, 52)(3, 37)(4, 59)(5, 66)(6, 68)(7, 39)(8, 58)(9, 43)(10, 53)(11, 72)(12, 62)(13, 54)(14, 57)(15, 50)(16, 44)(17, 40)(18, 55)(19, 60)(20, 51)(21, 56)(22, 38)(23, 46)(24, 49)(25, 64)(26, 42)(27, 65)(28, 67)(29, 69)(30, 47)(31, 70)(32, 48)(33, 71)(34, 61)(35, 63)(36, 41)(73, 110)(74, 113)(75, 118)(76, 117)(77, 109)(78, 112)(79, 119)(80, 115)(81, 114)(82, 120)(83, 116)(84, 111)(85, 122)(86, 125)(87, 142)(88, 141)(89, 121)(90, 124)(91, 131)(92, 127)(93, 138)(94, 132)(95, 128)(96, 135)(97, 134)(98, 137)(99, 130)(100, 129)(101, 133)(102, 136)(103, 143)(104, 139)(105, 126)(106, 144)(107, 140)(108, 123)(145, 216)(146, 183)(147, 212)(148, 206)(149, 202)(150, 181)(151, 196)(152, 210)(153, 197)(154, 187)(155, 189)(156, 203)(157, 190)(158, 204)(159, 191)(160, 193)(161, 195)(162, 209)(163, 201)(164, 184)(165, 205)(166, 215)(167, 198)(168, 188)(169, 207)(170, 214)(171, 199)(172, 185)(173, 192)(174, 194)(175, 186)(176, 213)(177, 182)(178, 200)(179, 208)(180, 211)

MAP           : A4.899
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 173)(92, 176)(93, 178)(94, 179)(95, 172)(96, 169)(97, 168)(98, 171)(99, 170)(100, 167)(101, 163)(102, 177)(103, 180)(104, 164)(105, 174)(106, 165)(107, 166)(108, 175)(181, 216)(182, 202)(183, 211)(184, 210)(185, 206)(186, 203)(187, 207)(188, 204)(189, 208)(190, 205)(191, 201)(192, 200)(193, 209)(194, 213)(195, 215)(196, 199)(197, 212)(198, 214)

MAP           : A4.900
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 171)(92, 175)(93, 166)(94, 165)(95, 179)(96, 176)(97, 180)(98, 177)(99, 163)(100, 178)(101, 174)(102, 173)(103, 164)(104, 168)(105, 170)(106, 172)(107, 167)(108, 169)(181, 204)(182, 214)(183, 212)(184, 199)(185, 210)(186, 202)(187, 209)(188, 200)(189, 201)(190, 211)(191, 215)(192, 216)(193, 213)(194, 207)(195, 208)(196, 206)(197, 205)(198, 203)

MAP           : A4.901
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 177)(92, 169)(93, 167)(94, 172)(95, 165)(96, 175)(97, 164)(98, 173)(99, 174)(100, 166)(101, 170)(102, 171)(103, 168)(104, 180)(105, 163)(106, 179)(107, 178)(108, 176)(181, 200)(182, 203)(183, 205)(184, 206)(185, 199)(186, 214)(187, 213)(188, 216)(189, 215)(190, 212)(191, 208)(192, 204)(193, 207)(194, 209)(195, 201)(196, 210)(197, 211)(198, 202)

MAP           : A4.902
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 42)(20, 52)(21, 50)(22, 37)(23, 48)(24, 40)(25, 47)(26, 38)(27, 39)(28, 49)(29, 53)(30, 54)(31, 51)(32, 45)(33, 46)(34, 44)(35, 43)(36, 41)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 172)(92, 173)(93, 174)(94, 175)(95, 176)(96, 177)(97, 178)(98, 179)(99, 180)(100, 163)(101, 164)(102, 165)(103, 166)(104, 167)(105, 168)(106, 169)(107, 170)(108, 171)(181, 206)(182, 216)(183, 215)(184, 214)(185, 202)(186, 200)(187, 211)(188, 210)(189, 209)(190, 201)(191, 213)(192, 199)(193, 212)(194, 205)(195, 207)(196, 203)(197, 208)(198, 204)

MAP           : A4.903
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 54)(20, 40)(21, 49)(22, 48)(23, 44)(24, 41)(25, 45)(26, 42)(27, 46)(28, 43)(29, 39)(30, 38)(31, 47)(32, 51)(33, 53)(34, 37)(35, 50)(36, 52)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 176)(92, 172)(93, 168)(94, 171)(95, 173)(96, 165)(97, 174)(98, 175)(99, 166)(100, 164)(101, 167)(102, 169)(103, 170)(104, 163)(105, 178)(106, 177)(107, 180)(108, 179)(181, 202)(182, 206)(183, 207)(184, 204)(185, 216)(186, 199)(187, 215)(188, 214)(189, 212)(190, 213)(191, 205)(192, 203)(193, 208)(194, 201)(195, 211)(196, 200)(197, 209)(198, 210)

MAP           : A4.904
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 175)(92, 179)(93, 180)(94, 177)(95, 171)(96, 172)(97, 170)(98, 169)(99, 167)(100, 168)(101, 178)(102, 176)(103, 163)(104, 174)(105, 166)(106, 173)(107, 164)(108, 165)(181, 214)(182, 210)(183, 209)(184, 200)(185, 204)(186, 206)(187, 208)(188, 203)(189, 205)(190, 207)(191, 211)(192, 202)(193, 201)(194, 215)(195, 212)(196, 216)(197, 213)(198, 199)

MAP           : A4.905
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 54)(20, 40)(21, 49)(22, 48)(23, 44)(24, 41)(25, 45)(26, 42)(27, 46)(28, 43)(29, 39)(30, 38)(31, 47)(32, 51)(33, 53)(34, 37)(35, 50)(36, 52)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 179)(92, 171)(93, 170)(94, 169)(95, 175)(96, 173)(97, 166)(98, 165)(99, 164)(100, 174)(101, 168)(102, 172)(103, 167)(104, 178)(105, 180)(106, 176)(107, 163)(108, 177)(181, 210)(182, 204)(183, 208)(184, 203)(185, 214)(186, 216)(187, 212)(188, 199)(189, 213)(190, 215)(191, 207)(192, 206)(193, 205)(194, 211)(195, 209)(196, 202)(197, 201)(198, 200)

MAP           : A4.906
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 134)(56, 144)(57, 143)(58, 142)(59, 130)(60, 128)(61, 139)(62, 138)(63, 137)(64, 129)(65, 141)(66, 127)(67, 140)(68, 133)(69, 135)(70, 131)(71, 136)(72, 132)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 176)(92, 172)(93, 168)(94, 171)(95, 173)(96, 165)(97, 174)(98, 175)(99, 166)(100, 164)(101, 167)(102, 169)(103, 170)(104, 163)(105, 178)(106, 177)(107, 180)(108, 179)(181, 202)(182, 206)(183, 207)(184, 204)(185, 216)(186, 199)(187, 215)(188, 214)(189, 212)(190, 213)(191, 205)(192, 203)(193, 208)(194, 201)(195, 211)(196, 200)(197, 209)(198, 210)

MAP           : A4.907
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 54)(20, 40)(21, 49)(22, 48)(23, 44)(24, 41)(25, 45)(26, 42)(27, 46)(28, 43)(29, 39)(30, 38)(31, 47)(32, 51)(33, 53)(34, 37)(35, 50)(36, 52)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 177)(92, 169)(93, 167)(94, 172)(95, 165)(96, 175)(97, 164)(98, 173)(99, 174)(100, 166)(101, 170)(102, 171)(103, 168)(104, 180)(105, 163)(106, 179)(107, 178)(108, 176)(181, 200)(182, 203)(183, 205)(184, 206)(185, 199)(186, 214)(187, 213)(188, 216)(189, 215)(190, 212)(191, 208)(192, 204)(193, 207)(194, 209)(195, 201)(196, 210)(197, 211)(198, 202)

MAP           : A4.908
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 54)(20, 40)(21, 49)(22, 48)(23, 44)(24, 41)(25, 45)(26, 42)(27, 46)(28, 43)(29, 39)(30, 38)(31, 47)(32, 51)(33, 53)(34, 37)(35, 50)(36, 52)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 172)(92, 173)(93, 174)(94, 175)(95, 176)(96, 177)(97, 178)(98, 179)(99, 180)(100, 163)(101, 164)(102, 165)(103, 166)(104, 167)(105, 168)(106, 169)(107, 170)(108, 171)(181, 206)(182, 216)(183, 215)(184, 214)(185, 202)(186, 200)(187, 211)(188, 210)(189, 209)(190, 201)(191, 213)(192, 199)(193, 212)(194, 205)(195, 207)(196, 203)(197, 208)(198, 204)

MAP           : A4.909
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.1^-1 * x.2^-1 * x.3^-1, (x.3^-1 * x.1)^2, x.1^4, x.3^4, x.2 * x.3^-2 * x.2^-1 * x.3 * x.1^-1 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 45)(2, 52)(3, 37)(4, 59)(5, 66)(6, 68)(7, 39)(8, 58)(9, 43)(10, 53)(11, 72)(12, 62)(13, 54)(14, 57)(15, 50)(16, 44)(17, 40)(18, 55)(19, 60)(20, 51)(21, 56)(22, 38)(23, 46)(24, 49)(25, 64)(26, 42)(27, 65)(28, 67)(29, 69)(30, 47)(31, 70)(32, 48)(33, 71)(34, 61)(35, 63)(36, 41)(73, 121)(74, 122)(75, 123)(76, 124)(77, 125)(78, 126)(79, 139)(80, 140)(81, 141)(82, 142)(83, 143)(84, 144)(85, 133)(86, 134)(87, 135)(88, 136)(89, 137)(90, 138)(91, 115)(92, 116)(93, 117)(94, 118)(95, 119)(96, 120)(97, 109)(98, 110)(99, 111)(100, 112)(101, 113)(102, 114)(103, 127)(104, 128)(105, 129)(106, 130)(107, 131)(108, 132)(145, 214)(146, 192)(147, 215)(148, 205)(149, 207)(150, 185)(151, 198)(152, 201)(153, 194)(154, 188)(155, 184)(156, 199)(157, 183)(158, 202)(159, 187)(160, 197)(161, 216)(162, 206)(163, 208)(164, 186)(165, 209)(166, 211)(167, 213)(168, 191)(169, 204)(170, 195)(171, 200)(172, 182)(173, 190)(174, 193)(175, 189)(176, 196)(177, 181)(178, 203)(179, 210)(180, 212)

MAP           : A4.910
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 42)(20, 52)(21, 50)(22, 37)(23, 48)(24, 40)(25, 47)(26, 38)(27, 39)(28, 49)(29, 53)(30, 54)(31, 51)(32, 45)(33, 46)(34, 44)(35, 43)(36, 41)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 175)(92, 179)(93, 180)(94, 177)(95, 171)(96, 172)(97, 170)(98, 169)(99, 167)(100, 168)(101, 178)(102, 176)(103, 163)(104, 174)(105, 166)(106, 173)(107, 164)(108, 165)(181, 214)(182, 210)(183, 209)(184, 200)(185, 204)(186, 206)(187, 208)(188, 203)(189, 205)(190, 207)(191, 211)(192, 202)(193, 201)(194, 215)(195, 212)(196, 216)(197, 213)(198, 199)

MAP           : A4.911
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 42)(20, 52)(21, 50)(22, 37)(23, 48)(24, 40)(25, 47)(26, 38)(27, 39)(28, 49)(29, 53)(30, 54)(31, 51)(32, 45)(33, 46)(34, 44)(35, 43)(36, 41)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 173)(92, 176)(93, 178)(94, 179)(95, 172)(96, 169)(97, 168)(98, 171)(99, 170)(100, 167)(101, 163)(102, 177)(103, 180)(104, 164)(105, 174)(106, 165)(107, 166)(108, 175)(181, 216)(182, 202)(183, 211)(184, 210)(185, 206)(186, 203)(187, 207)(188, 204)(189, 208)(190, 205)(191, 201)(192, 200)(193, 209)(194, 213)(195, 215)(196, 199)(197, 212)(198, 214)

MAP           : A4.912
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 176)(92, 172)(93, 168)(94, 171)(95, 173)(96, 165)(97, 174)(98, 175)(99, 166)(100, 164)(101, 167)(102, 169)(103, 170)(104, 163)(105, 178)(106, 177)(107, 180)(108, 179)(181, 202)(182, 206)(183, 207)(184, 204)(185, 216)(186, 199)(187, 215)(188, 214)(189, 212)(190, 213)(191, 205)(192, 203)(193, 208)(194, 201)(195, 211)(196, 200)(197, 209)(198, 210)

MAP           : A4.913
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.3 * x.2 * x.1, x.3^3, x.2^4, x.1^4, (x.2 * x.1^-1)^2 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 39)(2, 58)(3, 43)(4, 53)(5, 72)(6, 62)(7, 45)(8, 52)(9, 37)(10, 59)(11, 66)(12, 68)(13, 60)(14, 51)(15, 56)(16, 38)(17, 46)(18, 49)(19, 54)(20, 57)(21, 50)(22, 44)(23, 40)(24, 55)(25, 70)(26, 48)(27, 71)(28, 61)(29, 63)(30, 41)(31, 64)(32, 42)(33, 65)(34, 67)(35, 69)(36, 47)(73, 114)(74, 141)(75, 110)(76, 128)(77, 136)(78, 139)(79, 118)(80, 132)(81, 119)(82, 121)(83, 123)(84, 137)(85, 124)(86, 138)(87, 125)(88, 115)(89, 117)(90, 131)(91, 135)(92, 142)(93, 127)(94, 113)(95, 120)(96, 122)(97, 129)(98, 112)(99, 133)(100, 143)(101, 126)(102, 116)(103, 144)(104, 111)(105, 140)(106, 134)(107, 130)(108, 109)(145, 185)(146, 181)(147, 192)(148, 186)(149, 182)(150, 189)(151, 188)(152, 191)(153, 184)(154, 183)(155, 187)(156, 190)(157, 197)(158, 193)(159, 216)(160, 198)(161, 194)(162, 213)(163, 200)(164, 203)(165, 208)(166, 207)(167, 199)(168, 202)(169, 209)(170, 205)(171, 204)(172, 210)(173, 206)(174, 201)(175, 212)(176, 215)(177, 196)(178, 195)(179, 211)(180, 214)

MAP           : A4.914
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 54)(20, 40)(21, 49)(22, 48)(23, 44)(24, 41)(25, 45)(26, 42)(27, 46)(28, 43)(29, 39)(30, 38)(31, 47)(32, 51)(33, 53)(34, 37)(35, 50)(36, 52)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 169)(92, 165)(93, 164)(94, 173)(95, 177)(96, 179)(97, 163)(98, 176)(99, 178)(100, 180)(101, 166)(102, 175)(103, 174)(104, 170)(105, 167)(106, 171)(107, 168)(108, 172)(181, 203)(182, 199)(183, 213)(184, 216)(185, 200)(186, 210)(187, 201)(188, 202)(189, 211)(190, 209)(191, 212)(192, 214)(193, 215)(194, 208)(195, 205)(196, 204)(197, 207)(198, 206)

MAP           : A4.915
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.3 * x.2 * x.1, x.3^3, x.2^4, x.1^4, (x.2 * x.1^-1)^2 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 45)(2, 52)(3, 37)(4, 59)(5, 66)(6, 68)(7, 39)(8, 58)(9, 43)(10, 53)(11, 72)(12, 62)(13, 54)(14, 57)(15, 50)(16, 44)(17, 40)(18, 55)(19, 60)(20, 51)(21, 56)(22, 38)(23, 46)(24, 49)(25, 64)(26, 42)(27, 65)(28, 67)(29, 69)(30, 47)(31, 70)(32, 48)(33, 71)(34, 61)(35, 63)(36, 41)(73, 135)(74, 142)(75, 127)(76, 113)(77, 120)(78, 122)(79, 129)(80, 112)(81, 133)(82, 143)(83, 126)(84, 116)(85, 144)(86, 111)(87, 140)(88, 134)(89, 130)(90, 109)(91, 114)(92, 141)(93, 110)(94, 128)(95, 136)(96, 139)(97, 118)(98, 132)(99, 119)(100, 121)(101, 123)(102, 137)(103, 124)(104, 138)(105, 125)(106, 115)(107, 117)(108, 131)(145, 193)(146, 194)(147, 195)(148, 196)(149, 197)(150, 198)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 205)(158, 206)(159, 207)(160, 208)(161, 209)(162, 210)(163, 187)(164, 188)(165, 189)(166, 190)(167, 191)(168, 192)(169, 181)(170, 182)(171, 183)(172, 184)(173, 185)(174, 186)(175, 199)(176, 200)(177, 201)(178, 202)(179, 203)(180, 204)

MAP           : A4.916
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.1^-1 * x.2^-1 * x.3^-1, (x.3^-1 * x.1)^2, x.1^4, x.3^4, x.2 * x.3^-2 * x.2^-1 * x.3 * x.1^-1 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 39)(2, 58)(3, 43)(4, 53)(5, 72)(6, 62)(7, 45)(8, 52)(9, 37)(10, 59)(11, 66)(12, 68)(13, 60)(14, 51)(15, 56)(16, 38)(17, 46)(18, 49)(19, 54)(20, 57)(21, 50)(22, 44)(23, 40)(24, 55)(25, 70)(26, 48)(27, 71)(28, 61)(29, 63)(30, 41)(31, 64)(32, 42)(33, 65)(34, 67)(35, 69)(36, 47)(73, 121)(74, 122)(75, 123)(76, 124)(77, 125)(78, 126)(79, 139)(80, 140)(81, 141)(82, 142)(83, 143)(84, 144)(85, 133)(86, 134)(87, 135)(88, 136)(89, 137)(90, 138)(91, 115)(92, 116)(93, 117)(94, 118)(95, 119)(96, 120)(97, 109)(98, 110)(99, 111)(100, 112)(101, 113)(102, 114)(103, 127)(104, 128)(105, 129)(106, 130)(107, 131)(108, 132)(145, 208)(146, 186)(147, 209)(148, 211)(149, 213)(150, 191)(151, 204)(152, 195)(153, 200)(154, 182)(155, 190)(156, 193)(157, 189)(158, 196)(159, 181)(160, 203)(161, 210)(162, 212)(163, 214)(164, 192)(165, 215)(166, 205)(167, 207)(168, 185)(169, 198)(170, 201)(171, 194)(172, 188)(173, 184)(174, 199)(175, 183)(176, 202)(177, 187)(178, 197)(179, 216)(180, 206)

MAP           : A4.917
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 42)(20, 52)(21, 50)(22, 37)(23, 48)(24, 40)(25, 47)(26, 38)(27, 39)(28, 49)(29, 53)(30, 54)(31, 51)(32, 45)(33, 46)(34, 44)(35, 43)(36, 41)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 177)(92, 169)(93, 167)(94, 172)(95, 165)(96, 175)(97, 164)(98, 173)(99, 174)(100, 166)(101, 170)(102, 171)(103, 168)(104, 180)(105, 163)(106, 179)(107, 178)(108, 176)(181, 200)(182, 203)(183, 205)(184, 206)(185, 199)(186, 214)(187, 213)(188, 216)(189, 215)(190, 212)(191, 208)(192, 204)(193, 207)(194, 209)(195, 201)(196, 210)(197, 211)(198, 202)

MAP           : A4.918
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)   : <36, 10>
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^-1 * x.4)^2, (x.4^-1 * x.1)^2, x.4 * x.3^-1 * x.2 * x.3 * x.4^-1 * x.2, x.4 * x.3 * x.4 * x.3^-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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 112)(2, 114)(3, 144)(4, 143)(5, 142)(6, 141)(7, 128)(8, 127)(9, 133)(10, 139)(11, 134)(12, 140)(13, 110)(14, 109)(15, 115)(16, 121)(17, 116)(18, 122)(19, 111)(20, 113)(21, 119)(22, 120)(23, 117)(24, 118)(25, 130)(26, 132)(27, 126)(28, 125)(29, 124)(30, 123)(31, 129)(32, 131)(33, 137)(34, 138)(35, 135)(36, 136)(37, 77)(38, 75)(39, 94)(40, 93)(41, 96)(42, 95)(43, 83)(44, 81)(45, 88)(46, 87)(47, 90)(48, 89)(49, 84)(50, 82)(51, 86)(52, 80)(53, 85)(54, 79)(55, 78)(56, 76)(57, 92)(58, 74)(59, 91)(60, 73)(61, 108)(62, 106)(63, 98)(64, 104)(65, 97)(66, 103)(67, 107)(68, 105)(69, 100)(70, 99)(71, 102)(72, 101)(145, 150)(146, 148)(147, 164)(149, 163)(151, 180)(152, 178)(153, 170)(154, 176)(155, 169)(156, 175)(157, 179)(158, 177)(159, 172)(160, 171)(161, 174)(162, 173)(165, 166)(167, 168)(181, 182)(183, 187)(184, 193)(185, 188)(186, 194)(189, 191)(190, 192)(195, 216)(196, 215)(197, 214)(198, 213)(199, 200)(201, 205)(202, 211)(203, 206)(204, 212)(207, 209)(208, 210)

MAP           : A4.919
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 42)(20, 52)(21, 50)(22, 37)(23, 48)(24, 40)(25, 47)(26, 38)(27, 39)(28, 49)(29, 53)(30, 54)(31, 51)(32, 45)(33, 46)(34, 44)(35, 43)(36, 41)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 169)(92, 165)(93, 164)(94, 173)(95, 177)(96, 179)(97, 163)(98, 176)(99, 178)(100, 180)(101, 166)(102, 175)(103, 174)(104, 170)(105, 167)(106, 171)(107, 168)(108, 172)(181, 203)(182, 199)(183, 213)(184, 216)(185, 200)(186, 210)(187, 201)(188, 202)(189, 211)(190, 209)(191, 212)(192, 214)(193, 215)(194, 208)(195, 205)(196, 204)(197, 207)(198, 206)

MAP           : A4.920
NOTES         : type I, chiral, isomorphic to A4.918.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^-1 * x.1 * x.2, x.4^3, (x.4^-1 * x.3)^2, (x.4^-1 * x.2)^2, x.4^-1 * x.1 * x.3 * x.4^-1 * x.2, x.3^-2 * x.4 * x.1 * x.4^-1 * x.1, x.3^6 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 111)(2, 113)(3, 119)(4, 120)(5, 117)(6, 118)(7, 130)(8, 132)(9, 126)(10, 125)(11, 124)(12, 123)(13, 129)(14, 131)(15, 137)(16, 138)(17, 135)(18, 136)(19, 112)(20, 114)(21, 144)(22, 143)(23, 142)(24, 141)(25, 128)(26, 127)(27, 133)(28, 139)(29, 134)(30, 140)(31, 110)(32, 109)(33, 115)(34, 121)(35, 116)(36, 122)(37, 77)(38, 75)(39, 94)(40, 93)(41, 96)(42, 95)(43, 83)(44, 81)(45, 88)(46, 87)(47, 90)(48, 89)(49, 84)(50, 82)(51, 86)(52, 80)(53, 85)(54, 79)(55, 78)(56, 76)(57, 92)(58, 74)(59, 91)(60, 73)(61, 108)(62, 106)(63, 98)(64, 104)(65, 97)(66, 103)(67, 107)(68, 105)(69, 100)(70, 99)(71, 102)(72, 101)(145, 171)(146, 173)(147, 161)(148, 162)(149, 159)(150, 160)(151, 178)(152, 180)(153, 156)(154, 155)(157, 177)(158, 179)(163, 172)(164, 174)(165, 168)(166, 167)(169, 176)(170, 175)(181, 197)(182, 195)(183, 190)(184, 189)(185, 192)(186, 191)(187, 203)(188, 201)(193, 204)(194, 202)(196, 200)(198, 199)(205, 210)(206, 208)(207, 212)(209, 211)(213, 214)(215, 216)

MAP           : A4.921
NOTES         : type I, chiral, isomorphic to A4.918.
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)   : <36, 10>
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^-1 * x.4)^2, (x.4^-1 * x.1)^2, x.4 * x.3^-1 * x.2 * x.3 * x.4^-1 * x.2, x.4 * x.3 * x.4 * x.3^-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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 111)(2, 113)(3, 119)(4, 120)(5, 117)(6, 118)(7, 130)(8, 132)(9, 126)(10, 125)(11, 124)(12, 123)(13, 129)(14, 131)(15, 137)(16, 138)(17, 135)(18, 136)(19, 112)(20, 114)(21, 144)(22, 143)(23, 142)(24, 141)(25, 128)(26, 127)(27, 133)(28, 139)(29, 134)(30, 140)(31, 110)(32, 109)(33, 115)(34, 121)(35, 116)(36, 122)(37, 77)(38, 75)(39, 94)(40, 93)(41, 96)(42, 95)(43, 83)(44, 81)(45, 88)(46, 87)(47, 90)(48, 89)(49, 84)(50, 82)(51, 86)(52, 80)(53, 85)(54, 79)(55, 78)(56, 76)(57, 92)(58, 74)(59, 91)(60, 73)(61, 108)(62, 106)(63, 98)(64, 104)(65, 97)(66, 103)(67, 107)(68, 105)(69, 100)(70, 99)(71, 102)(72, 101)(145, 150)(146, 148)(147, 164)(149, 163)(151, 180)(152, 178)(153, 170)(154, 176)(155, 169)(156, 175)(157, 179)(158, 177)(159, 172)(160, 171)(161, 174)(162, 173)(165, 166)(167, 168)(181, 200)(182, 199)(183, 205)(184, 211)(185, 206)(186, 212)(187, 201)(188, 203)(189, 209)(190, 210)(191, 207)(192, 208)(193, 202)(194, 204)(195, 198)(196, 197)(213, 216)(214, 215)

MAP           : A4.922
NOTES         : type I, chiral, isomorphic to A4.918.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^-1 * x.1 * x.2, x.4^3, (x.4^-1 * x.3)^2, (x.4^-1 * x.2)^2, x.4^-1 * x.1 * x.3 * x.4^-1 * x.2, x.3^-2 * x.4 * x.1 * x.4^-1 * x.1, x.3^6 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 112)(2, 114)(3, 144)(4, 143)(5, 142)(6, 141)(7, 128)(8, 127)(9, 133)(10, 139)(11, 134)(12, 140)(13, 110)(14, 109)(15, 115)(16, 121)(17, 116)(18, 122)(19, 111)(20, 113)(21, 119)(22, 120)(23, 117)(24, 118)(25, 130)(26, 132)(27, 126)(28, 125)(29, 124)(30, 123)(31, 129)(32, 131)(33, 137)(34, 138)(35, 135)(36, 136)(37, 77)(38, 75)(39, 94)(40, 93)(41, 96)(42, 95)(43, 83)(44, 81)(45, 88)(46, 87)(47, 90)(48, 89)(49, 84)(50, 82)(51, 86)(52, 80)(53, 85)(54, 79)(55, 78)(56, 76)(57, 92)(58, 74)(59, 91)(60, 73)(61, 108)(62, 106)(63, 98)(64, 104)(65, 97)(66, 103)(67, 107)(68, 105)(69, 100)(70, 99)(71, 102)(72, 101)(145, 146)(147, 151)(148, 157)(149, 152)(150, 158)(153, 155)(154, 156)(159, 180)(160, 179)(161, 178)(162, 177)(163, 164)(165, 169)(166, 175)(167, 170)(168, 176)(171, 173)(172, 174)(181, 193)(182, 194)(183, 195)(184, 196)(185, 197)(186, 198)(187, 199)(188, 200)(189, 201)(190, 202)(191, 203)(192, 204)(205, 211)(206, 212)(207, 213)(208, 214)(209, 215)(210, 216)

MAP           : A4.923
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 42)(20, 52)(21, 50)(22, 37)(23, 48)(24, 40)(25, 47)(26, 38)(27, 39)(28, 49)(29, 53)(30, 54)(31, 51)(32, 45)(33, 46)(34, 44)(35, 43)(36, 41)(55, 130)(56, 134)(57, 135)(58, 132)(59, 144)(60, 127)(61, 143)(62, 142)(63, 140)(64, 141)(65, 133)(66, 131)(67, 136)(68, 129)(69, 139)(70, 128)(71, 137)(72, 138)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 179)(92, 171)(93, 170)(94, 169)(95, 175)(96, 173)(97, 166)(98, 165)(99, 164)(100, 174)(101, 168)(102, 172)(103, 167)(104, 178)(105, 180)(106, 176)(107, 163)(108, 177)(181, 210)(182, 204)(183, 208)(184, 203)(185, 214)(186, 216)(187, 212)(188, 199)(189, 213)(190, 215)(191, 207)(192, 206)(193, 205)(194, 211)(195, 209)(196, 202)(197, 201)(198, 200)

MAP           : A4.924
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 172)(92, 173)(93, 174)(94, 175)(95, 176)(96, 177)(97, 178)(98, 179)(99, 180)(100, 163)(101, 164)(102, 165)(103, 166)(104, 167)(105, 168)(106, 169)(107, 170)(108, 171)(181, 206)(182, 216)(183, 215)(184, 214)(185, 202)(186, 200)(187, 211)(188, 210)(189, 209)(190, 201)(191, 213)(192, 199)(193, 212)(194, 205)(195, 207)(196, 203)(197, 208)(198, 204)

MAP           : A4.925
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.3 * x.2 * x.1, x.3^3, x.2^4, x.1^4, (x.2 * x.1^-1)^2 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 45)(2, 52)(3, 37)(4, 59)(5, 66)(6, 68)(7, 39)(8, 58)(9, 43)(10, 53)(11, 72)(12, 62)(13, 54)(14, 57)(15, 50)(16, 44)(17, 40)(18, 55)(19, 60)(20, 51)(21, 56)(22, 38)(23, 46)(24, 49)(25, 64)(26, 42)(27, 65)(28, 67)(29, 69)(30, 47)(31, 70)(32, 48)(33, 71)(34, 61)(35, 63)(36, 41)(73, 144)(74, 111)(75, 140)(76, 134)(77, 130)(78, 109)(79, 124)(80, 138)(81, 125)(82, 115)(83, 117)(84, 131)(85, 118)(86, 132)(87, 119)(88, 121)(89, 123)(90, 137)(91, 129)(92, 112)(93, 133)(94, 143)(95, 126)(96, 116)(97, 135)(98, 142)(99, 127)(100, 113)(101, 120)(102, 122)(103, 114)(104, 141)(105, 110)(106, 128)(107, 136)(108, 139)(145, 206)(146, 209)(147, 202)(148, 201)(149, 205)(150, 208)(151, 203)(152, 199)(153, 210)(154, 204)(155, 200)(156, 207)(157, 182)(158, 185)(159, 190)(160, 189)(161, 181)(162, 184)(163, 215)(164, 211)(165, 198)(166, 216)(167, 212)(168, 195)(169, 194)(170, 197)(171, 214)(172, 213)(173, 193)(174, 196)(175, 191)(176, 187)(177, 186)(178, 192)(179, 188)(180, 183)

MAP           : A4.926
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <36, 9>
CTG (fp)      : < x.1, x.2, x.3 | x.2^3, x.1^-1 * x.2^-1 * x.3^-1, (x.3^-1 * x.1)^2, x.1^4, x.3^4, x.2 * x.3^-2 * x.2^-1 * x.3 * x.1^-1 >
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        : 216
R = (1, 37, 73, 109, 145, 181)(2, 38, 74, 110, 146, 182)(3, 39, 75, 111, 147, 183)(4, 40, 76, 112, 148, 184)(5, 41, 77, 113, 149, 185)(6, 42, 78, 114, 150, 186)(7, 43, 79, 115, 151, 187)(8, 44, 80, 116, 152, 188)(9, 45, 81, 117, 153, 189)(10, 46, 82, 118, 154, 190)(11, 47, 83, 119, 155, 191)(12, 48, 84, 120, 156, 192)(13, 49, 85, 121, 157, 193)(14, 50, 86, 122, 158, 194)(15, 51, 87, 123, 159, 195)(16, 52, 88, 124, 160, 196)(17, 53, 89, 125, 161, 197)(18, 54, 90, 126, 162, 198)(19, 55, 91, 127, 163, 199)(20, 56, 92, 128, 164, 200)(21, 57, 93, 129, 165, 201)(22, 58, 94, 130, 166, 202)(23, 59, 95, 131, 167, 203)(24, 60, 96, 132, 168, 204)(25, 61, 97, 133, 169, 205)(26, 62, 98, 134, 170, 206)(27, 63, 99, 135, 171, 207)(28, 64, 100, 136, 172, 208)(29, 65, 101, 137, 173, 209)(30, 66, 102, 138, 174, 210)(31, 67, 103, 139, 175, 211)(32, 68, 104, 140, 176, 212)(33, 69, 105, 141, 177, 213)(34, 70, 106, 142, 178, 214)(35, 71, 107, 143, 179, 215)(36, 72, 108, 144, 180, 216)
L = (1, 39)(2, 58)(3, 43)(4, 53)(5, 72)(6, 62)(7, 45)(8, 52)(9, 37)(10, 59)(11, 66)(12, 68)(13, 60)(14, 51)(15, 56)(16, 38)(17, 46)(18, 49)(19, 54)(20, 57)(21, 50)(22, 44)(23, 40)(24, 55)(25, 70)(26, 48)(27, 71)(28, 61)(29, 63)(30, 41)(31, 64)(32, 42)(33, 65)(34, 67)(35, 69)(36, 47)(73, 110)(74, 113)(75, 118)(76, 117)(77, 109)(78, 112)(79, 119)(80, 115)(81, 114)(82, 120)(83, 116)(84, 111)(85, 122)(86, 125)(87, 142)(88, 141)(89, 121)(90, 124)(91, 131)(92, 127)(93, 138)(94, 132)(95, 128)(96, 135)(97, 134)(98, 137)(99, 130)(100, 129)(101, 133)(102, 136)(103, 143)(104, 139)(105, 126)(106, 144)(107, 140)(108, 123)(145, 210)(146, 189)(147, 206)(148, 212)(149, 196)(150, 187)(151, 202)(152, 216)(153, 203)(154, 181)(155, 183)(156, 197)(157, 184)(158, 198)(159, 185)(160, 199)(161, 201)(162, 215)(163, 195)(164, 190)(165, 211)(166, 209)(167, 204)(168, 182)(169, 213)(170, 208)(171, 193)(172, 191)(173, 186)(174, 200)(175, 192)(176, 207)(177, 188)(178, 194)(179, 214)(180, 205)

MAP           : A4.927
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 54)(20, 40)(21, 49)(22, 48)(23, 44)(24, 41)(25, 45)(26, 42)(27, 46)(28, 43)(29, 39)(30, 38)(31, 47)(32, 51)(33, 53)(34, 37)(35, 50)(36, 52)(55, 142)(56, 138)(57, 137)(58, 128)(59, 132)(60, 134)(61, 136)(62, 131)(63, 133)(64, 135)(65, 139)(66, 130)(67, 129)(68, 143)(69, 140)(70, 144)(71, 141)(72, 127)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 171)(92, 175)(93, 166)(94, 165)(95, 179)(96, 176)(97, 180)(98, 177)(99, 163)(100, 178)(101, 174)(102, 173)(103, 164)(104, 168)(105, 170)(106, 172)(107, 167)(108, 169)(181, 204)(182, 214)(183, 212)(184, 199)(185, 210)(186, 202)(187, 209)(188, 200)(189, 201)(190, 211)(191, 215)(192, 216)(193, 213)(194, 207)(195, 208)(196, 206)(197, 205)(198, 203)

MAP           : A4.928
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 175)(92, 179)(93, 180)(94, 177)(95, 171)(96, 172)(97, 170)(98, 169)(99, 167)(100, 168)(101, 178)(102, 176)(103, 163)(104, 174)(105, 166)(106, 173)(107, 164)(108, 165)(181, 214)(182, 210)(183, 209)(184, 200)(185, 204)(186, 206)(187, 208)(188, 203)(189, 205)(190, 207)(191, 211)(192, 202)(193, 201)(194, 215)(195, 212)(196, 216)(197, 213)(198, 199)

MAP           : A4.929
NOTES         : type I, reflexible, isomorphic to A4.890.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.4^2, x.5 * x.4 * x.6, x.2^3, x.1 * x.2^-1 * x.3^-1, x.6^3, (x.5 * x.1^-1)^2, (x.3 * x.4)^2, x.5 * x.2 * x.5^-1 * x.3^-1, x.5 * x.3 * x.5^-1 * x.2^-1, (x.6^-1, x.2^-1), (x.6, x.3^-1) >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 4, 3, 4)
#DARTS        : 216
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)(109, 127, 145, 163, 181, 199)(110, 128, 146, 164, 182, 200)(111, 129, 147, 165, 183, 201)(112, 130, 148, 166, 184, 202)(113, 131, 149, 167, 185, 203)(114, 132, 150, 168, 186, 204)(115, 133, 151, 169, 187, 205)(116, 134, 152, 170, 188, 206)(117, 135, 153, 171, 189, 207)(118, 136, 154, 172, 190, 208)(119, 137, 155, 173, 191, 209)(120, 138, 156, 174, 192, 210)(121, 139, 157, 175, 193, 211)(122, 140, 158, 176, 194, 212)(123, 141, 159, 177, 195, 213)(124, 142, 160, 178, 196, 214)(125, 143, 161, 179, 197, 215)(126, 144, 162, 180, 198, 216)
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, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 128)(56, 131)(57, 133)(58, 134)(59, 127)(60, 142)(61, 141)(62, 144)(63, 143)(64, 140)(65, 136)(66, 132)(67, 135)(68, 137)(69, 129)(70, 138)(71, 139)(72, 130)(73, 111)(74, 123)(75, 109)(76, 122)(77, 115)(78, 117)(79, 113)(80, 118)(81, 114)(82, 116)(83, 126)(84, 125)(85, 124)(86, 112)(87, 110)(88, 121)(89, 120)(90, 119)(91, 173)(92, 176)(93, 178)(94, 179)(95, 172)(96, 169)(97, 168)(98, 171)(99, 170)(100, 167)(101, 163)(102, 177)(103, 180)(104, 164)(105, 174)(106, 165)(107, 166)(108, 175)(181, 216)(182, 202)(183, 211)(184, 210)(185, 206)(186, 203)(187, 207)(188, 204)(189, 208)(190, 205)(191, 201)(192, 200)(193, 209)(194, 213)(195, 215)(196, 199)(197, 212)(198, 214)

MAP           : A4.930
NOTES         : type I, chiral, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 4)(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^-1 * u.1 * u.2, (u.3 * u.4^-1)^2, u.4^4 >
CTG (small)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3 * x.2 * x.1, x.3^3, (x.3 * x.4^-1)^2, x.4^4, (x.4^-1 * x.1)^2, x.2 * x.4^-2 * x.3^-1 * x.4^-1, 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, 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, 86)(2, 88)(3, 85)(4, 87)(5, 91)(6, 89)(7, 92)(8, 90)(9, 76)(10, 75)(11, 74)(12, 73)(13, 82)(14, 84)(15, 81)(16, 83)(17, 95)(18, 93)(19, 96)(20, 94)(21, 80)(22, 79)(23, 78)(24, 77)(25, 50)(26, 52)(27, 49)(28, 51)(29, 55)(30, 53)(31, 56)(32, 54)(33, 64)(34, 63)(35, 62)(36, 61)(37, 70)(38, 72)(39, 69)(40, 71)(41, 59)(42, 57)(43, 60)(44, 58)(45, 68)(46, 67)(47, 66)(48, 65)(97, 104)(98, 103)(99, 102)(100, 101)(105, 115)(106, 113)(107, 116)(108, 114)(109, 119)(110, 117)(111, 120)(112, 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           : A4.931
NOTES         : type I, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 4)(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^-1 * u.1 * u.2, (u.3 * u.4^-1)^2, u.4^4 >
CTG (small)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.3^-1 * x.1 * x.2, (x.3 * x.4^-1)^2, x.4 * x.1 * x.4^-1 * x.2, x.4^4, x.4^-2 * x.1 * 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, 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, 86)(2, 88)(3, 85)(4, 87)(5, 91)(6, 89)(7, 92)(8, 90)(9, 76)(10, 75)(11, 74)(12, 73)(13, 82)(14, 84)(15, 81)(16, 83)(17, 95)(18, 93)(19, 96)(20, 94)(21, 80)(22, 79)(23, 78)(24, 77)(25, 50)(26, 52)(27, 49)(28, 51)(29, 55)(30, 53)(31, 56)(32, 54)(33, 64)(34, 63)(35, 62)(36, 61)(37, 70)(38, 72)(39, 69)(40, 71)(41, 59)(42, 57)(43, 60)(44, 58)(45, 68)(46, 67)(47, 66)(48, 65)(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, 140)(123, 137)(124, 139)(125, 135)(126, 133)(127, 136)(128, 134)(129, 144)(130, 143)(131, 142)(132, 141)

MAP           : A4.932
NOTES         : type I, chiral, isomorphic to A4.930.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 4)(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^-1 * u.1 * u.2, (u.3 * u.4^-1)^2, u.4^4 >
CTG (small)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.3^-1 * x.1 * x.2, (x.3 * x.4^-1)^2, x.4^4, (x.4 * x.2)^2, x.4 * x.1 * x.4^2 * x.3, x.1 * x.4^-1 * x.1 * x.4 * x.3, x.3 * x.4^-2 * x.3^-1 * x.4^-1 * x.2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 4, 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, 86)(2, 88)(3, 85)(4, 87)(5, 91)(6, 89)(7, 92)(8, 90)(9, 76)(10, 75)(11, 74)(12, 73)(13, 82)(14, 84)(15, 81)(16, 83)(17, 95)(18, 93)(19, 96)(20, 94)(21, 80)(22, 79)(23, 78)(24, 77)(25, 50)(26, 52)(27, 49)(28, 51)(29, 55)(30, 53)(31, 56)(32, 54)(33, 64)(34, 63)(35, 62)(36, 61)(37, 70)(38, 72)(39, 69)(40, 71)(41, 59)(42, 57)(43, 60)(44, 58)(45, 68)(46, 67)(47, 66)(48, 65)(97, 114)(98, 116)(99, 113)(100, 115)(101, 111)(102, 109)(103, 112)(104, 110)(105, 120)(106, 119)(107, 118)(108, 117)(121, 128)(122, 127)(123, 126)(124, 125)(129, 139)(130, 137)(131, 140)(132, 138)(133, 143)(134, 141)(135, 144)(136, 142)

MAP           : A4.933
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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^-1 * x.4^-1 * x.1, x.4^3, (x.2 * x.4^-1)^2, x.3^4, (x.2 * x.1)^2, x.2 * x.4 * x.3 * x.2 * x.1, x.2 * x.3^2 * x.4 * x.3^-1, x.4 * x.2 * x.3^-1 * x.1 * x.3 >
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        : 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, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 51)(26, 49)(27, 52)(28, 50)(29, 54)(30, 56)(31, 53)(32, 55)(33, 66)(34, 68)(35, 65)(36, 67)(37, 60)(38, 59)(39, 58)(40, 57)(41, 72)(42, 71)(43, 70)(44, 69)(45, 63)(46, 61)(47, 64)(48, 62)(73, 134)(74, 136)(75, 133)(76, 135)(77, 139)(78, 137)(79, 140)(80, 138)(81, 124)(82, 123)(83, 122)(84, 121)(85, 130)(86, 132)(87, 129)(88, 131)(89, 143)(90, 141)(91, 144)(92, 142)(93, 128)(94, 127)(95, 126)(96, 125)(97, 114)(98, 116)(99, 113)(100, 115)(101, 111)(102, 109)(103, 112)(104, 110)(105, 120)(106, 119)(107, 118)(108, 117)

MAP           : A4.934
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)   : <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.4^3, (x.4 * x.2)^2, (x.3 * x.2)^2, x.3^4, x.1 * x.2 * x.3^-1 * x.4 * x.3^-1 >
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        : 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, 12)(4, 10)(5, 22)(6, 24)(7, 21)(8, 23)(13, 20)(14, 19)(15, 18)(16, 17)(25, 64)(26, 63)(27, 62)(28, 61)(29, 68)(30, 67)(31, 66)(32, 65)(33, 59)(34, 57)(35, 60)(36, 58)(37, 55)(38, 53)(39, 56)(40, 54)(41, 50)(42, 52)(43, 49)(44, 51)(45, 70)(46, 72)(47, 69)(48, 71)(73, 134)(74, 136)(75, 133)(76, 135)(77, 139)(78, 137)(79, 140)(80, 138)(81, 124)(82, 123)(83, 122)(84, 121)(85, 130)(86, 132)(87, 129)(88, 131)(89, 143)(90, 141)(91, 144)(92, 142)(93, 128)(94, 127)(95, 126)(96, 125)(97, 114)(98, 116)(99, 113)(100, 115)(101, 111)(102, 109)(103, 112)(104, 110)(105, 120)(106, 119)(107, 118)(108, 117)

MAP           : A4.935
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)   : <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.4^3, x.3^4, x.3^-1 * x.1 * x.3 * x.2, (x.4 * x.2)^2, x.2 * x.3 * x.2 * x.4 * x.3^-1, (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, 4, 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, 72)(26, 71)(27, 70)(28, 69)(29, 60)(30, 59)(31, 58)(32, 57)(33, 51)(34, 49)(35, 52)(36, 50)(37, 63)(38, 61)(39, 64)(40, 62)(41, 66)(42, 68)(43, 65)(44, 67)(45, 54)(46, 56)(47, 53)(48, 55)(73, 134)(74, 136)(75, 133)(76, 135)(77, 139)(78, 137)(79, 140)(80, 138)(81, 124)(82, 123)(83, 122)(84, 121)(85, 130)(86, 132)(87, 129)(88, 131)(89, 143)(90, 141)(91, 144)(92, 142)(93, 128)(94, 127)(95, 126)(96, 125)(97, 114)(98, 116)(99, 113)(100, 115)(101, 111)(102, 109)(103, 112)(104, 110)(105, 120)(106, 119)(107, 118)(108, 117)

MAP           : A4.936
NOTES         : type I, chiral, isomorphic to A4.935.
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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.1 * x.4 * x.3^-1, x.3^3, x.4^4, (x.3^-1 * x.2)^2, x.4 * x.1 * x.4^-1 * x.2, x.2 * x.1 * x.3^-1 * x.4^-2, (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, 4, 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, 110)(2, 112)(3, 109)(4, 111)(5, 115)(6, 113)(7, 116)(8, 114)(9, 100)(10, 99)(11, 98)(12, 97)(13, 106)(14, 108)(15, 105)(16, 107)(17, 119)(18, 117)(19, 120)(20, 118)(21, 104)(22, 103)(23, 102)(24, 101)(25, 58)(26, 60)(27, 57)(28, 59)(29, 71)(30, 69)(31, 72)(32, 70)(33, 56)(34, 55)(35, 54)(36, 53)(37, 62)(38, 64)(39, 61)(40, 63)(41, 67)(42, 65)(43, 68)(44, 66)(45, 52)(46, 51)(47, 50)(48, 49)(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, 140)(123, 137)(124, 139)(125, 135)(126, 133)(127, 136)(128, 134)(129, 144)(130, 143)(131, 142)(132, 141)

MAP           : A4.937
NOTES         : type I, chiral, isomorphic to A4.933.
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)   : <24, 12>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.4 * x.3^-1 * x.1, x.3^3, (x.2 * x.3^-1)^2, (x.2 * x.1)^2, x.4^4, x.2 * x.4 * x.2 * x.3^-1 * x.4^-1, x.2 * x.4 * x.1 * x.3^-1 * x.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        : 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, 112)(3, 109)(4, 111)(5, 115)(6, 113)(7, 116)(8, 114)(9, 100)(10, 99)(11, 98)(12, 97)(13, 106)(14, 108)(15, 105)(16, 107)(17, 119)(18, 117)(19, 120)(20, 118)(21, 104)(22, 103)(23, 102)(24, 101)(25, 50)(26, 52)(27, 49)(28, 51)(29, 55)(30, 53)(31, 56)(32, 54)(33, 64)(34, 63)(35, 62)(36, 61)(37, 70)(38, 72)(39, 69)(40, 71)(41, 59)(42, 57)(43, 60)(44, 58)(45, 68)(46, 67)(47, 66)(48, 65)(73, 85)(74, 86)(75, 87)(76, 88)(77, 89)(78, 90)(79, 91)(80, 92)(81, 93)(82, 94)(83, 95)(84, 96)(121, 138)(122, 140)(123, 137)(124, 139)(125, 135)(126, 133)(127, 136)(128, 134)(129, 144)(130, 143)(131, 142)(132, 141)

MAP           : A4.938
NOTES         : type I, chiral, isomorphic to A4.934.
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)   : <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.3^3, x.4^4, (x.3^-1 * x.2)^2, (x.4 * x.2)^2, x.1 * x.2 * x.4 * x.3 * x.4, x.3 * x.1 * x.2 * x.1 * x.4^-1 >
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        : 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, 112)(3, 109)(4, 111)(5, 115)(6, 113)(7, 116)(8, 114)(9, 100)(10, 99)(11, 98)(12, 97)(13, 106)(14, 108)(15, 105)(16, 107)(17, 119)(18, 117)(19, 120)(20, 118)(21, 104)(22, 103)(23, 102)(24, 101)(25, 67)(26, 65)(27, 68)(28, 66)(29, 62)(30, 64)(31, 61)(32, 63)(33, 58)(34, 60)(35, 57)(36, 59)(37, 52)(38, 51)(39, 50)(40, 49)(41, 56)(42, 55)(43, 54)(44, 53)(45, 71)(46, 69)(47, 72)(48, 70)(73, 83)(74, 81)(75, 84)(76, 82)(77, 94)(78, 96)(79, 93)(80, 95)(85, 92)(86, 91)(87, 90)(88, 89)(121, 138)(122, 140)(123, 137)(124, 139)(125, 135)(126, 133)(127, 136)(128, 134)(129, 144)(130, 143)(131, 142)(132, 141)

MAP           : A4.939
NOTES         : type I, chiral, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.3^-1 * u.2)^2, u.4^5 >
CTG (small)   : <20, 4>
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.3^-1 * x.2)^2, (x.4 * x.2)^2, (x.2 * x.1)^2, x.4^5 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2)
LOCAL TYPE    : (3, 3, 4, 4, 3, 5)
#DARTS        : 120
R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120)
L = (1, 86)(2, 83)(3, 90)(4, 99)(5, 82)(6, 87)(7, 98)(8, 97)(9, 94)(10, 89)(11, 84)(12, 95)(13, 92)(14, 81)(15, 88)(16, 91)(17, 96)(18, 85)(19, 100)(20, 93)(21, 43)(22, 46)(23, 47)(24, 48)(25, 41)(26, 50)(27, 49)(28, 60)(29, 45)(30, 58)(31, 55)(32, 44)(33, 51)(34, 42)(35, 59)(36, 52)(37, 53)(38, 54)(39, 57)(40, 56)(61, 62)(63, 66)(64, 75)(65, 74)(67, 70)(68, 79)(69, 78)(71, 72)(73, 76)(77, 80)(101, 111)(102, 112)(103, 113)(104, 114)(105, 115)(106, 116)(107, 117)(108, 118)(109, 119)(110, 120)

MAP           : A4.940
NOTES         : type I, chiral, isomorphic to A4.939.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.3^-1 * u.2)^2, u.4^5 >
CTG (small)   : <20, 4>
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.3^-1 * x.2)^2, (x.4 * x.2)^2, (x.2 * x.1)^2, x.4^5 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2)
LOCAL TYPE    : (3, 3, 4, 4, 3, 5)
#DARTS        : 120
R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120)
L = (1, 98)(2, 89)(3, 94)(4, 93)(5, 90)(6, 85)(7, 82)(8, 91)(9, 86)(10, 81)(11, 100)(12, 97)(13, 88)(14, 87)(15, 96)(16, 99)(17, 84)(18, 83)(19, 92)(20, 95)(21, 49)(22, 58)(23, 45)(24, 56)(25, 47)(26, 54)(27, 41)(28, 52)(29, 43)(30, 42)(31, 57)(32, 60)(33, 59)(34, 50)(35, 53)(36, 48)(37, 55)(38, 46)(39, 51)(40, 44)(61, 62)(63, 66)(64, 75)(65, 74)(67, 70)(68, 79)(69, 78)(71, 72)(73, 76)(77, 80)(101, 111)(102, 112)(103, 113)(104, 114)(105, 115)(106, 116)(107, 117)(108, 118)(109, 119)(110, 120)

MAP           : A4.941
NOTES         : type I, chiral, isomorphic to A4.939.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.3^-1 * u.2)^2, u.4^5 >
CTG (small)   : <20, 4>
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.3^-1 * x.2)^2, (x.4 * x.2)^2, (x.2 * x.1)^2, x.4^5 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2)
LOCAL TYPE    : (3, 3, 4, 4, 3, 5)
#DARTS        : 120
R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120)
L = (1, 98)(2, 89)(3, 94)(4, 93)(5, 90)(6, 85)(7, 82)(8, 91)(9, 86)(10, 81)(11, 100)(12, 97)(13, 88)(14, 87)(15, 96)(16, 99)(17, 84)(18, 83)(19, 92)(20, 95)(21, 49)(22, 58)(23, 45)(24, 56)(25, 47)(26, 54)(27, 41)(28, 52)(29, 43)(30, 42)(31, 57)(32, 60)(33, 59)(34, 50)(35, 53)(36, 48)(37, 55)(38, 46)(39, 51)(40, 44)(61, 62)(63, 66)(64, 75)(65, 74)(67, 70)(68, 79)(69, 78)(71, 72)(73, 76)(77, 80)(101, 104)(102, 115)(103, 112)(105, 108)(106, 111)(107, 116)(109, 120)(110, 113)(114, 119)(117, 118)

MAP           : A4.942
NOTES         : type I, chiral, isomorphic to A4.939.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 5)(2, 3)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.3^-1 * u.2)^2, u.4^5 >
CTG (small)   : <20, 4>
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.3^-1 * x.2)^2, (x.4 * x.2)^2, (x.2 * x.1)^2, x.4^5 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.3^-1, x.2)
LOCAL TYPE    : (3, 3, 4, 4, 3, 5)
#DARTS        : 120
R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120)
L = (1, 86)(2, 83)(3, 90)(4, 99)(5, 82)(6, 87)(7, 98)(8, 97)(9, 94)(10, 89)(11, 84)(12, 95)(13, 92)(14, 81)(15, 88)(16, 91)(17, 96)(18, 85)(19, 100)(20, 93)(21, 43)(22, 46)(23, 47)(24, 48)(25, 41)(26, 50)(27, 49)(28, 60)(29, 45)(30, 58)(31, 55)(32, 44)(33, 51)(34, 42)(35, 59)(36, 52)(37, 53)(38, 54)(39, 57)(40, 56)(61, 62)(63, 66)(64, 75)(65, 74)(67, 70)(68, 79)(69, 78)(71, 72)(73, 76)(77, 80)(101, 104)(102, 115)(103, 112)(105, 108)(106, 111)(107, 116)(109, 120)(110, 113)(114, 119)(117, 118)

MAP           : A4.943
NOTES         : type I, chiral, isomorphic to A4.939.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.4 * u.2)^2, u.3^5 >
CTG (small)   : <20, 4>
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.1)^2, (x.4 * x.2)^2, (x.3^-1 * x.2)^2, x.3^5, x.3^2 * x.4^-1 * x.3 * x.4^-1 >
SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1)
LOCAL TYPE    : (3, 3, 5, 3, 4, 4)
#DARTS        : 120
R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120)
L = (1, 2)(3, 6)(4, 15)(5, 14)(7, 10)(8, 19)(9, 18)(11, 12)(13, 16)(17, 20)(21, 45)(22, 54)(23, 41)(24, 52)(25, 49)(26, 42)(27, 43)(28, 44)(29, 47)(30, 46)(31, 53)(32, 56)(33, 57)(34, 58)(35, 51)(36, 60)(37, 59)(38, 50)(39, 55)(40, 48)(61, 106)(62, 103)(63, 110)(64, 119)(65, 102)(66, 107)(67, 118)(68, 117)(69, 114)(70, 109)(71, 104)(72, 115)(73, 112)(74, 101)(75, 108)(76, 111)(77, 116)(78, 105)(79, 120)(80, 113)(81, 84)(82, 95)(83, 92)(85, 88)(86, 91)(87, 96)(89, 100)(90, 93)(94, 99)(97, 98)

MAP           : A4.944
NOTES         : type I, chiral, isomorphic to A4.939.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.4 * u.2)^2, u.3^5 >
CTG (small)   : <20, 4>
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.1)^2, (x.4 * x.2)^2, (x.3^-1 * x.2)^2, x.3^5, x.3^2 * x.4^-1 * x.3 * x.4^-1 >
SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1)
LOCAL TYPE    : (3, 3, 5, 3, 4, 4)
#DARTS        : 120
R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120)
L = (1, 2)(3, 6)(4, 15)(5, 14)(7, 10)(8, 19)(9, 18)(11, 12)(13, 16)(17, 20)(21, 47)(22, 50)(23, 49)(24, 60)(25, 43)(26, 58)(27, 45)(28, 56)(29, 41)(30, 54)(31, 59)(32, 48)(33, 55)(34, 46)(35, 57)(36, 44)(37, 51)(38, 42)(39, 53)(40, 52)(61, 118)(62, 109)(63, 114)(64, 113)(65, 110)(66, 105)(67, 102)(68, 111)(69, 106)(70, 101)(71, 120)(72, 117)(73, 108)(74, 107)(75, 116)(76, 119)(77, 104)(78, 103)(79, 112)(80, 115)(81, 91)(82, 92)(83, 93)(84, 94)(85, 95)(86, 96)(87, 97)(88, 98)(89, 99)(90, 100)

MAP           : A4.945
NOTES         : type I, chiral, isomorphic to A4.939.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.4 * u.2)^2, u.3^5 >
CTG (small)   : <20, 4>
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.1)^2, (x.4 * x.2)^2, (x.3^-1 * x.2)^2, x.3^5, x.3^2 * x.4^-1 * x.3 * x.4^-1 >
SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1)
LOCAL TYPE    : (3, 3, 5, 3, 4, 4)
#DARTS        : 120
R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120)
L = (1, 2)(3, 6)(4, 15)(5, 14)(7, 10)(8, 19)(9, 18)(11, 12)(13, 16)(17, 20)(21, 47)(22, 50)(23, 49)(24, 60)(25, 43)(26, 58)(27, 45)(28, 56)(29, 41)(30, 54)(31, 59)(32, 48)(33, 55)(34, 46)(35, 57)(36, 44)(37, 51)(38, 42)(39, 53)(40, 52)(61, 118)(62, 109)(63, 114)(64, 113)(65, 110)(66, 105)(67, 102)(68, 111)(69, 106)(70, 101)(71, 120)(72, 117)(73, 108)(74, 107)(75, 116)(76, 119)(77, 104)(78, 103)(79, 112)(80, 115)(81, 84)(82, 95)(83, 92)(85, 88)(86, 91)(87, 96)(89, 100)(90, 93)(94, 99)(97, 98)

MAP           : A4.946
NOTES         : type I, chiral, isomorphic to A4.939.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (2, 3)(4, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.4 * u.2)^2, u.3^5 >
CTG (small)   : <20, 4>
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.1)^2, (x.4 * x.2)^2, (x.3^-1 * x.2)^2, x.3^5, x.3^2 * x.4^-1 * x.3 * x.4^-1 >
SCHREIER VEC. : (x.1, x.3, x.3^-1, x.4, x.2, x.4^-1)
LOCAL TYPE    : (3, 3, 5, 3, 4, 4)
#DARTS        : 120
R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120)
L = (1, 2)(3, 6)(4, 15)(5, 14)(7, 10)(8, 19)(9, 18)(11, 12)(13, 16)(17, 20)(21, 45)(22, 54)(23, 41)(24, 52)(25, 49)(26, 42)(27, 43)(28, 44)(29, 47)(30, 46)(31, 53)(32, 56)(33, 57)(34, 58)(35, 51)(36, 60)(37, 59)(38, 50)(39, 55)(40, 48)(61, 106)(62, 103)(63, 110)(64, 119)(65, 102)(66, 107)(67, 118)(68, 117)(69, 114)(70, 109)(71, 104)(72, 115)(73, 112)(74, 101)(75, 108)(76, 111)(77, 116)(78, 105)(79, 120)(80, 113)(81, 91)(82, 92)(83, 93)(84, 94)(85, 95)(86, 96)(87, 97)(88, 98)(89, 99)(90, 100)

MAP           : A4.947
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3^5, u.6^5 >
CTG (small)   : <10, 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.7 * x.1 * x.3^-1, x.6 * x.2 * x.7^-1, x.1 * x.3 * x.7^-1, x.4 * x.2 * x.3, x.4 * x.5^-1 * x.7 * x.5, x.3^5, x.3^2 * x.7 * x.3 * x.4^-1, x.6^5 >
SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1)
LOCAL TYPE    : (3, 3, 5, 3, 4, 4)
#DARTS        : 120
R = (1, 11, 21, 31, 41, 51)(2, 12, 22, 32, 42, 52)(3, 13, 23, 33, 43, 53)(4, 14, 24, 34, 44, 54)(5, 15, 25, 35, 45, 55)(6, 16, 26, 36, 46, 56)(7, 17, 27, 37, 47, 57)(8, 18, 28, 38, 48, 58)(9, 19, 29, 39, 49, 59)(10, 20, 30, 40, 50, 60)(61, 71, 81, 91, 101, 111)(62, 72, 82, 92, 102, 112)(63, 73, 83, 93, 103, 113)(64, 74, 84, 94, 104, 114)(65, 75, 85, 95, 105, 115)(66, 76, 86, 96, 106, 116)(67, 77, 87, 97, 107, 117)(68, 78, 88, 98, 108, 118)(69, 79, 89, 99, 109, 119)(70, 80, 90, 100, 110, 120)
L = (1, 12)(2, 15)(3, 11)(4, 16)(5, 17)(6, 19)(7, 13)(8, 14)(9, 20)(10, 18)(21, 48)(22, 44)(23, 50)(24, 43)(25, 46)(26, 41)(27, 49)(28, 47)(29, 42)(30, 45)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(51, 54)(52, 56)(53, 58)(55, 59)(57, 60)(61, 112)(62, 115)(63, 111)(64, 116)(65, 117)(66, 119)(67, 113)(68, 114)(69, 120)(70, 118)(71, 74)(72, 76)(73, 78)(75, 79)(77, 80)(81, 106)(82, 109)(83, 104)(84, 102)(85, 110)(86, 105)(87, 108)(88, 101)(89, 107)(90, 103)

MAP           : A4.948
NOTES         : type II, reflexible, isomorphic to A4.947.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3^5, u.6^5 >
CTG (small)   : <10, 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.7 * x.1 * x.3^-1, x.6 * x.2 * x.7^-1, x.1 * x.3 * x.7^-1, x.4 * x.2 * x.3, x.4 * x.5^-1 * x.7 * x.5, x.3^5, x.3^2 * x.7 * x.3 * x.4^-1, x.6^5 >
SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1)
LOCAL TYPE    : (3, 3, 5, 3, 4, 4)
#DARTS        : 120
R = (1, 11, 21, 31, 41, 51)(2, 12, 22, 32, 42, 52)(3, 13, 23, 33, 43, 53)(4, 14, 24, 34, 44, 54)(5, 15, 25, 35, 45, 55)(6, 16, 26, 36, 46, 56)(7, 17, 27, 37, 47, 57)(8, 18, 28, 38, 48, 58)(9, 19, 29, 39, 49, 59)(10, 20, 30, 40, 50, 60)(61, 71, 81, 91, 101, 111)(62, 72, 82, 92, 102, 112)(63, 73, 83, 93, 103, 113)(64, 74, 84, 94, 104, 114)(65, 75, 85, 95, 105, 115)(66, 76, 86, 96, 106, 116)(67, 77, 87, 97, 107, 117)(68, 78, 88, 98, 108, 118)(69, 79, 89, 99, 109, 119)(70, 80, 90, 100, 110, 120)
L = (1, 15)(2, 17)(3, 12)(4, 19)(5, 13)(6, 20)(7, 11)(8, 16)(9, 18)(10, 14)(21, 50)(22, 48)(23, 49)(24, 47)(25, 44)(26, 43)(27, 46)(28, 45)(29, 41)(30, 42)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(51, 54)(52, 56)(53, 58)(55, 59)(57, 60)(61, 115)(62, 117)(63, 112)(64, 119)(65, 113)(66, 120)(67, 111)(68, 116)(69, 118)(70, 114)(71, 74)(72, 76)(73, 78)(75, 79)(77, 80)(81, 109)(82, 110)(83, 106)(84, 105)(85, 108)(86, 107)(87, 104)(88, 102)(89, 103)(90, 101)

MAP           : A4.949
NOTES         : type II, reflexible, isomorphic to A4.947.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3^5, u.6^5 >
CTG (small)   : <10, 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.7 * x.1 * x.3^-1, x.6 * x.2 * x.7^-1, x.1 * x.3 * x.7^-1, x.4 * x.2 * x.3, x.4 * x.5^-1 * x.7 * x.5, x.3^5, x.3^2 * x.7 * x.3 * x.4^-1, x.6^5 >
SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1)
LOCAL TYPE    : (3, 3, 5, 3, 4, 4)
#DARTS        : 120
R = (1, 11, 21, 31, 41, 51)(2, 12, 22, 32, 42, 52)(3, 13, 23, 33, 43, 53)(4, 14, 24, 34, 44, 54)(5, 15, 25, 35, 45, 55)(6, 16, 26, 36, 46, 56)(7, 17, 27, 37, 47, 57)(8, 18, 28, 38, 48, 58)(9, 19, 29, 39, 49, 59)(10, 20, 30, 40, 50, 60)(61, 71, 81, 91, 101, 111)(62, 72, 82, 92, 102, 112)(63, 73, 83, 93, 103, 113)(64, 74, 84, 94, 104, 114)(65, 75, 85, 95, 105, 115)(66, 76, 86, 96, 106, 116)(67, 77, 87, 97, 107, 117)(68, 78, 88, 98, 108, 118)(69, 79, 89, 99, 109, 119)(70, 80, 90, 100, 110, 120)
L = (1, 17)(2, 13)(3, 15)(4, 20)(5, 11)(6, 18)(7, 12)(8, 19)(9, 14)(10, 16)(21, 49)(22, 50)(23, 46)(24, 45)(25, 48)(26, 47)(27, 44)(28, 42)(29, 43)(30, 41)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(51, 54)(52, 56)(53, 58)(55, 59)(57, 60)(61, 117)(62, 113)(63, 115)(64, 120)(65, 111)(66, 118)(67, 112)(68, 119)(69, 114)(70, 116)(71, 74)(72, 76)(73, 78)(75, 79)(77, 80)(81, 110)(82, 108)(83, 109)(84, 107)(85, 104)(86, 103)(87, 106)(88, 105)(89, 101)(90, 102)

MAP           : A4.950
NOTES         : type II, reflexible, isomorphic to A4.947.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3^5, u.6^5 >
CTG (small)   : <10, 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.7 * x.1 * x.3^-1, x.6 * x.2 * x.7^-1, x.1 * x.3 * x.7^-1, x.4 * x.2 * x.3, x.4 * x.5^-1 * x.7 * x.5, x.3^5, x.3^2 * x.7 * x.3 * x.4^-1, x.6^5 >
SCHREIER VEC. : (x.3, x.3^-1, x.4, x.5, x.4^-1, x.1)
LOCAL TYPE    : (3, 3, 5, 3, 4, 4)
#DARTS        : 120
R = (1, 11, 21, 31, 41, 51)(2, 12, 22, 32, 42, 52)(3, 13, 23, 33, 43, 53)(4, 14, 24, 34, 44, 54)(5, 15, 25, 35, 45, 55)(6, 16, 26, 36, 46, 56)(7, 17, 27, 37, 47, 57)(8, 18, 28, 38, 48, 58)(9, 19, 29, 39, 49, 59)(10, 20, 30, 40, 50, 60)(61, 71, 81, 91, 101, 111)(62, 72, 82, 92, 102, 112)(63, 73, 83, 93, 103, 113)(64, 74, 84, 94, 104, 114)(65, 75, 85, 95, 105, 115)(66, 76, 86, 96, 106, 116)(67, 77, 87, 97, 107, 117)(68, 78, 88, 98, 108, 118)(69, 79, 89, 99, 109, 119)(70, 80, 90, 100, 110, 120)
L = (1, 13)(2, 11)(3, 17)(4, 18)(5, 12)(6, 14)(7, 15)(8, 20)(9, 16)(10, 19)(21, 46)(22, 49)(23, 44)(24, 42)(25, 50)(26, 45)(27, 48)(28, 41)(29, 47)(30, 43)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(51, 54)(52, 56)(53, 58)(55, 59)(57, 60)(61, 113)(62, 111)(63, 117)(64, 118)(65, 112)(66, 114)(67, 115)(68, 120)(69, 116)(70, 119)(71, 74)(72, 76)(73, 78)(75, 79)(77, 80)(81, 108)(82, 104)(83, 110)(84, 103)(85, 106)(86, 101)(87, 109)(88, 107)(89, 102)(90, 105)

MAP           : A4.951
NOTES         : type I, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6)
ORBIFOLD      : O(0, {5, 4, 4})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 5, 4, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.3^4, u.2^5 >
CTG (small)   : <20, 3>
CTG (fp)      : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.1^4, x.3^4, x.1^-1 * x.3^-1 * x.2^-2, (x.3^-1 * x.1)^2, x.3 * x.2^-1 * x.1 * x.2^-1, x.2^5 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 4, 3, 4, 3, 5)
#DARTS        : 120
R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120)
L = (1, 23)(2, 34)(3, 32)(4, 25)(5, 37)(6, 22)(7, 28)(8, 40)(9, 27)(10, 21)(11, 24)(12, 30)(13, 39)(14, 38)(15, 33)(16, 35)(17, 31)(18, 26)(19, 36)(20, 29)(41, 62)(42, 68)(43, 80)(44, 67)(45, 61)(46, 64)(47, 70)(48, 79)(49, 78)(50, 73)(51, 75)(52, 71)(53, 66)(54, 76)(55, 69)(56, 63)(57, 74)(58, 72)(59, 65)(60, 77)(81, 104)(82, 110)(83, 119)(84, 118)(85, 113)(86, 115)(87, 111)(88, 106)(89, 116)(90, 109)(91, 103)(92, 114)(93, 112)(94, 105)(95, 117)(96, 102)(97, 108)(98, 120)(99, 107)(100, 101)

MAP           : A4.952
NOTES         : type I, reflexible, isomorphic to A4.951.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6)
ORBIFOLD      : O(0, {5, 4, 4})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 4, 4, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.2^4, u.3^4, u.1^5 >
CTG (small)   : <20, 3>
CTG (fp)      : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2^4, x.3^4, x.1^-1 * x.3^-1 * x.2^-1 * x.1^-1, (x.3^-1 * x.2)^2, x.2 * x.1^-1 * x.3 * x.1^-1, x.1^5 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 4, 3, 4, 3, 5)
#DARTS        : 120
R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120)
L = (1, 22)(2, 28)(3, 40)(4, 27)(5, 21)(6, 24)(7, 30)(8, 39)(9, 38)(10, 33)(11, 35)(12, 31)(13, 26)(14, 36)(15, 29)(16, 23)(17, 34)(18, 32)(19, 25)(20, 37)(41, 70)(42, 66)(43, 61)(44, 71)(45, 64)(46, 78)(47, 69)(48, 67)(49, 80)(50, 72)(51, 77)(52, 63)(53, 75)(54, 62)(55, 76)(56, 79)(57, 65)(58, 74)(59, 73)(60, 68)(81, 116)(82, 117)(83, 118)(84, 119)(85, 120)(86, 101)(87, 102)(88, 103)(89, 104)(90, 105)(91, 106)(92, 107)(93, 108)(94, 109)(95, 110)(96, 111)(97, 112)(98, 113)(99, 114)(100, 115)

MAP           : A4.953
NOTES         : type I, reflexible, representative.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3 * u.4^-1)^2, u.2^5, u.6^5 >
CTG (small)   : <10, 1>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.4^2, x.2 * x.3, x.3^2 * x.6, x.2 * x.6^2, x.2^2 * x.6^-1, x.4 * x.5^-1 * x.6^-1, x.3 * x.6^-1 * x.5^-1 * x.4, x.3 * x.5 * x.6 * x.4, (x.5 * x.1^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 4, 3, 4, 3, 5)
#DARTS        : 120
R = (1, 11, 21, 31, 41, 51)(2, 12, 22, 32, 42, 52)(3, 13, 23, 33, 43, 53)(4, 14, 24, 34, 44, 54)(5, 15, 25, 35, 45, 55)(6, 16, 26, 36, 46, 56)(7, 17, 27, 37, 47, 57)(8, 18, 28, 38, 48, 58)(9, 19, 29, 39, 49, 59)(10, 20, 30, 40, 50, 60)(61, 71, 81, 91, 101, 111)(62, 72, 82, 92, 102, 112)(63, 73, 83, 93, 103, 113)(64, 74, 84, 94, 104, 114)(65, 75, 85, 95, 105, 115)(66, 76, 86, 96, 106, 116)(67, 77, 87, 97, 107, 117)(68, 78, 88, 98, 108, 118)(69, 79, 89, 99, 109, 119)(70, 80, 90, 100, 110, 120)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 24)(12, 21)(13, 29)(14, 28)(15, 22)(16, 27)(17, 30)(18, 25)(19, 26)(20, 23)(31, 72)(32, 75)(33, 80)(34, 71)(35, 78)(36, 79)(37, 76)(38, 74)(39, 73)(40, 77)(41, 63)(42, 69)(43, 61)(44, 70)(45, 66)(46, 65)(47, 68)(48, 67)(49, 62)(50, 64)(51, 97)(52, 100)(53, 95)(54, 96)(55, 93)(56, 94)(57, 91)(58, 99)(59, 98)(60, 92)(101, 118)(102, 114)(103, 116)(104, 115)(105, 111)(106, 120)(107, 113)(108, 112)(109, 117)(110, 119)

MAP           : A4.954
NOTES         : type I, reflexible, isomorphic to A4.951.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3 * u.4^-1)^2, u.2^5, u.6^5 >
CTG (small)   : <10, 1>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.4^2, x.3^-1 * x.2^-1, x.2^2 * x.6, x.2 * x.6^-2, x.4 * x.5^-1 * x.6^-1, x.3^2 * x.6^-1, (x.3 * x.4)^2, (x.5 * x.1^-1)^2, x.4 * x.6^-1 * x.5^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 4, 3, 4, 3, 5)
#DARTS        : 120
R = (1, 11, 21, 31, 41, 51)(2, 12, 22, 32, 42, 52)(3, 13, 23, 33, 43, 53)(4, 14, 24, 34, 44, 54)(5, 15, 25, 35, 45, 55)(6, 16, 26, 36, 46, 56)(7, 17, 27, 37, 47, 57)(8, 18, 28, 38, 48, 58)(9, 19, 29, 39, 49, 59)(10, 20, 30, 40, 50, 60)(61, 71, 81, 91, 101, 111)(62, 72, 82, 92, 102, 112)(63, 73, 83, 93, 103, 113)(64, 74, 84, 94, 104, 114)(65, 75, 85, 95, 105, 115)(66, 76, 86, 96, 106, 116)(67, 77, 87, 97, 107, 117)(68, 78, 88, 98, 108, 118)(69, 79, 89, 99, 109, 119)(70, 80, 90, 100, 110, 120)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 28)(12, 24)(13, 26)(14, 25)(15, 21)(16, 30)(17, 23)(18, 22)(19, 27)(20, 29)(31, 75)(32, 78)(33, 77)(34, 72)(35, 74)(36, 73)(37, 79)(38, 71)(39, 80)(40, 76)(41, 63)(42, 69)(43, 61)(44, 70)(45, 66)(46, 65)(47, 68)(48, 67)(49, 62)(50, 64)(51, 100)(52, 93)(53, 92)(54, 97)(55, 99)(56, 98)(57, 94)(58, 96)(59, 95)(60, 91)(101, 114)(102, 111)(103, 119)(104, 118)(105, 112)(106, 117)(107, 120)(108, 115)(109, 116)(110, 113)

MAP           : A4.955
NOTES         : type I, reflexible, isomorphic to A4.953.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6)
ORBIFOLD      : O(0, {5, 4, 4})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 5, 4, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.3^4, u.2^5 >
CTG (small)   : <20, 3>
CTG (fp)      : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.1^-1 * x.3^-1 * x.2^2, x.1^4, x.3^4, x.1^-1 * x.2 * x.3^-1 * x.2^-1, (x.3^-1 * x.1)^2, x.3 * x.1 * x.3 * x.1 * x.2 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 4, 3, 4, 3, 5)
#DARTS        : 120
R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120)
L = (1, 30)(2, 26)(3, 21)(4, 31)(5, 24)(6, 38)(7, 29)(8, 27)(9, 40)(10, 32)(11, 37)(12, 23)(13, 35)(14, 22)(15, 36)(16, 39)(17, 25)(18, 34)(19, 33)(20, 28)(41, 62)(42, 68)(43, 80)(44, 67)(45, 61)(46, 64)(47, 70)(48, 79)(49, 78)(50, 73)(51, 75)(52, 71)(53, 66)(54, 76)(55, 69)(56, 63)(57, 74)(58, 72)(59, 65)(60, 77)(81, 117)(82, 103)(83, 115)(84, 102)(85, 116)(86, 119)(87, 105)(88, 114)(89, 113)(90, 108)(91, 110)(92, 106)(93, 101)(94, 111)(95, 104)(96, 118)(97, 109)(98, 107)(99, 120)(100, 112)

MAP           : A4.956
NOTES         : type I, reflexible, isomorphic to A4.953.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6)
ORBIFOLD      : O(0, {5, 4, 4})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 4, 5, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^5 >
CTG (small)   : <20, 3>
CTG (fp)      : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.1 * x.3^-1 * x.2 * x.3, (x.1^-1 * x.2)^2, x.1^4, x.2^4, x.3^2 * x.2^-1 * x.1^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 4, 3, 4, 3, 5)
#DARTS        : 120
R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120)
L = (1, 23)(2, 34)(3, 32)(4, 25)(5, 37)(6, 22)(7, 28)(8, 40)(9, 27)(10, 21)(11, 24)(12, 30)(13, 39)(14, 38)(15, 33)(16, 35)(17, 31)(18, 26)(19, 36)(20, 29)(41, 73)(42, 64)(43, 62)(44, 75)(45, 67)(46, 72)(47, 78)(48, 70)(49, 77)(50, 71)(51, 74)(52, 80)(53, 69)(54, 68)(55, 63)(56, 65)(57, 61)(58, 76)(59, 66)(60, 79)(81, 105)(82, 101)(83, 116)(84, 106)(85, 119)(86, 113)(87, 104)(88, 102)(89, 115)(90, 107)(91, 112)(92, 118)(93, 110)(94, 117)(95, 111)(96, 114)(97, 120)(98, 109)(99, 108)(100, 103)

MAP           : A4.957
NOTES         : type I, reflexible, isomorphic to A4.951.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3 * u.4^-1)^2, u.2^5, u.6^5 >
CTG (small)   : <10, 1>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.4^2, x.3^-1 * x.2^-1, x.2^2 * x.6, x.2 * x.6^-2, x.4 * x.5^-1 * x.6^-1, x.3^2 * x.6^-1, (x.3 * x.4)^2, (x.5 * x.1^-1)^2, x.4 * x.6^-1 * x.5^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 4, 3, 4, 3, 5)
#DARTS        : 120
R = (1, 11, 21, 31, 41, 51)(2, 12, 22, 32, 42, 52)(3, 13, 23, 33, 43, 53)(4, 14, 24, 34, 44, 54)(5, 15, 25, 35, 45, 55)(6, 16, 26, 36, 46, 56)(7, 17, 27, 37, 47, 57)(8, 18, 28, 38, 48, 58)(9, 19, 29, 39, 49, 59)(10, 20, 30, 40, 50, 60)(61, 71, 81, 91, 101, 111)(62, 72, 82, 92, 102, 112)(63, 73, 83, 93, 103, 113)(64, 74, 84, 94, 104, 114)(65, 75, 85, 95, 105, 115)(66, 76, 86, 96, 106, 116)(67, 77, 87, 97, 107, 117)(68, 78, 88, 98, 108, 118)(69, 79, 89, 99, 109, 119)(70, 80, 90, 100, 110, 120)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 24)(12, 21)(13, 29)(14, 28)(15, 22)(16, 27)(17, 30)(18, 25)(19, 26)(20, 23)(31, 72)(32, 75)(33, 80)(34, 71)(35, 78)(36, 79)(37, 76)(38, 74)(39, 73)(40, 77)(41, 63)(42, 69)(43, 61)(44, 70)(45, 66)(46, 65)(47, 68)(48, 67)(49, 62)(50, 64)(51, 96)(52, 97)(53, 98)(54, 99)(55, 100)(56, 91)(57, 92)(58, 93)(59, 94)(60, 95)(101, 115)(102, 118)(103, 117)(104, 112)(105, 114)(106, 113)(107, 119)(108, 111)(109, 120)(110, 116)

MAP           : A4.958
NOTES         : type I, reflexible, isomorphic to A4.953.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3 * u.4^-1)^2, u.2^5, u.6^5 >
CTG (small)   : <10, 1>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.1, x.1, x.4^2, x.2 * x.3, x.3^2 * x.6, x.2 * x.6^2, x.2^2 * x.6^-1, x.4 * x.5^-1 * x.6^-1, x.3 * x.6^-1 * x.5^-1 * x.4, x.3 * x.5 * x.6 * x.4, (x.5 * x.1^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.2^-1, x.3, x.4, x.5)
LOCAL TYPE    : (3, 4, 3, 4, 3, 5)
#DARTS        : 120
R = (1, 11, 21, 31, 41, 51)(2, 12, 22, 32, 42, 52)(3, 13, 23, 33, 43, 53)(4, 14, 24, 34, 44, 54)(5, 15, 25, 35, 45, 55)(6, 16, 26, 36, 46, 56)(7, 17, 27, 37, 47, 57)(8, 18, 28, 38, 48, 58)(9, 19, 29, 39, 49, 59)(10, 20, 30, 40, 50, 60)(61, 71, 81, 91, 101, 111)(62, 72, 82, 92, 102, 112)(63, 73, 83, 93, 103, 113)(64, 74, 84, 94, 104, 114)(65, 75, 85, 95, 105, 115)(66, 76, 86, 96, 106, 116)(67, 77, 87, 97, 107, 117)(68, 78, 88, 98, 108, 118)(69, 79, 89, 99, 109, 119)(70, 80, 90, 100, 110, 120)
L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 28)(12, 24)(13, 26)(14, 25)(15, 21)(16, 30)(17, 23)(18, 22)(19, 27)(20, 29)(31, 75)(32, 78)(33, 77)(34, 72)(35, 74)(36, 73)(37, 79)(38, 71)(39, 80)(40, 76)(41, 63)(42, 69)(43, 61)(44, 70)(45, 66)(46, 65)(47, 68)(48, 67)(49, 62)(50, 64)(51, 99)(52, 96)(53, 94)(54, 93)(55, 97)(56, 92)(57, 95)(58, 100)(59, 91)(60, 98)(101, 112)(102, 115)(103, 120)(104, 111)(105, 118)(106, 119)(107, 116)(108, 114)(109, 113)(110, 117)

MAP           : A4.959
NOTES         : type I, reflexible, isomorphic to A4.951.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6)
ORBIFOLD      : O(0, {5, 4, 4})
EMBEDDING     : vertices: [ 1 ], faces: [ 4, 4, 5, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.1^4, u.2^4, u.3^5 >
CTG (small)   : <20, 3>
CTG (fp)      : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.1^4, x.2^4, x.3 * x.1^-1 * x.3 * x.2^-1, x.2^-1 * x.1^-1 * x.3^-2, (x.2 * x.1^-1)^2, x.3^5 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 4, 3, 4, 3, 5)
#DARTS        : 120
R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120)
L = (1, 30)(2, 26)(3, 21)(4, 31)(5, 24)(6, 38)(7, 29)(8, 27)(9, 40)(10, 32)(11, 37)(12, 23)(13, 35)(14, 22)(15, 36)(16, 39)(17, 25)(18, 34)(19, 33)(20, 28)(41, 77)(42, 63)(43, 75)(44, 62)(45, 76)(46, 79)(47, 65)(48, 74)(49, 73)(50, 68)(51, 70)(52, 66)(53, 61)(54, 71)(55, 64)(56, 78)(57, 69)(58, 67)(59, 80)(60, 72)(81, 119)(82, 105)(83, 114)(84, 113)(85, 108)(86, 110)(87, 106)(88, 101)(89, 111)(90, 104)(91, 118)(92, 109)(93, 107)(94, 120)(95, 112)(96, 117)(97, 103)(98, 115)(99, 102)(100, 116)

MAP           : A4.960
NOTES         : type I, reflexible, isomorphic to A4.953.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 2)(3, 4)(5, 6)
ORBIFOLD      : O(0, {5, 4, 4})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 4, 4, 1 ]
UNIGROUP      : < u.1, u.2, u.3 | u.1^-1 * u.2^-1 * u.3^-1, u.2^4, u.3^4, u.1^5 >
CTG (small)   : <20, 3>
CTG (fp)      : < x.1, x.2, x.3 | x.1^-1 * x.2^-1 * x.3^-1, x.2 * x.1^-1 * x.3 * x.1, x.2^4, x.3^4, (x.3^-1 * x.2)^2, x.2^-1 * x.1^2 * x.3^-1, x.2 * x.3 * x.2^-1 * x.1 * x.3^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.2^-1, x.3, x.3^-1)
LOCAL TYPE    : (3, 4, 3, 4, 3, 5)
#DARTS        : 120
R = (1, 21, 41, 61, 81, 101)(2, 22, 42, 62, 82, 102)(3, 23, 43, 63, 83, 103)(4, 24, 44, 64, 84, 104)(5, 25, 45, 65, 85, 105)(6, 26, 46, 66, 86, 106)(7, 27, 47, 67, 87, 107)(8, 28, 48, 68, 88, 108)(9, 29, 49, 69, 89, 109)(10, 30, 50, 70, 90, 110)(11, 31, 51, 71, 91, 111)(12, 32, 52, 72, 92, 112)(13, 33, 53, 73, 93, 113)(14, 34, 54, 74, 94, 114)(15, 35, 55, 75, 95, 115)(16, 36, 56, 76, 96, 116)(17, 37, 57, 77, 97, 117)(18, 38, 58, 78, 98, 118)(19, 39, 59, 79, 99, 119)(20, 40, 60, 80, 100, 120)
L = (1, 22)(2, 28)(3, 40)(4, 27)(5, 21)(6, 24)(7, 30)(8, 39)(9, 38)(10, 33)(11, 35)(12, 31)(13, 26)(14, 36)(15, 29)(16, 23)(17, 34)(18, 32)(19, 25)(20, 37)(41, 63)(42, 74)(43, 72)(44, 65)(45, 77)(46, 62)(47, 68)(48, 80)(49, 67)(50, 61)(51, 64)(52, 70)(53, 79)(54, 78)(55, 73)(56, 75)(57, 71)(58, 66)(59, 76)(60, 69)(81, 107)(82, 113)(83, 105)(84, 112)(85, 106)(86, 109)(87, 115)(88, 104)(89, 103)(90, 118)(91, 120)(92, 116)(93, 111)(94, 101)(95, 114)(96, 108)(97, 119)(98, 117)(99, 110)(100, 102)

MAP           : A4.961
NOTES         : type I, chiral, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 6)(2, 3)
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.4^3, u.3^3, u.3 * u.4^-1 * u.1 * u.2 >
CTG (small)   : <18, 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^-1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4^-1, x.4^-1 * x.1 * x.2 * x.3, x.3^-1 * x.1 * x.3 * x.2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.2, x.3^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)
L = (1, 106)(2, 99)(3, 108)(4, 107)(5, 103)(6, 92)(7, 94)(8, 105)(9, 96)(10, 95)(11, 91)(12, 98)(13, 100)(14, 93)(15, 102)(16, 101)(17, 97)(18, 104)(19, 41)(20, 54)(21, 44)(22, 37)(23, 40)(24, 39)(25, 47)(26, 42)(27, 50)(28, 43)(29, 46)(30, 45)(31, 53)(32, 48)(33, 38)(34, 49)(35, 52)(36, 51)(55, 56)(57, 71)(58, 69)(59, 72)(60, 67)(61, 63)(62, 70)(64, 66)(65, 68)(73, 84)(74, 89)(75, 82)(76, 86)(77, 81)(78, 83)(79, 80)(85, 87)(88, 90)

MAP           : A4.962
NOTES         : type I, chiral, isomorphic to A4.961.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 6)(2, 3)
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.4^3, u.3^3, u.3 * u.4^-1 * u.1 * u.2 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.4^3, (x.3, x.4^-1), x.3 * x.2 * x.3^-1 * x.2, x.3 * x.2 * x.4^-1 * x.1, x.2 * x.4^-1 * x.3 * x.1, x.4 * x.1 * x.4^-1 * x.2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.2, x.3^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)
L = (1, 94)(2, 105)(3, 96)(4, 95)(5, 91)(6, 98)(7, 100)(8, 93)(9, 102)(10, 101)(11, 97)(12, 104)(13, 106)(14, 99)(15, 108)(16, 107)(17, 103)(18, 92)(19, 47)(20, 42)(21, 50)(22, 43)(23, 46)(24, 45)(25, 53)(26, 48)(27, 38)(28, 49)(29, 52)(30, 51)(31, 41)(32, 54)(33, 44)(34, 37)(35, 40)(36, 39)(55, 56)(57, 71)(58, 69)(59, 72)(60, 67)(61, 63)(62, 70)(64, 66)(65, 68)(73, 84)(74, 89)(75, 82)(76, 86)(77, 81)(78, 83)(79, 80)(85, 87)(88, 90)

MAP           : A4.963
NOTES         : type I, chiral, isomorphic to A4.961.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 6)(2, 3)
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.4^3, u.3^3, u.3 * u.4^-1 * u.1 * u.2 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.4^3, (x.3, x.4^-1), x.3 * x.2 * x.3^-1 * x.2, x.3 * x.2 * x.4^-1 * x.1, x.2 * x.4^-1 * x.3 * x.1, x.4 * x.1 * x.4^-1 * x.2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.2, x.3^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)
L = (1, 95)(2, 108)(3, 98)(4, 91)(5, 94)(6, 93)(7, 101)(8, 96)(9, 104)(10, 97)(11, 100)(12, 99)(13, 107)(14, 102)(15, 92)(16, 103)(17, 106)(18, 105)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(25, 49)(26, 50)(27, 51)(28, 52)(29, 53)(30, 54)(31, 37)(32, 38)(33, 39)(34, 40)(35, 41)(36, 42)(55, 56)(57, 71)(58, 69)(59, 72)(60, 67)(61, 63)(62, 70)(64, 66)(65, 68)(73, 84)(74, 89)(75, 82)(76, 86)(77, 81)(78, 83)(79, 80)(85, 87)(88, 90)

MAP           : A4.964
NOTES         : type I, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 6)(2, 3)
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.4^3, u.3^3, u.3 * u.4^-1 * u.1 * u.2 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.4^3, x.4 * x.1 * x.3^-1 * x.1, x.4 * x.2 * x.4^-1 * x.1, x.1 * x.4 * x.3^-1 * x.2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.2, x.3^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)
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, 91)(14, 92)(15, 93)(16, 94)(17, 95)(18, 96)(19, 52)(20, 45)(21, 54)(22, 53)(23, 49)(24, 38)(25, 40)(26, 51)(27, 42)(28, 41)(29, 37)(30, 44)(31, 46)(32, 39)(33, 48)(34, 47)(35, 43)(36, 50)(55, 56)(57, 71)(58, 69)(59, 72)(60, 67)(61, 63)(62, 70)(64, 66)(65, 68)(73, 84)(74, 89)(75, 82)(76, 86)(77, 81)(78, 83)(79, 80)(85, 87)(88, 90)

MAP           : A4.965
NOTES         : type II, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.966
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.967
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.968
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.969
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.970
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.971
NOTES         : type I, chiral, isomorphic to A4.961.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 6)(2, 3)
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.4^3, u.3^3, u.3 * u.4^-1 * u.1 * u.2 >
CTG (small)   : <18, 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^-1 * x.2 * x.3, x.3 * x.1 * x.2 * x.4^-1, x.4^-1 * x.1 * x.2 * x.3, x.3^-1 * x.1 * x.3 * x.2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.2, x.3^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)
L = (1, 103)(2, 104)(3, 105)(4, 106)(5, 107)(6, 108)(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, 40)(20, 51)(21, 42)(22, 41)(23, 37)(24, 44)(25, 46)(26, 39)(27, 48)(28, 47)(29, 43)(30, 50)(31, 52)(32, 45)(33, 54)(34, 53)(35, 49)(36, 38)(55, 56)(57, 71)(58, 69)(59, 72)(60, 67)(61, 63)(62, 70)(64, 66)(65, 68)(73, 84)(74, 89)(75, 82)(76, 86)(77, 81)(78, 83)(79, 80)(85, 87)(88, 90)

MAP           : A4.972
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6) L = (1, 6)(2, 3)
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.4^3, u.3^3, u.3 * u.4^-1 * u.1 * u.2 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.4^3, x.4 * x.1 * x.3^-1 * x.1, x.4 * x.2 * x.4^-1 * x.1, x.1 * x.4 * x.3^-1 * x.2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.1, x.2, x.3^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)
L = (1, 101)(2, 96)(3, 104)(4, 97)(5, 100)(6, 99)(7, 107)(8, 102)(9, 92)(10, 103)(11, 106)(12, 105)(13, 95)(14, 108)(15, 98)(16, 91)(17, 94)(18, 93)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)(55, 56)(57, 71)(58, 69)(59, 72)(60, 67)(61, 63)(62, 70)(64, 66)(65, 68)(73, 84)(74, 89)(75, 82)(76, 86)(77, 81)(78, 83)(79, 80)(85, 87)(88, 90)

MAP           : A4.973
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.974
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.975
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.976
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.977
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.978
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.979
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.980
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.981
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.982
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.983
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.984
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.985
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.986
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.987
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.988
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.989
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.990
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.991
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.992
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.993
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.994
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.995
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.996
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.997
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.998
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.999
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.1000
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.1001
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.1002
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.1003
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.1004
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.1005
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.1006
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.1007
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1008
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1009
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1010
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.1011
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.1012
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.1013
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1014
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1015
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1016
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1017
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1018
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 96)(29, 99)(30, 91)(31, 92)(32, 97)(33, 93)(34, 98)(35, 95)(36, 94)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1019
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.1020
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1021
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1022
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 95)(29, 91)(30, 98)(31, 93)(32, 92)(33, 97)(34, 99)(35, 94)(36, 96)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1023
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1024
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1025
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1026
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1027
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 93)(29, 94)(30, 96)(31, 99)(32, 98)(33, 91)(34, 95)(35, 97)(36, 92)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1028
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.1029
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.1030
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.1031
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1032
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1033
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1034
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1035
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1036
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1037
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.1038
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.1039
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.1040
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1041
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1042
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1043
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1044
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1045
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1046
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1047
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1048
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1049
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.1050
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.1051
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.1052
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.1053
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.1054
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 97)(29, 96)(30, 95)(31, 91)(32, 99)(33, 98)(34, 94)(35, 92)(36, 93)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.1055
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1056
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1057
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1058
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.1059
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.1060
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.1061
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.1062
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1063
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1064
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1065
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.1066
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.1067
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 94)(29, 98)(30, 99)(31, 97)(32, 93)(33, 92)(34, 91)(35, 96)(36, 95)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.1068
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.1069
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.1070
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 80)(65, 75)(66, 79)(67, 78)(68, 76)(69, 77)(70, 74)(71, 81)(72, 73)

MAP           : A4.1071
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1072
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1073
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1074
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1075
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1076
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1077
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 54)(38, 52)(39, 47)(40, 50)(41, 51)(42, 49)(43, 48)(44, 46)(45, 53)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1078
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1079
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 53)(38, 48)(39, 52)(40, 51)(41, 49)(42, 50)(43, 47)(44, 54)(45, 46)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 81)(65, 79)(66, 74)(67, 77)(68, 78)(69, 76)(70, 75)(71, 73)(72, 80)

MAP           : A4.1080
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.1081
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.1082
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.1083
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.1084
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 92)(29, 95)(30, 94)(31, 98)(32, 91)(33, 99)(34, 96)(35, 93)(36, 97)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.1085
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1086
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.1087
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.1088
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1089
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1090
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1091
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1092
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.1093
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.1094
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.1095
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.1096
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1097
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(64, 77)(65, 73)(66, 80)(67, 75)(68, 74)(69, 79)(70, 81)(71, 76)(72, 78)

MAP           : A4.1098
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 50)(38, 46)(39, 53)(40, 48)(41, 47)(42, 52)(43, 54)(44, 49)(45, 51)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1099
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 47)(38, 50)(39, 49)(40, 53)(41, 46)(42, 54)(43, 51)(44, 48)(45, 52)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1100
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1101
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 78)(65, 81)(66, 73)(67, 74)(68, 79)(69, 75)(70, 80)(71, 77)(72, 76)

MAP           : A4.1102
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.1103
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 98)(29, 93)(30, 97)(31, 96)(32, 94)(33, 95)(34, 92)(35, 99)(36, 91)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 74)(65, 77)(66, 76)(67, 80)(68, 73)(69, 81)(70, 78)(71, 75)(72, 79)

MAP           : A4.1104
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.1105
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(64, 76)(65, 80)(66, 81)(67, 79)(68, 75)(69, 74)(70, 73)(71, 78)(72, 77)

MAP           : A4.1106
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 51)(38, 54)(39, 46)(40, 47)(41, 52)(42, 48)(43, 53)(44, 50)(45, 49)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1107
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1108
NOTES         : type I, reflexible, isomorphic to A4.964.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.3 * x.4^-1 * x.1^-1, x.3^3, x.6^3, x.5^3, x.4^3, x.3 * x.1^-1 * x.4^-1, x.1^3, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 49)(38, 53)(39, 54)(40, 52)(41, 48)(42, 47)(43, 46)(44, 51)(45, 50)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(64, 79)(65, 78)(66, 77)(67, 73)(68, 81)(69, 80)(70, 76)(71, 74)(72, 75)

MAP           : A4.1109
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.5^-1 * x.1^-1, x.1^3, x.4^3, x.3^3, x.6^3, x.5^3, x.1 * x.6 * x.3, x.1 * x.4^-1 * x.6^-1, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 52)(38, 51)(39, 50)(40, 46)(41, 54)(42, 53)(43, 49)(44, 47)(45, 48)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1110
NOTES         : type II, reflexible, isomorphic to A4.965.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 10)(4, 11)(5, 6)(7, 12)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.3 * u.4^-1, u.2 * u.3^-1 * u.5 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.6^-1 * x.4, x.1^3, x.6^3, x.4^3, x.1 * x.6 * x.3^-1, x.5^3, x.1 * x.4^-1 * x.5^-1, x.1 * x.3 * x.5, x.3^3, x.1 * x.5 * x.3, x.1 * x.3^-1 * x.4, x.1^-1 * x.2^-1 * x.3 * x.4^-1, x.2 * x.3^-1 * x.5 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.4^-1)
LOCAL TYPE    : (3, 4, 3, 4, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 99)(29, 97)(30, 92)(31, 95)(32, 96)(33, 94)(34, 93)(35, 91)(36, 98)(37, 48)(38, 49)(39, 51)(40, 54)(41, 53)(42, 46)(43, 50)(44, 52)(45, 47)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(64, 75)(65, 76)(66, 78)(67, 81)(68, 80)(69, 73)(70, 77)(71, 79)(72, 74)

MAP           : A4.1111
NOTES         : type I, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 38)(29, 41)(30, 40)(31, 44)(32, 37)(33, 45)(34, 42)(35, 39)(36, 43)(46, 72)(47, 70)(48, 65)(49, 68)(50, 69)(51, 67)(52, 66)(53, 64)(54, 71)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)

MAP           : A4.1112
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 38)(29, 41)(30, 40)(31, 44)(32, 37)(33, 45)(34, 42)(35, 39)(36, 43)(46, 66)(47, 67)(48, 69)(49, 72)(50, 71)(51, 64)(52, 68)(53, 70)(54, 65)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)

MAP           : A4.1113
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 41)(29, 37)(30, 44)(31, 39)(32, 38)(33, 43)(34, 45)(35, 40)(36, 42)(46, 69)(47, 72)(48, 64)(49, 65)(50, 70)(51, 66)(52, 71)(53, 68)(54, 67)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)

MAP           : A4.1114
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 41)(29, 37)(30, 44)(31, 39)(32, 38)(33, 43)(34, 45)(35, 40)(36, 42)(46, 66)(47, 67)(48, 69)(49, 72)(50, 71)(51, 64)(52, 68)(53, 70)(54, 65)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)

MAP           : A4.1115
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 41)(29, 37)(30, 44)(31, 39)(32, 38)(33, 43)(34, 45)(35, 40)(36, 42)(46, 66)(47, 67)(48, 69)(49, 72)(50, 71)(51, 64)(52, 68)(53, 70)(54, 65)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)

MAP           : A4.1116
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 41)(29, 37)(30, 44)(31, 39)(32, 38)(33, 43)(34, 45)(35, 40)(36, 42)(46, 69)(47, 72)(48, 64)(49, 65)(50, 70)(51, 66)(52, 71)(53, 68)(54, 67)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)

MAP           : A4.1117
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 38)(29, 41)(30, 40)(31, 44)(32, 37)(33, 45)(34, 42)(35, 39)(36, 43)(46, 70)(47, 69)(48, 68)(49, 64)(50, 72)(51, 71)(52, 67)(53, 65)(54, 66)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)

MAP           : A4.1118
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 38)(29, 41)(30, 40)(31, 44)(32, 37)(33, 45)(34, 42)(35, 39)(36, 43)(46, 70)(47, 69)(48, 68)(49, 64)(50, 72)(51, 71)(52, 67)(53, 65)(54, 66)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)

MAP           : A4.1119
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 38)(29, 41)(30, 40)(31, 44)(32, 37)(33, 45)(34, 42)(35, 39)(36, 43)(46, 71)(47, 66)(48, 70)(49, 69)(50, 67)(51, 68)(52, 65)(53, 72)(54, 64)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)

MAP           : A4.1120
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 38)(29, 41)(30, 40)(31, 44)(32, 37)(33, 45)(34, 42)(35, 39)(36, 43)(46, 71)(47, 66)(48, 70)(49, 69)(50, 67)(51, 68)(52, 65)(53, 72)(54, 64)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)

MAP           : A4.1121
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 38)(29, 41)(30, 40)(31, 44)(32, 37)(33, 45)(34, 42)(35, 39)(36, 43)(46, 72)(47, 70)(48, 65)(49, 68)(50, 69)(51, 67)(52, 66)(53, 64)(54, 71)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)

MAP           : A4.1122
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 43)(29, 42)(30, 41)(31, 37)(32, 45)(33, 44)(34, 40)(35, 38)(36, 39)(46, 66)(47, 67)(48, 69)(49, 72)(50, 71)(51, 64)(52, 68)(53, 70)(54, 65)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)

MAP           : A4.1123
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 42)(29, 45)(30, 37)(31, 38)(32, 43)(33, 39)(34, 44)(35, 41)(36, 40)(46, 68)(47, 64)(48, 71)(49, 66)(50, 65)(51, 70)(52, 72)(53, 67)(54, 69)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)

MAP           : A4.1124
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 42)(29, 45)(30, 37)(31, 38)(32, 43)(33, 39)(34, 44)(35, 41)(36, 40)(46, 68)(47, 64)(48, 71)(49, 66)(50, 65)(51, 70)(52, 72)(53, 67)(54, 69)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)

MAP           : A4.1125
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 42)(29, 45)(30, 37)(31, 38)(32, 43)(33, 39)(34, 44)(35, 41)(36, 40)(46, 67)(47, 71)(48, 72)(49, 70)(50, 66)(51, 65)(52, 64)(53, 69)(54, 68)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)

MAP           : A4.1126
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 42)(29, 45)(30, 37)(31, 38)(32, 43)(33, 39)(34, 44)(35, 41)(36, 40)(46, 67)(47, 71)(48, 72)(49, 70)(50, 66)(51, 65)(52, 64)(53, 69)(54, 68)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)

MAP           : A4.1127
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 42)(29, 45)(30, 37)(31, 38)(32, 43)(33, 39)(34, 44)(35, 41)(36, 40)(46, 70)(47, 69)(48, 68)(49, 64)(50, 72)(51, 71)(52, 67)(53, 65)(54, 66)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)

MAP           : A4.1128
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 42)(29, 45)(30, 37)(31, 38)(32, 43)(33, 39)(34, 44)(35, 41)(36, 40)(46, 70)(47, 69)(48, 68)(49, 64)(50, 72)(51, 71)(52, 67)(53, 65)(54, 66)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)

MAP           : A4.1129
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 42)(29, 45)(30, 37)(31, 38)(32, 43)(33, 39)(34, 44)(35, 41)(36, 40)(46, 71)(47, 66)(48, 70)(49, 69)(50, 67)(51, 68)(52, 65)(53, 72)(54, 64)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)

MAP           : A4.1130
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 42)(29, 45)(30, 37)(31, 38)(32, 43)(33, 39)(34, 44)(35, 41)(36, 40)(46, 71)(47, 66)(48, 70)(49, 69)(50, 67)(51, 68)(52, 65)(53, 72)(54, 64)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)

MAP           : A4.1131
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 42)(29, 45)(30, 37)(31, 38)(32, 43)(33, 39)(34, 44)(35, 41)(36, 40)(46, 72)(47, 70)(48, 65)(49, 68)(50, 69)(51, 67)(52, 66)(53, 64)(54, 71)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)

MAP           : A4.1132
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 42)(29, 45)(30, 37)(31, 38)(32, 43)(33, 39)(34, 44)(35, 41)(36, 40)(46, 72)(47, 70)(48, 65)(49, 68)(50, 69)(51, 67)(52, 66)(53, 64)(54, 71)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)

MAP           : A4.1133
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 40)(29, 44)(30, 45)(31, 43)(32, 39)(33, 38)(34, 37)(35, 42)(36, 41)(46, 65)(47, 68)(48, 67)(49, 71)(50, 64)(51, 72)(52, 69)(53, 66)(54, 70)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)

MAP           : A4.1134
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 40)(29, 44)(30, 45)(31, 43)(32, 39)(33, 38)(34, 37)(35, 42)(36, 41)(46, 65)(47, 68)(48, 67)(49, 71)(50, 64)(51, 72)(52, 69)(53, 66)(54, 70)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)

MAP           : A4.1135
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 40)(29, 44)(30, 45)(31, 43)(32, 39)(33, 38)(34, 37)(35, 42)(36, 41)(46, 68)(47, 64)(48, 71)(49, 66)(50, 65)(51, 70)(52, 72)(53, 67)(54, 69)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)

MAP           : A4.1136
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 40)(29, 44)(30, 45)(31, 43)(32, 39)(33, 38)(34, 37)(35, 42)(36, 41)(46, 68)(47, 64)(48, 71)(49, 66)(50, 65)(51, 70)(52, 72)(53, 67)(54, 69)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)

MAP           : A4.1137
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 40)(29, 44)(30, 45)(31, 43)(32, 39)(33, 38)(34, 37)(35, 42)(36, 41)(46, 66)(47, 67)(48, 69)(49, 72)(50, 71)(51, 64)(52, 68)(53, 70)(54, 65)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)

MAP           : A4.1138
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 40)(29, 44)(30, 45)(31, 43)(32, 39)(33, 38)(34, 37)(35, 42)(36, 41)(46, 66)(47, 67)(48, 69)(49, 72)(50, 71)(51, 64)(52, 68)(53, 70)(54, 65)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)

MAP           : A4.1139
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 40)(29, 44)(30, 45)(31, 43)(32, 39)(33, 38)(34, 37)(35, 42)(36, 41)(46, 69)(47, 72)(48, 64)(49, 65)(50, 70)(51, 66)(52, 71)(53, 68)(54, 67)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)

MAP           : A4.1140
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 40)(29, 44)(30, 45)(31, 43)(32, 39)(33, 38)(34, 37)(35, 42)(36, 41)(46, 69)(47, 72)(48, 64)(49, 65)(50, 70)(51, 66)(52, 71)(53, 68)(54, 67)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)

MAP           : A4.1141
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 41)(29, 37)(30, 44)(31, 39)(32, 38)(33, 43)(34, 45)(35, 40)(36, 42)(46, 67)(47, 71)(48, 72)(49, 70)(50, 66)(51, 65)(52, 64)(53, 69)(54, 68)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)

MAP           : A4.1142
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 41)(29, 37)(30, 44)(31, 39)(32, 38)(33, 43)(34, 45)(35, 40)(36, 42)(46, 67)(47, 71)(48, 72)(49, 70)(50, 66)(51, 65)(52, 64)(53, 69)(54, 68)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)

MAP           : A4.1143
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 41)(29, 37)(30, 44)(31, 39)(32, 38)(33, 43)(34, 45)(35, 40)(36, 42)(46, 70)(47, 69)(48, 68)(49, 64)(50, 72)(51, 71)(52, 67)(53, 65)(54, 66)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)

MAP           : A4.1144
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 41)(29, 37)(30, 44)(31, 39)(32, 38)(33, 43)(34, 45)(35, 40)(36, 42)(46, 70)(47, 69)(48, 68)(49, 64)(50, 72)(51, 71)(52, 67)(53, 65)(54, 66)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)

MAP           : A4.1145
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 41)(29, 37)(30, 44)(31, 39)(32, 38)(33, 43)(34, 45)(35, 40)(36, 42)(46, 71)(47, 66)(48, 70)(49, 69)(50, 67)(51, 68)(52, 65)(53, 72)(54, 64)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)

MAP           : A4.1146
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 41)(29, 37)(30, 44)(31, 39)(32, 38)(33, 43)(34, 45)(35, 40)(36, 42)(46, 71)(47, 66)(48, 70)(49, 69)(50, 67)(51, 68)(52, 65)(53, 72)(54, 64)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)

MAP           : A4.1147
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 41)(29, 37)(30, 44)(31, 39)(32, 38)(33, 43)(34, 45)(35, 40)(36, 42)(46, 72)(47, 70)(48, 65)(49, 68)(50, 69)(51, 67)(52, 66)(53, 64)(54, 71)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)

MAP           : A4.1148
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 41)(29, 37)(30, 44)(31, 39)(32, 38)(33, 43)(34, 45)(35, 40)(36, 42)(46, 72)(47, 70)(48, 65)(49, 68)(50, 69)(51, 67)(52, 66)(53, 64)(54, 71)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)

MAP           : A4.1149
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 39)(29, 40)(30, 42)(31, 45)(32, 44)(33, 37)(34, 41)(35, 43)(36, 38)(46, 65)(47, 68)(48, 67)(49, 71)(50, 64)(51, 72)(52, 69)(53, 66)(54, 70)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)

MAP           : A4.1150
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 39)(29, 40)(30, 42)(31, 45)(32, 44)(33, 37)(34, 41)(35, 43)(36, 38)(46, 65)(47, 68)(48, 67)(49, 71)(50, 64)(51, 72)(52, 69)(53, 66)(54, 70)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)

MAP           : A4.1151
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 39)(29, 40)(30, 42)(31, 45)(32, 44)(33, 37)(34, 41)(35, 43)(36, 38)(46, 68)(47, 64)(48, 71)(49, 66)(50, 65)(51, 70)(52, 72)(53, 67)(54, 69)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)

MAP           : A4.1152
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 39)(29, 40)(30, 42)(31, 45)(32, 44)(33, 37)(34, 41)(35, 43)(36, 38)(46, 68)(47, 64)(48, 71)(49, 66)(50, 65)(51, 70)(52, 72)(53, 67)(54, 69)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)

MAP           : A4.1153
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 39)(29, 40)(30, 42)(31, 45)(32, 44)(33, 37)(34, 41)(35, 43)(36, 38)(46, 67)(47, 71)(48, 72)(49, 70)(50, 66)(51, 65)(52, 64)(53, 69)(54, 68)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)

MAP           : A4.1154
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 39)(29, 40)(30, 42)(31, 45)(32, 44)(33, 37)(34, 41)(35, 43)(36, 38)(46, 67)(47, 71)(48, 72)(49, 70)(50, 66)(51, 65)(52, 64)(53, 69)(54, 68)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)

MAP           : A4.1155
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 39)(29, 40)(30, 42)(31, 45)(32, 44)(33, 37)(34, 41)(35, 43)(36, 38)(46, 70)(47, 69)(48, 68)(49, 64)(50, 72)(51, 71)(52, 67)(53, 65)(54, 66)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)

MAP           : A4.1156
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 39)(29, 40)(30, 42)(31, 45)(32, 44)(33, 37)(34, 41)(35, 43)(36, 38)(46, 70)(47, 69)(48, 68)(49, 64)(50, 72)(51, 71)(52, 67)(53, 65)(54, 66)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)

MAP           : A4.1157
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 39)(29, 40)(30, 42)(31, 45)(32, 44)(33, 37)(34, 41)(35, 43)(36, 38)(46, 71)(47, 66)(48, 70)(49, 69)(50, 67)(51, 68)(52, 65)(53, 72)(54, 64)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)

MAP           : A4.1158
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 39)(29, 40)(30, 42)(31, 45)(32, 44)(33, 37)(34, 41)(35, 43)(36, 38)(46, 71)(47, 66)(48, 70)(49, 69)(50, 67)(51, 68)(52, 65)(53, 72)(54, 64)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)

MAP           : A4.1159
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 39)(29, 40)(30, 42)(31, 45)(32, 44)(33, 37)(34, 41)(35, 43)(36, 38)(46, 72)(47, 70)(48, 65)(49, 68)(50, 69)(51, 67)(52, 66)(53, 64)(54, 71)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)

MAP           : A4.1160
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 39)(29, 40)(30, 42)(31, 45)(32, 44)(33, 37)(34, 41)(35, 43)(36, 38)(46, 72)(47, 70)(48, 65)(49, 68)(50, 69)(51, 67)(52, 66)(53, 64)(54, 71)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)

MAP           : A4.1161
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 42)(29, 45)(30, 37)(31, 38)(32, 43)(33, 39)(34, 44)(35, 41)(36, 40)(46, 65)(47, 68)(48, 67)(49, 71)(50, 64)(51, 72)(52, 69)(53, 66)(54, 70)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)

MAP           : A4.1162
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 42)(29, 45)(30, 37)(31, 38)(32, 43)(33, 39)(34, 44)(35, 41)(36, 40)(46, 65)(47, 68)(48, 67)(49, 71)(50, 64)(51, 72)(52, 69)(53, 66)(54, 70)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)

MAP           : A4.1163
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 44)(29, 39)(30, 43)(31, 42)(32, 40)(33, 41)(34, 38)(35, 45)(36, 37)(46, 69)(47, 72)(48, 64)(49, 65)(50, 70)(51, 66)(52, 71)(53, 68)(54, 67)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)

MAP           : A4.1164
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 44)(29, 39)(30, 43)(31, 42)(32, 40)(33, 41)(34, 38)(35, 45)(36, 37)(46, 69)(47, 72)(48, 64)(49, 65)(50, 70)(51, 66)(52, 71)(53, 68)(54, 67)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)

MAP           : A4.1165
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 44)(29, 39)(30, 43)(31, 42)(32, 40)(33, 41)(34, 38)(35, 45)(36, 37)(46, 67)(47, 71)(48, 72)(49, 70)(50, 66)(51, 65)(52, 64)(53, 69)(54, 68)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)

MAP           : A4.1166
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 44)(29, 39)(30, 43)(31, 42)(32, 40)(33, 41)(34, 38)(35, 45)(36, 37)(46, 67)(47, 71)(48, 72)(49, 70)(50, 66)(51, 65)(52, 64)(53, 69)(54, 68)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)

MAP           : A4.1167
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 44)(29, 39)(30, 43)(31, 42)(32, 40)(33, 41)(34, 38)(35, 45)(36, 37)(46, 70)(47, 69)(48, 68)(49, 64)(50, 72)(51, 71)(52, 67)(53, 65)(54, 66)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)

MAP           : A4.1168
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 44)(29, 39)(30, 43)(31, 42)(32, 40)(33, 41)(34, 38)(35, 45)(36, 37)(46, 70)(47, 69)(48, 68)(49, 64)(50, 72)(51, 71)(52, 67)(53, 65)(54, 66)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)

MAP           : A4.1169
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 45)(29, 43)(30, 38)(31, 41)(32, 42)(33, 40)(34, 39)(35, 37)(36, 44)(46, 65)(47, 68)(48, 67)(49, 71)(50, 64)(51, 72)(52, 69)(53, 66)(54, 70)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)

MAP           : A4.1170
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 45)(29, 43)(30, 38)(31, 41)(32, 42)(33, 40)(34, 39)(35, 37)(36, 44)(46, 65)(47, 68)(48, 67)(49, 71)(50, 64)(51, 72)(52, 69)(53, 66)(54, 70)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)

MAP           : A4.1171
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 45)(29, 43)(30, 38)(31, 41)(32, 42)(33, 40)(34, 39)(35, 37)(36, 44)(46, 68)(47, 64)(48, 71)(49, 66)(50, 65)(51, 70)(52, 72)(53, 67)(54, 69)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)

MAP           : A4.1172
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 45)(29, 43)(30, 38)(31, 41)(32, 42)(33, 40)(34, 39)(35, 37)(36, 44)(46, 68)(47, 64)(48, 71)(49, 66)(50, 65)(51, 70)(52, 72)(53, 67)(54, 69)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)

MAP           : A4.1173
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 45)(29, 43)(30, 38)(31, 41)(32, 42)(33, 40)(34, 39)(35, 37)(36, 44)(46, 66)(47, 67)(48, 69)(49, 72)(50, 71)(51, 64)(52, 68)(53, 70)(54, 65)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)

MAP           : A4.1174
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 45)(29, 43)(30, 38)(31, 41)(32, 42)(33, 40)(34, 39)(35, 37)(36, 44)(46, 66)(47, 67)(48, 69)(49, 72)(50, 71)(51, 64)(52, 68)(53, 70)(54, 65)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)

MAP           : A4.1175
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 45)(29, 43)(30, 38)(31, 41)(32, 42)(33, 40)(34, 39)(35, 37)(36, 44)(46, 69)(47, 72)(48, 64)(49, 65)(50, 70)(51, 66)(52, 71)(53, 68)(54, 67)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)

MAP           : A4.1176
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 45)(29, 43)(30, 38)(31, 41)(32, 42)(33, 40)(34, 39)(35, 37)(36, 44)(46, 69)(47, 72)(48, 64)(49, 65)(50, 70)(51, 66)(52, 71)(53, 68)(54, 67)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)

MAP           : A4.1177
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 45)(29, 43)(30, 38)(31, 41)(32, 42)(33, 40)(34, 39)(35, 37)(36, 44)(46, 67)(47, 71)(48, 72)(49, 70)(50, 66)(51, 65)(52, 64)(53, 69)(54, 68)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)

MAP           : A4.1178
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 45)(29, 43)(30, 38)(31, 41)(32, 42)(33, 40)(34, 39)(35, 37)(36, 44)(46, 67)(47, 71)(48, 72)(49, 70)(50, 66)(51, 65)(52, 64)(53, 69)(54, 68)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)

MAP           : A4.1179
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 45)(29, 43)(30, 38)(31, 41)(32, 42)(33, 40)(34, 39)(35, 37)(36, 44)(46, 70)(47, 69)(48, 68)(49, 64)(50, 72)(51, 71)(52, 67)(53, 65)(54, 66)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)

MAP           : A4.1180
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 45)(29, 43)(30, 38)(31, 41)(32, 42)(33, 40)(34, 39)(35, 37)(36, 44)(46, 70)(47, 69)(48, 68)(49, 64)(50, 72)(51, 71)(52, 67)(53, 65)(54, 66)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)

MAP           : A4.1181
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 40)(29, 44)(30, 45)(31, 43)(32, 39)(33, 38)(34, 37)(35, 42)(36, 41)(46, 71)(47, 66)(48, 70)(49, 69)(50, 67)(51, 68)(52, 65)(53, 72)(54, 64)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)

MAP           : A4.1182
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 40)(29, 44)(30, 45)(31, 43)(32, 39)(33, 38)(34, 37)(35, 42)(36, 41)(46, 71)(47, 66)(48, 70)(49, 69)(50, 67)(51, 68)(52, 65)(53, 72)(54, 64)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)

MAP           : A4.1183
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 40)(29, 44)(30, 45)(31, 43)(32, 39)(33, 38)(34, 37)(35, 42)(36, 41)(46, 72)(47, 70)(48, 65)(49, 68)(50, 69)(51, 67)(52, 66)(53, 64)(54, 71)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)

MAP           : A4.1184
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 40)(29, 44)(30, 45)(31, 43)(32, 39)(33, 38)(34, 37)(35, 42)(36, 41)(46, 72)(47, 70)(48, 65)(49, 68)(50, 69)(51, 67)(52, 66)(53, 64)(54, 71)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)

MAP           : A4.1185
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 43)(29, 42)(30, 41)(31, 37)(32, 45)(33, 44)(34, 40)(35, 38)(36, 39)(46, 65)(47, 68)(48, 67)(49, 71)(50, 64)(51, 72)(52, 69)(53, 66)(54, 70)(55, 107)(56, 102)(57, 106)(58, 105)(59, 103)(60, 104)(61, 101)(62, 108)(63, 100)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)

MAP           : A4.1186
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 43)(29, 42)(30, 41)(31, 37)(32, 45)(33, 44)(34, 40)(35, 38)(36, 39)(46, 65)(47, 68)(48, 67)(49, 71)(50, 64)(51, 72)(52, 69)(53, 66)(54, 70)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)

MAP           : A4.1187
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 43)(29, 42)(30, 41)(31, 37)(32, 45)(33, 44)(34, 40)(35, 38)(36, 39)(46, 68)(47, 64)(48, 71)(49, 66)(50, 65)(51, 70)(52, 72)(53, 67)(54, 69)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)

MAP           : A4.1188
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 43)(29, 42)(30, 41)(31, 37)(32, 45)(33, 44)(34, 40)(35, 38)(36, 39)(46, 68)(47, 64)(48, 71)(49, 66)(50, 65)(51, 70)(52, 72)(53, 67)(54, 69)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)

MAP           : A4.1189
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 43)(29, 42)(30, 41)(31, 37)(32, 45)(33, 44)(34, 40)(35, 38)(36, 39)(46, 66)(47, 67)(48, 69)(49, 72)(50, 71)(51, 64)(52, 68)(53, 70)(54, 65)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)

MAP           : A4.1190
NOTES         : type I, reflexible, isomorphic to A4.1111.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.4^3, x.4^-1 * x.2 * x.3^-1 * x.1, x.1 * x.3 * x.1 * x.3^-1, x.3^-1 * x.2 * x.1 * x.4^-1, x.4^-1 * x.1 * x.4 * x.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        : 108
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)
L = (1, 22)(2, 33)(3, 24)(4, 23)(5, 19)(6, 26)(7, 28)(8, 21)(9, 30)(10, 29)(11, 25)(12, 32)(13, 34)(14, 27)(15, 36)(16, 35)(17, 31)(18, 20)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 88)(56, 81)(57, 90)(58, 89)(59, 85)(60, 74)(61, 76)(62, 87)(63, 78)(64, 77)(65, 73)(66, 80)(67, 82)(68, 75)(69, 84)(70, 83)(71, 79)(72, 86)(91, 102)(92, 107)(93, 100)(94, 104)(95, 99)(96, 101)(97, 98)(103, 105)(106, 108)

MAP           : A4.1191
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 43)(29, 42)(30, 41)(31, 37)(32, 45)(33, 44)(34, 40)(35, 38)(36, 39)(46, 69)(47, 72)(48, 64)(49, 65)(50, 70)(51, 66)(52, 71)(53, 68)(54, 67)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)

MAP           : A4.1192
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 43)(29, 42)(30, 41)(31, 37)(32, 45)(33, 44)(34, 40)(35, 38)(36, 39)(46, 69)(47, 72)(48, 64)(49, 65)(50, 70)(51, 66)(52, 71)(53, 68)(54, 67)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)

MAP           : A4.1193
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 43)(29, 42)(30, 41)(31, 37)(32, 45)(33, 44)(34, 40)(35, 38)(36, 39)(46, 71)(47, 66)(48, 70)(49, 69)(50, 67)(51, 68)(52, 65)(53, 72)(54, 64)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)

MAP           : A4.1194
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 43)(29, 42)(30, 41)(31, 37)(32, 45)(33, 44)(34, 40)(35, 38)(36, 39)(46, 71)(47, 66)(48, 70)(49, 69)(50, 67)(51, 68)(52, 65)(53, 72)(54, 64)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)

MAP           : A4.1195
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 43)(29, 42)(30, 41)(31, 37)(32, 45)(33, 44)(34, 40)(35, 38)(36, 39)(46, 72)(47, 70)(48, 65)(49, 68)(50, 69)(51, 67)(52, 66)(53, 64)(54, 71)(55, 103)(56, 107)(57, 108)(58, 106)(59, 102)(60, 101)(61, 100)(62, 105)(63, 104)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)

MAP           : A4.1196
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 43)(29, 42)(30, 41)(31, 37)(32, 45)(33, 44)(34, 40)(35, 38)(36, 39)(46, 72)(47, 70)(48, 65)(49, 68)(50, 69)(51, 67)(52, 66)(53, 64)(54, 71)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)

MAP           : A4.1197
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 44)(29, 39)(30, 43)(31, 42)(32, 40)(33, 41)(34, 38)(35, 45)(36, 37)(46, 65)(47, 68)(48, 67)(49, 71)(50, 64)(51, 72)(52, 69)(53, 66)(54, 70)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)

MAP           : A4.1198
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 44)(29, 39)(30, 43)(31, 42)(32, 40)(33, 41)(34, 38)(35, 45)(36, 37)(46, 65)(47, 68)(48, 67)(49, 71)(50, 64)(51, 72)(52, 69)(53, 66)(54, 70)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)

MAP           : A4.1199
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 44)(29, 39)(30, 43)(31, 42)(32, 40)(33, 41)(34, 38)(35, 45)(36, 37)(46, 68)(47, 64)(48, 71)(49, 66)(50, 65)(51, 70)(52, 72)(53, 67)(54, 69)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)

MAP           : A4.1200
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 44)(29, 39)(30, 43)(31, 42)(32, 40)(33, 41)(34, 38)(35, 45)(36, 37)(46, 68)(47, 64)(48, 71)(49, 66)(50, 65)(51, 70)(52, 72)(53, 67)(54, 69)(55, 105)(56, 108)(57, 100)(58, 101)(59, 106)(60, 102)(61, 107)(62, 104)(63, 103)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)

MAP           : A4.1201
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 44)(29, 39)(30, 43)(31, 42)(32, 40)(33, 41)(34, 38)(35, 45)(36, 37)(46, 66)(47, 67)(48, 69)(49, 72)(50, 71)(51, 64)(52, 68)(53, 70)(54, 65)(55, 108)(56, 106)(57, 101)(58, 104)(59, 105)(60, 103)(61, 102)(62, 100)(63, 107)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)

MAP           : A4.1202
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 44)(29, 39)(30, 43)(31, 42)(32, 40)(33, 41)(34, 38)(35, 45)(36, 37)(46, 66)(47, 67)(48, 69)(49, 72)(50, 71)(51, 64)(52, 68)(53, 70)(54, 65)(55, 101)(56, 104)(57, 103)(58, 107)(59, 100)(60, 108)(61, 105)(62, 102)(63, 106)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)

MAP           : A4.1203
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 38)(29, 41)(30, 40)(31, 44)(32, 37)(33, 45)(34, 42)(35, 39)(36, 43)(46, 66)(47, 67)(48, 69)(49, 72)(50, 71)(51, 64)(52, 68)(53, 70)(54, 65)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)

MAP           : A4.1204
NOTES         : type I, reflexible, isomorphic to A4.1111.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.4^3, x.4^-1 * x.2 * x.3^-1 * x.1, x.1 * x.3 * x.1 * x.3^-1, x.3^-1 * x.2 * x.1 * x.4^-1, x.4^-1 * x.1 * x.4 * x.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        : 108
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)
L = (1, 23)(2, 36)(3, 26)(4, 19)(5, 22)(6, 21)(7, 29)(8, 24)(9, 32)(10, 25)(11, 28)(12, 27)(13, 35)(14, 30)(15, 20)(16, 31)(17, 34)(18, 33)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 85)(56, 86)(57, 87)(58, 88)(59, 89)(60, 90)(61, 73)(62, 74)(63, 75)(64, 76)(65, 77)(66, 78)(67, 79)(68, 80)(69, 81)(70, 82)(71, 83)(72, 84)(91, 102)(92, 107)(93, 100)(94, 104)(95, 99)(96, 101)(97, 98)(103, 105)(106, 108)

MAP           : A4.1205
NOTES         : type I, reflexible, isomorphic to A4.1111.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.4^3, x.2 * x.3^-1 * x.4^-1 * x.1, (x.4^-1, x.3), x.4 * x.1 * x.4^-1 * x.1, x.3^-1 * x.2 * x.3 * x.1 >
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        : 108
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)
L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 76)(56, 87)(57, 78)(58, 77)(59, 73)(60, 80)(61, 82)(62, 75)(63, 84)(64, 83)(65, 79)(66, 86)(67, 88)(68, 81)(69, 90)(70, 89)(71, 85)(72, 74)(91, 102)(92, 107)(93, 100)(94, 104)(95, 99)(96, 101)(97, 98)(103, 105)(106, 108)

MAP           : A4.1206
NOTES         : type I, reflexible, isomorphic to A4.1111.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2^2, x.3^3, x.4^3, x.2 * x.3^-1 * x.4^-1 * x.1, (x.4^-1, x.3), x.4 * x.1 * x.4^-1 * x.1, x.3^-1 * x.2 * x.3 * x.1 >
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        : 108
R = (1, 19, 37, 55, 73, 91)(2, 20, 38, 56, 74, 92)(3, 21, 39, 57, 75, 93)(4, 22, 40, 58, 76, 94)(5, 23, 41, 59, 77, 95)(6, 24, 42, 60, 78, 96)(7, 25, 43, 61, 79, 97)(8, 26, 44, 62, 80, 98)(9, 27, 45, 63, 81, 99)(10, 28, 46, 64, 82, 100)(11, 29, 47, 65, 83, 101)(12, 30, 48, 66, 84, 102)(13, 31, 49, 67, 85, 103)(14, 32, 50, 68, 86, 104)(15, 33, 51, 69, 87, 105)(16, 34, 52, 70, 88, 106)(17, 35, 53, 71, 89, 107)(18, 36, 54, 72, 90, 108)
L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(13, 25)(14, 26)(15, 27)(16, 28)(17, 29)(18, 30)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 77)(56, 90)(57, 80)(58, 73)(59, 76)(60, 75)(61, 83)(62, 78)(63, 86)(64, 79)(65, 82)(66, 81)(67, 89)(68, 84)(69, 74)(70, 85)(71, 88)(72, 87)(91, 93)(92, 100)(94, 96)(95, 98)(97, 108)(99, 106)(101, 105)(102, 107)(103, 104)

MAP           : A4.1207
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 38)(29, 41)(30, 40)(31, 44)(32, 37)(33, 45)(34, 42)(35, 39)(36, 43)(46, 67)(47, 71)(48, 72)(49, 70)(50, 66)(51, 65)(52, 64)(53, 69)(54, 68)(55, 102)(56, 103)(57, 105)(58, 108)(59, 107)(60, 100)(61, 104)(62, 106)(63, 101)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)

MAP           : A4.1208
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 38)(29, 41)(30, 40)(31, 44)(32, 37)(33, 45)(34, 42)(35, 39)(36, 43)(46, 69)(47, 72)(48, 64)(49, 65)(50, 70)(51, 66)(52, 71)(53, 68)(54, 67)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)

MAP           : A4.1209
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.2, x.6 * x.1^-1, x.6^3, x.5^3, x.3^3, x.1 * x.5^-1 * x.4^-1, x.3 * x.1^-1 * x.5^-1, x.3 * x.1 * x.4, x.1 * x.5 * x.3^-1, x.1^3, x.1 * x.3 * x.4, x.1^-1 * x.2^-1 * x.5 * x.4 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 38)(29, 41)(30, 40)(31, 44)(32, 37)(33, 45)(34, 42)(35, 39)(36, 43)(46, 69)(47, 72)(48, 64)(49, 65)(50, 70)(51, 66)(52, 71)(53, 68)(54, 67)(55, 106)(56, 105)(57, 104)(58, 100)(59, 108)(60, 107)(61, 103)(62, 101)(63, 102)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)

MAP           : A4.1210
NOTES         : type I, reflexible, isomorphic to A4.1111.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6)(7, 8, 9, 10, 11, 12) L = (1, 2)(3, 11)(4, 5)(6, 8)(7, 12)(9, 10)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.2, u.1^3, u.3^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.5 * u.4, u.2 * u.3^-1 * u.4^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.2, x.3^-1 * x.5^-1, x.1^3, x.5^3, x.3^3, x.6^3, x.1 * x.5 * x.6, x.1 * x.5^-1 * x.4^-1, x.1 * x.4 * x.6^-1, x.1 * x.6 * x.3^-1, x.1^-1 * x.2^-1 * x.5 * x.4, x.2 * x.3^-1 * x.4^-1 * x.6^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.3^-1, x.4)
LOCAL TYPE    : (3, 4, 4, 3, 4, 4)
#DARTS        : 108
R = (1, 10, 19, 28, 37, 46)(2, 11, 20, 29, 38, 47)(3, 12, 21, 30, 39, 48)(4, 13, 22, 31, 40, 49)(5, 14, 23, 32, 41, 50)(6, 15, 24, 33, 42, 51)(7, 16, 25, 34, 43, 52)(8, 17, 26, 35, 44, 53)(9, 18, 27, 36, 45, 54)(55, 64, 73, 82, 91, 100)(56, 65, 74, 83, 92, 101)(57, 66, 75, 84, 93, 102)(58, 67, 76, 85, 94, 103)(59, 68, 77, 86, 95, 104)(60, 69, 78, 87, 96, 105)(61, 70, 79, 88, 97, 106)(62, 71, 80, 89, 98, 107)(63, 72, 81, 90, 99, 108)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 38)(29, 41)(30, 40)(31, 44)(32, 37)(33, 45)(34, 42)(35, 39)(36, 43)(46, 67)(47, 71)(48, 72)(49, 70)(50, 66)(51, 65)(52, 64)(53, 69)(54, 68)(55, 104)(56, 100)(57, 107)(58, 102)(59, 101)(60, 106)(61, 108)(62, 103)(63, 105)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)

MAP           : A4.1211
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 160)(20, 156)(21, 155)(22, 146)(23, 150)(24, 152)(25, 154)(26, 149)(27, 151)(28, 153)(29, 157)(30, 148)(31, 147)(32, 161)(33, 158)(34, 162)(35, 159)(36, 145)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 137)(56, 140)(57, 142)(58, 143)(59, 136)(60, 133)(61, 132)(62, 135)(63, 134)(64, 131)(65, 127)(66, 141)(67, 144)(68, 128)(69, 138)(70, 129)(71, 130)(72, 139)(73, 92)(74, 95)(75, 97)(76, 98)(77, 91)(78, 106)(79, 105)(80, 108)(81, 107)(82, 104)(83, 100)(84, 96)(85, 99)(86, 101)(87, 93)(88, 102)(89, 103)(90, 94)(109, 244)(110, 245)(111, 246)(112, 247)(113, 248)(114, 249)(115, 250)(116, 251)(117, 252)(118, 235)(119, 236)(120, 237)(121, 238)(122, 239)(123, 240)(124, 241)(125, 242)(126, 243)(163, 198)(164, 184)(165, 193)(166, 192)(167, 188)(168, 185)(169, 189)(170, 186)(171, 190)(172, 187)(173, 183)(174, 182)(175, 191)(176, 195)(177, 197)(178, 181)(179, 194)(180, 196)(217, 226)(218, 227)(219, 228)(220, 229)(221, 230)(222, 231)(223, 232)(224, 233)(225, 234)

MAP           : A4.1212
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)   : <36, 10>
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.4^-1 * x.5 * x.3 * x.5^-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        : 252
R = (1, 37, 73, 109, 145, 181, 217)(2, 38, 74, 110, 146, 182, 218)(3, 39, 75, 111, 147, 183, 219)(4, 40, 76, 112, 148, 184, 220)(5, 41, 77, 113, 149, 185, 221)(6, 42, 78, 114, 150, 186, 222)(7, 43, 79, 115, 151, 187, 223)(8, 44, 80, 116, 152, 188, 224)(9, 45, 81, 117, 153, 189, 225)(10, 46, 82, 118, 154, 190, 226)(11, 47, 83, 119, 155, 191, 227)(12, 48, 84, 120, 156, 192, 228)(13, 49, 85, 121, 157, 193, 229)(14, 50, 86, 122, 158, 194, 230)(15, 51, 87, 123, 159, 195, 231)(16, 52, 88, 124, 160, 196, 232)(17, 53, 89, 125, 161, 197, 233)(18, 54, 90, 126, 162, 198, 234)(19, 55, 91, 127, 163, 199, 235)(20, 56, 92, 128, 164, 200, 236)(21, 57, 93, 129, 165, 201, 237)(22, 58, 94, 130, 166, 202, 238)(23, 59, 95, 131, 167, 203, 239)(24, 60, 96, 132, 168, 204, 240)(25, 61, 97, 133, 169, 205, 241)(26, 62, 98, 134, 170, 206, 242)(27, 63, 99, 135, 171, 207, 243)(28, 64, 100, 136, 172, 208, 244)(29, 65, 101, 137, 173, 209, 245)(30, 66, 102, 138, 174, 210, 246)(31, 67, 103, 139, 175, 211, 247)(32, 68, 104, 140, 176, 212, 248)(33, 69, 105, 141, 177, 213, 249)(34, 70, 106, 142, 178, 214, 250)(35, 71, 107, 143, 179, 215, 251)(36, 72, 108, 144, 180, 216, 252)
L = (1, 41)(2, 39)(3, 58)(4, 57)(5, 60)(6, 59)(7, 47)(8, 45)(9, 52)(10, 51)(11, 54)(12, 53)(13, 48)(14, 46)(15, 50)(16, 44)(17, 49)(18, 43)(19, 42)(20, 40)(21, 56)(22, 38)(23, 55)(24, 37)(25, 72)(26, 70)(27, 62)(28, 68)(29, 61)(30, 67)(31, 71)(32, 69)(33, 64)(34, 63)(35, 66)(36, 65)(73, 201)(74, 203)(75, 209)(76, 210)(77, 207)(78, 208)(79, 184)(80, 186)(81, 216)(82, 215)(83, 214)(84, 213)(85, 183)(86, 185)(87, 191)(88, 192)(89, 189)(90, 190)(91, 202)(92, 204)(93, 198)(94, 197)(95, 196)(96, 195)(97, 182)(98, 181)(99, 187)(100, 193)(101, 188)(102, 194)(103, 200)(104, 199)(105, 205)(106, 211)(107, 206)(108, 212)(109, 120)(110, 118)(111, 122)(112, 116)(113, 121)(114, 115)(117, 128)(119, 127)(123, 130)(124, 129)(125, 132)(126, 131)(133, 143)(134, 141)(135, 136)(137, 138)(139, 144)(140, 142)(145, 177)(146, 179)(147, 149)(148, 150)(151, 172)(152, 174)(153, 168)(154, 167)(155, 166)(156, 165)(157, 171)(158, 173)(159, 161)(160, 162)(163, 178)(164, 180)(169, 170)(175, 176)(217, 243)(218, 245)(219, 233)(220, 234)(221, 231)(222, 232)(223, 250)(224, 252)(225, 228)(226, 227)(229, 249)(230, 251)(235, 244)(236, 246)(237, 240)(238, 239)(241, 248)(242, 247)

MAP           : A4.1213
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 152)(20, 162)(21, 161)(22, 160)(23, 148)(24, 146)(25, 157)(26, 156)(27, 155)(28, 147)(29, 159)(30, 145)(31, 158)(32, 151)(33, 153)(34, 149)(35, 154)(36, 150)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 143)(56, 135)(57, 134)(58, 133)(59, 139)(60, 137)(61, 130)(62, 129)(63, 128)(64, 138)(65, 132)(66, 136)(67, 131)(68, 142)(69, 144)(70, 140)(71, 127)(72, 141)(73, 96)(74, 106)(75, 104)(76, 91)(77, 102)(78, 94)(79, 101)(80, 92)(81, 93)(82, 103)(83, 107)(84, 108)(85, 105)(86, 99)(87, 100)(88, 98)(89, 97)(90, 95)(109, 241)(110, 237)(111, 236)(112, 245)(113, 249)(114, 251)(115, 235)(116, 248)(117, 250)(118, 252)(119, 238)(120, 247)(121, 246)(122, 242)(123, 239)(124, 243)(125, 240)(126, 244)(163, 192)(164, 186)(165, 190)(166, 185)(167, 196)(168, 198)(169, 194)(170, 181)(171, 195)(172, 197)(173, 189)(174, 188)(175, 187)(176, 193)(177, 191)(178, 184)(179, 183)(180, 182)(217, 223)(218, 219)(220, 227)(221, 231)(222, 233)(224, 230)(225, 232)(226, 234)(228, 229)

MAP           : A4.1214
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 152)(20, 162)(21, 161)(22, 160)(23, 148)(24, 146)(25, 157)(26, 156)(27, 155)(28, 147)(29, 159)(30, 145)(31, 158)(32, 151)(33, 153)(34, 149)(35, 154)(36, 150)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 143)(56, 135)(57, 134)(58, 133)(59, 139)(60, 137)(61, 130)(62, 129)(63, 128)(64, 138)(65, 132)(66, 136)(67, 131)(68, 142)(69, 144)(70, 140)(71, 127)(72, 141)(73, 106)(74, 102)(75, 101)(76, 92)(77, 96)(78, 98)(79, 100)(80, 95)(81, 97)(82, 99)(83, 103)(84, 94)(85, 93)(86, 107)(87, 104)(88, 108)(89, 105)(90, 91)(109, 249)(110, 241)(111, 239)(112, 244)(113, 237)(114, 247)(115, 236)(116, 245)(117, 246)(118, 238)(119, 242)(120, 243)(121, 240)(122, 252)(123, 235)(124, 251)(125, 250)(126, 248)(163, 192)(164, 186)(165, 190)(166, 185)(167, 196)(168, 198)(169, 194)(170, 181)(171, 195)(172, 197)(173, 189)(174, 188)(175, 187)(176, 193)(177, 191)(178, 184)(179, 183)(180, 182)(217, 231)(218, 223)(219, 221)(220, 226)(222, 229)(224, 227)(225, 228)(230, 234)(232, 233)

MAP           : A4.1215
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 152)(20, 162)(21, 161)(22, 160)(23, 148)(24, 146)(25, 157)(26, 156)(27, 155)(28, 147)(29, 159)(30, 145)(31, 158)(32, 151)(33, 153)(34, 149)(35, 154)(36, 150)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 143)(56, 135)(57, 134)(58, 133)(59, 139)(60, 137)(61, 130)(62, 129)(63, 128)(64, 138)(65, 132)(66, 136)(67, 131)(68, 142)(69, 144)(70, 140)(71, 127)(72, 141)(73, 108)(74, 94)(75, 103)(76, 102)(77, 98)(78, 95)(79, 99)(80, 96)(81, 100)(82, 97)(83, 93)(84, 92)(85, 101)(86, 105)(87, 107)(88, 91)(89, 104)(90, 106)(109, 248)(110, 244)(111, 240)(112, 243)(113, 245)(114, 237)(115, 246)(116, 247)(117, 238)(118, 236)(119, 239)(120, 241)(121, 242)(122, 235)(123, 250)(124, 249)(125, 252)(126, 251)(163, 192)(164, 186)(165, 190)(166, 185)(167, 196)(168, 198)(169, 194)(170, 181)(171, 195)(172, 197)(173, 189)(174, 188)(175, 187)(176, 193)(177, 191)(178, 184)(179, 183)(180, 182)(217, 230)(218, 226)(219, 222)(220, 225)(221, 227)(223, 228)(224, 229)(231, 232)(233, 234)

MAP           : A4.1216
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 146)(20, 149)(21, 151)(22, 152)(23, 145)(24, 160)(25, 159)(26, 162)(27, 161)(28, 158)(29, 154)(30, 150)(31, 153)(32, 155)(33, 147)(34, 156)(35, 157)(36, 148)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 133)(56, 129)(57, 128)(58, 137)(59, 141)(60, 143)(61, 127)(62, 140)(63, 142)(64, 144)(65, 130)(66, 139)(67, 138)(68, 134)(69, 131)(70, 135)(71, 132)(72, 136)(73, 106)(74, 102)(75, 101)(76, 92)(77, 96)(78, 98)(79, 100)(80, 95)(81, 97)(82, 99)(83, 103)(84, 94)(85, 93)(86, 107)(87, 104)(88, 108)(89, 105)(90, 91)(109, 244)(110, 245)(111, 246)(112, 247)(113, 248)(114, 249)(115, 250)(116, 251)(117, 252)(118, 235)(119, 236)(120, 237)(121, 238)(122, 239)(123, 240)(124, 241)(125, 242)(126, 243)(163, 185)(164, 181)(165, 195)(166, 198)(167, 182)(168, 192)(169, 183)(170, 184)(171, 193)(172, 191)(173, 194)(174, 196)(175, 197)(176, 190)(177, 187)(178, 186)(179, 189)(180, 188)(217, 226)(218, 227)(219, 228)(220, 229)(221, 230)(222, 231)(223, 232)(224, 233)(225, 234)

MAP           : A4.1217
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 160)(20, 156)(21, 155)(22, 146)(23, 150)(24, 152)(25, 154)(26, 149)(27, 151)(28, 153)(29, 157)(30, 148)(31, 147)(32, 161)(33, 158)(34, 162)(35, 159)(36, 145)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 137)(56, 140)(57, 142)(58, 143)(59, 136)(60, 133)(61, 132)(62, 135)(63, 134)(64, 131)(65, 127)(66, 141)(67, 144)(68, 128)(69, 138)(70, 129)(71, 130)(72, 139)(73, 95)(74, 91)(75, 105)(76, 108)(77, 92)(78, 102)(79, 93)(80, 94)(81, 103)(82, 101)(83, 104)(84, 106)(85, 107)(86, 100)(87, 97)(88, 96)(89, 99)(90, 98)(109, 248)(110, 244)(111, 240)(112, 243)(113, 245)(114, 237)(115, 246)(116, 247)(117, 238)(118, 236)(119, 239)(120, 241)(121, 242)(122, 235)(123, 250)(124, 249)(125, 252)(126, 251)(163, 198)(164, 184)(165, 193)(166, 192)(167, 188)(168, 185)(169, 189)(170, 186)(171, 190)(172, 187)(173, 183)(174, 182)(175, 191)(176, 195)(177, 197)(178, 181)(179, 194)(180, 196)(217, 230)(218, 226)(219, 222)(220, 225)(221, 227)(223, 228)(224, 229)(231, 232)(233, 234)

MAP           : A4.1218
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 160)(20, 156)(21, 155)(22, 146)(23, 150)(24, 152)(25, 154)(26, 149)(27, 151)(28, 153)(29, 157)(30, 148)(31, 147)(32, 161)(33, 158)(34, 162)(35, 159)(36, 145)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 137)(56, 140)(57, 142)(58, 143)(59, 136)(60, 133)(61, 132)(62, 135)(63, 134)(64, 131)(65, 127)(66, 141)(67, 144)(68, 128)(69, 138)(70, 129)(71, 130)(72, 139)(73, 94)(74, 98)(75, 99)(76, 96)(77, 108)(78, 91)(79, 107)(80, 106)(81, 104)(82, 105)(83, 97)(84, 95)(85, 100)(86, 93)(87, 103)(88, 92)(89, 101)(90, 102)(109, 241)(110, 237)(111, 236)(112, 245)(113, 249)(114, 251)(115, 235)(116, 248)(117, 250)(118, 252)(119, 238)(120, 247)(121, 246)(122, 242)(123, 239)(124, 243)(125, 240)(126, 244)(163, 198)(164, 184)(165, 193)(166, 192)(167, 188)(168, 185)(169, 189)(170, 186)(171, 190)(172, 187)(173, 183)(174, 182)(175, 191)(176, 195)(177, 197)(178, 181)(179, 194)(180, 196)(217, 223)(218, 219)(220, 227)(221, 231)(222, 233)(224, 230)(225, 232)(226, 234)(228, 229)

MAP           : A4.1219
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 160)(20, 156)(21, 155)(22, 146)(23, 150)(24, 152)(25, 154)(26, 149)(27, 151)(28, 153)(29, 157)(30, 148)(31, 147)(32, 161)(33, 158)(34, 162)(35, 159)(36, 145)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 137)(56, 140)(57, 142)(58, 143)(59, 136)(60, 133)(61, 132)(62, 135)(63, 134)(64, 131)(65, 127)(66, 141)(67, 144)(68, 128)(69, 138)(70, 129)(71, 130)(72, 139)(73, 96)(74, 106)(75, 104)(76, 91)(77, 102)(78, 94)(79, 101)(80, 92)(81, 93)(82, 103)(83, 107)(84, 108)(85, 105)(86, 99)(87, 100)(88, 98)(89, 97)(90, 95)(109, 251)(110, 243)(111, 242)(112, 241)(113, 247)(114, 245)(115, 238)(116, 237)(117, 236)(118, 246)(119, 240)(120, 244)(121, 239)(122, 250)(123, 252)(124, 248)(125, 235)(126, 249)(163, 198)(164, 184)(165, 193)(166, 192)(167, 188)(168, 185)(169, 189)(170, 186)(171, 190)(172, 187)(173, 183)(174, 182)(175, 191)(176, 195)(177, 197)(178, 181)(179, 194)(180, 196)(217, 233)(218, 225)(219, 224)(220, 223)(221, 229)(222, 227)(226, 228)(230, 232)(231, 234)

MAP           : A4.1220
NOTES         : type I, chiral, isomorphic to A4.1212.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.2 * x.4^-1 * x.1, x.5 * x.4^-1 * x.3, x.5^3, (x.3 * x.1)^2, x.3 * x.4^-2 * x.5 * x.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        : 252
R = (1, 37, 73, 109, 145, 181, 217)(2, 38, 74, 110, 146, 182, 218)(3, 39, 75, 111, 147, 183, 219)(4, 40, 76, 112, 148, 184, 220)(5, 41, 77, 113, 149, 185, 221)(6, 42, 78, 114, 150, 186, 222)(7, 43, 79, 115, 151, 187, 223)(8, 44, 80, 116, 152, 188, 224)(9, 45, 81, 117, 153, 189, 225)(10, 46, 82, 118, 154, 190, 226)(11, 47, 83, 119, 155, 191, 227)(12, 48, 84, 120, 156, 192, 228)(13, 49, 85, 121, 157, 193, 229)(14, 50, 86, 122, 158, 194, 230)(15, 51, 87, 123, 159, 195, 231)(16, 52, 88, 124, 160, 196, 232)(17, 53, 89, 125, 161, 197, 233)(18, 54, 90, 126, 162, 198, 234)(19, 55, 91, 127, 163, 199, 235)(20, 56, 92, 128, 164, 200, 236)(21, 57, 93, 129, 165, 201, 237)(22, 58, 94, 130, 166, 202, 238)(23, 59, 95, 131, 167, 203, 239)(24, 60, 96, 132, 168, 204, 240)(25, 61, 97, 133, 169, 205, 241)(26, 62, 98, 134, 170, 206, 242)(27, 63, 99, 135, 171, 207, 243)(28, 64, 100, 136, 172, 208, 244)(29, 65, 101, 137, 173, 209, 245)(30, 66, 102, 138, 174, 210, 246)(31, 67, 103, 139, 175, 211, 247)(32, 68, 104, 140, 176, 212, 248)(33, 69, 105, 141, 177, 213, 249)(34, 70, 106, 142, 178, 214, 250)(35, 71, 107, 143, 179, 215, 251)(36, 72, 108, 144, 180, 216, 252)
L = (1, 27)(2, 29)(3, 17)(4, 18)(5, 15)(6, 16)(7, 34)(8, 36)(9, 12)(10, 11)(13, 33)(14, 35)(19, 28)(20, 30)(21, 24)(22, 23)(25, 32)(26, 31)(37, 53)(38, 51)(39, 46)(40, 45)(41, 48)(42, 47)(43, 59)(44, 57)(49, 60)(50, 58)(52, 56)(54, 55)(61, 66)(62, 64)(63, 68)(65, 67)(69, 70)(71, 72)(73, 219)(74, 221)(75, 227)(76, 228)(77, 225)(78, 226)(79, 238)(80, 240)(81, 234)(82, 233)(83, 232)(84, 231)(85, 237)(86, 239)(87, 245)(88, 246)(89, 243)(90, 244)(91, 220)(92, 222)(93, 252)(94, 251)(95, 250)(96, 249)(97, 236)(98, 235)(99, 241)(100, 247)(101, 242)(102, 248)(103, 218)(104, 217)(105, 223)(106, 229)(107, 224)(108, 230)(109, 151)(110, 152)(111, 153)(112, 154)(113, 155)(114, 156)(115, 175)(116, 176)(117, 177)(118, 178)(119, 179)(120, 180)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 157)(128, 158)(129, 159)(130, 160)(131, 161)(132, 162)(133, 163)(134, 164)(135, 165)(136, 166)(137, 167)(138, 168)(139, 145)(140, 146)(141, 147)(142, 148)(143, 149)(144, 150)(181, 182)(183, 187)(184, 193)(185, 188)(186, 194)(189, 191)(190, 192)(195, 216)(196, 215)(197, 214)(198, 213)(199, 200)(201, 205)(202, 211)(203, 206)(204, 212)(207, 209)(208, 210)

MAP           : A4.1221
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.2 * x.1 * x.4, x.5^3, x.4 * x.5^-1 * x.3, (x.5 * x.1)^2, (x.3 * x.2)^2, x.3 * x.5 * x.1 * x.4 * x.1, x.4^2 * x.3 * x.4^-1 * 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        : 252
R = (1, 37, 73, 109, 145, 181, 217)(2, 38, 74, 110, 146, 182, 218)(3, 39, 75, 111, 147, 183, 219)(4, 40, 76, 112, 148, 184, 220)(5, 41, 77, 113, 149, 185, 221)(6, 42, 78, 114, 150, 186, 222)(7, 43, 79, 115, 151, 187, 223)(8, 44, 80, 116, 152, 188, 224)(9, 45, 81, 117, 153, 189, 225)(10, 46, 82, 118, 154, 190, 226)(11, 47, 83, 119, 155, 191, 227)(12, 48, 84, 120, 156, 192, 228)(13, 49, 85, 121, 157, 193, 229)(14, 50, 86, 122, 158, 194, 230)(15, 51, 87, 123, 159, 195, 231)(16, 52, 88, 124, 160, 196, 232)(17, 53, 89, 125, 161, 197, 233)(18, 54, 90, 126, 162, 198, 234)(19, 55, 91, 127, 163, 199, 235)(20, 56, 92, 128, 164, 200, 236)(21, 57, 93, 129, 165, 201, 237)(22, 58, 94, 130, 166, 202, 238)(23, 59, 95, 131, 167, 203, 239)(24, 60, 96, 132, 168, 204, 240)(25, 61, 97, 133, 169, 205, 241)(26, 62, 98, 134, 170, 206, 242)(27, 63, 99, 135, 171, 207, 243)(28, 64, 100, 136, 172, 208, 244)(29, 65, 101, 137, 173, 209, 245)(30, 66, 102, 138, 174, 210, 246)(31, 67, 103, 139, 175, 211, 247)(32, 68, 104, 140, 176, 212, 248)(33, 69, 105, 141, 177, 213, 249)(34, 70, 106, 142, 178, 214, 250)(35, 71, 107, 143, 179, 215, 251)(36, 72, 108, 144, 180, 216, 252)
L = (1, 6)(2, 4)(3, 20)(5, 19)(7, 36)(8, 34)(9, 26)(10, 32)(11, 25)(12, 31)(13, 35)(14, 33)(15, 28)(16, 27)(17, 30)(18, 29)(21, 22)(23, 24)(37, 56)(38, 55)(39, 61)(40, 67)(41, 62)(42, 68)(43, 57)(44, 59)(45, 65)(46, 66)(47, 63)(48, 64)(49, 58)(50, 60)(51, 54)(52, 53)(69, 72)(70, 71)(73, 219)(74, 221)(75, 227)(76, 228)(77, 225)(78, 226)(79, 238)(80, 240)(81, 234)(82, 233)(83, 232)(84, 231)(85, 237)(86, 239)(87, 245)(88, 246)(89, 243)(90, 244)(91, 220)(92, 222)(93, 252)(94, 251)(95, 250)(96, 249)(97, 236)(98, 235)(99, 241)(100, 247)(101, 242)(102, 248)(103, 218)(104, 217)(105, 223)(106, 229)(107, 224)(108, 230)(109, 151)(110, 152)(111, 153)(112, 154)(113, 155)(114, 156)(115, 175)(116, 176)(117, 177)(118, 178)(119, 179)(120, 180)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 157)(128, 158)(129, 159)(130, 160)(131, 161)(132, 162)(133, 163)(134, 164)(135, 165)(136, 166)(137, 167)(138, 168)(139, 145)(140, 146)(141, 147)(142, 148)(143, 149)(144, 150)(181, 182)(183, 187)(184, 193)(185, 188)(186, 194)(189, 191)(190, 192)(195, 216)(196, 215)(197, 214)(198, 213)(199, 200)(201, 205)(202, 211)(203, 206)(204, 212)(207, 209)(208, 210)

MAP           : A4.1222
NOTES         : type I, chiral, isomorphic to A4.1212.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.2 * x.4^-1 * x.1, x.5 * x.4^-1 * x.3, x.5^3, (x.3 * x.1)^2, x.3 * x.4^-2 * x.5 * x.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        : 252
R = (1, 37, 73, 109, 145, 181, 217)(2, 38, 74, 110, 146, 182, 218)(3, 39, 75, 111, 147, 183, 219)(4, 40, 76, 112, 148, 184, 220)(5, 41, 77, 113, 149, 185, 221)(6, 42, 78, 114, 150, 186, 222)(7, 43, 79, 115, 151, 187, 223)(8, 44, 80, 116, 152, 188, 224)(9, 45, 81, 117, 153, 189, 225)(10, 46, 82, 118, 154, 190, 226)(11, 47, 83, 119, 155, 191, 227)(12, 48, 84, 120, 156, 192, 228)(13, 49, 85, 121, 157, 193, 229)(14, 50, 86, 122, 158, 194, 230)(15, 51, 87, 123, 159, 195, 231)(16, 52, 88, 124, 160, 196, 232)(17, 53, 89, 125, 161, 197, 233)(18, 54, 90, 126, 162, 198, 234)(19, 55, 91, 127, 163, 199, 235)(20, 56, 92, 128, 164, 200, 236)(21, 57, 93, 129, 165, 201, 237)(22, 58, 94, 130, 166, 202, 238)(23, 59, 95, 131, 167, 203, 239)(24, 60, 96, 132, 168, 204, 240)(25, 61, 97, 133, 169, 205, 241)(26, 62, 98, 134, 170, 206, 242)(27, 63, 99, 135, 171, 207, 243)(28, 64, 100, 136, 172, 208, 244)(29, 65, 101, 137, 173, 209, 245)(30, 66, 102, 138, 174, 210, 246)(31, 67, 103, 139, 175, 211, 247)(32, 68, 104, 140, 176, 212, 248)(33, 69, 105, 141, 177, 213, 249)(34, 70, 106, 142, 178, 214, 250)(35, 71, 107, 143, 179, 215, 251)(36, 72, 108, 144, 180, 216, 252)
L = (1, 2)(3, 7)(4, 13)(5, 8)(6, 14)(9, 11)(10, 12)(15, 36)(16, 35)(17, 34)(18, 33)(19, 20)(21, 25)(22, 31)(23, 26)(24, 32)(27, 29)(28, 30)(37, 59)(38, 57)(39, 40)(41, 42)(43, 65)(44, 63)(45, 70)(46, 69)(47, 72)(48, 71)(49, 66)(50, 64)(51, 68)(52, 62)(53, 67)(54, 61)(55, 60)(56, 58)(73, 242)(74, 241)(75, 229)(76, 223)(77, 230)(78, 224)(79, 243)(80, 245)(81, 233)(82, 234)(83, 231)(84, 232)(85, 244)(86, 246)(87, 240)(88, 239)(89, 238)(90, 237)(91, 248)(92, 247)(93, 217)(94, 235)(95, 218)(96, 236)(97, 249)(98, 251)(99, 221)(100, 222)(101, 219)(102, 220)(103, 250)(104, 252)(105, 228)(106, 227)(107, 226)(108, 225)(109, 175)(110, 176)(111, 177)(112, 178)(113, 179)(114, 180)(115, 145)(116, 146)(117, 147)(118, 148)(119, 149)(120, 150)(121, 163)(122, 164)(123, 165)(124, 166)(125, 167)(126, 168)(127, 169)(128, 170)(129, 171)(130, 172)(131, 173)(132, 174)(133, 157)(134, 158)(135, 159)(136, 160)(137, 161)(138, 162)(139, 151)(140, 152)(141, 153)(142, 154)(143, 155)(144, 156)(181, 207)(182, 209)(183, 197)(184, 198)(185, 195)(186, 196)(187, 214)(188, 216)(189, 192)(190, 191)(193, 213)(194, 215)(199, 208)(200, 210)(201, 204)(202, 203)(205, 212)(206, 211)

MAP           : A4.1223
NOTES         : type I, chiral, isomorphic to A4.1221.
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)   : <36, 10>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3^2, x.2 * x.1 * x.4, x.5^3, x.4 * x.5^-1 * x.3, (x.5 * x.1)^2, (x.3 * x.2)^2, x.3 * x.5 * x.1 * x.4 * x.1, x.4^2 * x.3 * x.4^-1 * 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        : 252
R = (1, 37, 73, 109, 145, 181, 217)(2, 38, 74, 110, 146, 182, 218)(3, 39, 75, 111, 147, 183, 219)(4, 40, 76, 112, 148, 184, 220)(5, 41, 77, 113, 149, 185, 221)(6, 42, 78, 114, 150, 186, 222)(7, 43, 79, 115, 151, 187, 223)(8, 44, 80, 116, 152, 188, 224)(9, 45, 81, 117, 153, 189, 225)(10, 46, 82, 118, 154, 190, 226)(11, 47, 83, 119, 155, 191, 227)(12, 48, 84, 120, 156, 192, 228)(13, 49, 85, 121, 157, 193, 229)(14, 50, 86, 122, 158, 194, 230)(15, 51, 87, 123, 159, 195, 231)(16, 52, 88, 124, 160, 196, 232)(17, 53, 89, 125, 161, 197, 233)(18, 54, 90, 126, 162, 198, 234)(19, 55, 91, 127, 163, 199, 235)(20, 56, 92, 128, 164, 200, 236)(21, 57, 93, 129, 165, 201, 237)(22, 58, 94, 130, 166, 202, 238)(23, 59, 95, 131, 167, 203, 239)(24, 60, 96, 132, 168, 204, 240)(25, 61, 97, 133, 169, 205, 241)(26, 62, 98, 134, 170, 206, 242)(27, 63, 99, 135, 171, 207, 243)(28, 64, 100, 136, 172, 208, 244)(29, 65, 101, 137, 173, 209, 245)(30, 66, 102, 138, 174, 210, 246)(31, 67, 103, 139, 175, 211, 247)(32, 68, 104, 140, 176, 212, 248)(33, 69, 105, 141, 177, 213, 249)(34, 70, 106, 142, 178, 214, 250)(35, 71, 107, 143, 179, 215, 251)(36, 72, 108, 144, 180, 216, 252)
L = (1, 12)(2, 10)(3, 14)(4, 8)(5, 13)(6, 7)(9, 20)(11, 19)(15, 22)(16, 21)(17, 24)(18, 23)(25, 35)(26, 33)(27, 28)(29, 30)(31, 36)(32, 34)(37, 69)(38, 71)(39, 41)(40, 42)(43, 64)(44, 66)(45, 60)(46, 59)(47, 58)(48, 57)(49, 63)(50, 65)(51, 53)(52, 54)(55, 70)(56, 72)(61, 62)(67, 68)(73, 242)(74, 241)(75, 229)(76, 223)(77, 230)(78, 224)(79, 243)(80, 245)(81, 233)(82, 234)(83, 231)(84, 232)(85, 244)(86, 246)(87, 240)(88, 239)(89, 238)(90, 237)(91, 248)(92, 247)(93, 217)(94, 235)(95, 218)(96, 236)(97, 249)(98, 251)(99, 221)(100, 222)(101, 219)(102, 220)(103, 250)(104, 252)(105, 228)(106, 227)(107, 226)(108, 225)(109, 175)(110, 176)(111, 177)(112, 178)(113, 179)(114, 180)(115, 145)(116, 146)(117, 147)(118, 148)(119, 149)(120, 150)(121, 163)(122, 164)(123, 165)(124, 166)(125, 167)(126, 168)(127, 169)(128, 170)(129, 171)(130, 172)(131, 173)(132, 174)(133, 157)(134, 158)(135, 159)(136, 160)(137, 161)(138, 162)(139, 151)(140, 152)(141, 153)(142, 154)(143, 155)(144, 156)(181, 207)(182, 209)(183, 197)(184, 198)(185, 195)(186, 196)(187, 214)(188, 216)(189, 192)(190, 191)(193, 213)(194, 215)(199, 208)(200, 210)(201, 204)(202, 203)(205, 212)(206, 211)

MAP           : A4.1224
NOTES         : type I, chiral, isomorphic to A4.1221.
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)   : <36, 10>
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^-1 * x.2)^2, (x.3 * x.1)^2, x.3 * x.4^-1 * x.2 * x.5 * x.2, x.5^2 * x.3 * x.5^-1 * x.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        : 252
R = (1, 37, 73, 109, 145, 181, 217)(2, 38, 74, 110, 146, 182, 218)(3, 39, 75, 111, 147, 183, 219)(4, 40, 76, 112, 148, 184, 220)(5, 41, 77, 113, 149, 185, 221)(6, 42, 78, 114, 150, 186, 222)(7, 43, 79, 115, 151, 187, 223)(8, 44, 80, 116, 152, 188, 224)(9, 45, 81, 117, 153, 189, 225)(10, 46, 82, 118, 154, 190, 226)(11, 47, 83, 119, 155, 191, 227)(12, 48, 84, 120, 156, 192, 228)(13, 49, 85, 121, 157, 193, 229)(14, 50, 86, 122, 158, 194, 230)(15, 51, 87, 123, 159, 195, 231)(16, 52, 88, 124, 160, 196, 232)(17, 53, 89, 125, 161, 197, 233)(18, 54, 90, 126, 162, 198, 234)(19, 55, 91, 127, 163, 199, 235)(20, 56, 92, 128, 164, 200, 236)(21, 57, 93, 129, 165, 201, 237)(22, 58, 94, 130, 166, 202, 238)(23, 59, 95, 131, 167, 203, 239)(24, 60, 96, 132, 168, 204, 240)(25, 61, 97, 133, 169, 205, 241)(26, 62, 98, 134, 170, 206, 242)(27, 63, 99, 135, 171, 207, 243)(28, 64, 100, 136, 172, 208, 244)(29, 65, 101, 137, 173, 209, 245)(30, 66, 102, 138, 174, 210, 246)(31, 67, 103, 139, 175, 211, 247)(32, 68, 104, 140, 176, 212, 248)(33, 69, 105, 141, 177, 213, 249)(34, 70, 106, 142, 178, 214, 250)(35, 71, 107, 143, 179, 215, 251)(36, 72, 108, 144, 180, 216, 252)
L = (1, 41)(2, 39)(3, 58)(4, 57)(5, 60)(6, 59)(7, 47)(8, 45)(9, 52)(10, 51)(11, 54)(12, 53)(13, 48)(14, 46)(15, 50)(16, 44)(17, 49)(18, 43)(19, 42)(20, 40)(21, 56)(22, 38)(23, 55)(24, 37)(25, 72)(26, 70)(27, 62)(28, 68)(29, 61)(30, 67)(31, 71)(32, 69)(33, 64)(34, 63)(35, 66)(36, 65)(73, 212)(74, 211)(75, 181)(76, 199)(77, 182)(78, 200)(79, 213)(80, 215)(81, 185)(82, 186)(83, 183)(84, 184)(85, 214)(86, 216)(87, 192)(88, 191)(89, 190)(90, 189)(91, 206)(92, 205)(93, 193)(94, 187)(95, 194)(96, 188)(97, 207)(98, 209)(99, 197)(100, 198)(101, 195)(102, 196)(103, 208)(104, 210)(105, 204)(106, 203)(107, 202)(108, 201)(109, 135)(110, 137)(111, 125)(112, 126)(113, 123)(114, 124)(115, 142)(116, 144)(117, 120)(118, 119)(121, 141)(122, 143)(127, 136)(128, 138)(129, 132)(130, 131)(133, 140)(134, 139)(145, 161)(146, 159)(147, 154)(148, 153)(149, 156)(150, 155)(151, 167)(152, 165)(157, 168)(158, 166)(160, 164)(162, 163)(169, 174)(170, 172)(171, 176)(173, 175)(177, 178)(179, 180)(217, 218)(219, 223)(220, 229)(221, 224)(222, 230)(225, 227)(226, 228)(231, 252)(232, 251)(233, 250)(234, 249)(235, 236)(237, 241)(238, 247)(239, 242)(240, 248)(243, 245)(244, 246)

MAP           : A4.1225
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 146)(20, 149)(21, 151)(22, 152)(23, 145)(24, 160)(25, 159)(26, 162)(27, 161)(28, 158)(29, 154)(30, 150)(31, 153)(32, 155)(33, 147)(34, 156)(35, 157)(36, 148)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 133)(56, 129)(57, 128)(58, 137)(59, 141)(60, 143)(61, 127)(62, 140)(63, 142)(64, 144)(65, 130)(66, 139)(67, 138)(68, 134)(69, 131)(70, 135)(71, 132)(72, 136)(73, 94)(74, 98)(75, 99)(76, 96)(77, 108)(78, 91)(79, 107)(80, 106)(81, 104)(82, 105)(83, 97)(84, 95)(85, 100)(86, 93)(87, 103)(88, 92)(89, 101)(90, 102)(109, 251)(110, 243)(111, 242)(112, 241)(113, 247)(114, 245)(115, 238)(116, 237)(117, 236)(118, 246)(119, 240)(120, 244)(121, 239)(122, 250)(123, 252)(124, 248)(125, 235)(126, 249)(163, 185)(164, 181)(165, 195)(166, 198)(167, 182)(168, 192)(169, 183)(170, 184)(171, 193)(172, 191)(173, 194)(174, 196)(175, 197)(176, 190)(177, 187)(178, 186)(179, 189)(180, 188)(217, 233)(218, 225)(219, 224)(220, 223)(221, 229)(222, 227)(226, 228)(230, 232)(231, 234)

MAP           : A4.1226
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 146)(20, 149)(21, 151)(22, 152)(23, 145)(24, 160)(25, 159)(26, 162)(27, 161)(28, 158)(29, 154)(30, 150)(31, 153)(32, 155)(33, 147)(34, 156)(35, 157)(36, 148)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 133)(56, 129)(57, 128)(58, 137)(59, 141)(60, 143)(61, 127)(62, 140)(63, 142)(64, 144)(65, 130)(66, 139)(67, 138)(68, 134)(69, 131)(70, 135)(71, 132)(72, 136)(73, 96)(74, 106)(75, 104)(76, 91)(77, 102)(78, 94)(79, 101)(80, 92)(81, 93)(82, 103)(83, 107)(84, 108)(85, 105)(86, 99)(87, 100)(88, 98)(89, 97)(90, 95)(109, 245)(110, 248)(111, 250)(112, 251)(113, 244)(114, 241)(115, 240)(116, 243)(117, 242)(118, 239)(119, 235)(120, 249)(121, 252)(122, 236)(123, 246)(124, 237)(125, 238)(126, 247)(163, 185)(164, 181)(165, 195)(166, 198)(167, 182)(168, 192)(169, 183)(170, 184)(171, 193)(172, 191)(173, 194)(174, 196)(175, 197)(176, 190)(177, 187)(178, 186)(179, 189)(180, 188)(217, 227)(218, 230)(219, 232)(220, 233)(221, 226)(222, 223)(224, 225)(228, 231)(229, 234)

MAP           : A4.1227
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 146)(20, 149)(21, 151)(22, 152)(23, 145)(24, 160)(25, 159)(26, 162)(27, 161)(28, 158)(29, 154)(30, 150)(31, 153)(32, 155)(33, 147)(34, 156)(35, 157)(36, 148)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 133)(56, 129)(57, 128)(58, 137)(59, 141)(60, 143)(61, 127)(62, 140)(63, 142)(64, 144)(65, 130)(66, 139)(67, 138)(68, 134)(69, 131)(70, 135)(71, 132)(72, 136)(73, 98)(74, 108)(75, 107)(76, 106)(77, 94)(78, 92)(79, 103)(80, 102)(81, 101)(82, 93)(83, 105)(84, 91)(85, 104)(86, 97)(87, 99)(88, 95)(89, 100)(90, 96)(109, 247)(110, 251)(111, 252)(112, 249)(113, 243)(114, 244)(115, 242)(116, 241)(117, 239)(118, 240)(119, 250)(120, 248)(121, 235)(122, 246)(123, 238)(124, 245)(125, 236)(126, 237)(163, 185)(164, 181)(165, 195)(166, 198)(167, 182)(168, 192)(169, 183)(170, 184)(171, 193)(172, 191)(173, 194)(174, 196)(175, 197)(176, 190)(177, 187)(178, 186)(179, 189)(180, 188)(217, 229)(218, 233)(219, 234)(220, 231)(221, 225)(222, 226)(223, 224)(227, 232)(228, 230)

MAP           : A4.1228
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 146)(20, 149)(21, 151)(22, 152)(23, 145)(24, 160)(25, 159)(26, 162)(27, 161)(28, 158)(29, 154)(30, 150)(31, 153)(32, 155)(33, 147)(34, 156)(35, 157)(36, 148)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 133)(56, 129)(57, 128)(58, 137)(59, 141)(60, 143)(61, 127)(62, 140)(63, 142)(64, 144)(65, 130)(66, 139)(67, 138)(68, 134)(69, 131)(70, 135)(71, 132)(72, 136)(73, 102)(74, 96)(75, 100)(76, 95)(77, 106)(78, 108)(79, 104)(80, 91)(81, 105)(82, 107)(83, 99)(84, 98)(85, 97)(86, 103)(87, 101)(88, 94)(89, 93)(90, 92)(109, 248)(110, 244)(111, 240)(112, 243)(113, 245)(114, 237)(115, 246)(116, 247)(117, 238)(118, 236)(119, 239)(120, 241)(121, 242)(122, 235)(123, 250)(124, 249)(125, 252)(126, 251)(163, 185)(164, 181)(165, 195)(166, 198)(167, 182)(168, 192)(169, 183)(170, 184)(171, 193)(172, 191)(173, 194)(174, 196)(175, 197)(176, 190)(177, 187)(178, 186)(179, 189)(180, 188)(217, 230)(218, 226)(219, 222)(220, 225)(221, 227)(223, 228)(224, 229)(231, 232)(233, 234)

MAP           : A4.1229
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 148)(20, 152)(21, 153)(22, 150)(23, 162)(24, 145)(25, 161)(26, 160)(27, 158)(28, 159)(29, 151)(30, 149)(31, 154)(32, 147)(33, 157)(34, 146)(35, 155)(36, 156)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 135)(56, 139)(57, 130)(58, 129)(59, 143)(60, 140)(61, 144)(62, 141)(63, 127)(64, 142)(65, 138)(66, 137)(67, 128)(68, 132)(69, 134)(70, 136)(71, 131)(72, 133)(73, 98)(74, 108)(75, 107)(76, 106)(77, 94)(78, 92)(79, 103)(80, 102)(81, 101)(82, 93)(83, 105)(84, 91)(85, 104)(86, 97)(87, 99)(88, 95)(89, 100)(90, 96)(109, 245)(110, 248)(111, 250)(112, 251)(113, 244)(114, 241)(115, 240)(116, 243)(117, 242)(118, 239)(119, 235)(120, 249)(121, 252)(122, 236)(123, 246)(124, 237)(125, 238)(126, 247)(163, 186)(164, 196)(165, 194)(166, 181)(167, 192)(168, 184)(169, 191)(170, 182)(171, 183)(172, 193)(173, 197)(174, 198)(175, 195)(176, 189)(177, 190)(178, 188)(179, 187)(180, 185)(217, 227)(218, 230)(219, 232)(220, 233)(221, 226)(222, 223)(224, 225)(228, 231)(229, 234)

MAP           : A4.1230
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 146)(20, 149)(21, 151)(22, 152)(23, 145)(24, 160)(25, 159)(26, 162)(27, 161)(28, 158)(29, 154)(30, 150)(31, 153)(32, 155)(33, 147)(34, 156)(35, 157)(36, 148)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 133)(56, 129)(57, 128)(58, 137)(59, 141)(60, 143)(61, 127)(62, 140)(63, 142)(64, 144)(65, 130)(66, 139)(67, 138)(68, 134)(69, 131)(70, 135)(71, 132)(72, 136)(73, 108)(74, 94)(75, 103)(76, 102)(77, 98)(78, 95)(79, 99)(80, 96)(81, 100)(82, 97)(83, 93)(84, 92)(85, 101)(86, 105)(87, 107)(88, 91)(89, 104)(90, 106)(109, 243)(110, 247)(111, 238)(112, 237)(113, 251)(114, 248)(115, 252)(116, 249)(117, 235)(118, 250)(119, 246)(120, 245)(121, 236)(122, 240)(123, 242)(124, 244)(125, 239)(126, 241)(163, 185)(164, 181)(165, 195)(166, 198)(167, 182)(168, 192)(169, 183)(170, 184)(171, 193)(172, 191)(173, 194)(174, 196)(175, 197)(176, 190)(177, 187)(178, 186)(179, 189)(180, 188)(217, 225)(218, 229)(219, 220)(221, 233)(222, 230)(223, 234)(224, 231)(226, 232)(227, 228)

MAP           : A4.1231
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 148)(20, 152)(21, 153)(22, 150)(23, 162)(24, 145)(25, 161)(26, 160)(27, 158)(28, 159)(29, 151)(30, 149)(31, 154)(32, 147)(33, 157)(34, 146)(35, 155)(36, 156)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 135)(56, 139)(57, 130)(58, 129)(59, 143)(60, 140)(61, 144)(62, 141)(63, 127)(64, 142)(65, 138)(66, 137)(67, 128)(68, 132)(69, 134)(70, 136)(71, 131)(72, 133)(73, 92)(74, 95)(75, 97)(76, 98)(77, 91)(78, 106)(79, 105)(80, 108)(81, 107)(82, 104)(83, 100)(84, 96)(85, 99)(86, 101)(87, 93)(88, 102)(89, 103)(90, 94)(109, 251)(110, 243)(111, 242)(112, 241)(113, 247)(114, 245)(115, 238)(116, 237)(117, 236)(118, 246)(119, 240)(120, 244)(121, 239)(122, 250)(123, 252)(124, 248)(125, 235)(126, 249)(163, 186)(164, 196)(165, 194)(166, 181)(167, 192)(168, 184)(169, 191)(170, 182)(171, 183)(172, 193)(173, 197)(174, 198)(175, 195)(176, 189)(177, 190)(178, 188)(179, 187)(180, 185)(217, 233)(218, 225)(219, 224)(220, 223)(221, 229)(222, 227)(226, 228)(230, 232)(231, 234)

MAP           : A4.1232
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 148)(20, 152)(21, 153)(22, 150)(23, 162)(24, 145)(25, 161)(26, 160)(27, 158)(28, 159)(29, 151)(30, 149)(31, 154)(32, 147)(33, 157)(34, 146)(35, 155)(36, 156)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 135)(56, 139)(57, 130)(58, 129)(59, 143)(60, 140)(61, 144)(62, 141)(63, 127)(64, 142)(65, 138)(66, 137)(67, 128)(68, 132)(69, 134)(70, 136)(71, 131)(72, 133)(73, 95)(74, 91)(75, 105)(76, 108)(77, 92)(78, 102)(79, 93)(80, 94)(81, 103)(82, 101)(83, 104)(84, 106)(85, 107)(86, 100)(87, 97)(88, 96)(89, 99)(90, 98)(109, 247)(110, 251)(111, 252)(112, 249)(113, 243)(114, 244)(115, 242)(116, 241)(117, 239)(118, 240)(119, 250)(120, 248)(121, 235)(122, 246)(123, 238)(124, 245)(125, 236)(126, 237)(163, 186)(164, 196)(165, 194)(166, 181)(167, 192)(168, 184)(169, 191)(170, 182)(171, 183)(172, 193)(173, 197)(174, 198)(175, 195)(176, 189)(177, 190)(178, 188)(179, 187)(180, 185)(217, 229)(218, 233)(219, 234)(220, 231)(221, 225)(222, 226)(223, 224)(227, 232)(228, 230)

MAP           : A4.1233
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 148)(20, 152)(21, 153)(22, 150)(23, 162)(24, 145)(25, 161)(26, 160)(27, 158)(28, 159)(29, 151)(30, 149)(31, 154)(32, 147)(33, 157)(34, 146)(35, 155)(36, 156)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 135)(56, 139)(57, 130)(58, 129)(59, 143)(60, 140)(61, 144)(62, 141)(63, 127)(64, 142)(65, 138)(66, 137)(67, 128)(68, 132)(69, 134)(70, 136)(71, 131)(72, 133)(73, 102)(74, 96)(75, 100)(76, 95)(77, 106)(78, 108)(79, 104)(80, 91)(81, 105)(82, 107)(83, 99)(84, 98)(85, 97)(86, 103)(87, 101)(88, 94)(89, 93)(90, 92)(109, 249)(110, 241)(111, 239)(112, 244)(113, 237)(114, 247)(115, 236)(116, 245)(117, 246)(118, 238)(119, 242)(120, 243)(121, 240)(122, 252)(123, 235)(124, 251)(125, 250)(126, 248)(163, 186)(164, 196)(165, 194)(166, 181)(167, 192)(168, 184)(169, 191)(170, 182)(171, 183)(172, 193)(173, 197)(174, 198)(175, 195)(176, 189)(177, 190)(178, 188)(179, 187)(180, 185)(217, 231)(218, 223)(219, 221)(220, 226)(222, 229)(224, 227)(225, 228)(230, 234)(232, 233)

MAP           : A4.1234
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 148)(20, 152)(21, 153)(22, 150)(23, 162)(24, 145)(25, 161)(26, 160)(27, 158)(28, 159)(29, 151)(30, 149)(31, 154)(32, 147)(33, 157)(34, 146)(35, 155)(36, 156)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 135)(56, 139)(57, 130)(58, 129)(59, 143)(60, 140)(61, 144)(62, 141)(63, 127)(64, 142)(65, 138)(66, 137)(67, 128)(68, 132)(69, 134)(70, 136)(71, 131)(72, 133)(73, 106)(74, 102)(75, 101)(76, 92)(77, 96)(78, 98)(79, 100)(80, 95)(81, 97)(82, 99)(83, 103)(84, 94)(85, 93)(86, 107)(87, 104)(88, 108)(89, 105)(90, 91)(109, 241)(110, 237)(111, 236)(112, 245)(113, 249)(114, 251)(115, 235)(116, 248)(117, 250)(118, 252)(119, 238)(120, 247)(121, 246)(122, 242)(123, 239)(124, 243)(125, 240)(126, 244)(163, 186)(164, 196)(165, 194)(166, 181)(167, 192)(168, 184)(169, 191)(170, 182)(171, 183)(172, 193)(173, 197)(174, 198)(175, 195)(176, 189)(177, 190)(178, 188)(179, 187)(180, 185)(217, 223)(218, 219)(220, 227)(221, 231)(222, 233)(224, 230)(225, 232)(226, 234)(228, 229)

MAP           : A4.1235
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 148)(20, 152)(21, 153)(22, 150)(23, 162)(24, 145)(25, 161)(26, 160)(27, 158)(28, 159)(29, 151)(30, 149)(31, 154)(32, 147)(33, 157)(34, 146)(35, 155)(36, 156)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 135)(56, 139)(57, 130)(58, 129)(59, 143)(60, 140)(61, 144)(62, 141)(63, 127)(64, 142)(65, 138)(66, 137)(67, 128)(68, 132)(69, 134)(70, 136)(71, 131)(72, 133)(73, 108)(74, 94)(75, 103)(76, 102)(77, 98)(78, 95)(79, 99)(80, 96)(81, 100)(82, 97)(83, 93)(84, 92)(85, 101)(86, 105)(87, 107)(88, 91)(89, 104)(90, 106)(109, 244)(110, 245)(111, 246)(112, 247)(113, 248)(114, 249)(115, 250)(116, 251)(117, 252)(118, 235)(119, 236)(120, 237)(121, 238)(122, 239)(123, 240)(124, 241)(125, 242)(126, 243)(163, 186)(164, 196)(165, 194)(166, 181)(167, 192)(168, 184)(169, 191)(170, 182)(171, 183)(172, 193)(173, 197)(174, 198)(175, 195)(176, 189)(177, 190)(178, 188)(179, 187)(180, 185)(217, 226)(218, 227)(219, 228)(220, 229)(221, 230)(222, 231)(223, 232)(224, 233)(225, 234)

MAP           : A4.1236
NOTES         : type I, chiral, isomorphic to A4.1221.
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)   : <36, 10>
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^-1 * x.2)^2, (x.3 * x.1)^2, x.3 * x.4^-1 * x.2 * x.5 * x.2, x.5^2 * x.3 * x.5^-1 * x.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        : 252
R = (1, 37, 73, 109, 145, 181, 217)(2, 38, 74, 110, 146, 182, 218)(3, 39, 75, 111, 147, 183, 219)(4, 40, 76, 112, 148, 184, 220)(5, 41, 77, 113, 149, 185, 221)(6, 42, 78, 114, 150, 186, 222)(7, 43, 79, 115, 151, 187, 223)(8, 44, 80, 116, 152, 188, 224)(9, 45, 81, 117, 153, 189, 225)(10, 46, 82, 118, 154, 190, 226)(11, 47, 83, 119, 155, 191, 227)(12, 48, 84, 120, 156, 192, 228)(13, 49, 85, 121, 157, 193, 229)(14, 50, 86, 122, 158, 194, 230)(15, 51, 87, 123, 159, 195, 231)(16, 52, 88, 124, 160, 196, 232)(17, 53, 89, 125, 161, 197, 233)(18, 54, 90, 126, 162, 198, 234)(19, 55, 91, 127, 163, 199, 235)(20, 56, 92, 128, 164, 200, 236)(21, 57, 93, 129, 165, 201, 237)(22, 58, 94, 130, 166, 202, 238)(23, 59, 95, 131, 167, 203, 239)(24, 60, 96, 132, 168, 204, 240)(25, 61, 97, 133, 169, 205, 241)(26, 62, 98, 134, 170, 206, 242)(27, 63, 99, 135, 171, 207, 243)(28, 64, 100, 136, 172, 208, 244)(29, 65, 101, 137, 173, 209, 245)(30, 66, 102, 138, 174, 210, 246)(31, 67, 103, 139, 175, 211, 247)(32, 68, 104, 140, 176, 212, 248)(33, 69, 105, 141, 177, 213, 249)(34, 70, 106, 142, 178, 214, 250)(35, 71, 107, 143, 179, 215, 251)(36, 72, 108, 144, 180, 216, 252)
L = (1, 41)(2, 39)(3, 58)(4, 57)(5, 60)(6, 59)(7, 47)(8, 45)(9, 52)(10, 51)(11, 54)(12, 53)(13, 48)(14, 46)(15, 50)(16, 44)(17, 49)(18, 43)(19, 42)(20, 40)(21, 56)(22, 38)(23, 55)(24, 37)(25, 72)(26, 70)(27, 62)(28, 68)(29, 61)(30, 67)(31, 71)(32, 69)(33, 64)(34, 63)(35, 66)(36, 65)(73, 201)(74, 203)(75, 209)(76, 210)(77, 207)(78, 208)(79, 184)(80, 186)(81, 216)(82, 215)(83, 214)(84, 213)(85, 183)(86, 185)(87, 191)(88, 192)(89, 189)(90, 190)(91, 202)(92, 204)(93, 198)(94, 197)(95, 196)(96, 195)(97, 182)(98, 181)(99, 187)(100, 193)(101, 188)(102, 194)(103, 200)(104, 199)(105, 205)(106, 211)(107, 206)(108, 212)(109, 110)(111, 115)(112, 121)(113, 116)(114, 122)(117, 119)(118, 120)(123, 144)(124, 143)(125, 142)(126, 141)(127, 128)(129, 133)(130, 139)(131, 134)(132, 140)(135, 137)(136, 138)(145, 167)(146, 165)(147, 148)(149, 150)(151, 173)(152, 171)(153, 178)(154, 177)(155, 180)(156, 179)(157, 174)(158, 172)(159, 176)(160, 170)(161, 175)(162, 169)(163, 168)(164, 166)(217, 243)(218, 245)(219, 233)(220, 234)(221, 231)(222, 232)(223, 250)(224, 252)(225, 228)(226, 227)(229, 249)(230, 251)(235, 244)(236, 246)(237, 240)(238, 239)(241, 248)(242, 247)

MAP           : A4.1237
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 152)(20, 162)(21, 161)(22, 160)(23, 148)(24, 146)(25, 157)(26, 156)(27, 155)(28, 147)(29, 159)(30, 145)(31, 158)(32, 151)(33, 153)(34, 149)(35, 154)(36, 150)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 143)(56, 135)(57, 134)(58, 133)(59, 139)(60, 137)(61, 130)(62, 129)(63, 128)(64, 138)(65, 132)(66, 136)(67, 131)(68, 142)(69, 144)(70, 140)(71, 127)(72, 141)(73, 94)(74, 98)(75, 99)(76, 96)(77, 108)(78, 91)(79, 107)(80, 106)(81, 104)(82, 105)(83, 97)(84, 95)(85, 100)(86, 93)(87, 103)(88, 92)(89, 101)(90, 102)(109, 245)(110, 248)(111, 250)(112, 251)(113, 244)(114, 241)(115, 240)(116, 243)(117, 242)(118, 239)(119, 235)(120, 249)(121, 252)(122, 236)(123, 246)(124, 237)(125, 238)(126, 247)(163, 192)(164, 186)(165, 190)(166, 185)(167, 196)(168, 198)(169, 194)(170, 181)(171, 195)(172, 197)(173, 189)(174, 188)(175, 187)(176, 193)(177, 191)(178, 184)(179, 183)(180, 182)(217, 227)(218, 230)(219, 232)(220, 233)(221, 226)(222, 223)(224, 225)(228, 231)(229, 234)

MAP           : A4.1238
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 160)(20, 156)(21, 155)(22, 146)(23, 150)(24, 152)(25, 154)(26, 149)(27, 151)(28, 153)(29, 157)(30, 148)(31, 147)(32, 161)(33, 158)(34, 162)(35, 159)(36, 145)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 137)(56, 140)(57, 142)(58, 143)(59, 136)(60, 133)(61, 132)(62, 135)(63, 134)(64, 131)(65, 127)(66, 141)(67, 144)(68, 128)(69, 138)(70, 129)(71, 130)(72, 139)(73, 102)(74, 96)(75, 100)(76, 95)(77, 106)(78, 108)(79, 104)(80, 91)(81, 105)(82, 107)(83, 99)(84, 98)(85, 97)(86, 103)(87, 101)(88, 94)(89, 93)(90, 92)(109, 243)(110, 247)(111, 238)(112, 237)(113, 251)(114, 248)(115, 252)(116, 249)(117, 235)(118, 250)(119, 246)(120, 245)(121, 236)(122, 240)(123, 242)(124, 244)(125, 239)(126, 241)(163, 198)(164, 184)(165, 193)(166, 192)(167, 188)(168, 185)(169, 189)(170, 186)(171, 190)(172, 187)(173, 183)(174, 182)(175, 191)(176, 195)(177, 197)(178, 181)(179, 194)(180, 196)(217, 225)(218, 229)(219, 220)(221, 233)(222, 230)(223, 234)(224, 231)(226, 232)(227, 228)

MAP           : A4.1239
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 160)(20, 156)(21, 155)(22, 146)(23, 150)(24, 152)(25, 154)(26, 149)(27, 151)(28, 153)(29, 157)(30, 148)(31, 147)(32, 161)(33, 158)(34, 162)(35, 159)(36, 145)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 137)(56, 140)(57, 142)(58, 143)(59, 136)(60, 133)(61, 132)(62, 135)(63, 134)(64, 131)(65, 127)(66, 141)(67, 144)(68, 128)(69, 138)(70, 129)(71, 130)(72, 139)(73, 98)(74, 108)(75, 107)(76, 106)(77, 94)(78, 92)(79, 103)(80, 102)(81, 101)(82, 93)(83, 105)(84, 91)(85, 104)(86, 97)(87, 99)(88, 95)(89, 100)(90, 96)(109, 249)(110, 241)(111, 239)(112, 244)(113, 237)(114, 247)(115, 236)(116, 245)(117, 246)(118, 238)(119, 242)(120, 243)(121, 240)(122, 252)(123, 235)(124, 251)(125, 250)(126, 248)(163, 198)(164, 184)(165, 193)(166, 192)(167, 188)(168, 185)(169, 189)(170, 186)(171, 190)(172, 187)(173, 183)(174, 182)(175, 191)(176, 195)(177, 197)(178, 181)(179, 194)(180, 196)(217, 231)(218, 223)(219, 221)(220, 226)(222, 229)(224, 227)(225, 228)(230, 234)(232, 233)

MAP           : A4.1240
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 152)(20, 162)(21, 161)(22, 160)(23, 148)(24, 146)(25, 157)(26, 156)(27, 155)(28, 147)(29, 159)(30, 145)(31, 158)(32, 151)(33, 153)(34, 149)(35, 154)(36, 150)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 143)(56, 135)(57, 134)(58, 133)(59, 139)(60, 137)(61, 130)(62, 129)(63, 128)(64, 138)(65, 132)(66, 136)(67, 131)(68, 142)(69, 144)(70, 140)(71, 127)(72, 141)(73, 95)(74, 91)(75, 105)(76, 108)(77, 92)(78, 102)(79, 93)(80, 94)(81, 103)(82, 101)(83, 104)(84, 106)(85, 107)(86, 100)(87, 97)(88, 96)(89, 99)(90, 98)(109, 243)(110, 247)(111, 238)(112, 237)(113, 251)(114, 248)(115, 252)(116, 249)(117, 235)(118, 250)(119, 246)(120, 245)(121, 236)(122, 240)(123, 242)(124, 244)(125, 239)(126, 241)(163, 192)(164, 186)(165, 190)(166, 185)(167, 196)(168, 198)(169, 194)(170, 181)(171, 195)(172, 197)(173, 189)(174, 188)(175, 187)(176, 193)(177, 191)(178, 184)(179, 183)(180, 182)(217, 225)(218, 229)(219, 220)(221, 233)(222, 230)(223, 234)(224, 231)(226, 232)(227, 228)

MAP           : A4.1241
NOTES         : type II, reflexible, isomorphic to A4.1211.
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)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.5^2, x.1^2, x.2^2, x.7^-1 * x.2, x.8 * x.4, x.4 * x.1 * x.5, x.8^3, x.6^3, x.2 * x.5 * x.6^-1, (x.6, x.4^-1), x.4 * x.2 * x.8^-1 * x.2, (x.8^-1, x.6^-1), (x.6^-1 * 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        : 252
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)(127, 145, 163, 181, 199, 217, 235)(128, 146, 164, 182, 200, 218, 236)(129, 147, 165, 183, 201, 219, 237)(130, 148, 166, 184, 202, 220, 238)(131, 149, 167, 185, 203, 221, 239)(132, 150, 168, 186, 204, 222, 240)(133, 151, 169, 187, 205, 223, 241)(134, 152, 170, 188, 206, 224, 242)(135, 153, 171, 189, 207, 225, 243)(136, 154, 172, 190, 208, 226, 244)(137, 155, 173, 191, 209, 227, 245)(138, 156, 174, 192, 210, 228, 246)(139, 157, 175, 193, 211, 229, 247)(140, 158, 176, 194, 212, 230, 248)(141, 159, 177, 195, 213, 231, 249)(142, 160, 178, 196, 214, 232, 250)(143, 161, 179, 197, 215, 233, 251)(144, 162, 180, 198, 216, 234, 252)
L = (1, 199)(2, 200)(3, 201)(4, 202)(5, 203)(6, 204)(7, 205)(8, 206)(9, 207)(10, 208)(11, 209)(12, 210)(13, 211)(14, 212)(15, 213)(16, 214)(17, 215)(18, 216)(19, 152)(20, 162)(21, 161)(22, 160)(23, 148)(24, 146)(25, 157)(26, 156)(27, 155)(28, 147)(29, 159)(30, 145)(31, 158)(32, 151)(33, 153)(34, 149)(35, 154)(36, 150)(37, 39)(38, 51)(40, 50)(41, 43)(42, 45)(44, 46)(47, 54)(48, 53)(49, 52)(55, 143)(56, 135)(57, 134)(58, 133)(59, 139)(60, 137)(61, 130)(62, 129)(63, 128)(64, 138)(65, 132)(66, 136)(67, 131)(68, 142)(69, 144)(70, 140)(71, 127)(72, 141)(73, 92)(74, 95)(75, 97)(76, 98)(77, 91)(78, 106)(79, 105)(80, 108)(81, 107)(82, 104)(83, 100)(84, 96)(85, 99)(86, 101)(87, 93)(88, 102)(89, 103)(90, 94)(109, 247)(110, 251)(111, 252)(112, 249)(113, 243)(114, 244)(115, 242)(116, 241)(117, 239)(118, 240)(119, 250)(120, 248)(121, 235)(122, 246)(123, 238)(124, 245)(125, 236)(126, 237)(163, 192)(164, 186)(165, 190)(166, 185)(167, 196)(168, 198)(169, 194)(170, 181)(171, 195)(172, 197)(173, 189)(174, 188)(175, 187)(176, 193)(177, 191)(178, 184)(179, 183)(180, 182)(217, 229)(218, 233)(219, 234)(220, 231)(221, 225)(222, 226)(223, 224)(227, 232)(228, 230)

MAP           : A4.1242
NOTES         : type I, chiral, representative.
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)   : <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.2 * x.1 * x.5^-1, x.4^-1 * x.5^-1 * x.3, x.1 * x.3 * x.2 * x.4^-1, x.4^4, x.4 * x.3 * x.2 * x.1, x.3 * x.1 * x.4^-1 * x.5 * x.4^-1, x.4 * x.2 * 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, 4)
#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, 28)(3, 25)(4, 27)(5, 31)(6, 29)(7, 32)(8, 30)(9, 40)(10, 39)(11, 38)(12, 37)(13, 46)(14, 48)(15, 45)(16, 47)(17, 35)(18, 33)(19, 36)(20, 34)(21, 44)(22, 43)(23, 42)(24, 41)(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, 164)(147, 161)(148, 163)(149, 159)(150, 157)(151, 160)(152, 158)(153, 168)(154, 167)(155, 166)(156, 165)

MAP           : A4.1243
NOTES         : type I, chiral, isomorphic to A4.1242.
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)   : <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.4 * x.5^-1 * x.3, x.5 * x.4^2 * x.3, x.5^-1 * x.1 * x.3 * x.2, x.5^4, x.4 * x.3 * x.2 * x.3 * x.5^-1, x.1 * x.5^2 * x.4 * 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, 4)
#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, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(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, 153)(50, 154)(51, 155)(52, 156)(53, 165)(54, 166)(55, 167)(56, 168)(57, 161)(58, 162)(59, 163)(60, 164)(61, 149)(62, 150)(63, 151)(64, 152)(65, 145)(66, 146)(67, 147)(68, 148)(69, 157)(70, 158)(71, 159)(72, 160)(73, 120)(74, 119)(75, 118)(76, 117)(77, 108)(78, 107)(79, 106)(80, 105)(81, 99)(82, 97)(83, 100)(84, 98)(85, 111)(86, 109)(87, 112)(88, 110)(89, 114)(90, 116)(91, 113)(92, 115)(93, 102)(94, 104)(95, 101)(96, 103)(121, 138)(122, 140)(123, 137)(124, 139)(125, 135)(126, 133)(127, 136)(128, 134)(129, 144)(130, 143)(131, 142)(132, 141)

MAP           : A4.1244
NOTES         : type I, chiral, representative.
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)   : <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^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.4^4, x.4 * x.2 * x.4^-1 * x.3, x.4 * x.1 * x.4^-1 * x.2, (x.3 * x.1)^2, x.4^-1 * x.2 * x.4^-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, 4)
#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, 28)(3, 25)(4, 27)(5, 31)(6, 29)(7, 32)(8, 30)(9, 40)(10, 39)(11, 38)(12, 37)(13, 46)(14, 48)(15, 45)(16, 47)(17, 35)(18, 33)(19, 36)(20, 34)(21, 44)(22, 43)(23, 42)(24, 41)(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, 164)(147, 161)(148, 163)(149, 159)(150, 157)(151, 160)(152, 158)(153, 168)(154, 167)(155, 166)(156, 165)

MAP           : A4.1245
NOTES         : type I, chiral, isomorphic to A4.1244.
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)   : <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.4 * x.5^-1 * x.3, x.5^4, x.5 * x.3 * x.5^-1 * x.1, (x.3 * x.2)^2, x.5 * x.1 * x.5^-1 * x.2, x.1 * x.3 * x.4^-1 * x.5^-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, 4)
#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, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)(49, 153)(50, 154)(51, 155)(52, 156)(53, 165)(54, 166)(55, 167)(56, 168)(57, 161)(58, 162)(59, 163)(60, 164)(61, 149)(62, 150)(63, 151)(64, 152)(65, 145)(66, 146)(67, 147)(68, 148)(69, 157)(70, 158)(71, 159)(72, 160)(73, 120)(74, 119)(75, 118)(76, 117)(77, 108)(78, 107)(79, 106)(80, 105)(81, 99)(82, 97)(83, 100)(84, 98)(85, 111)(86, 109)(87, 112)(88, 110)(89, 114)(90, 116)(91, 113)(92, 115)(93, 102)(94, 104)(95, 101)(96, 103)(121, 138)(122, 140)(123, 137)(124, 139)(125, 135)(126, 133)(127, 136)(128, 134)(129, 144)(130, 143)(131, 142)(132, 141)

MAP           : A4.1246
NOTES         : type I, chiral, representative.
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)   : <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^-1 * x.5^-1 * x.3, x.5 * x.1 * x.2, x.1 * x.5 * x.2 * x.5^-1, x.4^4, x.4 * x.1 * x.4^-1 * x.3, (x.4^-1 * x.2)^2, x.1 * x.3 * x.4 * 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, 4)
#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, 28)(3, 25)(4, 27)(5, 31)(6, 29)(7, 32)(8, 30)(9, 40)(10, 39)(11, 38)(12, 37)(13, 46)(14, 48)(15, 45)(16, 47)(17, 35)(18, 33)(19, 36)(20, 34)(21, 44)(22, 43)(23, 42)(24, 41)(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, 164)(147, 161)(148, 163)(149, 159)(150, 157)(151, 160)(152, 158)(153, 168)(154, 167)(155, 166)(156, 165)

MAP           : A4.1247
NOTES         : type I, chiral, isomorphic to A4.1246.
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)   : <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.4 * x.5^-1 * x.3, x.2 * x.5 * x.3 * x.5^-1, x.2 * x.4 * x.1 * x.4^-1, (x.5^-1 * x.1)^2, x.5^4 >
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        : 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, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(49, 153)(50, 154)(51, 155)(52, 156)(53, 165)(54, 166)(55, 167)(56, 168)(57, 161)(58, 162)(59, 163)(60, 164)(61, 149)(62, 150)(63, 151)(64, 152)(65, 145)(66, 146)(67, 147)(68, 148)(69, 157)(70, 158)(71, 159)(72, 160)(73, 120)(74, 119)(75, 118)(76, 117)(77, 108)(78, 107)(79, 106)(80, 105)(81, 99)(82, 97)(83, 100)(84, 98)(85, 111)(86, 109)(87, 112)(88, 110)(89, 114)(90, 116)(91, 113)(92, 115)(93, 102)(94, 104)(95, 101)(96, 103)(121, 138)(122, 140)(123, 137)(124, 139)(125, 135)(126, 133)(127, 136)(128, 134)(129, 144)(130, 143)(131, 142)(132, 141)

MAP           : A4.1248
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3^5, u.7^5 >
CTG (small)   : <10, 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.2 * x.1, x.7 * x.3^-1, x.4 * x.6, x.6 * x.1 * x.3^-1, x.4 * x.2 * x.3, x.7 * x.2 * x.8^-1, x.1 * x.3 * x.6^-1, x.5 * x.6^-1 * x.8, x.3^2 * x.6 * x.3 * x.4^-1, x.3^5, x.7^5 >
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, 5)
#DARTS        : 140
R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140)
L = (1, 13)(2, 11)(3, 17)(4, 18)(5, 12)(6, 14)(7, 15)(8, 20)(9, 16)(10, 19)(21, 56)(22, 59)(23, 54)(24, 52)(25, 60)(26, 55)(27, 58)(28, 51)(29, 57)(30, 53)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 118)(42, 114)(43, 120)(44, 113)(45, 116)(46, 111)(47, 119)(48, 117)(49, 112)(50, 115)(61, 64)(62, 66)(63, 68)(65, 69)(67, 70)(71, 133)(72, 131)(73, 137)(74, 138)(75, 132)(76, 134)(77, 135)(78, 140)(79, 136)(80, 139)(81, 84)(82, 86)(83, 88)(85, 89)(87, 90)(91, 128)(92, 124)(93, 130)(94, 123)(95, 126)(96, 121)(97, 129)(98, 127)(99, 122)(100, 125)

MAP           : A4.1249
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.6^5, u.8^5 >
CTG (small)   : <10, 1>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.7^-1 * x.2, x.8^-1 * x.4^-1, x.2 * x.5 * x.6^-1, x.4 * x.1 * x.5, x.6^-2 * x.4, x.1 * x.2 * x.4^-1, x.1 * x.4 * x.2, x.4 * x.6 * x.4, x.8^5 >
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, 5)
#DARTS        : 140
R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140)
L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 85)(12, 88)(13, 87)(14, 82)(15, 84)(16, 83)(17, 89)(18, 81)(19, 90)(20, 86)(21, 23)(22, 29)(24, 30)(25, 26)(27, 28)(31, 77)(32, 80)(33, 75)(34, 76)(35, 73)(36, 74)(37, 71)(38, 79)(39, 78)(40, 72)(41, 52)(42, 55)(43, 60)(44, 51)(45, 58)(46, 59)(47, 56)(48, 54)(49, 53)(50, 57)(61, 136)(62, 137)(63, 138)(64, 139)(65, 140)(66, 131)(67, 132)(68, 133)(69, 134)(70, 135)(91, 108)(92, 104)(93, 106)(94, 105)(95, 101)(96, 110)(97, 103)(98, 102)(99, 107)(100, 109)(121, 126)(122, 127)(123, 128)(124, 129)(125, 130)

MAP           : A4.1250
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.6^5, u.8^5 >
CTG (small)   : <10, 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 * x.4^-1, x.6^-1 * x.8^-1, x.5 * x.6^-1 * x.7^-1, x.7 * x.3^-1 * x.2, x.3 * x.4^-1 * x.8^-1, x.8 * x.1 * x.5, x.4 * x.2 * x.5^-1, x.8^5, x.6^5 >
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, 5)
#DARTS        : 140
R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140)
L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 83)(12, 81)(13, 87)(14, 88)(15, 82)(16, 84)(17, 85)(18, 90)(19, 86)(20, 89)(21, 24)(22, 26)(23, 28)(25, 29)(27, 30)(31, 78)(32, 74)(33, 80)(34, 73)(35, 76)(36, 71)(37, 79)(38, 77)(39, 72)(40, 75)(41, 53)(42, 51)(43, 57)(44, 58)(45, 52)(46, 54)(47, 55)(48, 60)(49, 56)(50, 59)(61, 134)(62, 136)(63, 138)(64, 131)(65, 139)(66, 132)(67, 140)(68, 133)(69, 135)(70, 137)(91, 102)(92, 105)(93, 101)(94, 106)(95, 107)(96, 109)(97, 103)(98, 104)(99, 110)(100, 108)(121, 124)(122, 126)(123, 128)(125, 129)(127, 130)

MAP           : A4.1251
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.6^5, u.8^5 >
CTG (small)   : <10, 1>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.5^2, x.1^2, x.2^2, x.8 * x.4, x.4 * x.6^2, x.7 * x.3^-1 * x.2, x.5 * x.6^-1 * x.7^-1, x.2 * x.1 * x.6, x.1 * x.2 * x.6^-1, x.4 * x.1 * x.5, x.4^2 * x.6^-1, x.8^5 >
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, 5)
#DARTS        : 140
R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140)
L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 82)(12, 85)(13, 90)(14, 81)(15, 88)(16, 89)(17, 86)(18, 84)(19, 83)(20, 87)(21, 23)(22, 29)(24, 30)(25, 26)(27, 28)(31, 80)(32, 73)(33, 72)(34, 77)(35, 79)(36, 78)(37, 74)(38, 76)(39, 75)(40, 71)(41, 55)(42, 58)(43, 57)(44, 52)(45, 54)(46, 53)(47, 59)(48, 51)(49, 60)(50, 56)(61, 136)(62, 137)(63, 138)(64, 139)(65, 140)(66, 131)(67, 132)(68, 133)(69, 134)(70, 135)(91, 104)(92, 101)(93, 109)(94, 108)(95, 102)(96, 107)(97, 110)(98, 105)(99, 106)(100, 103)(121, 126)(122, 127)(123, 128)(124, 129)(125, 130)

MAP           : A4.1252
NOTES         : type II, reflexible, isomorphic to A4.1248.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3^5, u.7^5 >
CTG (small)   : <10, 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.2 * x.1, x.7 * x.3^-1, x.4 * x.6, x.6 * x.1 * x.3^-1, x.4 * x.2 * x.3, x.7 * x.2 * x.8^-1, x.1 * x.3 * x.6^-1, x.5 * x.6^-1 * x.8, x.3^2 * x.6 * x.3 * x.4^-1, x.3^5, x.7^5 >
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, 5)
#DARTS        : 140
R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140)
L = (1, 15)(2, 17)(3, 12)(4, 19)(5, 13)(6, 20)(7, 11)(8, 16)(9, 18)(10, 14)(21, 60)(22, 58)(23, 59)(24, 57)(25, 54)(26, 53)(27, 56)(28, 55)(29, 51)(30, 52)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 119)(42, 120)(43, 116)(44, 115)(45, 118)(46, 117)(47, 114)(48, 112)(49, 113)(50, 111)(61, 64)(62, 66)(63, 68)(65, 69)(67, 70)(71, 135)(72, 137)(73, 132)(74, 139)(75, 133)(76, 140)(77, 131)(78, 136)(79, 138)(80, 134)(81, 84)(82, 86)(83, 88)(85, 89)(87, 90)(91, 129)(92, 130)(93, 126)(94, 125)(95, 128)(96, 127)(97, 124)(98, 122)(99, 123)(100, 121)

MAP           : A4.1253
NOTES         : type II, reflexible, isomorphic to A4.1248.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3^5, u.7^5 >
CTG (small)   : <10, 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.2 * x.1, x.7 * x.3^-1, x.4 * x.6, x.6 * x.1 * x.3^-1, x.4 * x.2 * x.3, x.7 * x.2 * x.8^-1, x.1 * x.3 * x.6^-1, x.5 * x.6^-1 * x.8, x.3^2 * x.6 * x.3 * x.4^-1, x.3^5, x.7^5 >
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, 5)
#DARTS        : 140
R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140)
L = (1, 17)(2, 13)(3, 15)(4, 20)(5, 11)(6, 18)(7, 12)(8, 19)(9, 14)(10, 16)(21, 59)(22, 60)(23, 56)(24, 55)(25, 58)(26, 57)(27, 54)(28, 52)(29, 53)(30, 51)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 120)(42, 118)(43, 119)(44, 117)(45, 114)(46, 113)(47, 116)(48, 115)(49, 111)(50, 112)(61, 64)(62, 66)(63, 68)(65, 69)(67, 70)(71, 137)(72, 133)(73, 135)(74, 140)(75, 131)(76, 138)(77, 132)(78, 139)(79, 134)(80, 136)(81, 84)(82, 86)(83, 88)(85, 89)(87, 90)(91, 130)(92, 128)(93, 129)(94, 127)(95, 124)(96, 123)(97, 126)(98, 125)(99, 121)(100, 122)

MAP           : A4.1254
NOTES         : type I, chiral, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.5^5 >
CTG (small)   : <20, 4>
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 * x.1)^2, (x.3 * x.1)^2, x.5^5 >
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, 5)
#DARTS        : 140
R = (1, 21, 41, 61, 81, 101, 121)(2, 22, 42, 62, 82, 102, 122)(3, 23, 43, 63, 83, 103, 123)(4, 24, 44, 64, 84, 104, 124)(5, 25, 45, 65, 85, 105, 125)(6, 26, 46, 66, 86, 106, 126)(7, 27, 47, 67, 87, 107, 127)(8, 28, 48, 68, 88, 108, 128)(9, 29, 49, 69, 89, 109, 129)(10, 30, 50, 70, 90, 110, 130)(11, 31, 51, 71, 91, 111, 131)(12, 32, 52, 72, 92, 112, 132)(13, 33, 53, 73, 93, 113, 133)(14, 34, 54, 74, 94, 114, 134)(15, 35, 55, 75, 95, 115, 135)(16, 36, 56, 76, 96, 116, 136)(17, 37, 57, 77, 97, 117, 137)(18, 38, 58, 78, 98, 118, 138)(19, 39, 59, 79, 99, 119, 139)(20, 40, 60, 80, 100, 120, 140)
L = (1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10, 20)(21, 36)(22, 33)(23, 40)(24, 29)(25, 32)(26, 37)(27, 28)(30, 39)(31, 34)(35, 38)(41, 126)(42, 123)(43, 130)(44, 139)(45, 122)(46, 127)(47, 138)(48, 137)(49, 134)(50, 129)(51, 124)(52, 135)(53, 132)(54, 121)(55, 128)(56, 131)(57, 136)(58, 125)(59, 140)(60, 133)(61, 83)(62, 86)(63, 87)(64, 88)(65, 81)(66, 90)(67, 89)(68, 100)(69, 85)(70, 98)(71, 95)(72, 84)(73, 91)(74, 82)(75, 99)(76, 92)(77, 93)(78, 94)(79, 97)(80, 96)(101, 102)(103, 106)(104, 115)(105, 114)(107, 110)(108, 119)(109, 118)(111, 112)(113, 116)(117, 120)

MAP           : A4.1255
NOTES         : type I, chiral, isomorphic to A4.1254.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.5^5 >
CTG (small)   : <20, 4>
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 * x.1)^2, (x.3 * x.1)^2, x.5^5 >
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, 5)
#DARTS        : 140
R = (1, 21, 41, 61, 81, 101, 121)(2, 22, 42, 62, 82, 102, 122)(3, 23, 43, 63, 83, 103, 123)(4, 24, 44, 64, 84, 104, 124)(5, 25, 45, 65, 85, 105, 125)(6, 26, 46, 66, 86, 106, 126)(7, 27, 47, 67, 87, 107, 127)(8, 28, 48, 68, 88, 108, 128)(9, 29, 49, 69, 89, 109, 129)(10, 30, 50, 70, 90, 110, 130)(11, 31, 51, 71, 91, 111, 131)(12, 32, 52, 72, 92, 112, 132)(13, 33, 53, 73, 93, 113, 133)(14, 34, 54, 74, 94, 114, 134)(15, 35, 55, 75, 95, 115, 135)(16, 36, 56, 76, 96, 116, 136)(17, 37, 57, 77, 97, 117, 137)(18, 38, 58, 78, 98, 118, 138)(19, 39, 59, 79, 99, 119, 139)(20, 40, 60, 80, 100, 120, 140)
L = (1, 4)(2, 15)(3, 12)(5, 8)(6, 11)(7, 16)(9, 20)(10, 13)(14, 19)(17, 18)(21, 37)(22, 40)(23, 39)(24, 30)(25, 33)(26, 28)(27, 35)(29, 31)(32, 38)(34, 36)(41, 138)(42, 129)(43, 134)(44, 133)(45, 130)(46, 125)(47, 122)(48, 131)(49, 126)(50, 121)(51, 140)(52, 137)(53, 128)(54, 127)(55, 136)(56, 139)(57, 124)(58, 123)(59, 132)(60, 135)(61, 89)(62, 98)(63, 85)(64, 96)(65, 87)(66, 94)(67, 81)(68, 92)(69, 83)(70, 82)(71, 97)(72, 100)(73, 99)(74, 90)(75, 93)(76, 88)(77, 95)(78, 86)(79, 91)(80, 84)(101, 102)(103, 106)(104, 115)(105, 114)(107, 110)(108, 119)(109, 118)(111, 112)(113, 116)(117, 120)

MAP           : A4.1256
NOTES         : type I, chiral, isomorphic to A4.1254.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.5^5 >
CTG (small)   : <20, 4>
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 * x.1)^2, (x.3 * x.1)^2, x.5^5 >
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, 5)
#DARTS        : 140
R = (1, 21, 41, 61, 81, 101, 121)(2, 22, 42, 62, 82, 102, 122)(3, 23, 43, 63, 83, 103, 123)(4, 24, 44, 64, 84, 104, 124)(5, 25, 45, 65, 85, 105, 125)(6, 26, 46, 66, 86, 106, 126)(7, 27, 47, 67, 87, 107, 127)(8, 28, 48, 68, 88, 108, 128)(9, 29, 49, 69, 89, 109, 129)(10, 30, 50, 70, 90, 110, 130)(11, 31, 51, 71, 91, 111, 131)(12, 32, 52, 72, 92, 112, 132)(13, 33, 53, 73, 93, 113, 133)(14, 34, 54, 74, 94, 114, 134)(15, 35, 55, 75, 95, 115, 135)(16, 36, 56, 76, 96, 116, 136)(17, 37, 57, 77, 97, 117, 137)(18, 38, 58, 78, 98, 118, 138)(19, 39, 59, 79, 99, 119, 139)(20, 40, 60, 80, 100, 120, 140)
L = (1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10, 20)(21, 28)(22, 39)(23, 24)(25, 40)(26, 35)(27, 32)(29, 36)(30, 31)(33, 38)(34, 37)(41, 138)(42, 129)(43, 134)(44, 133)(45, 130)(46, 125)(47, 122)(48, 131)(49, 126)(50, 121)(51, 140)(52, 137)(53, 128)(54, 127)(55, 136)(56, 139)(57, 124)(58, 123)(59, 132)(60, 135)(61, 89)(62, 98)(63, 85)(64, 96)(65, 87)(66, 94)(67, 81)(68, 92)(69, 83)(70, 82)(71, 97)(72, 100)(73, 99)(74, 90)(75, 93)(76, 88)(77, 95)(78, 86)(79, 91)(80, 84)(101, 102)(103, 106)(104, 115)(105, 114)(107, 110)(108, 119)(109, 118)(111, 112)(113, 116)(117, 120)

MAP           : A4.1257
NOTES         : type I, chiral, isomorphic to A4.1254.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (3, 7)(4, 5)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.5^5 >
CTG (small)   : <20, 4>
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 * x.1)^2, (x.3 * x.1)^2, x.5^5 >
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, 5)
#DARTS        : 140
R = (1, 21, 41, 61, 81, 101, 121)(2, 22, 42, 62, 82, 102, 122)(3, 23, 43, 63, 83, 103, 123)(4, 24, 44, 64, 84, 104, 124)(5, 25, 45, 65, 85, 105, 125)(6, 26, 46, 66, 86, 106, 126)(7, 27, 47, 67, 87, 107, 127)(8, 28, 48, 68, 88, 108, 128)(9, 29, 49, 69, 89, 109, 129)(10, 30, 50, 70, 90, 110, 130)(11, 31, 51, 71, 91, 111, 131)(12, 32, 52, 72, 92, 112, 132)(13, 33, 53, 73, 93, 113, 133)(14, 34, 54, 74, 94, 114, 134)(15, 35, 55, 75, 95, 115, 135)(16, 36, 56, 76, 96, 116, 136)(17, 37, 57, 77, 97, 117, 137)(18, 38, 58, 78, 98, 118, 138)(19, 39, 59, 79, 99, 119, 139)(20, 40, 60, 80, 100, 120, 140)
L = (1, 4)(2, 15)(3, 12)(5, 8)(6, 11)(7, 16)(9, 20)(10, 13)(14, 19)(17, 18)(21, 31)(22, 32)(23, 33)(24, 34)(25, 35)(26, 36)(27, 37)(28, 38)(29, 39)(30, 40)(41, 126)(42, 123)(43, 130)(44, 139)(45, 122)(46, 127)(47, 138)(48, 137)(49, 134)(50, 129)(51, 124)(52, 135)(53, 132)(54, 121)(55, 128)(56, 131)(57, 136)(58, 125)(59, 140)(60, 133)(61, 83)(62, 86)(63, 87)(64, 88)(65, 81)(66, 90)(67, 89)(68, 100)(69, 85)(70, 98)(71, 95)(72, 84)(73, 91)(74, 82)(75, 99)(76, 92)(77, 93)(78, 94)(79, 97)(80, 96)(101, 102)(103, 106)(104, 115)(105, 114)(107, 110)(108, 119)(109, 118)(111, 112)(113, 116)(117, 120)

MAP           : A4.1258
NOTES         : type I, chiral, isomorphic to A4.1254.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.4^5 >
CTG (small)   : <20, 4>
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^-1 * x.2)^2, (x.3 * x.1)^2, x.4 * x.5^-4, x.4^5 >
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, 5)
#DARTS        : 140
R = (1, 21, 41, 61, 81, 101, 121)(2, 22, 42, 62, 82, 102, 122)(3, 23, 43, 63, 83, 103, 123)(4, 24, 44, 64, 84, 104, 124)(5, 25, 45, 65, 85, 105, 125)(6, 26, 46, 66, 86, 106, 126)(7, 27, 47, 67, 87, 107, 127)(8, 28, 48, 68, 88, 108, 128)(9, 29, 49, 69, 89, 109, 129)(10, 30, 50, 70, 90, 110, 130)(11, 31, 51, 71, 91, 111, 131)(12, 32, 52, 72, 92, 112, 132)(13, 33, 53, 73, 93, 113, 133)(14, 34, 54, 74, 94, 114, 134)(15, 35, 55, 75, 95, 115, 135)(16, 36, 56, 76, 96, 116, 136)(17, 37, 57, 77, 97, 117, 137)(18, 38, 58, 78, 98, 118, 138)(19, 39, 59, 79, 99, 119, 139)(20, 40, 60, 80, 100, 120, 140)
L = (1, 23)(2, 26)(3, 27)(4, 28)(5, 21)(6, 30)(7, 29)(8, 40)(9, 25)(10, 38)(11, 35)(12, 24)(13, 31)(14, 22)(15, 39)(16, 32)(17, 33)(18, 34)(19, 37)(20, 36)(41, 114)(42, 105)(43, 102)(44, 111)(45, 118)(46, 101)(47, 106)(48, 115)(49, 110)(50, 103)(51, 116)(52, 113)(53, 120)(54, 109)(55, 112)(56, 117)(57, 108)(58, 107)(59, 104)(60, 119)(61, 64)(62, 75)(63, 72)(65, 68)(66, 71)(67, 76)(69, 80)(70, 73)(74, 79)(77, 78)(81, 91)(82, 92)(83, 93)(84, 94)(85, 95)(86, 96)(87, 97)(88, 98)(89, 99)(90, 100)(121, 122)(123, 126)(124, 135)(125, 134)(127, 130)(128, 139)(129, 138)(131, 132)(133, 136)(137, 140)

MAP           : A4.1259
NOTES         : type II, reflexible, isomorphic to A4.1251.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.6^5, u.8^5 >
CTG (small)   : <10, 1>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.5^2, x.1^2, x.2^2, x.8 * x.4, x.4 * x.6^2, x.7 * x.3^-1 * x.2, x.5 * x.6^-1 * x.7^-1, x.2 * x.1 * x.6, x.1 * x.2 * x.6^-1, x.4 * x.1 * x.5, x.4^2 * x.6^-1, x.8^5 >
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, 5)
#DARTS        : 140
R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140)
L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 85)(12, 88)(13, 87)(14, 82)(15, 84)(16, 83)(17, 89)(18, 81)(19, 90)(20, 86)(21, 23)(22, 29)(24, 30)(25, 26)(27, 28)(31, 77)(32, 80)(33, 75)(34, 76)(35, 73)(36, 74)(37, 71)(38, 79)(39, 78)(40, 72)(41, 54)(42, 51)(43, 59)(44, 58)(45, 52)(46, 57)(47, 60)(48, 55)(49, 56)(50, 53)(61, 140)(62, 133)(63, 132)(64, 137)(65, 139)(66, 138)(67, 134)(68, 136)(69, 135)(70, 131)(91, 108)(92, 104)(93, 106)(94, 105)(95, 101)(96, 110)(97, 103)(98, 102)(99, 107)(100, 109)(121, 130)(122, 123)(124, 127)(125, 129)(126, 128)

MAP           : A4.1260
NOTES         : type II, reflexible, isomorphic to A4.1250.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.6^5, u.8^5 >
CTG (small)   : <10, 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 * x.4^-1, x.6^-1 * x.8^-1, x.5 * x.6^-1 * x.7^-1, x.7 * x.3^-1 * x.2, x.3 * x.4^-1 * x.8^-1, x.8 * x.1 * x.5, x.4 * x.2 * x.5^-1, x.8^5, x.6^5 >
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, 5)
#DARTS        : 140
R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140)
L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 82)(12, 85)(13, 81)(14, 86)(15, 87)(16, 89)(17, 83)(18, 84)(19, 90)(20, 88)(21, 24)(22, 26)(23, 28)(25, 29)(27, 30)(31, 76)(32, 79)(33, 74)(34, 72)(35, 80)(36, 75)(37, 78)(38, 71)(39, 77)(40, 73)(41, 52)(42, 55)(43, 51)(44, 56)(45, 57)(46, 59)(47, 53)(48, 54)(49, 60)(50, 58)(61, 134)(62, 136)(63, 138)(64, 131)(65, 139)(66, 132)(67, 140)(68, 133)(69, 135)(70, 137)(91, 103)(92, 101)(93, 107)(94, 108)(95, 102)(96, 104)(97, 105)(98, 110)(99, 106)(100, 109)(121, 124)(122, 126)(123, 128)(125, 129)(127, 130)

MAP           : A4.1261
NOTES         : type II, reflexible, isomorphic to A4.1249.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.6^5, u.8^5 >
CTG (small)   : <10, 1>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.3, x.1^2, x.2^2, x.5^2, x.7^-1 * x.2, x.8^-1 * x.4^-1, x.2 * x.5 * x.6^-1, x.4 * x.1 * x.5, x.6^-2 * x.4, x.1 * x.2 * x.4^-1, x.1 * x.4 * x.2, x.4 * x.6 * x.4, x.8^5 >
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, 5)
#DARTS        : 140
R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140)
L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 82)(12, 85)(13, 90)(14, 81)(15, 88)(16, 89)(17, 86)(18, 84)(19, 83)(20, 87)(21, 23)(22, 29)(24, 30)(25, 26)(27, 28)(31, 80)(32, 73)(33, 72)(34, 77)(35, 79)(36, 78)(37, 74)(38, 76)(39, 75)(40, 71)(41, 58)(42, 54)(43, 56)(44, 55)(45, 51)(46, 60)(47, 53)(48, 52)(49, 57)(50, 59)(61, 139)(62, 136)(63, 134)(64, 133)(65, 137)(66, 132)(67, 135)(68, 140)(69, 131)(70, 138)(91, 104)(92, 101)(93, 109)(94, 108)(95, 102)(96, 107)(97, 110)(98, 105)(99, 106)(100, 103)(121, 129)(122, 126)(123, 124)(125, 127)(128, 130)

MAP           : A4.1262
NOTES         : type II, reflexible, isomorphic to A4.1250.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.6^5, u.8^5 >
CTG (small)   : <10, 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 * x.4^-1, x.6^-1 * x.8^-1, x.5 * x.6^-1 * x.7^-1, x.7 * x.3^-1 * x.2, x.3 * x.4^-1 * x.8^-1, x.8 * x.1 * x.5, x.4 * x.2 * x.5^-1, x.8^5, x.6^5 >
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, 5)
#DARTS        : 140
R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140)
L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 87)(12, 83)(13, 85)(14, 90)(15, 81)(16, 88)(17, 82)(18, 89)(19, 84)(20, 86)(21, 24)(22, 26)(23, 28)(25, 29)(27, 30)(31, 80)(32, 78)(33, 79)(34, 77)(35, 74)(36, 73)(37, 76)(38, 75)(39, 71)(40, 72)(41, 57)(42, 53)(43, 55)(44, 60)(45, 51)(46, 58)(47, 52)(48, 59)(49, 54)(50, 56)(61, 134)(62, 136)(63, 138)(64, 131)(65, 139)(66, 132)(67, 140)(68, 133)(69, 135)(70, 137)(91, 105)(92, 107)(93, 102)(94, 109)(95, 103)(96, 110)(97, 101)(98, 106)(99, 108)(100, 104)(121, 124)(122, 126)(123, 128)(125, 129)(127, 130)

MAP           : A4.1263
NOTES         : type I, chiral, isomorphic to A4.1254.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.4^5 >
CTG (small)   : <20, 4>
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^-1 * x.2)^2, (x.3 * x.1)^2, x.4 * x.5^-4, x.4^5 >
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, 5)
#DARTS        : 140
R = (1, 21, 41, 61, 81, 101, 121)(2, 22, 42, 62, 82, 102, 122)(3, 23, 43, 63, 83, 103, 123)(4, 24, 44, 64, 84, 104, 124)(5, 25, 45, 65, 85, 105, 125)(6, 26, 46, 66, 86, 106, 126)(7, 27, 47, 67, 87, 107, 127)(8, 28, 48, 68, 88, 108, 128)(9, 29, 49, 69, 89, 109, 129)(10, 30, 50, 70, 90, 110, 130)(11, 31, 51, 71, 91, 111, 131)(12, 32, 52, 72, 92, 112, 132)(13, 33, 53, 73, 93, 113, 133)(14, 34, 54, 74, 94, 114, 134)(15, 35, 55, 75, 95, 115, 135)(16, 36, 56, 76, 96, 116, 136)(17, 37, 57, 77, 97, 117, 137)(18, 38, 58, 78, 98, 118, 138)(19, 39, 59, 79, 99, 119, 139)(20, 40, 60, 80, 100, 120, 140)
L = (1, 27)(2, 30)(3, 29)(4, 40)(5, 23)(6, 38)(7, 25)(8, 36)(9, 21)(10, 34)(11, 39)(12, 28)(13, 35)(14, 26)(15, 37)(16, 24)(17, 31)(18, 22)(19, 33)(20, 32)(41, 118)(42, 109)(43, 114)(44, 113)(45, 110)(46, 105)(47, 102)(48, 111)(49, 106)(50, 101)(51, 120)(52, 117)(53, 108)(54, 107)(55, 116)(56, 119)(57, 104)(58, 103)(59, 112)(60, 115)(61, 64)(62, 75)(63, 72)(65, 68)(66, 71)(67, 76)(69, 80)(70, 73)(74, 79)(77, 78)(81, 93)(82, 96)(83, 97)(84, 98)(85, 91)(86, 100)(87, 99)(88, 90)(89, 95)(92, 94)(121, 122)(123, 126)(124, 135)(125, 134)(127, 130)(128, 139)(129, 138)(131, 132)(133, 136)(137, 140)

MAP           : A4.1264
NOTES         : type II, reflexible, isomorphic to A4.1248.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.3^5, u.7^5 >
CTG (small)   : <10, 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.2 * x.1, x.7 * x.3^-1, x.4 * x.6, x.6 * x.1 * x.3^-1, x.4 * x.2 * x.3, x.7 * x.2 * x.8^-1, x.1 * x.3 * x.6^-1, x.5 * x.6^-1 * x.8, x.3^2 * x.6 * x.3 * x.4^-1, x.3^5, x.7^5 >
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, 5)
#DARTS        : 140
R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140)
L = (1, 12)(2, 15)(3, 11)(4, 16)(5, 17)(6, 19)(7, 13)(8, 14)(9, 20)(10, 18)(21, 58)(22, 54)(23, 60)(24, 53)(25, 56)(26, 51)(27, 59)(28, 57)(29, 52)(30, 55)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 116)(42, 119)(43, 114)(44, 112)(45, 120)(46, 115)(47, 118)(48, 111)(49, 117)(50, 113)(61, 64)(62, 66)(63, 68)(65, 69)(67, 70)(71, 132)(72, 135)(73, 131)(74, 136)(75, 137)(76, 139)(77, 133)(78, 134)(79, 140)(80, 138)(81, 84)(82, 86)(83, 88)(85, 89)(87, 90)(91, 126)(92, 129)(93, 124)(94, 122)(95, 130)(96, 125)(97, 128)(98, 121)(99, 127)(100, 123)

MAP           : A4.1265
NOTES         : type II, reflexible, isomorphic to A4.1250.
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, {5, 5, 2, 2})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 5, 5, 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.6^5, u.8^5 >
CTG (small)   : <10, 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 * x.4^-1, x.6^-1 * x.8^-1, x.5 * x.6^-1 * x.7^-1, x.7 * x.3^-1 * x.2, x.3 * x.4^-1 * x.8^-1, x.8 * x.1 * x.5, x.4 * x.2 * x.5^-1, x.8^5, x.6^5 >
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, 5)
#DARTS        : 140
R = (1, 11, 21, 31, 41, 51, 61)(2, 12, 22, 32, 42, 52, 62)(3, 13, 23, 33, 43, 53, 63)(4, 14, 24, 34, 44, 54, 64)(5, 15, 25, 35, 45, 55, 65)(6, 16, 26, 36, 46, 56, 66)(7, 17, 27, 37, 47, 57, 67)(8, 18, 28, 38, 48, 58, 68)(9, 19, 29, 39, 49, 59, 69)(10, 20, 30, 40, 50, 60, 70)(71, 81, 91, 101, 111, 121, 131)(72, 82, 92, 102, 112, 122, 132)(73, 83, 93, 103, 113, 123, 133)(74, 84, 94, 104, 114, 124, 134)(75, 85, 95, 105, 115, 125, 135)(76, 86, 96, 106, 116, 126, 136)(77, 87, 97, 107, 117, 127, 137)(78, 88, 98, 108, 118, 128, 138)(79, 89, 99, 109, 119, 129, 139)(80, 90, 100, 110, 120, 130, 140)
L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 85)(12, 87)(13, 82)(14, 89)(15, 83)(16, 90)(17, 81)(18, 86)(19, 88)(20, 84)(21, 24)(22, 26)(23, 28)(25, 29)(27, 30)(31, 79)(32, 80)(33, 76)(34, 75)(35, 78)(36, 77)(37, 74)(38, 72)(39, 73)(40, 71)(41, 55)(42, 57)(43, 52)(44, 59)(45, 53)(46, 60)(47, 51)(48, 56)(49, 58)(50, 54)(61, 134)(62, 136)(63, 138)(64, 131)(65, 139)(66, 132)(67, 140)(68, 133)(69, 135)(70, 137)(91, 107)(92, 103)(93, 105)(94, 110)(95, 101)(96, 108)(97, 102)(98, 109)(99, 104)(100, 106)(121, 124)(122, 126)(123, 128)(125, 129)(127, 130)

MAP           : A4.1266
NOTES         : type I, chiral, isomorphic to A4.1254.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 2)(3, 6)
ORBIFOLD      : O(0, {5, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 5, 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.4^5 >
CTG (small)   : <20, 4>
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^-1 * x.2)^2, (x.3 * x.1)^2, x.4 * x.5^-4, x.4^5 >
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, 5)
#DARTS        : 140
R = (1, 21, 41, 61, 81, 101, 121)(2, 22, 42, 62, 82, 102, 122)(3, 23, 43, 63, 83, 103, 123)(4, 24, 44, 64, 84, 104, 124)(5, 25, 45, 65, 85, 105, 125)(6, 26, 46, 66, 86, 106, 126)(7, 27, 47, 67, 87, 107, 127)(8, 28, 48, 68, 88, 108, 128)(9, 29, 49, 69, 89, 109, 129)(10, 30, 50, 70, 90, 110, 130)(11, 31, 51, 71, 91, 111, 131)(12, 32, 52, 72, 92, 112, 132)(13, 33, 53, 73, 93, 113, 133)(14, 34, 54, 74, 94, 114, 134)(15, 35, 55, 75, 95, 115, 135)(16, 36, 56, 76, 96, 116, 136)(17, 37, 57, 77, 97, 117, 137)(18, 38, 58, 78, 98, 118, 138)(19, 39, 59, 79, 99, 119, 139)(20, 40, 60, 80, 100, 120, 140)
L = (1, 27)(2, 30)(3, 29)(4, 40)(5, 23)(6, 38)(7, 25)(8, 36)(9, 21)(10, 34)(11, 39)(12, 28)(13, 35)(14, 26)(15, 37)(16, 24)(17, 31)(18, 22)(19, 33)(20, 32)(41, 118)(42, 109)(43, 114)(44, 113)(45, 110)(46, 105)(47, 102)(48, 111)(49, 106)(50, 101)(51, 120)(52, 117)(53, 108)(54, 107)(55, 116)(56, 119)(57, 104)(58, 103)(59, 112)(60, 115)(61, 71)(62, 72)(63, 73)(64, 74)(65, 75)(66, 76)(67, 77)(68, 78)(69, 79)(70, 80)(81, 100)(82, 97)(83, 88)(84, 87)(85, 96)(86, 99)(89, 92)(90, 95)(91, 98)(93, 94)(121, 122)(123, 126)(124, 135)(125, 134)(127, 130)(128, 139)(129, 138)(131, 132)(133, 136)(137, 140)

MAP           : A4.1267
NOTES         : type I, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 110)(2, 113)(3, 115)(4, 116)(5, 109)(6, 124)(7, 123)(8, 126)(9, 125)(10, 122)(11, 118)(12, 114)(13, 117)(14, 119)(15, 111)(16, 120)(17, 121)(18, 112)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1268
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 120)(2, 114)(3, 118)(4, 113)(5, 124)(6, 126)(7, 122)(8, 109)(9, 123)(10, 125)(11, 117)(12, 116)(13, 115)(14, 121)(15, 119)(16, 112)(17, 111)(18, 110)(19, 54)(20, 40)(21, 49)(22, 48)(23, 44)(24, 41)(25, 45)(26, 42)(27, 46)(28, 43)(29, 39)(30, 38)(31, 47)(32, 51)(33, 53)(34, 37)(35, 50)(36, 52)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1269
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 113)(2, 109)(3, 123)(4, 126)(5, 110)(6, 120)(7, 111)(8, 112)(9, 121)(10, 119)(11, 122)(12, 124)(13, 125)(14, 118)(15, 115)(16, 114)(17, 117)(18, 116)(19, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1270
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 116)(2, 126)(3, 125)(4, 124)(5, 112)(6, 110)(7, 121)(8, 120)(9, 119)(10, 111)(11, 123)(12, 109)(13, 122)(14, 115)(15, 117)(16, 113)(17, 118)(18, 114)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1271
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 112)(2, 116)(3, 117)(4, 114)(5, 126)(6, 109)(7, 125)(8, 124)(9, 122)(10, 123)(11, 115)(12, 113)(13, 118)(14, 111)(15, 121)(16, 110)(17, 119)(18, 120)(19, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1272
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 124)(2, 120)(3, 119)(4, 110)(5, 114)(6, 116)(7, 118)(8, 113)(9, 115)(10, 117)(11, 121)(12, 112)(13, 111)(14, 125)(15, 122)(16, 126)(17, 123)(18, 109)(19, 44)(20, 54)(21, 53)(22, 52)(23, 40)(24, 38)(25, 49)(26, 48)(27, 47)(28, 39)(29, 51)(30, 37)(31, 50)(32, 43)(33, 45)(34, 41)(35, 46)(36, 42)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1273
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 126)(2, 112)(3, 121)(4, 120)(5, 116)(6, 113)(7, 117)(8, 114)(9, 118)(10, 115)(11, 111)(12, 110)(13, 119)(14, 123)(15, 125)(16, 109)(17, 122)(18, 124)(19, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 94)(56, 98)(57, 99)(58, 96)(59, 108)(60, 91)(61, 107)(62, 106)(63, 104)(64, 105)(65, 97)(66, 95)(67, 100)(68, 93)(69, 103)(70, 92)(71, 101)(72, 102)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1274
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 110)(2, 113)(3, 115)(4, 116)(5, 109)(6, 124)(7, 123)(8, 126)(9, 125)(10, 122)(11, 118)(12, 114)(13, 117)(14, 119)(15, 111)(16, 120)(17, 121)(18, 112)(19, 42)(20, 52)(21, 50)(22, 37)(23, 48)(24, 40)(25, 47)(26, 38)(27, 39)(28, 49)(29, 53)(30, 54)(31, 51)(32, 45)(33, 46)(34, 44)(35, 43)(36, 41)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1275
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 124)(2, 120)(3, 119)(4, 110)(5, 114)(6, 116)(7, 118)(8, 113)(9, 115)(10, 117)(11, 121)(12, 112)(13, 111)(14, 125)(15, 122)(16, 126)(17, 123)(18, 109)(19, 42)(20, 52)(21, 50)(22, 37)(23, 48)(24, 40)(25, 47)(26, 38)(27, 39)(28, 49)(29, 53)(30, 54)(31, 51)(32, 45)(33, 46)(34, 44)(35, 43)(36, 41)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1276
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 126)(2, 112)(3, 121)(4, 120)(5, 116)(6, 113)(7, 117)(8, 114)(9, 118)(10, 115)(11, 111)(12, 110)(13, 119)(14, 123)(15, 125)(16, 109)(17, 122)(18, 124)(19, 44)(20, 54)(21, 53)(22, 52)(23, 40)(24, 38)(25, 49)(26, 48)(27, 47)(28, 39)(29, 51)(30, 37)(31, 50)(32, 43)(33, 45)(34, 41)(35, 46)(36, 42)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1277
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, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1278
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1279
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 114)(2, 124)(3, 122)(4, 109)(5, 120)(6, 112)(7, 119)(8, 110)(9, 111)(10, 121)(11, 125)(12, 126)(13, 123)(14, 117)(15, 118)(16, 116)(17, 115)(18, 113)(19, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1280
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 116)(2, 126)(3, 125)(4, 124)(5, 112)(6, 110)(7, 121)(8, 120)(9, 119)(10, 111)(11, 123)(12, 109)(13, 122)(14, 115)(15, 117)(16, 113)(17, 118)(18, 114)(19, 42)(20, 52)(21, 50)(22, 37)(23, 48)(24, 40)(25, 47)(26, 38)(27, 39)(28, 49)(29, 53)(30, 54)(31, 51)(32, 45)(33, 46)(34, 44)(35, 43)(36, 41)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1281
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 120)(2, 114)(3, 118)(4, 113)(5, 124)(6, 126)(7, 122)(8, 109)(9, 123)(10, 125)(11, 117)(12, 116)(13, 115)(14, 121)(15, 119)(16, 112)(17, 111)(18, 110)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1282
NOTES         : type I, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1283
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1284
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 113)(2, 109)(3, 123)(4, 126)(5, 110)(6, 120)(7, 111)(8, 112)(9, 121)(10, 119)(11, 122)(12, 124)(13, 125)(14, 118)(15, 115)(16, 114)(17, 117)(18, 116)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1285
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1286
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 114)(2, 124)(3, 122)(4, 109)(5, 120)(6, 112)(7, 119)(8, 110)(9, 111)(10, 121)(11, 125)(12, 126)(13, 123)(14, 117)(15, 118)(16, 116)(17, 115)(18, 113)(19, 54)(20, 40)(21, 49)(22, 48)(23, 44)(24, 41)(25, 45)(26, 42)(27, 46)(28, 43)(29, 39)(30, 38)(31, 47)(32, 51)(33, 53)(34, 37)(35, 50)(36, 52)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1287
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 124)(2, 120)(3, 119)(4, 110)(5, 114)(6, 116)(7, 118)(8, 113)(9, 115)(10, 117)(11, 121)(12, 112)(13, 111)(14, 125)(15, 122)(16, 126)(17, 123)(18, 109)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1288
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 126)(2, 112)(3, 121)(4, 120)(5, 116)(6, 113)(7, 117)(8, 114)(9, 118)(10, 115)(11, 111)(12, 110)(13, 119)(14, 123)(15, 125)(16, 109)(17, 122)(18, 124)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 98)(56, 108)(57, 107)(58, 106)(59, 94)(60, 92)(61, 103)(62, 102)(63, 101)(64, 93)(65, 105)(66, 91)(67, 104)(68, 97)(69, 99)(70, 95)(71, 100)(72, 96)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1289
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 110)(2, 113)(3, 115)(4, 116)(5, 109)(6, 124)(7, 123)(8, 126)(9, 125)(10, 122)(11, 118)(12, 114)(13, 117)(14, 119)(15, 111)(16, 120)(17, 121)(18, 112)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1290
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 113)(2, 109)(3, 123)(4, 126)(5, 110)(6, 120)(7, 111)(8, 112)(9, 121)(10, 119)(11, 122)(12, 124)(13, 125)(14, 118)(15, 115)(16, 114)(17, 117)(18, 116)(19, 44)(20, 54)(21, 53)(22, 52)(23, 40)(24, 38)(25, 49)(26, 48)(27, 47)(28, 39)(29, 51)(30, 37)(31, 50)(32, 43)(33, 45)(34, 41)(35, 46)(36, 42)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1291
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 112)(2, 116)(3, 117)(4, 114)(5, 126)(6, 109)(7, 125)(8, 124)(9, 122)(10, 123)(11, 115)(12, 113)(13, 118)(14, 111)(15, 121)(16, 110)(17, 119)(18, 120)(19, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 106)(56, 102)(57, 101)(58, 92)(59, 96)(60, 98)(61, 100)(62, 95)(63, 97)(64, 99)(65, 103)(66, 94)(67, 93)(68, 107)(69, 104)(70, 108)(71, 105)(72, 91)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1292
NOTES         : type I, chiral, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.4 * x.3 * x.2^-1, x.3^3, x.2 * x.4^-1 * x.3^-1, x.4^3, x.2^3, (x.4 * x.1)^2, x.2 * x.1 * x.2^-1 * x.1, x.1 * x.2 * x.3 * x.1 * x.3 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 112)(2, 123)(3, 114)(4, 113)(5, 109)(6, 116)(7, 118)(8, 111)(9, 120)(10, 119)(11, 115)(12, 122)(13, 124)(14, 117)(15, 126)(16, 125)(17, 121)(18, 110)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)(55, 100)(56, 93)(57, 102)(58, 101)(59, 97)(60, 104)(61, 106)(62, 99)(63, 108)(64, 107)(65, 103)(66, 92)(67, 94)(68, 105)(69, 96)(70, 95)(71, 91)(72, 98)(73, 74)(75, 89)(76, 87)(77, 90)(78, 85)(79, 81)(80, 88)(82, 84)(83, 86)

MAP           : A4.1293
NOTES         : type I, chiral, isomorphic to A4.1292.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.4 * x.3 * x.2^-1, x.3^3, x.2 * x.4^-1 * x.3^-1, x.4^3, x.2^3, (x.4 * x.1)^2, x.2 * x.1 * x.2^-1 * x.1, x.1 * x.2 * x.3 * x.1 * x.3 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 113)(2, 126)(3, 116)(4, 109)(5, 112)(6, 111)(7, 119)(8, 114)(9, 122)(10, 115)(11, 118)(12, 117)(13, 125)(14, 120)(15, 110)(16, 121)(17, 124)(18, 123)(19, 52)(20, 45)(21, 54)(22, 53)(23, 49)(24, 38)(25, 40)(26, 51)(27, 42)(28, 41)(29, 37)(30, 44)(31, 46)(32, 39)(33, 48)(34, 47)(35, 43)(36, 50)(55, 100)(56, 93)(57, 102)(58, 101)(59, 97)(60, 104)(61, 106)(62, 99)(63, 108)(64, 107)(65, 103)(66, 92)(67, 94)(68, 105)(69, 96)(70, 95)(71, 91)(72, 98)(73, 74)(75, 89)(76, 87)(77, 90)(78, 85)(79, 81)(80, 88)(82, 84)(83, 86)

MAP           : A4.1294
NOTES         : type I, chiral, isomorphic to A4.1292.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.4 * x.3 * x.2^-1, x.2 * x.4^-1 * x.3^-1, x.4^3, x.3^3, x.2^3, x.4^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3^-1 * x.1 * x.3 * x.1, (x.4 * x.1)^2, x.4 * x.1 * x.2^-1 * x.1 * x.2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 115)(2, 116)(3, 117)(4, 118)(5, 119)(6, 120)(7, 121)(8, 122)(9, 123)(10, 124)(11, 125)(12, 126)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 41)(20, 54)(21, 44)(22, 37)(23, 40)(24, 39)(25, 47)(26, 42)(27, 50)(28, 43)(29, 46)(30, 45)(31, 53)(32, 48)(33, 38)(34, 49)(35, 52)(36, 51)(55, 100)(56, 93)(57, 102)(58, 101)(59, 97)(60, 104)(61, 106)(62, 99)(63, 108)(64, 107)(65, 103)(66, 92)(67, 94)(68, 105)(69, 96)(70, 95)(71, 91)(72, 98)(73, 74)(75, 89)(76, 87)(77, 90)(78, 85)(79, 81)(80, 88)(82, 84)(83, 86)

MAP           : A4.1295
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.4 * x.3 * x.2^-1, x.2 * x.4^-1 * x.3^-1, x.3^3, x.2^3, x.4^3, (x.4 * x.1)^2, x.3 * x.1 * x.2^-1 * x.1 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 124)(2, 117)(3, 126)(4, 125)(5, 121)(6, 110)(7, 112)(8, 123)(9, 114)(10, 113)(11, 109)(12, 116)(13, 118)(14, 111)(15, 120)(16, 119)(17, 115)(18, 122)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(25, 49)(26, 50)(27, 51)(28, 52)(29, 53)(30, 54)(31, 37)(32, 38)(33, 39)(34, 40)(35, 41)(36, 42)(55, 100)(56, 93)(57, 102)(58, 101)(59, 97)(60, 104)(61, 106)(62, 99)(63, 108)(64, 107)(65, 103)(66, 92)(67, 94)(68, 105)(69, 96)(70, 95)(71, 91)(72, 98)(73, 74)(75, 89)(76, 87)(77, 90)(78, 85)(79, 81)(80, 88)(82, 84)(83, 86)

MAP           : A4.1296
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.4 * x.3 * x.2^-1, x.2 * x.4^-1 * x.3^-1, x.3^3, x.2^3, x.4^3, (x.4 * x.1)^2, x.3 * x.1 * x.2^-1 * x.1 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 109)(8, 110)(9, 111)(10, 112)(11, 113)(12, 114)(13, 115)(14, 116)(15, 117)(16, 118)(17, 119)(18, 120)(19, 47)(20, 42)(21, 50)(22, 43)(23, 46)(24, 45)(25, 53)(26, 48)(27, 38)(28, 49)(29, 52)(30, 51)(31, 41)(32, 54)(33, 44)(34, 37)(35, 40)(36, 39)(55, 100)(56, 93)(57, 102)(58, 101)(59, 97)(60, 104)(61, 106)(62, 99)(63, 108)(64, 107)(65, 103)(66, 92)(67, 94)(68, 105)(69, 96)(70, 95)(71, 91)(72, 98)(73, 74)(75, 89)(76, 87)(77, 90)(78, 85)(79, 81)(80, 88)(82, 84)(83, 86)

MAP           : A4.1297
NOTES         : type I, chiral, isomorphic to A4.1292.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.4 * x.3 * x.2^-1, x.2 * x.4^-1 * x.3^-1, x.4^3, x.3^3, x.2^3, x.4^-1 * x.2^-1 * x.3^-1 * x.2^-1, x.3^-1 * x.1 * x.3 * x.1, (x.4 * x.1)^2, x.4 * x.1 * x.2^-1 * x.1 * x.2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 119)(2, 114)(3, 122)(4, 115)(5, 118)(6, 117)(7, 125)(8, 120)(9, 110)(10, 121)(11, 124)(12, 123)(13, 113)(14, 126)(15, 116)(16, 109)(17, 112)(18, 111)(19, 40)(20, 51)(21, 42)(22, 41)(23, 37)(24, 44)(25, 46)(26, 39)(27, 48)(28, 47)(29, 43)(30, 50)(31, 52)(32, 45)(33, 54)(34, 53)(35, 49)(36, 38)(55, 100)(56, 93)(57, 102)(58, 101)(59, 97)(60, 104)(61, 106)(62, 99)(63, 108)(64, 107)(65, 103)(66, 92)(67, 94)(68, 105)(69, 96)(70, 95)(71, 91)(72, 98)(73, 74)(75, 89)(76, 87)(77, 90)(78, 85)(79, 81)(80, 88)(82, 84)(83, 86)

MAP           : A4.1298
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 112)(2, 116)(3, 117)(4, 114)(5, 126)(6, 109)(7, 125)(8, 124)(9, 122)(10, 123)(11, 115)(12, 113)(13, 118)(14, 111)(15, 121)(16, 110)(17, 119)(18, 120)(19, 54)(20, 40)(21, 49)(22, 48)(23, 44)(24, 41)(25, 45)(26, 42)(27, 46)(28, 43)(29, 39)(30, 38)(31, 47)(32, 51)(33, 53)(34, 37)(35, 50)(36, 52)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1299
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 114)(2, 124)(3, 122)(4, 109)(5, 120)(6, 112)(7, 119)(8, 110)(9, 111)(10, 121)(11, 125)(12, 126)(13, 123)(14, 117)(15, 118)(16, 116)(17, 115)(18, 113)(19, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1300
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 116)(2, 126)(3, 125)(4, 124)(5, 112)(6, 110)(7, 121)(8, 120)(9, 119)(10, 111)(11, 123)(12, 109)(13, 122)(14, 115)(15, 117)(16, 113)(17, 118)(18, 114)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1301
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7) L = (1, 7)(2, 3)(4, 6)
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.4^-1, u.3^3, u.2^3, (u.4 * u.1)^2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.4^-1, x.3^3, x.2^3, x.2 * x.4^-1 * x.3^-1, x.4^3, (x.4 * x.1)^2, (x.2 * x.1)^2, (x.3^-1 * x.1)^2 >
SCHREIER VEC. : (x.2, x.3, x.3^-1, x.4, x.1, x.4^-1, x.2^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 120)(2, 114)(3, 118)(4, 113)(5, 124)(6, 126)(7, 122)(8, 109)(9, 123)(10, 125)(11, 117)(12, 116)(13, 115)(14, 121)(15, 119)(16, 112)(17, 111)(18, 110)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 92)(56, 95)(57, 97)(58, 98)(59, 91)(60, 106)(61, 105)(62, 108)(63, 107)(64, 104)(65, 100)(66, 96)(67, 99)(68, 101)(69, 93)(70, 102)(71, 103)(72, 94)(73, 75)(74, 87)(76, 86)(77, 79)(78, 81)(80, 82)(83, 90)(84, 89)(85, 88)

MAP           : A4.1302
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1303
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1304
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1305
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1306
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1307
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1308
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1309
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1310
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1311
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1312
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1313
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1314
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1315
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1316
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1317
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1318
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1319
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1320
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1321
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1322
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1323
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1324
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1325
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1326
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1327
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1328
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1329
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1330
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1331
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1332
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1333
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1334
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1335
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1336
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1337
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1338
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1339
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1340
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1341
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1342
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1343
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1344
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1345
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1346
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1347
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1348
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1349
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1350
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1351
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1352
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1353
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1354
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1355
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1356
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1357
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1358
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1359
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1360
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1361
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1362
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1363
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1364
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1365
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1366
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1367
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1368
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1369
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1370
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1371
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1372
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1373
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1374
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1375
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1376
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1377
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1378
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1379
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1380
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1381
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1382
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1383
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1384
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1385
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1386
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1387
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1388
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1389
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1390
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1391
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1392
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1393
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1394
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1395
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1396
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1397
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1398
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1399
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1400
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1401
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1402
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1403
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1404
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1405
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1406
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1407
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1408
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1409
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1410
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1411
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1412
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1413
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1414
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1415
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1416
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1417
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1418
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1419
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1420
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1421
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1422
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1423
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1424
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1425
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1426
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1427
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1428
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1429
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1430
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1431
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1432
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1433
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1434
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1435
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1436
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1437
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1438
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1439
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1440
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1441
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 44)(20, 39)(21, 43)(22, 42)(23, 40)(24, 41)(25, 38)(26, 45)(27, 37)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 117)(92, 115)(93, 110)(94, 113)(95, 114)(96, 112)(97, 111)(98, 109)(99, 116)

MAP           : A4.1442
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1443
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1444
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1445
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 45)(20, 43)(21, 38)(22, 41)(23, 42)(24, 40)(25, 39)(26, 37)(27, 44)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 116)(92, 111)(93, 115)(94, 114)(95, 112)(96, 113)(97, 110)(98, 117)(99, 109)

MAP           : A4.1446
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1447
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1448
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1449
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1450
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1451
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1452
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1453
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1454
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1455
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1456
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1457
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1458
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1459
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1460
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1461
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1462
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1463
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 90)(74, 88)(75, 83)(76, 86)(77, 87)(78, 85)(79, 84)(80, 82)(81, 89)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1464
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1465
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1466
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1467
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1468
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1469
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1470
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1471
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1472
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 38)(20, 41)(21, 40)(22, 44)(23, 37)(24, 45)(25, 42)(26, 39)(27, 43)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 113)(92, 109)(93, 116)(94, 111)(95, 110)(96, 115)(97, 117)(98, 112)(99, 114)

MAP           : A4.1473
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1474
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 120)(65, 121)(66, 123)(67, 126)(68, 125)(69, 118)(70, 122)(71, 124)(72, 119)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1475
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 121)(65, 125)(66, 126)(67, 124)(68, 120)(69, 119)(70, 118)(71, 123)(72, 122)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1476
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 85)(74, 89)(75, 90)(76, 88)(77, 84)(78, 83)(79, 82)(80, 87)(81, 86)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1477
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 41)(20, 37)(21, 44)(22, 39)(23, 38)(24, 43)(25, 45)(26, 40)(27, 42)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 110)(92, 113)(93, 112)(94, 116)(95, 109)(96, 117)(97, 114)(98, 111)(99, 115)

MAP           : A4.1478
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1479
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1480
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1481
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 39)(20, 40)(21, 42)(22, 45)(23, 44)(24, 37)(25, 41)(26, 43)(27, 38)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 114)(92, 117)(93, 109)(94, 110)(95, 115)(96, 111)(97, 116)(98, 113)(99, 112)

MAP           : A4.1482
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 122)(65, 118)(66, 125)(67, 120)(68, 119)(69, 124)(70, 126)(71, 121)(72, 123)(73, 88)(74, 87)(75, 86)(76, 82)(77, 90)(78, 89)(79, 85)(80, 83)(81, 84)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1483
NOTES         : type I, reflexible, isomorphic to A4.1267.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.4, x.1^-1 * x.6^-1, x.4^3, x.6^3, x.2^2 * x.7^-1, x.5^3, x.1^-1 * x.2^-1 * x.4^-1, x.1^3, x.1 * x.5 * x.7^-1, x.5 * x.6^-1 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 42)(20, 45)(21, 37)(22, 38)(23, 43)(24, 39)(25, 44)(26, 41)(27, 40)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 124)(65, 123)(66, 122)(67, 118)(68, 126)(69, 125)(70, 121)(71, 119)(72, 120)(73, 89)(74, 84)(75, 88)(76, 87)(77, 85)(78, 86)(79, 83)(80, 90)(81, 82)(91, 111)(92, 112)(93, 114)(94, 117)(95, 116)(96, 109)(97, 113)(98, 115)(99, 110)

MAP           : A4.1484
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.5^-1 * x.1^-1, x.4^3, x.5^3, x.5 * x.6^-1 * x.7^-1, x.6^3, x.2 * x.4 * x.5^-1, x.1^3, x.1 * x.6 * x.2^-1, x.4 * x.1 * x.7^-1, x.1^-1 * x.2^-1 * x.4^-1, x.2^2 * x.7^-1, x.1 * x.4^-1 * x.6^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 125)(65, 120)(66, 124)(67, 123)(68, 121)(69, 122)(70, 119)(71, 126)(72, 118)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1485
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 86)(74, 82)(75, 89)(76, 84)(77, 83)(78, 88)(79, 90)(80, 85)(81, 87)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1486
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 119)(65, 122)(66, 121)(67, 125)(68, 118)(69, 126)(70, 123)(71, 120)(72, 124)(73, 87)(74, 90)(75, 82)(76, 83)(77, 88)(78, 84)(79, 89)(80, 86)(81, 85)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1487
NOTES         : type II, reflexible, isomorphic to A4.1277.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.6 * x.4^-1, x.6^3, x.5^3, x.4^3, x.1 * x.5 * x.2^-1, x.1 * x.2 * x.4, x.1^3, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.1 * x.7 * x.5, x.1^-1 * x.2^-1 * x.4^-1, x.1 * x.6 * x.7^-1, x.1 * x.4^-1 * x.5^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 40)(20, 44)(21, 45)(22, 43)(23, 39)(24, 38)(25, 37)(26, 42)(27, 41)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 123)(65, 126)(66, 118)(67, 119)(68, 124)(69, 120)(70, 125)(71, 122)(72, 121)(73, 83)(74, 86)(75, 85)(76, 89)(77, 82)(78, 90)(79, 87)(80, 84)(81, 88)(91, 115)(92, 114)(93, 113)(94, 109)(95, 117)(96, 116)(97, 112)(98, 110)(99, 111)

MAP           : A4.1488
NOTES         : type I, reflexible, isomorphic to A4.1282.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14) L = (1, 2)(3, 5)(4, 12)(6, 7)(8, 14)(9, 10)(11, 13)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.3, u.1^3, u.4^3, u.6^3, u.5^3, u.1^-1 * u.2^-1 * u.4^-1, u.5 * u.6^-1 * u.7^-1, u.2 * u.3^-1 * u.7 * u.3 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.2^-1, x.5^-1 * x.1, x.4^-1 * x.6^-1, x.1^3, x.2 * x.4 * x.1, x.5^3, x.6^3, x.4^3, x.1^-1 * x.2^-1 * x.4^-1, x.5 * x.6^-1 * x.7^-1, x.2^2 * x.7^-1, x.2 * x.3^-1 * x.7 * x.3 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.2^-1, x.4, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 4)
#DARTS        : 126
R = (1, 10, 19, 28, 37, 46, 55)(2, 11, 20, 29, 38, 47, 56)(3, 12, 21, 30, 39, 48, 57)(4, 13, 22, 31, 40, 49, 58)(5, 14, 23, 32, 41, 50, 59)(6, 15, 24, 33, 42, 51, 60)(7, 16, 25, 34, 43, 52, 61)(8, 17, 26, 35, 44, 53, 62)(9, 18, 27, 36, 45, 54, 63)(64, 73, 82, 91, 100, 109, 118)(65, 74, 83, 92, 101, 110, 119)(66, 75, 84, 93, 102, 111, 120)(67, 76, 85, 94, 103, 112, 121)(68, 77, 86, 95, 104, 113, 122)(69, 78, 87, 96, 105, 114, 123)(70, 79, 88, 97, 106, 115, 124)(71, 80, 89, 98, 107, 116, 125)(72, 81, 90, 99, 108, 117, 126)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 43)(20, 42)(21, 41)(22, 37)(23, 45)(24, 44)(25, 40)(26, 38)(27, 39)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 126)(65, 124)(66, 119)(67, 122)(68, 123)(69, 121)(70, 120)(71, 118)(72, 125)(73, 84)(74, 85)(75, 87)(76, 90)(77, 89)(78, 82)(79, 86)(80, 88)(81, 83)(91, 112)(92, 116)(93, 117)(94, 115)(95, 111)(96, 110)(97, 109)(98, 114)(99, 113)

MAP           : A4.1489
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.1, x.1 * x.2^-1 * x.3, x.4^3, x.2^3, (x.3 * x.4^-1)^2, x.4^-1 * x.1 * x.4^-1 * x.3^-1, (x.4, x.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        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 112)(2, 123)(3, 114)(4, 113)(5, 109)(6, 116)(7, 118)(8, 111)(9, 120)(10, 119)(11, 115)(12, 122)(13, 124)(14, 117)(15, 126)(16, 125)(17, 121)(18, 110)(19, 78)(20, 83)(21, 76)(22, 80)(23, 75)(24, 77)(25, 74)(26, 73)(27, 89)(28, 87)(29, 90)(30, 85)(31, 81)(32, 88)(33, 79)(34, 84)(35, 86)(36, 82)(37, 67)(38, 68)(39, 69)(40, 70)(41, 71)(42, 72)(43, 55)(44, 56)(45, 57)(46, 58)(47, 59)(48, 60)(49, 61)(50, 62)(51, 63)(52, 64)(53, 65)(54, 66)(91, 93)(92, 100)(94, 96)(95, 98)(97, 108)(99, 106)(101, 105)(102, 107)(103, 104)

MAP           : A4.1490
NOTES         : type I, chiral, isomorphic to A4.1489.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.1, x.2 * x.1 * x.3^-1, x.3^3, x.4^3, (x.3, x.4^-1), x.4 * x.1 * x.4 * x.2^-1, (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        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 78)(2, 83)(3, 76)(4, 80)(5, 75)(6, 77)(7, 74)(8, 73)(9, 89)(10, 87)(11, 90)(12, 85)(13, 81)(14, 88)(15, 79)(16, 84)(17, 86)(18, 82)(19, 40)(20, 51)(21, 42)(22, 41)(23, 37)(24, 44)(25, 46)(26, 39)(27, 48)(28, 47)(29, 43)(30, 50)(31, 52)(32, 45)(33, 54)(34, 53)(35, 49)(36, 38)(55, 57)(56, 64)(58, 60)(59, 62)(61, 72)(63, 70)(65, 69)(66, 71)(67, 68)(91, 115)(92, 116)(93, 117)(94, 118)(95, 119)(96, 120)(97, 121)(98, 122)(99, 123)(100, 124)(101, 125)(102, 126)(103, 109)(104, 110)(105, 111)(106, 112)(107, 113)(108, 114)

MAP           : A4.1491
NOTES         : type I, chiral, isomorphic to A4.1489.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.1, x.2 * x.1 * x.3^-1, x.3^3, x.4^3, (x.3, x.4^-1), x.4 * x.1 * x.4 * x.2^-1, (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        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 80)(2, 79)(3, 77)(4, 75)(5, 78)(6, 73)(7, 87)(8, 76)(9, 85)(10, 90)(11, 74)(12, 88)(13, 84)(14, 89)(15, 82)(16, 86)(17, 81)(18, 83)(19, 41)(20, 54)(21, 44)(22, 37)(23, 40)(24, 39)(25, 47)(26, 42)(27, 50)(28, 43)(29, 46)(30, 45)(31, 53)(32, 48)(33, 38)(34, 49)(35, 52)(36, 51)(55, 57)(56, 64)(58, 60)(59, 62)(61, 72)(63, 70)(65, 69)(66, 71)(67, 68)(91, 121)(92, 122)(93, 123)(94, 124)(95, 125)(96, 126)(97, 109)(98, 110)(99, 111)(100, 112)(101, 113)(102, 114)(103, 115)(104, 116)(105, 117)(106, 118)(107, 119)(108, 120)

MAP           : A4.1492
NOTES         : type I, chiral, isomorphic to A4.1489.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.1^2, x.2 * x.3^-1 * x.1, x.1 * x.2^-1 * x.3, x.4^3, x.2^3, (x.3 * x.4^-1)^2, x.4^-1 * x.1 * x.4^-1 * x.3^-1, (x.4, x.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        : 126
R = (1, 19, 37, 55, 73, 91, 109)(2, 20, 38, 56, 74, 92, 110)(3, 21, 39, 57, 75, 93, 111)(4, 22, 40, 58, 76, 94, 112)(5, 23, 41, 59, 77, 95, 113)(6, 24, 42, 60, 78, 96, 114)(7, 25, 43, 61, 79, 97, 115)(8, 26, 44, 62, 80, 98, 116)(9, 27, 45, 63, 81, 99, 117)(10, 28, 46, 64, 82, 100, 118)(11, 29, 47, 65, 83, 101, 119)(12, 30, 48, 66, 84, 102, 120)(13, 31, 49, 67, 85, 103, 121)(14, 32, 50, 68, 86, 104, 122)(15, 33, 51, 69, 87, 105, 123)(16, 34, 52, 70, 88, 106, 124)(17, 35, 53, 71, 89, 107, 125)(18, 36, 54, 72, 90, 108, 126)
L = (1, 113)(2, 126)(3, 116)(4, 109)(5, 112)(6, 111)(7, 119)(8, 114)(9, 122)(10, 115)(11, 118)(12, 117)(13, 125)(14, 120)(15, 110)(16, 121)(17, 124)(18, 123)(19, 80)(20, 79)(21, 77)(22, 75)(23, 78)(24, 73)(25, 87)(26, 76)(27, 85)(28, 90)(29, 74)(30, 88)(31, 84)(32, 89)(33, 82)(34, 86)(35, 81)(36, 83)(37, 61)(38, 62)(39, 63)(40, 64)(41, 65)(42, 66)(43, 67)(44, 68)(45, 69)(46, 70)(47, 71)(48, 72)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(91, 93)(92, 100)(94, 96)(95, 98)(97, 108)(99, 106)(101, 105)(102, 107)(103, 104)

MAP           : A4.1493
NOTES         : type II, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1494
NOTES         : type I, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1495
NOTES         : type I, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1496
NOTES         : type I, reflexible, 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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.4 * x.3^-1 * x.1, x.4^3, x.5^3, x.2 * x.3^-1 * x.4, x.1 * x.5 * x.3, x.3^-1 * x.2 * x.5^-1, x.4^-1 * x.5^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4^-1 * x.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        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 78)(2, 83)(3, 76)(4, 80)(5, 75)(6, 77)(7, 74)(8, 73)(9, 89)(10, 87)(11, 90)(12, 85)(13, 81)(14, 88)(15, 79)(16, 84)(17, 86)(18, 82)(19, 47)(20, 42)(21, 50)(22, 43)(23, 46)(24, 45)(25, 53)(26, 48)(27, 38)(28, 49)(29, 52)(30, 51)(31, 41)(32, 54)(33, 44)(34, 37)(35, 40)(36, 39)(55, 66)(56, 71)(57, 64)(58, 68)(59, 63)(60, 65)(61, 62)(67, 69)(70, 72)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)(109, 133)(110, 134)(111, 135)(112, 136)(113, 137)(114, 138)(115, 139)(116, 140)(117, 141)(118, 142)(119, 143)(120, 144)(121, 127)(122, 128)(123, 129)(124, 130)(125, 131)(126, 132)

MAP           : A4.1497
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4 * x.3, x.3 * x.4^-1 * x.1, x.5^3, x.4^3, x.3^-1 * x.2 * x.5^-1, x.3 * x.1 * x.4^-1, x.5 * x.4 * x.2 * x.1, x.5^-1 * x.1 * x.4^-1 * x.2, x.5 * x.1 * x.5^-1 * x.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        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 78)(2, 83)(3, 76)(4, 80)(5, 75)(6, 77)(7, 74)(8, 73)(9, 89)(10, 87)(11, 90)(12, 85)(13, 81)(14, 88)(15, 79)(16, 84)(17, 86)(18, 82)(19, 40)(20, 51)(21, 42)(22, 41)(23, 37)(24, 44)(25, 46)(26, 39)(27, 48)(28, 47)(29, 43)(30, 50)(31, 52)(32, 45)(33, 54)(34, 53)(35, 49)(36, 38)(55, 57)(56, 64)(58, 60)(59, 62)(61, 72)(63, 70)(65, 69)(66, 71)(67, 68)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)(109, 133)(110, 134)(111, 135)(112, 136)(113, 137)(114, 138)(115, 139)(116, 140)(117, 141)(118, 142)(119, 143)(120, 144)(121, 127)(122, 128)(123, 129)(124, 130)(125, 131)(126, 132)

MAP           : A4.1498
NOTES         : type I, chiral, isomorphic to A4.1497.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.5^-1 * x.3^2, x.3 * x.4^-1 * x.1, x.4^3, x.5^3, x.3^-1 * x.2 * x.5^-1, x.2 * x.5 * x.3, x.4^-1 * x.2 * x.4 * x.1, x.3^-1 * x.4^-1 * x.5 * x.1, x.2 * x.4^-1 * x.5^-1 * x.1 >
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        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 87)(2, 76)(3, 85)(4, 90)(5, 74)(6, 88)(7, 84)(8, 89)(9, 82)(10, 86)(11, 81)(12, 83)(13, 80)(14, 79)(15, 77)(16, 75)(17, 78)(18, 73)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)(55, 66)(56, 71)(57, 64)(58, 68)(59, 63)(60, 65)(61, 62)(67, 69)(70, 72)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)(109, 131)(110, 144)(111, 134)(112, 127)(113, 130)(114, 129)(115, 137)(116, 132)(117, 140)(118, 133)(119, 136)(120, 135)(121, 143)(122, 138)(123, 128)(124, 139)(125, 142)(126, 141)

MAP           : A4.1499
NOTES         : type I, reflexible, isomorphic to A4.1496.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.4 * x.3^-1 * x.1, x.4^3, x.5^3, x.2 * x.3^-1 * x.4, x.1 * x.5 * x.3, x.3^-1 * x.2 * x.5^-1, x.4^-1 * x.5^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4^-1 * x.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        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 80)(2, 79)(3, 77)(4, 75)(5, 78)(6, 73)(7, 87)(8, 76)(9, 85)(10, 90)(11, 74)(12, 88)(13, 84)(14, 89)(15, 82)(16, 86)(17, 81)(18, 83)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(25, 49)(26, 50)(27, 51)(28, 52)(29, 53)(30, 54)(31, 37)(32, 38)(33, 39)(34, 40)(35, 41)(36, 42)(55, 66)(56, 71)(57, 64)(58, 68)(59, 63)(60, 65)(61, 62)(67, 69)(70, 72)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)(109, 137)(110, 132)(111, 140)(112, 133)(113, 136)(114, 135)(115, 143)(116, 138)(117, 128)(118, 139)(119, 142)(120, 141)(121, 131)(122, 144)(123, 134)(124, 127)(125, 130)(126, 129)

MAP           : A4.1500
NOTES         : type I, chiral, isomorphic to A4.1497.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4 * x.3, x.3 * x.4^-1 * x.1, x.5^3, x.4^3, x.3^-1 * x.2 * x.5^-1, x.3 * x.1 * x.4^-1, x.5 * x.4 * x.2 * x.1, x.5^-1 * x.1 * x.4^-1 * x.2, x.5 * x.1 * x.5^-1 * x.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        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 80)(2, 79)(3, 77)(4, 75)(5, 78)(6, 73)(7, 87)(8, 76)(9, 85)(10, 90)(11, 74)(12, 88)(13, 84)(14, 89)(15, 82)(16, 86)(17, 81)(18, 83)(19, 41)(20, 54)(21, 44)(22, 37)(23, 40)(24, 39)(25, 47)(26, 42)(27, 50)(28, 43)(29, 46)(30, 45)(31, 53)(32, 48)(33, 38)(34, 49)(35, 52)(36, 51)(55, 57)(56, 64)(58, 60)(59, 62)(61, 72)(63, 70)(65, 69)(66, 71)(67, 68)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)(109, 137)(110, 132)(111, 140)(112, 133)(113, 136)(114, 135)(115, 143)(116, 138)(117, 128)(118, 139)(119, 142)(120, 141)(121, 131)(122, 144)(123, 134)(124, 127)(125, 130)(126, 129)

MAP           : A4.1501
NOTES         : type I, chiral, isomorphic to A4.1497.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.5^-1 * x.3^2, x.3 * x.4^-1 * x.1, x.4^3, x.5^3, x.3^-1 * x.2 * x.5^-1, x.2 * x.5 * x.3, x.4^-1 * x.2 * x.4 * x.1, x.3^-1 * x.4^-1 * x.5 * x.1, x.2 * x.4^-1 * x.5^-1 * x.1 >
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        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 90)(2, 77)(3, 88)(4, 74)(5, 87)(6, 89)(7, 86)(8, 85)(9, 83)(10, 81)(11, 84)(12, 79)(13, 75)(14, 82)(15, 73)(16, 78)(17, 80)(18, 76)(19, 52)(20, 45)(21, 54)(22, 53)(23, 49)(24, 38)(25, 40)(26, 51)(27, 42)(28, 41)(29, 37)(30, 44)(31, 46)(32, 39)(33, 48)(34, 47)(35, 43)(36, 50)(55, 66)(56, 71)(57, 64)(58, 68)(59, 63)(60, 65)(61, 62)(67, 69)(70, 72)(91, 92)(93, 107)(94, 105)(95, 108)(96, 103)(97, 99)(98, 106)(100, 102)(101, 104)(109, 130)(110, 141)(111, 132)(112, 131)(113, 127)(114, 134)(115, 136)(116, 129)(117, 138)(118, 137)(119, 133)(120, 140)(121, 142)(122, 135)(123, 144)(124, 143)(125, 139)(126, 128)

MAP           : A4.1502
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1503
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1504
NOTES         : type II, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1505
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1506
NOTES         : type I, chiral, representative.
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)   : <18, 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.1 * x.4 * x.3, x.3^-1 * x.1 * x.4^-1, x.4 * x.5^-1 * x.2, x.5 * x.2 * x.5^-1 * x.1, x.2 * x.3 * x.5 * x.1 >
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        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 22)(2, 33)(3, 24)(4, 23)(5, 19)(6, 26)(7, 28)(8, 21)(9, 30)(10, 29)(11, 25)(12, 32)(13, 34)(14, 27)(15, 36)(16, 35)(17, 31)(18, 20)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 144)(56, 131)(57, 142)(58, 128)(59, 141)(60, 143)(61, 140)(62, 139)(63, 137)(64, 135)(65, 138)(66, 133)(67, 129)(68, 136)(69, 127)(70, 132)(71, 134)(72, 130)(73, 106)(74, 99)(75, 108)(76, 107)(77, 103)(78, 92)(79, 94)(80, 105)(81, 96)(82, 95)(83, 91)(84, 98)(85, 100)(86, 93)(87, 102)(88, 101)(89, 97)(90, 104)(109, 120)(110, 125)(111, 118)(112, 122)(113, 117)(114, 119)(115, 116)(121, 123)(124, 126)

MAP           : A4.1507
NOTES         : type I, chiral, isomorphic to A4.1506.
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)   : <18, 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.1 * x.4 * x.3, x.3^-1 * x.1 * x.4^-1, x.4 * x.5^-1 * x.2, x.5 * x.2 * x.5^-1 * x.1, x.2 * x.3 * x.5 * x.1 >
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        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 23)(2, 36)(3, 26)(4, 19)(5, 22)(6, 21)(7, 29)(8, 24)(9, 32)(10, 25)(11, 28)(12, 27)(13, 35)(14, 30)(15, 20)(16, 31)(17, 34)(18, 33)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 141)(56, 130)(57, 139)(58, 144)(59, 128)(60, 142)(61, 138)(62, 143)(63, 136)(64, 140)(65, 135)(66, 137)(67, 134)(68, 133)(69, 131)(70, 129)(71, 132)(72, 127)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 91)(80, 92)(81, 93)(82, 94)(83, 95)(84, 96)(85, 97)(86, 98)(87, 99)(88, 100)(89, 101)(90, 102)(109, 120)(110, 125)(111, 118)(112, 122)(113, 117)(114, 119)(115, 116)(121, 123)(124, 126)

MAP           : A4.1508
NOTES         : type I, chiral, isomorphic to A4.1506.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.4 * x.5 * x.4, x.3^3, x.3^-1 * x.1 * x.4^-1, x.5^3, x.4 * x.5^-1 * x.2, x.4 * x.2 * x.5^-1, (x.3^-1, x.5^-1), x.5^-1 * x.3^-1 * x.1 * x.2, x.3 * x.1 * x.3^-1 * x.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        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 140)(56, 139)(57, 137)(58, 135)(59, 138)(60, 133)(61, 129)(62, 136)(63, 127)(64, 132)(65, 134)(66, 130)(67, 144)(68, 131)(69, 142)(70, 128)(71, 141)(72, 143)(73, 94)(74, 105)(75, 96)(76, 95)(77, 91)(78, 98)(79, 100)(80, 93)(81, 102)(82, 101)(83, 97)(84, 104)(85, 106)(86, 99)(87, 108)(88, 107)(89, 103)(90, 92)(109, 120)(110, 125)(111, 118)(112, 122)(113, 117)(114, 119)(115, 116)(121, 123)(124, 126)

MAP           : A4.1509
NOTES         : type I, chiral, isomorphic to A4.1506.
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)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.4 * x.5 * x.4, x.3^3, x.3^-1 * x.1 * x.4^-1, x.5^3, x.4 * x.5^-1 * x.2, x.4 * x.2 * x.5^-1, (x.3^-1, x.5^-1), x.5^-1 * x.3^-1 * x.1 * x.2, x.3 * x.1 * x.3^-1 * x.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        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(13, 25)(14, 26)(15, 27)(16, 28)(17, 29)(18, 30)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 134)(56, 133)(57, 131)(58, 129)(59, 132)(60, 127)(61, 141)(62, 130)(63, 139)(64, 144)(65, 128)(66, 142)(67, 138)(68, 143)(69, 136)(70, 140)(71, 135)(72, 137)(73, 95)(74, 108)(75, 98)(76, 91)(77, 94)(78, 93)(79, 101)(80, 96)(81, 104)(82, 97)(83, 100)(84, 99)(85, 107)(86, 102)(87, 92)(88, 103)(89, 106)(90, 105)(109, 111)(110, 118)(112, 114)(113, 116)(115, 126)(117, 124)(119, 123)(120, 125)(121, 122)

MAP           : A4.1510
NOTES         : type I, chiral, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 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.5^-1, x.3^3, x.4^3, x.5^3, x.5 * x.3^-1 * x.4, x.3^-1 * x.1 * x.2, x.5 * x.1 * x.5^-1 * x.2, x.4 * x.1 * x.4^-1 * x.1 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 100)(2, 93)(3, 102)(4, 101)(5, 97)(6, 104)(7, 106)(8, 99)(9, 108)(10, 107)(11, 103)(12, 92)(13, 94)(14, 105)(15, 96)(16, 95)(17, 91)(18, 98)(19, 40)(20, 51)(21, 42)(22, 41)(23, 37)(24, 44)(25, 46)(26, 39)(27, 48)(28, 47)(29, 43)(30, 50)(31, 52)(32, 45)(33, 54)(34, 53)(35, 49)(36, 38)(55, 79)(56, 80)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67, 73)(68, 74)(69, 75)(70, 76)(71, 77)(72, 78)(109, 110)(111, 125)(112, 123)(113, 126)(114, 121)(115, 117)(116, 124)(118, 120)(119, 122)(127, 138)(128, 143)(129, 136)(130, 140)(131, 135)(132, 137)(133, 134)(139, 141)(142, 144)

MAP           : A4.1511
NOTES         : type I, chiral, isomorphic to A4.1510.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 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.5^-1, x.3^3, x.4^3, x.5^3, x.5 * x.3^-1 * x.4, x.3^-1 * x.1 * x.2, x.5 * x.1 * x.5^-1 * x.2, x.4 * x.1 * x.4^-1 * x.1 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 100)(2, 93)(3, 102)(4, 101)(5, 97)(6, 104)(7, 106)(8, 99)(9, 108)(10, 107)(11, 103)(12, 92)(13, 94)(14, 105)(15, 96)(16, 95)(17, 91)(18, 98)(19, 41)(20, 54)(21, 44)(22, 37)(23, 40)(24, 39)(25, 47)(26, 42)(27, 50)(28, 43)(29, 46)(30, 45)(31, 53)(32, 48)(33, 38)(34, 49)(35, 52)(36, 51)(55, 83)(56, 78)(57, 86)(58, 79)(59, 82)(60, 81)(61, 89)(62, 84)(63, 74)(64, 85)(65, 88)(66, 87)(67, 77)(68, 90)(69, 80)(70, 73)(71, 76)(72, 75)(109, 110)(111, 125)(112, 123)(113, 126)(114, 121)(115, 117)(116, 124)(118, 120)(119, 122)(127, 138)(128, 143)(129, 136)(130, 140)(131, 135)(132, 137)(133, 134)(139, 141)(142, 144)

MAP           : A4.1512
NOTES         : type I, chiral, isomorphic to A4.1510.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.5 * x.4 * x.3^-1, x.3^3, x.3^-1 * x.1 * x.2, x.3 * x.5^-1 * x.4^-1, x.4^3, x.5^3, x.5 * x.2 * x.5^-1 * x.2, x.5 * x.1 * x.5^-1 * x.1, x.4 * x.1 * x.4^-1 * x.2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 100)(2, 93)(3, 102)(4, 101)(5, 97)(6, 104)(7, 106)(8, 99)(9, 108)(10, 107)(11, 103)(12, 92)(13, 94)(14, 105)(15, 96)(16, 95)(17, 91)(18, 98)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(25, 49)(26, 50)(27, 51)(28, 52)(29, 53)(30, 54)(31, 37)(32, 38)(33, 39)(34, 40)(35, 41)(36, 42)(55, 76)(56, 87)(57, 78)(58, 77)(59, 73)(60, 80)(61, 82)(62, 75)(63, 84)(64, 83)(65, 79)(66, 86)(67, 88)(68, 81)(69, 90)(70, 89)(71, 85)(72, 74)(109, 110)(111, 125)(112, 123)(113, 126)(114, 121)(115, 117)(116, 124)(118, 120)(119, 122)(127, 138)(128, 143)(129, 136)(130, 140)(131, 135)(132, 137)(133, 134)(139, 141)(142, 144)

MAP           : A4.1513
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 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.5^-1, x.3^3, x.5^3, x.3^-1 * x.1 * x.2, x.4^3, x.5 * x.3^-1 * x.4, x.4 * x.1 * x.5 * x.1 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 100)(2, 93)(3, 102)(4, 101)(5, 97)(6, 104)(7, 106)(8, 99)(9, 108)(10, 107)(11, 103)(12, 92)(13, 94)(14, 105)(15, 96)(16, 95)(17, 91)(18, 98)(19, 52)(20, 45)(21, 54)(22, 53)(23, 49)(24, 38)(25, 40)(26, 51)(27, 42)(28, 41)(29, 37)(30, 44)(31, 46)(32, 39)(33, 48)(34, 47)(35, 43)(36, 50)(55, 85)(56, 86)(57, 87)(58, 88)(59, 89)(60, 90)(61, 73)(62, 74)(63, 75)(64, 76)(65, 77)(66, 78)(67, 79)(68, 80)(69, 81)(70, 82)(71, 83)(72, 84)(109, 110)(111, 125)(112, 123)(113, 126)(114, 121)(115, 117)(116, 124)(118, 120)(119, 122)(127, 138)(128, 143)(129, 136)(130, 140)(131, 135)(132, 137)(133, 134)(139, 141)(142, 144)

MAP           : A4.1514
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 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.5^-1, x.3^3, x.5^3, x.3^-1 * x.1 * x.2, x.4^3, x.5 * x.3^-1 * x.4, x.4 * x.1 * x.5 * x.1 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 100)(2, 93)(3, 102)(4, 101)(5, 97)(6, 104)(7, 106)(8, 99)(9, 108)(10, 107)(11, 103)(12, 92)(13, 94)(14, 105)(15, 96)(16, 95)(17, 91)(18, 98)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)(55, 88)(56, 81)(57, 90)(58, 89)(59, 85)(60, 74)(61, 76)(62, 87)(63, 78)(64, 77)(65, 73)(66, 80)(67, 82)(68, 75)(69, 84)(70, 83)(71, 79)(72, 86)(109, 110)(111, 125)(112, 123)(113, 126)(114, 121)(115, 117)(116, 124)(118, 120)(119, 122)(127, 138)(128, 143)(129, 136)(130, 140)(131, 135)(132, 137)(133, 134)(139, 141)(142, 144)

MAP           : A4.1515
NOTES         : type I, chiral, isomorphic to A4.1510.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.5 * x.4 * x.3^-1, x.3^3, x.3^-1 * x.1 * x.2, x.3 * x.5^-1 * x.4^-1, x.4^3, x.5^3, x.5 * x.2 * x.5^-1 * x.2, x.5 * x.1 * x.5^-1 * x.1, x.4 * x.1 * x.4^-1 * x.2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 100)(2, 93)(3, 102)(4, 101)(5, 97)(6, 104)(7, 106)(8, 99)(9, 108)(10, 107)(11, 103)(12, 92)(13, 94)(14, 105)(15, 96)(16, 95)(17, 91)(18, 98)(19, 47)(20, 42)(21, 50)(22, 43)(23, 46)(24, 45)(25, 53)(26, 48)(27, 38)(28, 49)(29, 52)(30, 51)(31, 41)(32, 54)(33, 44)(34, 37)(35, 40)(36, 39)(55, 77)(56, 90)(57, 80)(58, 73)(59, 76)(60, 75)(61, 83)(62, 78)(63, 86)(64, 79)(65, 82)(66, 81)(67, 89)(68, 84)(69, 74)(70, 85)(71, 88)(72, 87)(109, 110)(111, 125)(112, 123)(113, 126)(114, 121)(115, 117)(116, 124)(118, 120)(119, 122)(127, 138)(128, 143)(129, 136)(130, 140)(131, 135)(132, 137)(133, 134)(139, 141)(142, 144)

MAP           : A4.1516
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 95)(2, 91)(3, 105)(4, 108)(5, 92)(6, 102)(7, 93)(8, 94)(9, 103)(10, 101)(11, 104)(12, 106)(13, 107)(14, 100)(15, 97)(16, 96)(17, 99)(18, 98)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 84)(56, 78)(57, 82)(58, 77)(59, 88)(60, 90)(61, 86)(62, 73)(63, 87)(64, 89)(65, 81)(66, 80)(67, 79)(68, 85)(69, 83)(70, 76)(71, 75)(72, 74)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 133)(128, 129)(130, 137)(131, 141)(132, 143)(134, 140)(135, 142)(136, 144)(138, 139)

MAP           : A4.1517
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 96)(2, 106)(3, 104)(4, 91)(5, 102)(6, 94)(7, 101)(8, 92)(9, 93)(10, 103)(11, 107)(12, 108)(13, 105)(14, 99)(15, 100)(16, 98)(17, 97)(18, 95)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 84)(56, 78)(57, 82)(58, 77)(59, 88)(60, 90)(61, 86)(62, 73)(63, 87)(64, 89)(65, 81)(66, 80)(67, 79)(68, 85)(69, 83)(70, 76)(71, 75)(72, 74)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 135)(128, 139)(129, 130)(131, 143)(132, 140)(133, 144)(134, 141)(136, 142)(137, 138)

MAP           : A4.1518
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 96)(2, 106)(3, 104)(4, 91)(5, 102)(6, 94)(7, 101)(8, 92)(9, 93)(10, 103)(11, 107)(12, 108)(13, 105)(14, 99)(15, 100)(16, 98)(17, 97)(18, 95)(19, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 88)(56, 84)(57, 83)(58, 74)(59, 78)(60, 80)(61, 82)(62, 77)(63, 79)(64, 81)(65, 85)(66, 76)(67, 75)(68, 89)(69, 86)(70, 90)(71, 87)(72, 73)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 135)(128, 139)(129, 130)(131, 143)(132, 140)(133, 144)(134, 141)(136, 142)(137, 138)

MAP           : A4.1519
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 96)(2, 106)(3, 104)(4, 91)(5, 102)(6, 94)(7, 101)(8, 92)(9, 93)(10, 103)(11, 107)(12, 108)(13, 105)(14, 99)(15, 100)(16, 98)(17, 97)(18, 95)(19, 44)(20, 54)(21, 53)(22, 52)(23, 40)(24, 38)(25, 49)(26, 48)(27, 47)(28, 39)(29, 51)(30, 37)(31, 50)(32, 43)(33, 45)(34, 41)(35, 46)(36, 42)(55, 90)(56, 76)(57, 85)(58, 84)(59, 80)(60, 77)(61, 81)(62, 78)(63, 82)(64, 79)(65, 75)(66, 74)(67, 83)(68, 87)(69, 89)(70, 73)(71, 86)(72, 88)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 135)(128, 139)(129, 130)(131, 143)(132, 140)(133, 144)(134, 141)(136, 142)(137, 138)

MAP           : A4.1520
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 96)(2, 106)(3, 104)(4, 91)(5, 102)(6, 94)(7, 101)(8, 92)(9, 93)(10, 103)(11, 107)(12, 108)(13, 105)(14, 99)(15, 100)(16, 98)(17, 97)(18, 95)(19, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 74)(56, 77)(57, 79)(58, 80)(59, 73)(60, 88)(61, 87)(62, 90)(63, 89)(64, 86)(65, 82)(66, 78)(67, 81)(68, 83)(69, 75)(70, 84)(71, 85)(72, 76)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 135)(128, 139)(129, 130)(131, 143)(132, 140)(133, 144)(134, 141)(136, 142)(137, 138)

MAP           : A4.1521
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 96)(2, 106)(3, 104)(4, 91)(5, 102)(6, 94)(7, 101)(8, 92)(9, 93)(10, 103)(11, 107)(12, 108)(13, 105)(14, 99)(15, 100)(16, 98)(17, 97)(18, 95)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 77)(56, 73)(57, 87)(58, 90)(59, 74)(60, 84)(61, 75)(62, 76)(63, 85)(64, 83)(65, 86)(66, 88)(67, 89)(68, 82)(69, 79)(70, 78)(71, 81)(72, 80)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 135)(128, 139)(129, 130)(131, 143)(132, 140)(133, 144)(134, 141)(136, 142)(137, 138)

MAP           : A4.1522
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 96)(2, 106)(3, 104)(4, 91)(5, 102)(6, 94)(7, 101)(8, 92)(9, 93)(10, 103)(11, 107)(12, 108)(13, 105)(14, 99)(15, 100)(16, 98)(17, 97)(18, 95)(19, 54)(20, 40)(21, 49)(22, 48)(23, 44)(24, 41)(25, 45)(26, 42)(27, 46)(28, 43)(29, 39)(30, 38)(31, 47)(32, 51)(33, 53)(34, 37)(35, 50)(36, 52)(55, 80)(56, 90)(57, 89)(58, 88)(59, 76)(60, 74)(61, 85)(62, 84)(63, 83)(64, 75)(65, 87)(66, 73)(67, 86)(68, 79)(69, 81)(70, 77)(71, 82)(72, 78)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 135)(128, 139)(129, 130)(131, 143)(132, 140)(133, 144)(134, 141)(136, 142)(137, 138)

MAP           : A4.1523
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 102)(2, 96)(3, 100)(4, 95)(5, 106)(6, 108)(7, 104)(8, 91)(9, 105)(10, 107)(11, 99)(12, 98)(13, 97)(14, 103)(15, 101)(16, 94)(17, 93)(18, 92)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 88)(56, 84)(57, 83)(58, 74)(59, 78)(60, 80)(61, 82)(62, 77)(63, 79)(64, 81)(65, 85)(66, 76)(67, 75)(68, 89)(69, 86)(70, 90)(71, 87)(72, 73)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 143)(128, 135)(129, 134)(130, 133)(131, 139)(132, 137)(136, 138)(140, 142)(141, 144)

MAP           : A4.1524
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 102)(2, 96)(3, 100)(4, 95)(5, 106)(6, 108)(7, 104)(8, 91)(9, 105)(10, 107)(11, 99)(12, 98)(13, 97)(14, 103)(15, 101)(16, 94)(17, 93)(18, 92)(19, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 78)(56, 88)(57, 86)(58, 73)(59, 84)(60, 76)(61, 83)(62, 74)(63, 75)(64, 85)(65, 89)(66, 90)(67, 87)(68, 81)(69, 82)(70, 80)(71, 79)(72, 77)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 143)(128, 135)(129, 134)(130, 133)(131, 139)(132, 137)(136, 138)(140, 142)(141, 144)

MAP           : A4.1525
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 102)(2, 96)(3, 100)(4, 95)(5, 106)(6, 108)(7, 104)(8, 91)(9, 105)(10, 107)(11, 99)(12, 98)(13, 97)(14, 103)(15, 101)(16, 94)(17, 93)(18, 92)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 90)(56, 76)(57, 85)(58, 84)(59, 80)(60, 77)(61, 81)(62, 78)(63, 82)(64, 79)(65, 75)(66, 74)(67, 83)(68, 87)(69, 89)(70, 73)(71, 86)(72, 88)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 143)(128, 135)(129, 134)(130, 133)(131, 139)(132, 137)(136, 138)(140, 142)(141, 144)

MAP           : A4.1526
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 102)(2, 96)(3, 100)(4, 95)(5, 106)(6, 108)(7, 104)(8, 91)(9, 105)(10, 107)(11, 99)(12, 98)(13, 97)(14, 103)(15, 101)(16, 94)(17, 93)(18, 92)(19, 42)(20, 52)(21, 50)(22, 37)(23, 48)(24, 40)(25, 47)(26, 38)(27, 39)(28, 49)(29, 53)(30, 54)(31, 51)(32, 45)(33, 46)(34, 44)(35, 43)(36, 41)(55, 77)(56, 73)(57, 87)(58, 90)(59, 74)(60, 84)(61, 75)(62, 76)(63, 85)(64, 83)(65, 86)(66, 88)(67, 89)(68, 82)(69, 79)(70, 78)(71, 81)(72, 80)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 143)(128, 135)(129, 134)(130, 133)(131, 139)(132, 137)(136, 138)(140, 142)(141, 144)

MAP           : A4.1527
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 102)(2, 96)(3, 100)(4, 95)(5, 106)(6, 108)(7, 104)(8, 91)(9, 105)(10, 107)(11, 99)(12, 98)(13, 97)(14, 103)(15, 101)(16, 94)(17, 93)(18, 92)(19, 52)(20, 48)(21, 47)(22, 38)(23, 42)(24, 44)(25, 46)(26, 41)(27, 43)(28, 45)(29, 49)(30, 40)(31, 39)(32, 53)(33, 50)(34, 54)(35, 51)(36, 37)(55, 74)(56, 77)(57, 79)(58, 80)(59, 73)(60, 88)(61, 87)(62, 90)(63, 89)(64, 86)(65, 82)(66, 78)(67, 81)(68, 83)(69, 75)(70, 84)(71, 85)(72, 76)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 143)(128, 135)(129, 134)(130, 133)(131, 139)(132, 137)(136, 138)(140, 142)(141, 144)

MAP           : A4.1528
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 102)(2, 96)(3, 100)(4, 95)(5, 106)(6, 108)(7, 104)(8, 91)(9, 105)(10, 107)(11, 99)(12, 98)(13, 97)(14, 103)(15, 101)(16, 94)(17, 93)(18, 92)(19, 54)(20, 40)(21, 49)(22, 48)(23, 44)(24, 41)(25, 45)(26, 42)(27, 46)(28, 43)(29, 39)(30, 38)(31, 47)(32, 51)(33, 53)(34, 37)(35, 50)(36, 52)(55, 76)(56, 80)(57, 81)(58, 78)(59, 90)(60, 73)(61, 89)(62, 88)(63, 86)(64, 87)(65, 79)(66, 77)(67, 82)(68, 75)(69, 85)(70, 74)(71, 83)(72, 84)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 143)(128, 135)(129, 134)(130, 133)(131, 139)(132, 137)(136, 138)(140, 142)(141, 144)

MAP           : A4.1529
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 108)(2, 94)(3, 103)(4, 102)(5, 98)(6, 95)(7, 99)(8, 96)(9, 100)(10, 97)(11, 93)(12, 92)(13, 101)(14, 105)(15, 107)(16, 91)(17, 104)(18, 106)(19, 38)(20, 41)(21, 43)(22, 44)(23, 37)(24, 52)(25, 51)(26, 54)(27, 53)(28, 50)(29, 46)(30, 42)(31, 45)(32, 47)(33, 39)(34, 48)(35, 49)(36, 40)(55, 80)(56, 90)(57, 89)(58, 88)(59, 76)(60, 74)(61, 85)(62, 84)(63, 83)(64, 75)(65, 87)(66, 73)(67, 86)(68, 79)(69, 81)(70, 77)(71, 82)(72, 78)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 137)(128, 140)(129, 142)(130, 143)(131, 136)(132, 133)(134, 135)(138, 141)(139, 144)

MAP           : A4.1530
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 108)(2, 94)(3, 103)(4, 102)(5, 98)(6, 95)(7, 99)(8, 96)(9, 100)(10, 97)(11, 93)(12, 92)(13, 101)(14, 105)(15, 107)(16, 91)(17, 104)(18, 106)(19, 41)(20, 37)(21, 51)(22, 54)(23, 38)(24, 48)(25, 39)(26, 40)(27, 49)(28, 47)(29, 50)(30, 52)(31, 53)(32, 46)(33, 43)(34, 42)(35, 45)(36, 44)(55, 76)(56, 80)(57, 81)(58, 78)(59, 90)(60, 73)(61, 89)(62, 88)(63, 86)(64, 87)(65, 79)(66, 77)(67, 82)(68, 75)(69, 85)(70, 74)(71, 83)(72, 84)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 137)(128, 140)(129, 142)(130, 143)(131, 136)(132, 133)(134, 135)(138, 141)(139, 144)

MAP           : A4.1531
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 108)(2, 94)(3, 103)(4, 102)(5, 98)(6, 95)(7, 99)(8, 96)(9, 100)(10, 97)(11, 93)(12, 92)(13, 101)(14, 105)(15, 107)(16, 91)(17, 104)(18, 106)(19, 40)(20, 44)(21, 45)(22, 42)(23, 54)(24, 37)(25, 53)(26, 52)(27, 50)(28, 51)(29, 43)(30, 41)(31, 46)(32, 39)(33, 49)(34, 38)(35, 47)(36, 48)(55, 77)(56, 73)(57, 87)(58, 90)(59, 74)(60, 84)(61, 75)(62, 76)(63, 85)(64, 83)(65, 86)(66, 88)(67, 89)(68, 82)(69, 79)(70, 78)(71, 81)(72, 80)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 137)(128, 140)(129, 142)(130, 143)(131, 136)(132, 133)(134, 135)(138, 141)(139, 144)

MAP           : A4.1532
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 108)(2, 94)(3, 103)(4, 102)(5, 98)(6, 95)(7, 99)(8, 96)(9, 100)(10, 97)(11, 93)(12, 92)(13, 101)(14, 105)(15, 107)(16, 91)(17, 104)(18, 106)(19, 42)(20, 52)(21, 50)(22, 37)(23, 48)(24, 40)(25, 47)(26, 38)(27, 39)(28, 49)(29, 53)(30, 54)(31, 51)(32, 45)(33, 46)(34, 44)(35, 43)(36, 41)(55, 84)(56, 78)(57, 82)(58, 77)(59, 88)(60, 90)(61, 86)(62, 73)(63, 87)(64, 89)(65, 81)(66, 80)(67, 79)(68, 85)(69, 83)(70, 76)(71, 75)(72, 74)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 137)(128, 140)(129, 142)(130, 143)(131, 136)(132, 133)(134, 135)(138, 141)(139, 144)

MAP           : A4.1533
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 108)(2, 94)(3, 103)(4, 102)(5, 98)(6, 95)(7, 99)(8, 96)(9, 100)(10, 97)(11, 93)(12, 92)(13, 101)(14, 105)(15, 107)(16, 91)(17, 104)(18, 106)(19, 44)(20, 54)(21, 53)(22, 52)(23, 40)(24, 38)(25, 49)(26, 48)(27, 47)(28, 39)(29, 51)(30, 37)(31, 50)(32, 43)(33, 45)(34, 41)(35, 46)(36, 42)(55, 74)(56, 77)(57, 79)(58, 80)(59, 73)(60, 88)(61, 87)(62, 90)(63, 89)(64, 86)(65, 82)(66, 78)(67, 81)(68, 83)(69, 75)(70, 84)(71, 85)(72, 76)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 137)(128, 140)(129, 142)(130, 143)(131, 136)(132, 133)(134, 135)(138, 141)(139, 144)

MAP           : A4.1534
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 6)(2, 3)(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.5^-1, u.4^3, u.5^3, u.3^-1 * u.1 * u.2 >
CTG (small)   : <18, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2^2, x.3 * x.4^-1 * x.5^-1, x.3^3, x.4^3, x.5^3, x.3^-1 * x.1 * x.2, x.5 * x.3^-1 * x.4, (x.4 * x.1)^2, (x.5 * x.1)^2 >
SCHREIER VEC. : (x.3, x.4, x.4^-1, x.5, x.5^-1, x.3^-1, x.1, x.2)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 108)(2, 94)(3, 103)(4, 102)(5, 98)(6, 95)(7, 99)(8, 96)(9, 100)(10, 97)(11, 93)(12, 92)(13, 101)(14, 105)(15, 107)(16, 91)(17, 104)(18, 106)(19, 48)(20, 42)(21, 46)(22, 41)(23, 52)(24, 54)(25, 50)(26, 37)(27, 51)(28, 53)(29, 45)(30, 44)(31, 43)(32, 49)(33, 47)(34, 40)(35, 39)(36, 38)(55, 78)(56, 88)(57, 86)(58, 73)(59, 84)(60, 76)(61, 83)(62, 74)(63, 75)(64, 85)(65, 89)(66, 90)(67, 87)(68, 81)(69, 82)(70, 80)(71, 79)(72, 77)(109, 111)(110, 123)(112, 122)(113, 115)(114, 117)(116, 118)(119, 126)(120, 125)(121, 124)(127, 137)(128, 140)(129, 142)(130, 143)(131, 136)(132, 133)(134, 135)(138, 141)(139, 144)

MAP           : A4.1535
NOTES         : type I, chiral, isomorphic to A4.1506.
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)   : <18, 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.3^3, x.5^3, x.4 * x.1 * x.5^-1, x.3 * x.2 * x.4^-1, x.5 * x.3^-1 * x.1 * x.2, x.5 * x.2 * x.5^-1 * x.1, x.3^-1 * x.5^-1 * x.4^-1 * x.1 >
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        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 130)(2, 141)(3, 132)(4, 131)(5, 127)(6, 134)(7, 136)(8, 129)(9, 138)(10, 137)(11, 133)(12, 140)(13, 142)(14, 135)(15, 144)(16, 143)(17, 139)(18, 128)(19, 96)(20, 101)(21, 94)(22, 98)(23, 93)(24, 95)(25, 92)(26, 91)(27, 107)(28, 105)(29, 108)(30, 103)(31, 99)(32, 106)(33, 97)(34, 102)(35, 104)(36, 100)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 83)(56, 78)(57, 86)(58, 79)(59, 82)(60, 81)(61, 89)(62, 84)(63, 74)(64, 85)(65, 88)(66, 87)(67, 77)(68, 90)(69, 80)(70, 73)(71, 76)(72, 75)(109, 111)(110, 118)(112, 114)(113, 116)(115, 126)(117, 124)(119, 123)(120, 125)(121, 122)

MAP           : A4.1536
NOTES         : type I, chiral, isomorphic to A4.1506.
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)   : <18, 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.4^2 * x.5, x.1 * x.4 * x.5^-1, x.3^-1 * x.5 * x.2 * x.1, x.3^-1 * x.1 * x.3 * x.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        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 139)(2, 140)(3, 141)(4, 142)(5, 143)(6, 144)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 105)(20, 94)(21, 103)(22, 108)(23, 92)(24, 106)(25, 102)(26, 107)(27, 100)(28, 104)(29, 99)(30, 101)(31, 98)(32, 97)(33, 95)(34, 93)(35, 96)(36, 91)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 76)(56, 87)(57, 78)(58, 77)(59, 73)(60, 80)(61, 82)(62, 75)(63, 84)(64, 83)(65, 79)(66, 86)(67, 88)(68, 81)(69, 90)(70, 89)(71, 85)(72, 74)(109, 120)(110, 125)(111, 118)(112, 122)(113, 117)(114, 119)(115, 116)(121, 123)(124, 126)

MAP           : A4.1537
NOTES         : type I, chiral, isomorphic to A4.1506.
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)   : <18, 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.3^3, x.5^3, x.4 * x.1 * x.5^-1, x.3 * x.2 * x.4^-1, x.5 * x.3^-1 * x.1 * x.2, x.5 * x.2 * x.5^-1 * x.1, x.3^-1 * x.5^-1 * x.4^-1 * x.1 >
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        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 131)(2, 144)(3, 134)(4, 127)(5, 130)(6, 129)(7, 137)(8, 132)(9, 140)(10, 133)(11, 136)(12, 135)(13, 143)(14, 138)(15, 128)(16, 139)(17, 142)(18, 141)(19, 98)(20, 97)(21, 95)(22, 93)(23, 96)(24, 91)(25, 105)(26, 94)(27, 103)(28, 108)(29, 92)(30, 106)(31, 102)(32, 107)(33, 100)(34, 104)(35, 99)(36, 101)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 79)(56, 80)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67, 73)(68, 74)(69, 75)(70, 76)(71, 77)(72, 78)(109, 111)(110, 118)(112, 114)(113, 116)(115, 126)(117, 124)(119, 123)(120, 125)(121, 122)

MAP           : A4.1538
NOTES         : type I, chiral, isomorphic to A4.1506.
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)   : <18, 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.4^2 * x.5, x.1 * x.4 * x.5^-1, x.3^-1 * x.5 * x.2 * x.1, x.3^-1 * x.1 * x.3 * x.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        : 144
R = (1, 19, 37, 55, 73, 91, 109, 127)(2, 20, 38, 56, 74, 92, 110, 128)(3, 21, 39, 57, 75, 93, 111, 129)(4, 22, 40, 58, 76, 94, 112, 130)(5, 23, 41, 59, 77, 95, 113, 131)(6, 24, 42, 60, 78, 96, 114, 132)(7, 25, 43, 61, 79, 97, 115, 133)(8, 26, 44, 62, 80, 98, 116, 134)(9, 27, 45, 63, 81, 99, 117, 135)(10, 28, 46, 64, 82, 100, 118, 136)(11, 29, 47, 65, 83, 101, 119, 137)(12, 30, 48, 66, 84, 102, 120, 138)(13, 31, 49, 67, 85, 103, 121, 139)(14, 32, 50, 68, 86, 104, 122, 140)(15, 33, 51, 69, 87, 105, 123, 141)(16, 34, 52, 70, 88, 106, 124, 142)(17, 35, 53, 71, 89, 107, 125, 143)(18, 36, 54, 72, 90, 108, 126, 144)
L = (1, 142)(2, 135)(3, 144)(4, 143)(5, 139)(6, 128)(7, 130)(8, 141)(9, 132)(10, 131)(11, 127)(12, 134)(13, 136)(14, 129)(15, 138)(16, 137)(17, 133)(18, 140)(19, 108)(20, 95)(21, 106)(22, 92)(23, 105)(24, 107)(25, 104)(26, 103)(27, 101)(28, 99)(29, 102)(30, 97)(31, 93)(32, 100)(33, 91)(34, 96)(35, 98)(36, 94)(37, 38)(39, 53)(40, 51)(41, 54)(42, 49)(43, 45)(44, 52)(46, 48)(47, 50)(55, 77)(56, 90)(57, 80)(58, 73)(59, 76)(60, 75)(61, 83)(62, 78)(63, 86)(64, 79)(65, 82)(66, 81)(67, 89)(68, 84)(69, 74)(70, 85)(71, 88)(72, 87)(109, 120)(110, 125)(111, 118)(112, 122)(113, 117)(114, 119)(115, 116)(121, 123)(124, 126)

MAP           : A4.1539
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1540
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1541
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1542
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1543
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1544
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1545
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1546
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1547
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1548
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1549
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1550
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1551
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1552
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1553
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1554
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1555
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1556
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 83)(11, 86)(12, 85)(13, 89)(14, 82)(15, 90)(16, 87)(17, 84)(18, 88)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 104)(92, 100)(93, 107)(94, 102)(95, 101)(96, 106)(97, 108)(98, 103)(99, 105)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1557
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1558
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1559
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1560
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1561
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1562
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1563
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1564
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1565
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1566
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1567
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1568
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1569
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1570
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1571
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1572
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1573
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1574
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 86)(11, 82)(12, 89)(13, 84)(14, 83)(15, 88)(16, 90)(17, 85)(18, 87)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 101)(92, 104)(93, 103)(94, 107)(95, 100)(96, 108)(97, 105)(98, 102)(99, 106)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1575
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1576
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1577
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1578
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1579
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1580
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1581
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1582
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1583
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1584
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1585
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1586
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1587
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1588
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1589
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1590
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1591
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1592
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 84)(11, 85)(12, 87)(13, 90)(14, 89)(15, 82)(16, 86)(17, 88)(18, 83)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 105)(92, 108)(93, 100)(94, 101)(95, 106)(96, 102)(97, 107)(98, 104)(99, 103)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1593
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1594
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1595
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1596
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1597
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1598
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1599
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1600
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1601
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1602
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1603
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1604
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1605
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1606
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1607
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1608
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1609
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1610
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 87)(11, 90)(12, 82)(13, 83)(14, 88)(15, 84)(16, 89)(17, 86)(18, 85)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 102)(92, 103)(93, 105)(94, 108)(95, 107)(96, 100)(97, 104)(98, 106)(99, 101)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1611
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1612
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1613
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1614
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1615
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1616
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1617
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1618
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1619
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1620
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1621
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1622
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1623
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1624
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1625
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1626
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1627
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1628
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 85)(11, 89)(12, 90)(13, 88)(14, 84)(15, 83)(16, 82)(17, 87)(18, 86)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 106)(92, 105)(93, 104)(94, 100)(95, 108)(96, 107)(97, 103)(98, 101)(99, 102)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1629
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1630
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1631
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 81)(38, 79)(39, 74)(40, 77)(41, 78)(42, 76)(43, 75)(44, 73)(45, 80)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1632
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1633
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1634
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1635
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1636
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1637
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 80)(38, 75)(39, 79)(40, 78)(41, 76)(42, 77)(43, 74)(44, 81)(45, 73)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1638
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1639
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1640
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1641
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1642
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1643
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 35)(20, 30)(21, 34)(22, 33)(23, 31)(24, 32)(25, 29)(26, 36)(27, 28)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1644
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 144)(65, 142)(66, 137)(67, 140)(68, 141)(69, 139)(70, 138)(71, 136)(72, 143)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 135)(119, 133)(120, 128)(121, 131)(122, 132)(123, 130)(124, 129)(125, 127)(126, 134)

MAP           : A4.1645
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1646
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 88)(11, 87)(12, 86)(13, 82)(14, 90)(15, 89)(16, 85)(17, 83)(18, 84)(19, 36)(20, 34)(21, 29)(22, 32)(23, 33)(24, 31)(25, 30)(26, 28)(27, 35)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 143)(65, 138)(66, 142)(67, 141)(68, 139)(69, 140)(70, 137)(71, 144)(72, 136)(91, 103)(92, 107)(93, 108)(94, 106)(95, 102)(96, 101)(97, 100)(98, 105)(99, 104)(118, 134)(119, 129)(120, 133)(121, 132)(122, 130)(123, 131)(124, 128)(125, 135)(126, 127)

MAP           : A4.1647
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1648
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1649
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1650
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1651
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1652
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1653
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1654
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1655
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1656
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1657
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1658
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1659
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1660
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1661
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1662
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1663
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1664
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 89)(11, 84)(12, 88)(13, 87)(14, 85)(15, 86)(16, 83)(17, 90)(18, 82)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 108)(92, 106)(93, 101)(94, 104)(95, 105)(96, 103)(97, 102)(98, 100)(99, 107)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1665
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 61)(47, 60)(48, 59)(49, 55)(50, 63)(51, 62)(52, 58)(53, 56)(54, 57)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1666
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1667
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 29)(20, 32)(21, 31)(22, 35)(23, 28)(24, 36)(25, 33)(26, 30)(27, 34)(37, 78)(38, 81)(39, 73)(40, 74)(41, 79)(42, 75)(43, 80)(44, 77)(45, 76)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1668
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 60)(47, 63)(48, 55)(49, 56)(50, 61)(51, 57)(52, 62)(53, 59)(54, 58)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1669
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1670
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 32)(20, 28)(21, 35)(22, 30)(23, 29)(24, 34)(25, 36)(26, 31)(27, 33)(37, 79)(38, 78)(39, 77)(40, 73)(41, 81)(42, 80)(43, 76)(44, 74)(45, 75)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1671
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 56)(47, 59)(48, 58)(49, 62)(50, 55)(51, 63)(52, 60)(53, 57)(54, 61)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1672
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 140)(65, 136)(66, 143)(67, 138)(68, 137)(69, 142)(70, 144)(71, 139)(72, 141)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 131)(119, 127)(120, 134)(121, 129)(122, 128)(123, 133)(124, 135)(125, 130)(126, 132)

MAP           : A4.1673
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 30)(20, 31)(21, 33)(22, 36)(23, 35)(24, 28)(25, 32)(26, 34)(27, 29)(37, 76)(38, 80)(39, 81)(40, 79)(41, 75)(42, 74)(43, 73)(44, 78)(45, 77)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1674
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 58)(47, 62)(48, 63)(49, 61)(50, 57)(51, 56)(52, 55)(53, 60)(54, 59)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1675
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1676
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 33)(20, 36)(21, 28)(22, 29)(23, 34)(24, 30)(25, 35)(26, 32)(27, 31)(37, 74)(38, 77)(39, 76)(40, 80)(41, 73)(42, 81)(43, 78)(44, 75)(45, 79)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 138)(65, 139)(66, 141)(67, 144)(68, 143)(69, 136)(70, 140)(71, 142)(72, 137)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 129)(119, 130)(120, 132)(121, 135)(122, 134)(123, 127)(124, 131)(125, 133)(126, 128)

MAP           : A4.1677
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 59)(47, 55)(48, 62)(49, 57)(50, 56)(51, 61)(52, 63)(53, 58)(54, 60)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1678
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 137)(65, 140)(66, 139)(67, 143)(68, 136)(69, 144)(70, 141)(71, 138)(72, 142)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 128)(119, 131)(120, 130)(121, 134)(122, 127)(123, 135)(124, 132)(125, 129)(126, 133)

MAP           : A4.1679
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 31)(20, 35)(21, 36)(22, 34)(23, 30)(24, 29)(25, 28)(26, 33)(27, 32)(37, 75)(38, 76)(39, 78)(40, 81)(41, 80)(42, 73)(43, 77)(44, 79)(45, 74)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1680
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.6^-1 * x.3, x.6 * x.1^-1 * x.8^-1, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.7^3, x.3^3, x.3 * x.4^-1 * x.5, x.2 * x.4 * x.5, x.8^3, x.1 * x.2^-1 * x.7^-1, x.2 * x.5 * x.4, x.2 * x.4^-1 * x.3^-1, x.2 * x.3 * x.5^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 57)(47, 58)(48, 60)(49, 63)(50, 62)(51, 55)(52, 59)(53, 61)(54, 56)(64, 142)(65, 141)(66, 140)(67, 136)(68, 144)(69, 143)(70, 139)(71, 137)(72, 138)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 133)(119, 132)(120, 131)(121, 127)(122, 135)(123, 134)(124, 130)(125, 128)(126, 129)

MAP           : A4.1681
NOTES         : type II, reflexible, isomorphic to A4.1493.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.7 * x.5^-1, x.5^-1 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.7^3, x.4 * x.5^-1 * x.6^-1, x.8^3, x.3^3, x.5^3, x.3 * x.4^-1 * x.6^-1, x.2 * x.4^-1 * x.3^-1, x.1 * x.2^-1 * x.7^-1, x.2 * x.3^-1 * x.4^-1, x.2 * x.3 * x.6, x.2 * x.6 * x.3, x.2 * x.4 * x.6^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 62)(47, 57)(48, 61)(49, 60)(50, 58)(51, 59)(52, 56)(53, 63)(54, 55)(64, 141)(65, 144)(66, 136)(67, 137)(68, 142)(69, 138)(70, 143)(71, 140)(72, 139)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 132)(119, 135)(120, 127)(121, 128)(122, 133)(123, 129)(124, 134)(125, 131)(126, 130)

MAP           : A4.1682
NOTES         : type I, reflexible, isomorphic to A4.1496.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 13)(2, 10)(3, 4)(5, 9)(6, 7)(8, 16)(11, 12)(14, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 3, 3, 1, 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.8, u.4, u.5, u.6, u.7 | u.1, u.6 * u.1^-1 * u.8^-1, u.3^3, u.5^3, u.7^3, u.8^3, u.1 * u.2^-1 * u.7^-1, u.2 * u.3^-1 * u.4^-1, u.4 * u.5^-1 * u.6^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.1, x.5^-1 * x.7^-1, x.3^-1 * x.6^-1, x.5 * x.2^-1, x.6 * x.1^-1 * x.8^-1, x.3^3, x.5^3, x.7^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5^-1 * x.6^-1, x.8^3, x.1 * x.2^-1 * x.7^-1, x.4 * x.5 * x.3^-1 * x.4, x.3 * x.5 * x.3^-1 * x.2^-1 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.5, x.5^-1, x.6)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 90)(11, 88)(12, 83)(13, 86)(14, 87)(15, 85)(16, 84)(17, 82)(18, 89)(19, 34)(20, 33)(21, 32)(22, 28)(23, 36)(24, 35)(25, 31)(26, 29)(27, 30)(37, 77)(38, 73)(39, 80)(40, 75)(41, 74)(42, 79)(43, 81)(44, 76)(45, 78)(46, 63)(47, 61)(48, 56)(49, 59)(50, 60)(51, 58)(52, 57)(53, 55)(54, 62)(64, 139)(65, 143)(66, 144)(67, 142)(68, 138)(69, 137)(70, 136)(71, 141)(72, 140)(91, 107)(92, 102)(93, 106)(94, 105)(95, 103)(96, 104)(97, 101)(98, 108)(99, 100)(118, 130)(119, 134)(120, 135)(121, 133)(122, 129)(123, 128)(124, 127)(125, 132)(126, 131)

MAP           : A4.1683
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1684
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1685
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1686
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1687
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1688
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1689
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1690
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1691
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1692
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1693
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1694
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1695
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1696
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1697
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1698
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1699
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1700
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1701
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1702
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1703
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1704
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1705
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1706
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 11)(2, 14)(3, 13)(4, 17)(5, 10)(6, 18)(7, 15)(8, 12)(9, 16)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1707
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1708
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1709
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1710
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1711
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1712
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1713
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1714
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1715
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1716
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1717
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1718
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1719
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1720
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1721
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1722
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1723
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1724
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1725
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1726
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1727
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1728
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1729
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1730
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 14)(2, 10)(3, 17)(4, 12)(5, 11)(6, 16)(7, 18)(8, 13)(9, 15)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1731
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1732
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1733
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1734
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1735
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1736
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1737
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1738
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1739
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1740
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1741
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1742
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1743
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1744
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1745
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1746
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1747
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1748
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1749
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1750
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1751
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1752
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1753
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1754
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 12)(2, 13)(3, 15)(4, 18)(5, 17)(6, 10)(7, 14)(8, 16)(9, 11)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1755
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1756
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1757
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1758
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1759
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1760
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1761
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1762
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1763
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1764
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1765
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1766
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1767
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1768
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1769
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1770
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1771
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1772
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1773
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1774
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1775
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1776
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1777
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1778
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 15)(2, 18)(3, 10)(4, 11)(5, 16)(6, 12)(7, 17)(8, 14)(9, 13)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1779
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1780
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1781
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1782
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1783
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1784
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1785
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1786
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1787
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1788
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1789
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1790
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1791
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1792
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1793
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1794
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1795
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1796
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1797
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1798
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1799
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1800
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1801
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1802
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 13)(2, 17)(3, 18)(4, 16)(5, 12)(6, 11)(7, 10)(8, 15)(9, 14)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1803
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1804
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1805
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1806
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1807
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1808
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1809
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1810
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 71)(56, 66)(57, 70)(58, 69)(59, 67)(60, 68)(61, 65)(62, 72)(63, 64)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1811
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1812
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1813
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1814
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1815
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1816
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1817
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1818
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 72)(56, 70)(57, 65)(58, 68)(59, 69)(60, 67)(61, 66)(62, 64)(63, 71)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1819
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1820
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1821
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1822
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 53)(20, 48)(21, 52)(22, 51)(23, 49)(24, 50)(25, 47)(26, 54)(27, 46)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 126)(38, 124)(39, 119)(40, 122)(41, 123)(42, 121)(43, 120)(44, 118)(45, 125)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 135)(101, 133)(102, 128)(103, 131)(104, 132)(105, 130)(106, 129)(107, 127)(108, 134)

MAP           : A4.1823
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1824
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1825
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1826
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 16)(2, 15)(3, 14)(4, 10)(5, 18)(6, 17)(7, 13)(8, 11)(9, 12)(19, 54)(20, 52)(21, 47)(22, 50)(23, 51)(24, 49)(25, 48)(26, 46)(27, 53)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 125)(38, 120)(39, 124)(40, 123)(41, 121)(42, 122)(43, 119)(44, 126)(45, 118)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 134)(101, 129)(102, 133)(103, 132)(104, 130)(105, 131)(106, 128)(107, 135)(108, 127)

MAP           : A4.1827
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1828
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1829
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1830
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1831
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1832
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1833
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1834
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1835
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1836
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1837
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1838
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1839
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1840
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1841
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1842
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1843
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1844
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1845
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1846
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1847
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 99)(83, 97)(84, 92)(85, 95)(86, 96)(87, 94)(88, 93)(89, 91)(90, 98)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1848
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1849
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 17)(2, 12)(3, 16)(4, 15)(5, 13)(6, 14)(7, 11)(8, 18)(9, 10)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1850
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 140)(74, 136)(75, 143)(76, 138)(77, 137)(78, 142)(79, 144)(80, 139)(81, 141)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1851
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1852
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1853
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1854
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 47)(20, 50)(21, 49)(22, 53)(23, 46)(24, 54)(25, 51)(26, 48)(27, 52)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 122)(38, 118)(39, 125)(40, 120)(41, 119)(42, 124)(43, 126)(44, 121)(45, 123)(55, 67)(56, 71)(57, 72)(58, 70)(59, 66)(60, 65)(61, 64)(62, 69)(63, 68)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 131)(101, 127)(102, 134)(103, 129)(104, 128)(105, 133)(106, 135)(107, 130)(108, 132)

MAP           : A4.1855
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 138)(74, 139)(75, 141)(76, 144)(77, 143)(78, 136)(79, 140)(80, 142)(81, 137)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1856
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 139)(74, 143)(75, 144)(76, 142)(77, 138)(78, 137)(79, 136)(80, 141)(81, 140)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1857
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 50)(20, 46)(21, 53)(22, 48)(23, 47)(24, 52)(25, 54)(26, 49)(27, 51)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 119)(38, 122)(39, 121)(40, 125)(41, 118)(42, 126)(43, 123)(44, 120)(45, 124)(55, 66)(56, 67)(57, 69)(58, 72)(59, 71)(60, 64)(61, 68)(62, 70)(63, 65)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 94)(83, 98)(84, 99)(85, 97)(86, 93)(87, 92)(88, 91)(89, 96)(90, 95)(100, 128)(101, 131)(102, 130)(103, 134)(104, 127)(105, 135)(106, 132)(107, 129)(108, 133)

MAP           : A4.1858
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 137)(74, 140)(75, 139)(76, 143)(77, 136)(78, 144)(79, 141)(80, 138)(81, 142)(82, 96)(83, 99)(84, 91)(85, 92)(86, 97)(87, 93)(88, 98)(89, 95)(90, 94)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1859
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 141)(74, 144)(75, 136)(76, 137)(77, 142)(78, 138)(79, 143)(80, 140)(81, 139)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1860
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.5, x.2 * x.3^-1 * x.4, x.5^3, x.1 * x.5^-1 * x.6^-1, x.7^3, x.6^3, x.1^3, x.1 * x.2 * x.5, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.7 * x.4^-1, x.1 * x.4 * x.6, x.1 * x.6 * x.2^-1, x.2^2 * x.4^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1861
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 97)(83, 96)(84, 95)(85, 91)(86, 99)(87, 98)(88, 94)(89, 92)(90, 93)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1862
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 48)(20, 49)(21, 51)(22, 54)(23, 53)(24, 46)(25, 50)(26, 52)(27, 47)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 123)(38, 126)(39, 118)(40, 119)(41, 124)(42, 120)(43, 125)(44, 122)(45, 121)(55, 68)(56, 64)(57, 71)(58, 66)(59, 65)(60, 70)(61, 72)(62, 67)(63, 69)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 132)(101, 135)(102, 127)(103, 128)(104, 133)(105, 129)(106, 134)(107, 131)(108, 130)

MAP           : A4.1863
NOTES         : type I, reflexible, isomorphic to A4.1495.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.7^-1 * x.1^-1, x.6^-1 * x.5, x.2 * x.3^-1 * x.4, x.1^3, x.5^3, x.7^3, x.1^-1 * x.2^-1 * x.5^-1, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6^3, x.1 * x.6 * x.4^-1, x.6 * x.7^-1 * x.8^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 142)(74, 141)(75, 140)(76, 136)(77, 144)(78, 143)(79, 139)(80, 137)(81, 138)(82, 98)(83, 93)(84, 97)(85, 96)(86, 94)(87, 95)(88, 92)(89, 99)(90, 91)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1864
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 51)(20, 54)(21, 46)(22, 47)(23, 52)(24, 48)(25, 53)(26, 50)(27, 49)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 120)(38, 121)(39, 123)(40, 126)(41, 125)(42, 118)(43, 122)(44, 124)(45, 119)(55, 70)(56, 69)(57, 68)(58, 64)(59, 72)(60, 71)(61, 67)(62, 65)(63, 66)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 129)(101, 130)(102, 132)(103, 135)(104, 134)(105, 127)(106, 131)(107, 133)(108, 128)

MAP           : A4.1865
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 49)(20, 53)(21, 54)(22, 52)(23, 48)(24, 47)(25, 46)(26, 51)(27, 50)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 124)(38, 123)(39, 122)(40, 118)(41, 126)(42, 125)(43, 121)(44, 119)(45, 120)(55, 65)(56, 68)(57, 67)(58, 71)(59, 64)(60, 72)(61, 69)(62, 66)(63, 70)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 95)(83, 91)(84, 98)(85, 93)(86, 92)(87, 97)(88, 99)(89, 94)(90, 96)(100, 133)(101, 132)(102, 131)(103, 127)(104, 135)(105, 134)(106, 130)(107, 128)(108, 129)

MAP           : A4.1866
NOTES         : type II, reflexible, isomorphic to A4.1504.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.1^-1 * x.6^-1, x.1^3, x.5^3, x.7^3, x.6^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^-1 * x.2^-1 * x.5^-1, x.1 * x.5^-1 * x.7^-1, x.1 * x.2 * x.5, x.1 * x.7 * x.2^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 143)(74, 138)(75, 142)(76, 141)(77, 139)(78, 140)(79, 137)(80, 144)(81, 136)(82, 92)(83, 95)(84, 94)(85, 98)(86, 91)(87, 99)(88, 96)(89, 93)(90, 97)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1867
NOTES         : type I, reflexible, isomorphic to A4.1494.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8)(9, 10, 11, 12, 13, 14, 15, 16) L = (1, 2)(3, 6)(4, 13)(5, 14)(7, 8)(9, 16)(10, 11)(12, 15)
ORBIFOLD      : O(0, {3, 3, 3, 3})
EMBEDDING     : vertices: [ 1, 1 ], faces: [ 3, 3, 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.2 * u.3^-1 * u.4, u.1^3, u.5^3, u.7^3, u.6^3, u.1^-1 * u.2^-1 * u.5^-1, u.3 * u.4^-1 * u.8, u.6 * u.7^-1 * u.8^-1 >
CTG (small)   : <9, 2>
CTG (fp)      : < x.1, x.2, x.3, x.8, x.4, x.5, x.6, x.7 | x.3, x.3, x.4 * x.2, x.5^-1 * x.7^-1, x.6 * x.1^-1, x.7^3, x.6^3, x.5^3, x.2^2 * x.4^-1, x.3 * x.4^-1 * x.8, x.6 * x.7^-1 * x.8^-1, x.1^3, x.2 * x.5 * x.1, x.1^-1 * x.2^-1 * x.5^-1 >
SCHREIER VEC. : (x.1, x.1^-1, x.2, x.3, x.4, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 144
R = (1, 10, 19, 28, 37, 46, 55, 64)(2, 11, 20, 29, 38, 47, 56, 65)(3, 12, 21, 30, 39, 48, 57, 66)(4, 13, 22, 31, 40, 49, 58, 67)(5, 14, 23, 32, 41, 50, 59, 68)(6, 15, 24, 33, 42, 51, 60, 69)(7, 16, 25, 34, 43, 52, 61, 70)(8, 17, 26, 35, 44, 53, 62, 71)(9, 18, 27, 36, 45, 54, 63, 72)(73, 82, 91, 100, 109, 118, 127, 136)(74, 83, 92, 101, 110, 119, 128, 137)(75, 84, 93, 102, 111, 120, 129, 138)(76, 85, 94, 103, 112, 121, 130, 139)(77, 86, 95, 104, 113, 122, 131, 140)(78, 87, 96, 105, 114, 123, 132, 141)(79, 88, 97, 106, 115, 124, 133, 142)(80, 89, 98, 107, 116, 125, 134, 143)(81, 90, 99, 108, 117, 126, 135, 144)
L = (1, 18)(2, 16)(3, 11)(4, 14)(5, 15)(6, 13)(7, 12)(8, 10)(9, 17)(19, 52)(20, 51)(21, 50)(22, 46)(23, 54)(24, 53)(25, 49)(26, 47)(27, 48)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 121)(38, 125)(39, 126)(40, 124)(41, 120)(42, 119)(43, 118)(44, 123)(45, 122)(55, 69)(56, 72)(57, 64)(58, 65)(59, 70)(60, 66)(61, 71)(62, 68)(63, 67)(73, 144)(74, 142)(75, 137)(76, 140)(77, 141)(78, 139)(79, 138)(80, 136)(81, 143)(82, 93)(83, 94)(84, 96)(85, 99)(86, 98)(87, 91)(88, 95)(89, 97)(90, 92)(100, 130)(101, 134)(102, 135)(103, 133)(104, 129)(105, 128)(106, 127)(107, 132)(108, 131)

MAP           : A4.1868
NOTES         : type I, chiral, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (2, 4)(5, 8)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 2, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1^2, u.2^2, u.3^2, u.4^2, u.1 * u.5^-1 * u.6^-1, u.6 * u.3 * u.4, (u.5 * u.2)^2 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.4^2, x.1^2, x.2^2, x.3^2, x.1 * x.5^-1 * x.6^-1, x.3 * x.2 * x.6^-1, x.2 * x.4 * x.6^-1, x.6 * x.3 * x.4, x.1 * x.5 * x.6, x.2 * x.3 * x.6, x.3 * x.5 * x.4 * x.1, (x.5 * x.2)^2, (x.2 * x.1)^2 >
SCHREIER VEC. : (x.1, x.5, x.2, x.5^-1, x.6, x.3, x.4, x.6^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 4, 4)
#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, 3)(2, 4)(5, 6)(7, 9)(8, 10)(11, 12)(13, 42)(14, 48)(15, 41)(16, 47)(17, 46)(18, 44)(19, 40)(20, 39)(21, 38)(22, 37)(23, 45)(24, 43)(25, 26)(27, 28)(29, 31)(30, 33)(32, 35)(34, 36)(49, 92)(50, 91)(51, 94)(52, 93)(53, 85)(54, 87)(55, 95)(56, 89)(57, 96)(58, 90)(59, 86)(60, 88)(61, 67)(62, 68)(63, 69)(64, 70)(65, 71)(66, 72)(73, 83)(74, 77)(75, 84)(76, 78)(79, 80)(81, 82)

MAP           : A4.1869
NOTES         : type I, chiral, isomorphic to A4.1868.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 4)(5, 7)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 2, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1^2, u.2^2, u.3^2, u.4^2, u.5 * u.1 * u.2, u.5^-1 * u.6^-1 * u.4, (u.6 * u.3)^2 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.4^2, x.1^2, x.2^2, x.3^2, x.6^2 * x.5^-1, x.6 * x.4 * x.5, x.5 * x.1 * x.2, x.1 * x.3 * x.5^-1, x.5^-1 * x.6^-1 * x.4, x.2 * x.3 * x.5, x.1 * x.5 * x.3, x.2 * x.5^-1 * x.3, (x.6 * x.3)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.5, x.1, x.2, x.5^-1, x.6, x.3, x.6^-1, x.4)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 4, 4)
#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, 44)(2, 43)(3, 46)(4, 45)(5, 37)(6, 39)(7, 47)(8, 41)(9, 48)(10, 42)(11, 38)(12, 40)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 35)(26, 29)(27, 36)(28, 30)(31, 32)(33, 34)(49, 78)(50, 84)(51, 77)(52, 83)(53, 82)(54, 80)(55, 76)(56, 75)(57, 74)(58, 73)(59, 81)(60, 79)(61, 62)(63, 64)(65, 67)(66, 69)(68, 71)(70, 72)(85, 87)(86, 88)(89, 90)(91, 93)(92, 94)(95, 96)

MAP           : A4.1870
NOTES         : type I, chiral, isomorphic to A4.1868.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (2, 4)(5, 8)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 2, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1^2, u.2^2, u.3^2, u.4^2, u.1 * u.5^-1 * u.6^-1, u.6 * u.3 * u.4, (u.5 * u.2)^2 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.4^2, x.1^2, x.2^2, x.3^2, x.1 * x.5^-1 * x.6^-1, x.3 * x.2 * x.6^-1, x.2 * x.4 * x.6^-1, x.6 * x.3 * x.4, x.1 * x.5 * x.6, x.2 * x.3 * x.6, x.3 * x.5 * x.4 * x.1, (x.5 * x.2)^2, (x.2 * x.1)^2 >
SCHREIER VEC. : (x.1, x.5, x.2, x.5^-1, x.6, x.3, x.4, x.6^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 4, 4)
#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, 3)(2, 4)(5, 6)(7, 9)(8, 10)(11, 12)(13, 42)(14, 48)(15, 41)(16, 47)(17, 46)(18, 44)(19, 40)(20, 39)(21, 38)(22, 37)(23, 45)(24, 43)(25, 28)(26, 27)(29, 33)(30, 31)(32, 36)(34, 35)(49, 92)(50, 91)(51, 94)(52, 93)(53, 85)(54, 87)(55, 95)(56, 89)(57, 96)(58, 90)(59, 86)(60, 88)(61, 69)(62, 70)(63, 67)(64, 68)(65, 72)(66, 71)(73, 84)(74, 78)(75, 83)(76, 77)(79, 82)(80, 81)

MAP           : A4.1871
NOTES         : type I, chiral, isomorphic to A4.1868.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 4)(5, 7)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 2, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6 | u.1^2, u.2^2, u.3^2, u.4^2, u.5 * u.1 * u.2, u.5^-1 * u.6^-1 * u.4, (u.6 * u.3)^2 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6 | x.4^2, x.1^2, x.2^2, x.3^2, x.6^2 * x.5^-1, x.6 * x.4 * x.5, x.5 * x.1 * x.2, x.1 * x.3 * x.5^-1, x.5^-1 * x.6^-1 * x.4, x.2 * x.3 * x.5, x.1 * x.5 * x.3, x.2 * x.5^-1 * x.3, (x.6 * x.3)^2, (x.4 * x.1)^2 >
SCHREIER VEC. : (x.5, x.1, x.2, x.5^-1, x.6, x.3, x.6^-1, x.4)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 4, 4)
#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, 44)(2, 43)(3, 46)(4, 45)(5, 37)(6, 39)(7, 47)(8, 41)(9, 48)(10, 42)(11, 38)(12, 40)(13, 21)(14, 22)(15, 19)(16, 20)(17, 24)(18, 23)(25, 36)(26, 30)(27, 35)(28, 29)(31, 34)(32, 33)(49, 78)(50, 84)(51, 77)(52, 83)(53, 82)(54, 80)(55, 76)(56, 75)(57, 74)(58, 73)(59, 81)(60, 79)(61, 64)(62, 63)(65, 69)(66, 67)(68, 72)(70, 71)(85, 87)(86, 88)(89, 90)(91, 93)(92, 94)(95, 96)

MAP           : A4.1872
NOTES         : type I, reflexible, 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, 3, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 3, 3, 3, 2, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1 * u.2^-1 * u.4^-1, u.3^3, u.4^3, u.1^3, (u.2 * u.3^-1)^2 >
CTG (small)   : <12, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.4 * x.2 * x.1^-1, x.1 * x.3^-1 * x.2^-1, x.4^3, x.1^3, x.1 * x.4^-1 * x.3^-1, x.2^3, x.3^3, x.2 * x.4 * x.3, (x.2 * x.3^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.2^-1, x.4, x.4^-1, x.1^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 3, 4)
#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, 91)(2, 95)(3, 89)(4, 93)(5, 92)(6, 85)(7, 90)(8, 87)(9, 94)(10, 88)(11, 96)(12, 86)(13, 56)(14, 49)(15, 54)(16, 51)(17, 58)(18, 52)(19, 60)(20, 50)(21, 55)(22, 59)(23, 53)(24, 57)(25, 45)(26, 46)(27, 47)(28, 48)(29, 37)(30, 38)(31, 39)(32, 40)(33, 41)(34, 42)(35, 43)(36, 44)(61, 83)(62, 75)(63, 81)(64, 73)(65, 84)(66, 77)(67, 82)(68, 79)(69, 74)(70, 80)(71, 76)(72, 78)

MAP           : A4.1873
NOTES         : type I, reflexible, isomorphic to A4.1872.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8) L = (1, 8)(2, 5)(3, 4)(6, 7)
ORBIFOLD      : O(0, {3, 3, 3, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 3, 3, 3, 2, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4 | u.1 * u.2^-1 * u.4^-1, u.3^3, u.4^3, u.1^3, (u.2 * u.3^-1)^2 >
CTG (small)   : <12, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4 | x.4 * x.2 * x.1^-1, x.1 * x.3^-1 * x.2^-1, x.4^3, x.1^3, x.1 * x.4^-1 * x.3^-1, x.2^3, x.3^3, x.2 * x.4 * x.3, (x.2 * x.3^-1)^2 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.2^-1, x.4, x.4^-1, x.1^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 4, 3, 4)
#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, 95)(2, 87)(3, 93)(4, 85)(5, 96)(6, 89)(7, 94)(8, 91)(9, 86)(10, 92)(11, 88)(12, 90)(13, 50)(14, 56)(15, 52)(16, 54)(17, 59)(18, 51)(19, 57)(20, 49)(21, 60)(22, 53)(23, 58)(24, 55)(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, 79)(62, 83)(63, 77)(64, 81)(65, 80)(66, 73)(67, 78)(68, 75)(69, 82)(70, 76)(71, 84)(72, 74)

MAP           : A4.1874
NOTES         : type I, non-Cayley, reflexible, representative.
QUOTIENT      : R = (1, 2, 3, 4) L = (1, 2)
ORBIFOLD      : O(0, {4, 2, 2, 2})
EMBEDDING     : vertices: [ 2 ], faces: [ 4, 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)^4 >
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 * x.2)^2, (x.4 * x.2)^3, (x.4 * x.1)^3, (x.2 * x.1 * x.4 * x.1)^2 >
SCHREIER VEC. : (x.3, x.3^-1, x.1, x.2)^2
LOCAL TYPE    : (3, 3, 3, 4, 3, 3, 3, 4)
#DARTS        : 96
R = (1, 35, 59, 83, 11, 25, 49, 73)(2, 33, 57, 81, 9, 26, 50, 74)(3, 36, 60, 84, 12, 27, 51, 75)(4, 34, 58, 82, 10, 28, 52, 76)(5, 46, 70, 94, 22, 29, 53, 77)(6, 48, 72, 96, 24, 30, 54, 78)(7, 45, 69, 93, 21, 31, 55, 79)(8, 47, 71, 95, 23, 32, 56, 80)(13, 44, 68, 92, 20, 37, 61, 85)(14, 43, 67, 91, 19, 38, 62, 86)(15, 42, 66, 90, 18, 39, 63, 87)(16, 41, 65, 89, 17, 40, 64, 88)
L = (1, 38)(2, 40)(3, 37)(4, 39)(5, 43)(6, 41)(7, 44)(8, 42)(9, 28)(10, 27)(11, 26)(12, 25)(13, 34)(14, 36)(15, 33)(16, 35)(17, 47)(18, 45)(19, 48)(20, 46)(21, 32)(22, 31)(23, 30)(24, 29)(49, 66)(50, 68)(51, 65)(52, 67)(53, 63)(54, 61)(55, 64)(56, 62)(57, 72)(58, 71)(59, 70)(60, 69)(73, 80)(74, 79)(75, 78)(76, 77)(81, 91)(82, 89)(83, 92)(84, 90)(85, 95)(86, 93)(87, 96)(88, 94)

MAP           : A4.1875
NOTES         : type I, chiral, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (1, 7)(3, 6)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.1^2, u.2^2, u.3^2, u.4^2, u.5^2, u.6 * u.1 * u.7^-1, u.7 * u.2 * u.3, u.6^-1 * u.4 * u.5 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.4^2, x.1^2, x.2^2, x.3^2, x.5^2, x.6 * x.1 * x.7^-1, x.6^-1 * x.4 * x.5, x.7 * x.2 * x.3, x.1 * x.3 * x.5, x.3 * x.1 * x.5, x.2 * x.7 * x.4, x.1 * x.6 * x.7^-1, x.2 * x.4 * x.7^-1, (x.2 * x.1)^2 >
SCHREIER VEC. : (x.6, x.1, x.7, x.2, x.3, x.7^-1, x.6^-1, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 108
R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108)
L = (1, 78)(2, 84)(3, 77)(4, 83)(5, 82)(6, 80)(7, 76)(8, 75)(9, 74)(10, 73)(11, 81)(12, 79)(13, 15)(14, 16)(17, 18)(19, 21)(20, 22)(23, 24)(25, 65)(26, 71)(27, 66)(28, 72)(29, 68)(30, 70)(31, 62)(32, 61)(33, 64)(34, 63)(35, 67)(36, 69)(37, 38)(39, 40)(41, 43)(42, 45)(44, 47)(46, 48)(49, 59)(50, 53)(51, 60)(52, 54)(55, 56)(57, 58)(85, 91)(86, 92)(87, 93)(88, 94)(89, 95)(90, 96)(97, 108)(98, 102)(99, 107)(100, 101)(103, 106)(104, 105)

MAP           : A4.1876
NOTES         : type I, chiral, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (1, 7)(3, 6)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.1^2, u.2^2, u.3^2, u.4^2, u.5^2, u.6 * u.1 * u.7^-1, u.7 * u.2 * u.3, u.6^-1 * u.4 * u.5 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.4^2, x.1^2, x.2^2, x.3^2, x.5^2, x.6 * x.1 * x.7^-1, x.6^-1 * x.4 * x.5, x.1 * x.4 * x.2, x.3 * x.5 * x.7, x.2 * x.7 * x.5, x.1 * x.2 * x.4, x.7 * x.2 * x.3, x.1 * x.6 * x.7^-1, x.3 * x.7^-1 * x.5, (x.3 * x.1)^2 >
SCHREIER VEC. : (x.6, x.1, x.7, x.2, x.3, x.7^-1, x.6^-1, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 108
R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108)
L = (1, 78)(2, 84)(3, 77)(4, 83)(5, 82)(6, 80)(7, 76)(8, 75)(9, 74)(10, 73)(11, 81)(12, 79)(13, 15)(14, 16)(17, 18)(19, 21)(20, 22)(23, 24)(25, 65)(26, 71)(27, 66)(28, 72)(29, 68)(30, 70)(31, 62)(32, 61)(33, 64)(34, 63)(35, 67)(36, 69)(37, 38)(39, 40)(41, 43)(42, 45)(44, 47)(46, 48)(49, 59)(50, 53)(51, 60)(52, 54)(55, 56)(57, 58)(85, 88)(86, 87)(89, 93)(90, 91)(92, 96)(94, 95)(97, 103)(98, 104)(99, 105)(100, 106)(101, 107)(102, 108)

MAP           : A4.1877
NOTES         : type I, chiral, isomorphic to A4.1876.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (1, 7)(3, 6)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.1^2, u.2^2, u.3^2, u.4^2, u.5^2, u.6 * u.1 * u.7^-1, u.7 * u.2 * u.3, u.6^-1 * u.4 * u.5 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.4^2, x.1^2, x.2^2, x.3^2, x.5^2, x.6 * x.1 * x.7^-1, x.2 * x.4 * x.6^-1, x.7 * x.2 * x.3, x.6^-1 * x.4 * x.5, x.1 * x.3 * x.5, x.1 * x.5 * x.3, x.1 * x.6 * x.7^-1, x.4 * x.2 * x.6, x.2 * x.7 * x.4 * x.1 >
SCHREIER VEC. : (x.6, x.1, x.7, x.2, x.3, x.7^-1, x.6^-1, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 108
R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108)
L = (1, 77)(2, 83)(3, 78)(4, 84)(5, 80)(6, 82)(7, 74)(8, 73)(9, 76)(10, 75)(11, 79)(12, 81)(13, 15)(14, 16)(17, 18)(19, 21)(20, 22)(23, 24)(25, 66)(26, 72)(27, 65)(28, 71)(29, 70)(30, 68)(31, 64)(32, 63)(33, 62)(34, 61)(35, 69)(36, 67)(37, 38)(39, 40)(41, 43)(42, 45)(44, 47)(46, 48)(49, 60)(50, 54)(51, 59)(52, 53)(55, 58)(56, 57)(85, 91)(86, 92)(87, 93)(88, 94)(89, 95)(90, 96)(97, 107)(98, 101)(99, 108)(100, 102)(103, 104)(105, 106)

MAP           : A4.1878
NOTES         : type I, chiral, isomorphic to A4.1875.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (1, 7)(3, 6)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.1^2, u.2^2, u.3^2, u.4^2, u.5^2, u.6 * u.1 * u.7^-1, u.7 * u.2 * u.3, u.6^-1 * u.4 * u.5 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.4^2, x.1^2, x.2^2, x.3^2, x.5^2, x.6 * x.1 * x.7^-1, x.6^-1 * x.4 * x.5, x.7 * x.2 * x.3, x.1 * x.2 * x.4, x.2 * x.7 * x.5, x.3 * x.5 * x.6, x.1 * x.6 * x.7^-1, x.1 * x.4 * x.2, x.3 * x.7^-1 * x.5 * x.1 >
SCHREIER VEC. : (x.6, x.1, x.7, x.2, x.3, x.7^-1, x.6^-1, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 108
R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108)
L = (1, 77)(2, 83)(3, 78)(4, 84)(5, 80)(6, 82)(7, 74)(8, 73)(9, 76)(10, 75)(11, 79)(12, 81)(13, 15)(14, 16)(17, 18)(19, 21)(20, 22)(23, 24)(25, 66)(26, 72)(27, 65)(28, 71)(29, 70)(30, 68)(31, 64)(32, 63)(33, 62)(34, 61)(35, 69)(36, 67)(37, 38)(39, 40)(41, 43)(42, 45)(44, 47)(46, 48)(49, 60)(50, 54)(51, 59)(52, 53)(55, 58)(56, 57)(85, 88)(86, 87)(89, 93)(90, 91)(92, 96)(94, 95)(97, 105)(98, 106)(99, 103)(100, 104)(101, 108)(102, 107)

MAP           : A4.1879
NOTES         : type I, chiral, isomorphic to A4.1875.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (1, 7)(3, 6)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.1^2, u.2^2, u.3^2, u.4^2, u.5^2, u.6 * u.1 * u.7^-1, u.7 * u.2 * u.3, u.6^-1 * u.4 * u.5 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.4^2, x.1^2, x.2^2, x.3^2, x.5^2, x.6 * x.1 * x.7^-1, x.6^-1 * x.4 * x.5, x.7 * x.2 * x.3, x.1 * x.2 * x.4, x.2 * x.7 * x.5, x.3 * x.5 * x.6, x.1 * x.6 * x.7^-1, x.1 * x.4 * x.2, x.3 * x.7^-1 * x.5 * x.1 >
SCHREIER VEC. : (x.6, x.1, x.7, x.2, x.3, x.7^-1, x.6^-1, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 108
R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108)
L = (1, 77)(2, 83)(3, 78)(4, 84)(5, 80)(6, 82)(7, 74)(8, 73)(9, 76)(10, 75)(11, 79)(12, 81)(13, 15)(14, 16)(17, 18)(19, 21)(20, 22)(23, 24)(25, 66)(26, 72)(27, 65)(28, 71)(29, 70)(30, 68)(31, 64)(32, 63)(33, 62)(34, 61)(35, 69)(36, 67)(37, 40)(38, 39)(41, 45)(42, 43)(44, 48)(46, 47)(49, 59)(50, 53)(51, 60)(52, 54)(55, 56)(57, 58)(85, 86)(87, 88)(89, 91)(90, 93)(92, 95)(94, 96)(97, 103)(98, 104)(99, 105)(100, 106)(101, 107)(102, 108)

MAP           : A4.1880
NOTES         : type I, chiral, isomorphic to A4.1876.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (1, 7)(3, 6)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.1^2, u.2^2, u.3^2, u.4^2, u.5^2, u.6 * u.1 * u.7^-1, u.7 * u.2 * u.3, u.6^-1 * u.4 * u.5 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.4^2, x.1^2, x.2^2, x.3^2, x.5^2, x.6 * x.1 * x.7^-1, x.2 * x.4 * x.6^-1, x.7 * x.2 * x.3, x.6^-1 * x.4 * x.5, x.1 * x.3 * x.5, x.1 * x.5 * x.3, x.1 * x.6 * x.7^-1, x.4 * x.2 * x.6, x.2 * x.7 * x.4 * x.1 >
SCHREIER VEC. : (x.6, x.1, x.7, x.2, x.3, x.7^-1, x.6^-1, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 108
R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108)
L = (1, 77)(2, 83)(3, 78)(4, 84)(5, 80)(6, 82)(7, 74)(8, 73)(9, 76)(10, 75)(11, 79)(12, 81)(13, 15)(14, 16)(17, 18)(19, 21)(20, 22)(23, 24)(25, 66)(26, 72)(27, 65)(28, 71)(29, 70)(30, 68)(31, 64)(32, 63)(33, 62)(34, 61)(35, 69)(36, 67)(37, 40)(38, 39)(41, 45)(42, 43)(44, 48)(46, 47)(49, 59)(50, 53)(51, 60)(52, 54)(55, 56)(57, 58)(85, 93)(86, 94)(87, 91)(88, 92)(89, 96)(90, 95)(97, 108)(98, 102)(99, 107)(100, 101)(103, 106)(104, 105)

MAP           : A4.1881
NOTES         : type I, chiral, isomorphic to A4.1876.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (1, 7)(3, 6)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.1^2, u.2^2, u.3^2, u.4^2, u.5^2, u.6 * u.1 * u.7^-1, u.7 * u.2 * u.3, u.6^-1 * u.4 * u.5 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.4^2, x.1^2, x.2^2, x.3^2, x.5^2, x.6 * x.1 * x.7^-1, x.6^-1 * x.4 * x.5, x.1 * x.4 * x.2, x.3 * x.5 * x.7, x.2 * x.7 * x.5, x.1 * x.2 * x.4, x.7 * x.2 * x.3, x.1 * x.6 * x.7^-1, x.3 * x.7^-1 * x.5, (x.3 * x.1)^2 >
SCHREIER VEC. : (x.6, x.1, x.7, x.2, x.3, x.7^-1, x.6^-1, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 108
R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108)
L = (1, 78)(2, 84)(3, 77)(4, 83)(5, 82)(6, 80)(7, 76)(8, 75)(9, 74)(10, 73)(11, 81)(12, 79)(13, 15)(14, 16)(17, 18)(19, 21)(20, 22)(23, 24)(25, 65)(26, 71)(27, 66)(28, 72)(29, 68)(30, 70)(31, 62)(32, 61)(33, 64)(34, 63)(35, 67)(36, 69)(37, 40)(38, 39)(41, 45)(42, 43)(44, 48)(46, 47)(49, 60)(50, 54)(51, 59)(52, 53)(55, 58)(56, 57)(85, 86)(87, 88)(89, 91)(90, 93)(92, 95)(94, 96)(97, 105)(98, 106)(99, 103)(100, 104)(101, 108)(102, 107)

MAP           : A4.1882
NOTES         : type I, chiral, isomorphic to A4.1875.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (1, 7)(3, 6)
ORBIFOLD      : O(0, {2, 2, 2, 2, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 1, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5, u.6, u.7 | u.1^2, u.2^2, u.3^2, u.4^2, u.5^2, u.6 * u.1 * u.7^-1, u.7 * u.2 * u.3, u.6^-1 * u.4 * u.5 >
CTG (small)   : <12, 4>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5, x.6, x.7 | x.4^2, x.1^2, x.2^2, x.3^2, x.5^2, x.6 * x.1 * x.7^-1, x.6^-1 * x.4 * x.5, x.7 * x.2 * x.3, x.1 * x.3 * x.5, x.3 * x.1 * x.5, x.2 * x.7 * x.4, x.1 * x.6 * x.7^-1, x.2 * x.4 * x.7^-1, (x.2 * x.1)^2 >
SCHREIER VEC. : (x.6, x.1, x.7, x.2, x.3, x.7^-1, x.6^-1, x.4, x.5)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 108
R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108)
L = (1, 78)(2, 84)(3, 77)(4, 83)(5, 82)(6, 80)(7, 76)(8, 75)(9, 74)(10, 73)(11, 81)(12, 79)(13, 15)(14, 16)(17, 18)(19, 21)(20, 22)(23, 24)(25, 65)(26, 71)(27, 66)(28, 72)(29, 68)(30, 70)(31, 62)(32, 61)(33, 64)(34, 63)(35, 67)(36, 69)(37, 40)(38, 39)(41, 45)(42, 43)(44, 48)(46, 47)(49, 60)(50, 54)(51, 59)(52, 53)(55, 58)(56, 57)(85, 93)(86, 94)(87, 91)(88, 92)(89, 96)(90, 95)(97, 107)(98, 101)(99, 108)(100, 102)(103, 104)(105, 106)

MAP           : A4.1883
NOTES         : type I, chiral, representative.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (2, 7)(3, 4)(5, 6)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.1 * u.2^-1 * u.5^-1, u.3^3, u.4^3, u.5^3, u.2 * u.3^-1 * u.4^-1 >
CTG (small)   : <12, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2 * x.4^-1 * x.5^-1, x.1 * x.2^-1 * x.5^-1, x.2 * x.5^-1 * x.3^-1, x.3^3, x.4^3, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5 * x.3, x.1 * x.5^-1 * x.4, x.1 * x.3 * x.4^-1, x.1 * x.2 * x.3, x.2^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.4^-1, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 108
R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108)
L = (1, 12)(2, 5)(3, 10)(4, 7)(6, 8)(9, 11)(13, 74)(14, 80)(15, 76)(16, 78)(17, 83)(18, 75)(19, 81)(20, 73)(21, 84)(22, 77)(23, 82)(24, 79)(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, 71)(50, 63)(51, 69)(52, 61)(53, 72)(54, 65)(55, 70)(56, 67)(57, 62)(58, 68)(59, 64)(60, 66)(85, 102)(86, 108)(87, 104)(88, 106)(89, 99)(90, 103)(91, 97)(92, 101)(93, 100)(94, 105)(95, 98)(96, 107)

MAP           : A4.1884
NOTES         : type I, chiral, isomorphic to A4.1883.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (2, 7)(3, 4)(5, 6)(8, 9)
ORBIFOLD      : O(0, {3, 3, 3, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.1 * u.2^-1 * u.5^-1, u.3^3, u.4^3, u.5^3, u.2 * u.3^-1 * u.4^-1 >
CTG (small)   : <12, 3>
CTG (fp)      : < x.1, x.2, x.3, x.4, x.5 | x.1^2, x.2 * x.4^-1 * x.5^-1, x.1 * x.2^-1 * x.5^-1, x.2 * x.5^-1 * x.3^-1, x.3^3, x.4^3, x.5^3, x.2 * x.3^-1 * x.4^-1, x.4 * x.5 * x.3, x.1 * x.5^-1 * x.4, x.1 * x.3 * x.4^-1, x.1 * x.2 * x.3, x.2^3 >
SCHREIER VEC. : (x.1, x.2, x.3, x.3^-1, x.4, x.4^-1, x.2^-1, x.5, x.5^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 108
R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108)
L = (1, 10)(2, 4)(3, 12)(5, 7)(6, 11)(8, 9)(13, 80)(14, 73)(15, 78)(16, 75)(17, 82)(18, 76)(19, 84)(20, 74)(21, 79)(22, 83)(23, 77)(24, 81)(25, 41)(26, 42)(27, 43)(28, 44)(29, 45)(30, 46)(31, 47)(32, 48)(33, 37)(34, 38)(35, 39)(36, 40)(49, 67)(50, 71)(51, 65)(52, 69)(53, 68)(54, 61)(55, 66)(56, 63)(57, 70)(58, 64)(59, 72)(60, 62)(85, 100)(86, 105)(87, 98)(88, 107)(89, 102)(90, 108)(91, 104)(92, 106)(93, 99)(94, 103)(95, 97)(96, 101)

MAP           : A4.1885
NOTES         : type I, chiral, isomorphic to A4.1883.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (1, 2)(3, 4)(5, 9)(7, 8)
ORBIFOLD      : O(0, {3, 3, 3, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^3, u.3^3, u.5^3, u.2^-1 * u.3^-1 * u.4^-1, 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.2^3, x.5^3, x.3^3, x.3 * x.4 * x.5, x.2^-1 * x.3^-1 * x.4^-1, x.4 * x.1 * x.5^-1, x.1 * x.5 * x.2^-1, x.4^3, x.1 * x.4 * x.3^-1, x.2 * x.3 * x.5, x.4 * x.5^-1 * x.3 * x.2^-1 >
SCHREIER VEC. : (x.2, x.2^-1, x.3, x.3^-1, x.4, x.1, x.5, x.5^-1, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 108
R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108)
L = (1, 14)(2, 20)(3, 16)(4, 18)(5, 23)(6, 15)(7, 21)(8, 13)(9, 24)(10, 17)(11, 22)(12, 19)(25, 41)(26, 42)(27, 43)(28, 44)(29, 45)(30, 46)(31, 47)(32, 48)(33, 37)(34, 38)(35, 39)(36, 40)(49, 103)(50, 107)(51, 101)(52, 105)(53, 104)(54, 97)(55, 102)(56, 99)(57, 106)(58, 100)(59, 108)(60, 98)(61, 70)(62, 64)(63, 72)(65, 67)(66, 71)(68, 69)(73, 88)(74, 93)(75, 86)(76, 95)(77, 90)(78, 96)(79, 92)(80, 94)(81, 87)(82, 91)(83, 85)(84, 89)

MAP           : A4.1886
NOTES         : type I, chiral, isomorphic to A4.1883.
QUOTIENT      : R = (1, 2, 3, 4, 5, 6, 7, 8, 9) L = (1, 2)(3, 4)(5, 9)(7, 8)
ORBIFOLD      : O(0, {3, 3, 3, 2})
EMBEDDING     : vertices: [ 1 ], faces: [ 3, 3, 3, 1, 1 ]
UNIGROUP      : < u.1, u.2, u.3, u.4, u.5 | u.1^2, u.2^3, u.3^3, u.5^3, u.2^-1 * u.3^-1 * u.4^-1, 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.2^3, x.5^3, x.3^3, x.3 * x.4 * x.5, x.2^-1 * x.3^-1 * x.4^-1, x.4 * x.1 * x.5^-1, x.1 * x.5 * x.2^-1, x.4^3, x.1 * x.4 * x.3^-1, x.2 * x.3 * x.5, x.4 * x.5^-1 * x.3 * x.2^-1 >
SCHREIER VEC. : (x.2, x.2^-1, x.3, x.3^-1, x.4, x.1, x.5, x.5^-1, x.4^-1)
LOCAL TYPE    : (3, 3, 3, 3, 3, 3, 3, 3, 3)
#DARTS        : 108
R = (1, 13, 25, 37, 49, 61, 73, 85, 97)(2, 14, 26, 38, 50, 62, 74, 86, 98)(3, 15, 27, 39, 51, 63, 75, 87, 99)(4, 16, 28, 40, 52, 64, 76, 88, 100)(5, 17, 29, 41, 53, 65, 77, 89, 101)(6, 18, 30, 42, 54, 66, 78, 90, 102)(7, 19, 31, 43, 55, 67, 79, 91, 103)(8, 20, 32, 44, 56, 68, 80, 92, 104)(9, 21, 33, 45, 57, 69, 81, 93, 105)(10, 22, 34, 46, 58, 70, 82, 94, 106)(11, 23, 35, 47, 59, 71, 83, 95, 107)(12, 24, 36, 48, 60, 72, 84, 96, 108)
L = (1, 20)(2, 13)(3, 18)(4, 15)(5, 22)(6, 16)(7, 24)(8, 14)(9, 19)(10, 23)(11, 17)(12, 21)(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, 107)(50, 99)(51, 105)(52, 97)(53, 108)(54, 101)(55, 106)(56, 103)(57, 98)(58, 104)(59, 100)(60, 102)(61, 72)(62, 65)(63, 70)(64, 67)(66, 68)(69, 71)(73, 90)(74, 96)(75, 92)(76, 94)(77, 87)(78, 91)(79, 85)(80, 89)(81, 88)(82, 93)(83, 86)(84, 95)