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Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 2131 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,64)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,69,70,49,50,93)(34,67,68,52,48,61)(37,42,66,54,55,62)(40,82,80,58,59,57)(51,98,99,72,73,128)(53,96,97,75,71,90)(56,65,95,77,78,91)(60,111,112,83,84,86)(63,117,109,87,88,81)(74,133,134,101,102,169)(76,131,132,104,100,125)(79,94,130,106,107,126)(85,146,147,113,114,121)(89,153,151,118,119,116)(92,158,144,122,123,110)(103,174,175,136,137,216)(105,172,173,139,135,166)(108,129,171,141,142,167)(115,187,188,148,149,162)(120,194,195,154,155,157)(124,200,192,159,160,152)(127,205,185,163,164,145)(138,221,222,177,178,269)(140,219,220,180,176,213)(143,170,218,182,183,214)(150,234,235,189,190,209)(156,241,242,196,197,204)(161,248,246,201,202,199)(165,253,239,206,207,193)(168,258,232,210,211,186)(179,274,275,224,225,328)(181,272,273,227,223,266)(184,217,271,229,230,267)(191,287,288,236,237,262)(198,294,295,243,244,257)(203,301,302,249,250,252)(208,307,299,254,255,247)(212,312,292,259,260,240)(215,317,285,263,264,233)(226,333,334,277,278,393)(228,331,332,280,276,325)(231,270,330,282,283,326)(238,346,347,289,290,321)(245,353,354,296,297,316)(251,360,361,303,304,311)(256,367,365,308,309,306)(261,372,358,313,314,300)(265,377,351,318,319,293)(268,382,344,322,323,286)(279,398,399,336,337,464)(281,396,397,339,335,390)(284,329,395,341,342,391)(291,411,412,348,349,386)(298,418,419,355,356,381)(305,425,426,362,363,376)(310,432,433,368,369,371)(315,438,430,373,374,366)(320,443,423,378,379,359)(324,448,416,383,384,352)(327,453,409,387,388,345)(338,469,470,401,402,541)(340,467,468,404,400,461)(343,394,466,406,407,462)(350,482,483,413,414,457)(357,489,490,420,421,452)(364,496,497,427,428,447)(370,503,504,434,435,442)(375,510,508,439,440,437)(380,515,501,444,445,431)(385,520,494,449,450,424)(389,525,487,454,455,417)(392,530,480,458,459,410)(403,546,547,472,473,624)(405,544,545,475,471,538)(408,465,543,477,478,539)(415,559,560,484,485,534)(422,566,567,491,492,529)(429,573,574,498,499,524)(436,580,581,505,506,519)(441,587,588,511,512,514)(446,593,585,516,517,509)(451,598,578,521,522,502)(456,603,571,526,527,495)(460,608,564,531,532,488)(463,613,557,535,536,481)(474,629,630,549,550,713)(476,627,628,552,548,621)(479,542,626,554,555,622)(486,642,643,561,562,617)(493,649,650,568,569,612)(500,656,657,575,576,607)(507,663,664,582,583,602)(513,670,671,589,590,597)(518,677,675,594,595,592)(523,682,668,599,600,586)(528,687,661,604,605,579)(533,692,654,609,610,572)(537,697,647,614,615,565)(540,702,640,618,619,558)(551,718,719,632,633,808)(553,716,717,635,631,710)(556,625,715,637,638,711)(563,731,732,644,645,706)(570,738,739,651,652,701)(577,745,746,658,659,696)(584,752,753,665,666,691)(591,759,760,672,673,686)(596,766,767,678,679,681)(601,772,764,683,684,676)(606,777,757,688,689,669)(611,782,750,693,694,662)(616,787,743,698,699,655)(620,792,736,703,704,648)(623,797,729,707,708,641)(634,813,814,721,722,909)(636,811,812,724,720,805)(639,714,810,726,727,806)(646,826,827,733,734,801)(653,833,834,740,741,796)(660,840,841,747,748,791)(667,847,848,754,755,786)(674,854,855,761,762,781)(680,861,862,768,769,776)(685,868,866,773,774,771)(690,873,859,778,779,765)(695,878,852,783,784,758)(700,883,845,788,789,751)(705,888,838,793,794,744)(709,893,831,798,799,737)(712,898,824,802,803,730)(723,914,915,816,817,1016)(725,912,913,819,815,906)(728,809,911,821,822,907)(735,927,928,828,829,902)(742,934,935,835,836,897)(749,941,942,842,843,892)(756,948,949,849,850,887)(763,955,956,856,857,882)(770,962,963,863,864,877)(775,969,970,869,870,872)(780,975,967,874,875,867)(785,980,960,879,880,860)(790,985,953,884,885,853)(795,990,946,889,890,846)(800,995,939,894,895,839)(804,1000,932,899,900,832)(807,1005,925,903,904,825)(818,1021,1022,917,918,1129)(820,1019,1020,920,916,1013)(823,910,1018,922,923,1014)(830,1034,1035,929,930,1009)(837,1041,1042,936,937,1004)(844,1048,1049,943,944,999)(851,1055,1056,950,951,994)(858,1062,1063,957,958,989)(865,1069,1070,964,965,984)(871,1076,1077,971,972,979)(876,1083,1081,976,977,974)(881,1088,1074,981,982,968)(886,1093,1067,986,987,961)(891,1098,1060,991,992,954)(896,1103,1053,996,997,947)(901,1108,1046,1001,1002,940)(905,1113,1039,1006,1007,933)(908,1118,1032,1010,1011,926)(919,1134,1135,1024,1025,1248)(921,1132,1133,1027,1023,1126)(924,1017,1131,1029,1030,1127)(931,1147,1148,1036,1037,1122)(938,1154,1155,1043,1044,1117)(945,1161,1162,1050,1051,1112)(952,1168,1169,1057,1058,1107)(959,1175,1176,1064,1065,1102)(966,1182,1183,1071,1072,1097)(973,1189,1190,1078,1079,1092)(978,1196,1197,1084,1085,1087)(983,1202,1194,1089,1090,1082)(988,1207,1187,1094,1095,1075)(993,1212,1180,1099,1100,1068)(998,1217,1173,1104,1105,1061)(1003,1222,1166,1109,1110,1054)(1008,1227,1159,1114,1115,1047)(1012,1232,1152,1119,1120,1040)(1015,1237,1145,1123,1124,1033)(1026,1253,1254,1137,1138,1373)(1028,1251,1252,1140,1136,1245)(1031,1130,1250,1142,1143,1246)(1038,1266,1267,1149,1150,1241)(1045,1273,1274,1156,1157,1236)(1052,1280,1281,1163,1164,1231)(1059,1287,1288,1170,1171,1226)(1066,1294,1295,1177,1178,1221)(1073,1301,1302,1184,1185,1216)(1080,1308,1309,1191,1192,1211)(1086,1315,1316,1198,1199,1206)(1091,1322,1320,1203,1204,1201)(1096,1327,1313,1208,1209,1195)(1101,1332,1306,1213,1214,1188)(1106,1337,1299,1218,1219,1181)(1111,1342,1292,1223,1224,1174)(1116,1347,1285,1228,1229,1167)(1121,1352,1278,1233,1234,1160)(1125,1357,1271,1238,1239,1153)(1128,1362,1264,1242,1243,1146)(1139,1378,1379,1256,1257,1504)(1141,1376,1377,1259,1255,1370)(1144,1249,1375,1261,1262,1371)(1151,1391,1392,1268,1269,1366)(1158,1398,1399,1275,1276,1361)(1165,1405,1406,1282,1283,1356)(1172,1412,1413,1289,1290,1351)(1179,1419,1420,1296,1297,1346)(1186,1426,1427,1303,1304,1341)(1193,1433,1434,1310,1311,1336)(1200,1440,1441,1317,1318,1331)(1205,1447,1448,1323,1324,1326)(1210,1453,1445,1328,1329,1321)(1215,1458,1438,1333,1334,1314)(1220,1463,1431,1338,1339,1307)(1225,1468,1424,1343,1344,1300)(1230,1473,1417,1348,1349,1293)(1235,1478,1410,1353,1354,1286)(1240,1483,1403,1358,1359,1279)(1244,1488,1396,1363,1364,1272)(1247,1493,1389,1367,1368,1265)(1258,1509,1510,1381,1382,1641)(1260,1507,1508,1384,1380,1501)(1263,1374,1506,1386,1387,1502)(1270,1522,1523,1393,1394,1497)(1277,1529,1530,1400,1401,1492)(1284,1536,1537,1407,1408,1487)(1291,1543,1544,1414,1415,1482)(1298,1550,1551,1421,1422,1477)(1305,1557,1558,1428,1429,1472)(1312,1564,1565,1435,1436,1467)(1319,1571,1572,1442,1443,1462)(1325,1578,1579,1449,1450,1457)(1330,1585,1583,1454,1455,1452)(1335,1590,1576,1459,1460,1446)(1340,1595,1569,1464,1465,1439)(1345,1600,1562,1469,1470,1432)(1350,1605,1555,1474,1475,1425)(1355,1610,1548,1479,1480,1418)(1360,1615,1541,1484,1485,1411)(1365,1620,1534,1489,1490,1404)(1369,1625,1527,1494,1495,1397)(1372,1630,1520,1498,1499,1390)(1383,1646,1647,1512,1513,1783)(1385,1644,1645,1515,1511,1638)(1388,1505,1643,1517,1518,1639)(1395,1659,1660,1524,1525,1634)(1402,1666,1667,1531,1532,1629)(1409,1673,1674,1538,1539,1624)(1416,1680,1681,1545,1546,1619)(1423,1687,1688,1552,1553,1614)(1430,1694,1695,1559,1560,1609)(1437,1701,1702,1566,1567,1604)(1444,1708,1709,1573,1574,1599)(1451,1715,1716,1580,1581,1594)(1456,1722,1723,1586,1587,1589)(1461,1728,1720,1591,1592,1584)(1466,1733,1713,1596,1597,1577)(1471,1738,1706,1601,1602,1570)(1476,1743,1699,1606,1607,1563)(1481,1748,1692,1611,1612,1556)(1486,1752,1685,1616,1617,1549)(1491,1757,1678,1621,1622,1542)(1496,1762,1671,1626,1627,1535)(1500,1767,1664,1631,1632,1528)(1503,1772,1657,1635,1636,1521)(1514,1788,1789,1649,1650,1906)(1516,1786,1787,1652,1648,1780)(1519,1642,1785,1654,1655,1781)(1526,1797,1798,1661,1662,1776)(1533,1804,1805,1668,1669,1771)(1540,1811,1812,1675,1676,1766)(1547,1818,1819,1682,1683,1761)(1554,1825,1826,1689,1690,1756)(1561,1832,1833,1696,1697,1751)(1568,1837,1838,1703,1704,1747)(1575,1842,1843,1710,1711,1742)(1582,1849,1850,1717,1718,1737)(1588,1856,1857,1724,1725,1732)(1593,1863,1861,1729,1730,1727)(1598,1868,1854,1734,1735,1721)(1603,1873,1847,1739,1740,1714)(1608,1878,1651,1744,1745,1707)(1613,1883,1794,1749,1750,1700)(1618,1885,1830,1753,1754,1693)(1623,1888,1823,1758,1759,1686)(1628,1891,1816,1763,1764,1679)(1633,1894,1809,1768,1769,1672)(1637,1897,1802,1773,1774,1665)(1640,1900,1795,1777,1778,1658)(1653,1907,1908,1791,1790,1904)(1656,1784,1886,1793,1755,1905)(1663,1909,1910,1799,1800,1902)(1670,1913,1914,1806,1807,1899)(1677,1918,1919,1813,1814,1896)(1684,1923,1924,1820,1821,1893)(1691,1928,1929,1827,1828,1890)(1698,1933,1934,1834,1835,1887)(1705,1938,1939,1839,1840,1884)(1712,1943,1944,1844,1845,1882)(1719,1948,1949,1851,1852,1877)(1726,1953,1954,1858,1859,1872)(1731,1960,1961,1864,1865,1867)(1736,1966,1958,1869,1870,1862)(1741,1971,1912,1874,1875,1855)(1746,1976,1792,1879,1880,1848)(1760,1903,1796,1782,1889,1831)(1765,1901,1803,1779,1892,1824)(1770,1898,1810,1775,1895,1817)(1801,1977,1978,1911,1881,1987)(1808,1988,1989,1915,1916,1986)(1815,1990,1991,1920,1921,1985)(1822,1994,1995,1925,1926,1984)(1829,1999,2000,1930,1931,1983)(1836,2004,2005,1935,1936,1982)(1841,2009,2010,1940,1941,1981)(1846,2014,2015,1945,1946,1980)(1853,2019,2020,1950,1951,1979)(1860,2024,2025,1955,1956,1975)(1866,2029,2030,1962,1963,1970)(1871,2034,1993,1967,1968,1965)(1876,2039,1917,1972,1973,1959)(1922,2040,2041,1992,1974,2050)(1927,2051,2052,1996,1997,2049)(1932,2053,2054,2001,2002,2048)(1937,2057,2058,2006,2007,2047)(1942,2062,2063,2011,2012,2046)(1947,2067,2068,2016,2017,2045)(1952,2072,2073,2021,2022,2044)(1957,2077,2078,2026,2027,2043)(1964,2082,2056,2031,2032,2042)(1969,2086,1998,2035,2036,2038)(2003,2087,2088,2055,2037,2095)(2008,2096,2097,2059,2060,2094)(2013,2098,2099,2064,2065,2093)(2018,2102,2103,2069,2070,2092)(2023,2107,2108,2074,2075,2091)(2028,2112,2101,2079,2080,2090)(2033,2116,2061,2083,2084,2089)(2066,2117,2118,2100,2085,2122)(2071,2123,2124,2104,2105,2121)(2076,2125,2126,2109,2110,2120)(2081,2128,2106,2113,2114,2119)(2111,2129,2130,2127,2115,2131);(1,2,5,11,19,32,51,74,103,138,179,226,279,338,403,474,551,634,723,818,919,1026,1139,1258,1383,1514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Polycyclic presentation:
2,3,2131|c^a=c^2130,c^b=c^468
Conjugacy classes & character table
361 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12786, 1);
Finite Group Databasebeta