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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 2212 points:
(2,3)(4,5,7,10,14,19,25,32,40,49,59,70,82,95,109,124,140,157,175,194,214,235,257,280,304,329,355,382,410,439,469,500,532,565,599,634,670,707,745,784,824,865,907,950,994,1039,1085,6,8,11,15,20,26,33,41,50,60,71,83,96,110,125,141,158,176,195,215,236,258,281,305,330,356,383,411,440,470,501,533,566,600,635,671,708,746,785,825,866,908,951,995,1040,1086,1132,9,12,16,21,27,34,42,51,61,72,84,97,111,126,142,159,177,196,216,237,259,282,306,331,357,384,412,441,471,502,534,567,601,636,672,709,747,786,826,867,909,952,996,1041,1087,1133,1178,13,17,22,28,35,43,52,62,73,85,98,112,127,143,160,178,197,217,238,260,283,307,332,358,385,413,442,472,503,535,568,602,637,673,710,748,787,827,868,910,953,997,1042,1088,1134,1179,1223,18,23,29,36,44,53,63,74,86,99,113,128,144,161,179,198,218,239,261,284,308,333,359,386,414,443,473,504,536,569,603,638,674,711,749,788,828,869,911,954,998,1043,1089,1135,1180,1224,1267,24,30,37,45,54,64,75,87,100,114,129,145,162,180,199,219,240,262,285,309,334,360,387,415,444,474,505,537,570,604,639,675,712,750,789,829,870,912,955,999,1044,1090,1136,1181,1225,1268,1310,31,38,46,55,65,76,88,101,115,130,146,163,181,200,220,241,263,286,310,335,361,388,416,445,475,506,538,571,605,640,676,713,751,790,830,871,913,956,1000,1045,1091,1137,1182,1226,1269,1311,1352,39,47,56,66,77,89,102,116,131,147,164,182,201,221,242,264,287,311,336,362,389,417,446,476,507,539,572,606,641,677,714,752,791,831,872,914,957,1001,1046,1092,1138,1183,1227,1270,1312,1353,1393,48,57,67,78,90,103,117,132,148,165,183,202,222,243,265,288,312,337,363,390,418,447,477,508,540,573,607,642,678,715,753,792,832,873,915,958,1002,1047,1093,1139,1184,1228,1271,1313,1354,1394,1433,58,68,79,91,104,118,133,149,166,184,203,223,244,266,289,313,338,364,391,419,448,478,509,541,574,608,643,679,716,754,793,833,874,916,959,1003,1048,1094,1140,1185,1229,1272,1314,1355,1395,1434,1472,69,80,92,105,119,134,150,167,185,204,224,245,267,290,314,339,365,392,420,449,479,510,542,575,609,644,680,717,755,794,834,875,917,960,1004,1049,1095,1141,1186,1230,1273,1315,1356,1396,1435,1473,1510,81,93,106,120,135,151,168,186,205,225,246,268,291,315,340,366,393,421,450,480,511,543,576,610,645,681,718,756,795,835,876,918,961,1005,1050,1096,1142,1187,1231,1274,1316,1357,1397,1436,1474,1511,1547,94,107,121,136,152,169,187,206,226,247,269,292,316,341,367,394,422,451,481,512,544,577,611,646,682,719,757,796,836,877,919,962,1006,1051,1097,1143,1188,1232,1275,1317,1358,1398,1437,1475,1512,1548,1583,108,122,137,153,170,188,207,227,248,270,293,317,342,368,395,423,452,482,513,545,578,612,647,683,720,758,797,837,878,920,963,1007,1052,1098,1144,1189,1233,1276,1318,1359,1399,1438,1476,1513,1549,1584,1618,123,138,154,171,189,208,228,249,271,294,318,343,369,396,424,453,483,514,546,579,613,648,684,721,759,798,838,879,921,964,1008,1053,1099,1145,1190,1234,1277,1319,1360,1400,1439,1477,1514,1550,1585,1619,1652,139,155,172,190,209,229,250,272,295,319,344,370,397,425,454,484,515,547,580,614,649,685,722,760,799,839,880,922,965,1009,1054,1100,1146,1191,1235,1278,1320,1361,1401,1440,1478,1515,1551,1586,1620,1653,1685,156,173,191,210,230,251,273,296,320,345,371,398,426,455,485,516,548,581,615,650,686,723,761,800,840,881,923,966,1010,1055,1101,1147,1192,1236,1279,1321,1362,1402,1441,1479,1516,1552,1587,1621,1654,1686,1717,174,192,211,231,252,274,297,321,346,372,399,427,456,486,517,549,582,616,651,687,724,762,801,841,882,924,967,1011,1056,1102,1148,1193,1237,1280,1322,1363,1403,1442,1480,1517,1553,1588,1622,1655,1687,1718,1748,193,212,232,253,275,298,322,347,373,400,428,457,487,518,550,583,617,652,688,725,763,802,842,883,925,968,1012,1057,1103,1149,1194,1238,1281,1323,1364,1404,1443,1481,1518,1554,1589,1623,1656,1688,1719,1749,1778,213,233,254,276,299,323,348,374,401,429,458,488,519,551,584,618,653,689,726,764,803,843,884,926,969,1013,1058,1104,1150,1195,1239,1282,1324,1365,1405,1444,1482,1519,1555,1590,1624,1657,1689,1720,1750,1779,1807,234,255,277,300,324,349,375,402,430,459,489,520,552,585,619,654,690,727,765,804,844,885,927,970,1014,1059,1105,1151,1196,1240,1283,1325,1366,1406,1445,1483,1520,1556,1591,1625,1658,1690,1721,1751,1780,1808,1835,256,278,301,325,350,376,403,431,460,490,521,553,586,620,655,691,728,766,805,845,886,928,971,1015,1060,1106,1152,1197,1241,1284,1326,1367,1407,1446,1484,1521,1557,1592,1626,1659,1691,1722,1752,1781,1809,1836,1862,279,302,326,351,377,404,432,461,491,522,554,587,621,656,692,729,767,806,846,887,929,972,1016,1061,1107,1153,1198,1242,1285,1327,1368,1408,1447,1485,1522,1558,1593,1627,1660,1692,1723,1753,1782,1810,1837,1863,1888,303,327,352,378,405,433,462,492,523,555,588,622,657,693,730,768,807,847,888,930,973,1017,1062,1108,1154,1199,1243,1286,1328,1369,1409,1448,1486,1523,1559,1594,1628,1661,1693,1724,1754,1783,1811,1838,1864,1889,1913,328,353,379,406,434,463,493,524,556,589,623,658,694,731,769,808,848,889,931,974,1018,1063,1109,1155,1200,1244,1287,1329,1370,1410,1449,1487,1524,1560,1595,1629,1662,1694,1725,1755,1784,1812,1839,1865,1890,1914,1937,354,380,407,435,464,494,525,557,590,624,659,695,732,770,809,849,890,932,975,1019,1064,1110,1156,1201,1245,1288,1330,1371,1411,1450,1488,1525,1561,1596,1630,1663,1695,1726,1756,1785,1813,1840,1866,1891,1915,1938,1960,381,408,436,465,495,526,558,591,625,660,696,733,771,810,850,891,933,976,1020,1065,1111,1157,1202,1246,1289,1331,1372,1412,1451,1489,1526,1562,1597,1631,1664,1696,1727,1757,1786,1814,1841,1867,1892,1916,1939,1961,1982,409,437,466,496,527,559,592,626,661,697,734,772,811,851,892,934,977,1021,1066,1112,1158,1203,1247,1290,1332,1373,1413,1452,1490,1527,1563,1598,1632,1665,1697,1728,1758,1787,1815,1842,1868,1893,1917,1940,1962,1983,2003,438,467,497,528,560,593,627,662,698,735,773,812,852,893,935,978,1022,1067,1113,1159,1204,1248,1291,1333,1374,1414,1453,1491,1528,1564,1599,1633,1666,1698,1729,1759,1788,1816,1843,1869,1894,1918,1941,1963,1984,2004,2023,468,498,529,561,594,628,663,699,736,774,813,853,894,936,979,1023,1068,1114,1160,1205,1249,1292,1334,1375,1415,1454,1492,1529,1565,1600,1634,1667,1699,1730,1760,1789,1817,1844,1870,1895,1919,1942,1964,1985,2005,2024,2042,499,530,562,595,629,664,700,737,775,814,854,895,937,980,1024,1069,1115,1161,1206,1250,1293,1335,1376,1416,1455,1493,1530,1566,1601,1635,1668,1700,1731,1761,1790,1818,1845,1871,1896,1920,1943,1965,1986,2006,2025,2043,2060,531,563,596,630,665,701,738,776,815,855,896,938,981,1025,1070,1116,1162,1207,1251,1294,1336,1377,1417,1456,1494,1531,1567,1602,1636,1669,1701,1732,1762,1791,1819,1846,1872,1897,1921,1944,1966,1987,2007,2026,2044,2061,2077,564,597,631,666,702,739,777,816,856,897,939,982,1026,1071,1117,1163,1208,1252,1295,1337,1378,1418,1457,1495,1532,1568,1603,1637,1670,1702,1733,1763,1792,1820,1847,1873,1898,1922,1945,1967,1988,2008,2027,2045,2062,2078,2093,598,632,667,703,740,778,817,857,898,940,983,1027,1072,1118,1164,1209,1253,1296,1338,1379,1419,1458,1496,1533,1569,1604,1638,1671,1703,1734,1764,1793,1821,1848,1874,1899,1923,1946,1968,1989,2009,2028,2046,2063,2079,2094,2108,633,668,704,741,779,818,858,899,941,984,1028,1073,1119,1165,1210,1254,1297,1339,1380,1420,1459,1497,1534,1570,1605,1639,1672,1704,1735,1765,1794,1822,1849,1875,1900,1924,1947,1969,1990,2010,2029,2047,2064,2080,2095,2109,2122,669,705,742,780,819,859,900,942,985,1029,1074,1120,1166,1211,1255,1298,1340,1381,1421,1460,1498,1535,1571,1606,1640,1673,1705,1736,1766,1795,1823,1850,1876,1901,1925,1948,1970,1991,2011,2030,2048,2065,2081,2096,2110,2123,2135,706,743,781,820,860,901,943,986,1030,1075,1121,1167,1212,1256,1299,1341,1382,1422,1461,1499,1536,1572,1607,1641,1674,1706,1737,1767,1796,1824,1851,1877,1902,1926,1949,1971,1992,2012,2031,2049,2066,2082,2097,2111,2124,2136,2147,744,782,821,861,902,944,987,1031,1076,1122,1168,1213,1257,1300,1342,1383,1423,1462,1500,1537,1573,1608,1642,1675,1707,1738,1768,1797,1825,1852,1878,1903,1927,1950,1972,1993,2013,2032,2050,2067,2083,2098,2112,2125,2137,2148,2158,783,822,862,903,945,988,1032,1077,1123,1169,1214,1258,1301,1343,1384,1424,1463,1501,1538,1574,1609,1643,1676,1708,1739,1769,1798,1826,1853,1879,1904,1928,1951,1973,1994,2014,2033,2051,2068,2084,2099,2113,2126,2138,2149,2159,2168,823,863,904,946,989,1033,1078,1124,1170,1215,1259,1302,1344,1385,1425,1464,1502,1539,1575,1610,1644,1677,1709,1740,1770,1799,1827,1854,1880,1905,1929,1952,1974,1995,2015,2034,2052,2069,2085,2100,2114,2127,2139,2150,2160,2169,2177,864,905,947,990,1034,1079,1125,1171,1216,1260,1303,1345,1386,1426,1465,1503,1540,1576,1611,1645,1678,1710,1741,1771,1800,1828,1855,1881,1906,1930,1953,1975,1996,2016,2035,2053,2070,2086,2101,2115,2128,2140,2151,2161,2170,2178,2185,906,948,991,1035,1080,1126,1172,1217,1261,1304,1346,1387,1427,1466,1504,1541,1577,1612,1646,1679,1711,1742,1772,1801,1829,1856,1882,1907,1931,1954,1976,1997,2017,2036,2054,2071,2087,2102,2116,2129,2141,2152,2162,2171,2179,2186,2192,949,992,1036,1081,1127,1173,1218,1262,1305,1347,1388,1428,1467,1505,1542,1578,1613,1647,1680,1712,1743,1773,1802,1830,1857,1883,1908,1932,1955,1977,1998,2018,2037,2055,2072,2088,2103,2117,2130,2142,2153,2163,2172,2180,2187,2193,2198,993,1037,1082,1128,1174,1219,1263,1306,1348,1389,1429,1468,1506,1543,1579,1614,1648,1681,1713,1744,1774,1803,1831,1858,1884,1909,1933,1956,1978,1999,2019,2038,2056,2073,2089,2104,2118,2131,2143,2154,2164,2173,2181,2188,2194,2199,2203,1038,1083,1129,1175,1220,1264,1307,1349,1390,1430,1469,1507,1544,1580,1615,1649,1682,1714,1745,1775,1804,1832,1859,1885,1910,1934,1957,1979,2000,2020,2039,2057,2074,2090,2105,2119,2132,2144,2155,2165,2174,2182,2189,2195,2200,2204,2207,1084,1130,1176,1221,1265,1308,1350,1391,1431,1470,1508,1545,1581,1616,1650,1683,1715,1746,1776,1805,1833,1860,1886,1911,1935,1958,1980,2001,2021,2040,2058,2075,2091,2106,2120,2133,2145,2156,2166,2175,2183,2190,2196,2201,2205,2208,2210,1131,1177,1222,1266,1309,1351,1392,1432,1471,1509,1546,1582,1617,1651,1684,1716,1747,1777,1806,1834,1861,1887,1912,1936,1959,1981,2002,2022,2041,2059,2076,2092,2107,2121,2134,2146,2157,2167,2176,2184,2191,2197,2202,2206,2209,2211,2212);(1,2,3)
Conjugacy classes & character table
6627 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13254, 2);
Finite Group Databasebeta