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Aliases
Splittings
Subgroups
10 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 3595 points:
(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,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7,2302)(1298,2301)(1299,2300)(1300,2299)(1301,2298)(1302,2297)(1303,2296)(1304,2295)(1305,2294)(1306,2293)(1307,2292)(1308,2291)(1309,2290)(1310,2289)(1311,2288)(1312,2287)(1313,2286)(1314,2285)(1315,2284)(1316,2283)(1317,2282)(1318,2281)(1319,2280)(1320,2279)(1321,2278)(1322,2277)(1323,2276)(1324,2275)(1325,2274)(1326,2273)(1327,2272)(1328,2271)(1329,2270)(1330,2269)(1331,2268)(1332,2267)(1333,2266)(1334,2265)(1335,2264)(1336,2263)(1337,2262)(1338,2261)(1339,2260)(1340,2259)(1341,2258)(1342,2257)(1343,2256)(1344,2255)(1345,2254)(1346,2253)(1347,2252)(1348,2251)(1349,2250)(1350,2249)(1351,2248)(1352,2247)(1353,2246)(1354,2245)(1355,2244)(1356,2243)(1357,2242)(1358,2241)(1359,2240)(1360,2239)(1361,2238)(1362,2237)(1363,2236)(1364,2235)(1365,2234)(1366,2233)(1367,2232)(1368,2231)(1369,2230)(1370,2229)(1371,2228)(1372,2227)(1373,2226)(1374,2225)(1375,2224)(1376,2223)(1377,2222)(1378,2221)(1379,2220)(1380,2219)(1381,2218)(1382,2217)(1383,2216)(1384,2215)(1385,2214)(1386,2213)(1387,2212)(1388,2211)(1389,2210)(1390,2209)(1391,2208)(1392,2207)(1393,2206)(1394,2205)(1395,2204)(1396,2203)(1397,2202)(1398,2201)(1399,2200)(1400,2199)(1401,2198)(1402,2197)(1403,2196)(1404,2195)(1405,2194)(1406,2193)(1407,2192)(1408,2191)(1409,2190)(1410,2189)(1411,2188)(1412,2187)(1413,2186)(1414,2185)(1415,2184)(1416,2183)(1417,2182)(1418,2181)(1419,2180)(1420,2179)(1421,2178)(1422,2177)(1423,2176)(1424,2175)(1425,2174)(1426,2173)(1427,2172)(1428,2171)(1429,2170)(1430,2169)(1431,2168)(1432,2167)(1433,2166)(1434,2165)(1435,2164)(1436,2163)(1437,2162)(1438,2161)(1439,2160)(1440,2159)(1441,2158)(1442,2157)(1443,2156)(1444,2155)(1445,2154)(1446,2153)(1447,2152)(1448,2151)(1449,2150)(1450,2149)(1451,2148)(1452,2147)(1453,2146)(1454,2145)(1455,2144)(1456,2143)(1457,2142)(1458,2141)(1459,2140)(1460,2139)(1461,2138)(1462,2137)(1463,2136)(1464,2135)(1465,2134)(1466,2133)(1467,2132)(1468,2131)(1469,2130)(1470,2129)(1471,2128)(1472,2127)(1473,2126)(1474,2125)(1475,2124)(1476,2123)(1477,2122)(1478,2121)(1479,2120)(1480,2119)(1481,2118)(1482,2117)(1483,2116)(1484,2115)(1485,2114)(1486,2113)(1487,2112)(1488,2111)(1489,2110)(1490,2109)(1491,2108)(1492,2107)(1493,2106)(1494,2105)(1495,2104)(1496,2103)(1497,2102)(1498,2101)(1499,2100)(1500,2099)(1501,2098)(1502,2097)(1503,2096)(1504,2095)(1505,2094)(1506,2093)(1507,2092)(1508,2091)(1509,2090)(1510,2089)(1511,2088)(1512,2087)(1513,2086)(1514,2085)(1515,2084)(1516,2083)(1517,2082)(1518,2081)(1519,2080)(1520,2079)(1521,2078)(1522,2077)(1523,2076)(1524,2075)(1525,2074)(1526,2073)(1527,2072)(1528,2071)(1529,2070)(1530,2069)(1531,2068)(1532,2067)(1533,2066)(1534,2065)(1535,2064)(1536,2063)(1537,2062)(1538,2061)(1539,2060)(1540,2059)(1541,2058)(1542,2057)(1543,2056)(1544,2055)(1545,2054)(1546,2053)(1547,2052)(1548,2051)(1549,2050)(1550,2049)(1551,2048)(1552,2047)(1553,2046)(1554,2045)(1555,2044)(1556,2043)(1557,2042)(1558,2041)(1559,2040)(1560,2039)(1561,2038)(1562,2037)(1563,2036)(1564,2035)(1565,2034)(1566,2033)(1567,2032)(1568,2031)(1569,2030)(1570,2029)(1571,2028)(1572,2027)(1573,2026)(1574,2025)(1575,2024)(1576,2023)(1577,2022)(1578,2021)(1579,2020)(1580,2019)(1581,2018)(1582,2017)(1583,2016)(1584,2015)(1585,2014)(1586,2013)(1587,2012)(1588,2011)(1589,2010)(1590,2009)(1591,2008)(1592,2007)(1593,2006)(1594,2005)(1595,2004)(1596,2003)(1597,2002)(1598,2001)(1599,2000)(1600,1999)(1601,1998)(1602,1997)(1603,1996)(1604,1995)(1605,1994)(1606,1993)(1607,1992)(1608,1991)(1609,1990)(1610,1989)(1611,1988)(1612,1987)(1613,1986)(1614,1985)(1615,1984)(1616,1983)(1617,1982)(1618,1981)(1619,1980)(1620,1979)(1621,1978)(1622,1977)(1623,1976)(1624,1975)(1625,1974)(1626,1973)(1627,1972)(1628,1971)(1629,1970)(1630,1969)(1631,1968)(1632,1967)(1633,1966)(1634,1965)(1635,1964)(1636,1963)(1637,1962)(1638,1961)(1639,1960)(1640,1959)(1641,1958)(1642,1957)(1643,1956)(1644,1955)(1645,1954)(1646,1953)(1647,1952)(1648,1951)(1649,1950)(1650,1949)(1651,1948)(1652,1947)(1653,1946)(1654,1945)(1655,1944)(1656,1943)(1657,1942)(1658,1941)(1659,1940)(1660,1939)(1661,1938)(1662,1937)(1663,1936)(1664,1935)(1665,1934)(1666,1933)(1667,1932)(1668,1931)(1669,1930)(1670,1929)(1671,1928)(1672,1927)(1673,1926)(1674,1925)(1675,1924)(1676,1923)(1677,1922)(1678,1921)(1679,1920)(1680,1919)(1681,1918)(1682,1917)(1683,1916)(1684,1915)(1685,1914)(1686,1913)(1687,1912)(1688,1911)(1689,1910)(1690,1909)(1691,1908)(1692,1907)(1693,1906)(1694,1905)(1695,1904)(1696,1903)(1697,1902)(1698,1901)(1699,1900)(1700,1899)(1701,1898)(1702,1897)(1703,1896)(1704,1895)(1705,1894)(1706,1893)(1707,1892)(1708,1891)(1709,1890)(1710,1889)(1711,1888)(1712,1887)(1713,1886)(1714,1885)(1715,1884)(1716,1883)(1717,1882)(1718,1881)(1719,1880)(1720,1879)(1721,1878)(1722,1877)(1723,1876)(1724,1875)(1725,1874)(1726,1873)(1727,1872)(1728,1871)(1729,1870)(1730,1869)(1731,1868)(1732,1867)(1733,1866)(1734,1865)(1735,1864)(1736,1863)(1737,1862)(1738,1861)(1739,1860)(1740,1859)(1741,1858)(1742,1857)(1743,1856)(1744,1855)(1745,1854)(1746,1853)(1747,1852)(1748,1851)(1749,1850)(1750,1849)(1751,1848)(1752,1847)(1753,1846)(1754,1845)(1755,1844)(1756,1843)(1757,1842)(1758,1841)(1759,1840)(1760,1839)(1761,1838)(1762,1837)(1763,1836)(1764,1835)(1765,1834)(1766,1833)(1767,1832)(1768,1831)(1769,1830)(1770,1829)(1771,1828)(1772,1827)(1773,1826)(1774,1825)(1775,1824)(1776,1823)(1777,1822)(1778,1821)(1779,1820)(1780,1819)(1781,1818)(1782,1817)(1783,1816)(1784,1815)(1785,1814)(1786,1813)(1787,1812)(1788,1811)(1789,1810)(1790,1809)(1791,1808)(1792,1807)(1793,1806)(1794,1805)(1795,1804)(1796,1803)(1797,1802)(1798,1801)(1799,1800)
Conjugacy classes & character table
3596 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14372, 4);
Finite Group Databasebeta