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Dic3593 #28385452
Aliases
Splittings
Subgroups
6 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 3597 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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(1297,2306)(1298,2305)(1299,2304)(1300,2303)(1301,2302)(1302,2301)(1303,2300)(1304,2299)(1305,2298)(1306,2297)(1307,2296)(1308,2295)(1309,2294)(1310,2293)(1311,2292)(1312,2291)(1313,2290)(1314,2289)(1315,2288)(1316,2287)(1317,2286)(1318,2285)(1319,2284)(1320,2283)(1321,2282)(1322,2281)(1323,2280)(1324,2279)(1325,2278)(1326,2277)(1327,2276)(1328,2275)(1329,2274)(1330,2273)(1331,2272)(1332,2271)(1333,2270)(1334,2269)(1335,2268)(1336,2267)(1337,2266)(1338,2265)(1339,2264)(1340,2263)(1341,2262)(1342,2261)(1343,2260)(1344,2259)(1345,2258)(1346,2257)(1347,2256)(1348,2255)(1349,2254)(1350,2253)(1351,2252)(1352,2251)(1353,2250)(1354,2249)(1355,2248)(1356,2247)(1357,2246)(1358,2245)(1359,2244)(1360,2243)(1361,2242)(1362,2241)(1363,2240)(1364,2239)(1365,2238)(1366,2237)(1367,2236)(1368,2235)(1369,2234)(1370,2233)(1371,2232)(1372,2231)(1373,2230)(1374,2229)(1375,2228)(1376,2227)(1377,2226)(1378,2225)(1379,2224)(1380,2223)(1381,2222)(1382,2221)(1383,2220)(1384,2219)(1385,2218)(1386,2217)(1387,2216)(1388,2215)(1389,2214)(1390,2213)(1391,2212)(1392,2211)(1393,2210)(1394,2209)(1395,2208)(1396,2207)(1397,2206)(1398,2205)(1399,2204)(1400,2203)(1401,2202)(1402,2201)(1403,2200)(1404,2199)(1405,2198)(1406,2197)(1407,2196)(1408,2195)(1409,2194)(1410,2193)(1411,2192)(1412,2191)(1413,2190)(1414,2189)(1415,2188)(1416,2187)(1417,2186)(1418,2185)(1419,2184)(1420,2183)(1421,2182)(1422,2181)(1423,2180)(1424,2179)(1425,2178)(1426,2177)(1427,2176)(1428,2175)(1429,2174)(1430,2173)(1431,2172)(1432,2171)(1433,2170)(1434,2169)(1435,2168)(1436,2167)(1437,2166)(1438,2165)(1439,2164)(1440,2163)(1441,2162)(1442,2161)(1443,2160)(1444,2159)(1445,2158)(1446,2157)(1447,2156)(1448,2155)(1449,2154)(1450,2153)(1451,2152)(1452,2151)(1453,2150)(1454,2149)(1455,2148)(1456,2147)(1457,2146)(1458,2145)(1459,2144)(1460,2143)(1461,2142)(1462,2141)(1463,2140)(1464,2139)(1465,2138)(1466,2137)(1467,2136)(1468,2135)(1469,2134)(1470,2133)(1471,2132)(1472,2131)(1473,2130)(1474,2129)(1475,2128)(1476,2127)(1477,2126)(1478,2125)(1479,2124)(1480,2123)(1481,2122)(1482,2121)(1483,2120)(1484,2119)(1485,2118)(1486,2117)(1487,2116)(1488,2115)(1489,2114)(1490,2113)(1491,2112)(1492,2111)(1493,2110)(1494,2109)(1495,2108)(1496,2107)(1497,2106)(1498,2105)(1499,2104)(1500,2103)(1501,2102)(1502,2101)(1503,2100)(1504,2099)(1505,2098)(1506,2097)(1507,2096)(1508,2095)(1509,2094)(1510,2093)(1511,2092)(1512,2091)(1513,2090)(1514,2089)(1515,2088)(1516,2087)(1517,2086)(1518,2085)(1519,2084)(1520,2083)(1521,2082)(1522,2081)(1523,2080)(1524,2079)(1525,2078)(1526,2077)(1527,2076)(1528,2075)(1529,2074)(1530,2073)(1531,2072)(1532,2071)(1533,2070)(1534,2069)(1535,2068)(1536,2067)(1537,2066)(1538,2065)(1539,2064)(1540,2063)(1541,2062)(1542,2061)(1543,2060)(1544,2059)(1545,2058)(1546,2057)(1547,2056)(1548,2055)(1549,2054)(1550,2053)(1551,2052)(1552,2051)(1553,2050)(1554,2049)(1555,2048)(1556,2047)(1557,2046)(1558,2045)(1559,2044)(1560,2043)(1561,2042)(1562,2041)(1563,2040)(1564,2039)(1565,2038)(1566,2037)(1567,2036)(1568,2035)(1569,2034)(1570,2033)(1571,2032)(1572,2031)(1573,2030)(1574,2029)(1575,2028)(1576,2027)(1577,2026)(1578,2025)(1579,2024)(1580,2023)(1581,2022)(1582,2021)(1583,2020)(1584,2019)(1585,2018)(1586,2017)(1587,2016)(1588,2015)(1589,2014)(1590,2013)(1591,2012)(1592,2011)(1593,2010)(1594,2009)(1595,2008)(1596,2007)(1597,2006)(1598,2005)(1599,2004)(1600,2003)(1601,2002)(1602,2001)(1603,2000)(1604,1999)(1605,1998)(1606,1997)(1607,1996)(1608,1995)(1609,1994)(1610,1993)(1611,1992)(1612,1991)(1613,1990)(1614,1989)(1615,1988)(1616,1987)(1617,1986)(1618,1985)(1619,1984)(1620,1983)(1621,1982)(1622,1981)(1623,1980)(1624,1979)(1625,1978)(1626,1977)(1627,1976)(1628,1975)(1629,1974)(1630,1973)(1631,1972)(1632,1971)(1633,1970)(1634,1969)(1635,1968)(1636,1967)(1637,1966)(1638,1965)(1639,1964)(1640,1963)(1641,1962)(1642,1961)(1643,1960)(1644,1959)(1645,1958)(1646,1957)(1647,1956)(1648,1955)(1649,1954)(1650,1953)(1651,1952)(1652,1951)(1653,1950)(1654,1949)(1655,1948)(1656,1947)(1657,1946)(1658,1945)(1659,1944)(1660,1943)(1661,1942)(1662,1941)(1663,1940)(1664,1939)(1665,1938)(1666,1937)(1667,1936)(1668,1935)(1669,1934)(1670,1933)(1671,1932)(1672,1931)(1673,1930)(1674,1929)(1675,1928)(1676,1927)(1677,1926)(1678,1925)(1679,1924)(1680,1923)(1681,1922)(1682,1921)(1683,1920)(1684,1919)(1685,1918)(1686,1917)(1687,1916)(1688,1915)(1689,1914)(1690,1913)(1691,1912)(1692,1911)(1693,1910)(1694,1909)(1695,1908)(1696,1907)(1697,1906)(1698,1905)(1699,1904)(1700,1903)(1701,1902)(1702,1901)(1703,1900)(1704,1899)(1705,1898)(1706,1897)(1707,1896)(1708,1895)(1709,1894)(1710,1893)(1711,1892)(1712,1891)(1713,1890)(1714,1889)(1715,1888)(1716,1887)(1717,1886)(1718,1885)(1719,1884)(1720,1883)(1721,1882)(1722,1881)(1723,1880)(1724,1879)(1725,1878)(1726,1877)(1727,1876)(1728,1875)(1729,1874)(1730,1873)(1731,1872)(1732,1871)(1733,1870)(1734,1869)(1735,1868)(1736,1867)(1737,1866)(1738,1865)(1739,1864)(1740,1863)(1741,1862)(1742,1861)(1743,1860)(1744,1859)(1745,1858)(1746,1857)(1747,1856)(1748,1855)(1749,1854)(1750,1853)(1751,1852)(1752,1851)(1753,1850)(1754,1849)(1755,1848)(1756,1847)(1757,1846)(1758,1845)(1759,1844)(1760,1843)(1761,1842)(1762,1841)(1763,1840)(1764,1839)(1765,1838)(1766,1837)(1767,1836)(1768,1835)(1769,1834)(1770,1833)(1771,1832)(1772,1831)(1773,1830)(1774,1829)(1775,1828)(1776,1827)(1777,1826)(1778,1825)(1779,1824)(1780,1823)(1781,1822)(1782,1821)(1783,1820)(1784,1819)(1785,1818)(1786,1817)(1787,1816)(1788,1815)(1789,1814)(1790,1813)(1791,1812)(1792,1811)(1793,1810)(1794,1809)(1795,1808)(1796,1807)(1797,1806)(1798,1805)(1799,1804)(1800,1803)(1801,1802)
Polycyclic presentation:
2^2,3593|a^2=b,c^a=c^3592
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, 1);
Finite Group Databasebeta