Finite Group Databasebeta

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Dic₆₂₃₈ #38735644

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 3127 points:

(1,2,3,4)(5,8,7,6)(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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058,2079)(1059,2078)(1060,2077)(1061,2076)(1062,2075)(1063,2074)(1064,2073)(1065,2072)(1066,2071)(1067,2070)(1068,2069)(1069,2068)(1070,2067)(1071,2066)(1072,2065)(1073,2064)(1074,2063)(1075,2062)(1076,2061)(1077,2060)(1078,2059)(1079,2058)(1080,2057)(1081,2056)(1082,2055)(1083,2054)(1084,2053)(1085,2052)(1086,2051)(1087,2050)(1088,2049)(1089,2048)(1090,2047)(1091,2046)(1092,2045)(1093,2044)(1094,2043)(1095,2042)(1096,2041)(1097,2040)(1098,2039)(1099,2038)(1100,2037)(1101,2036)(1102,2035)(1103,2034)(1104,2033)(1105,2032)(1106,2031)(1107,2030)(1108,2029)(1109,2028)(1110,2027)(1111,2026)(1112,2025)(1113,2024)(1114,2023)(1115,2022)(1116,2021)(1117,2020)(1118,2019)(1119,2018)(1120,2017)(1121,2016)(1122,2015)(1123,2014)(1124,2013)(1125,2012)(1126,2011)(1127,2010)(1128,2009)(1129,2008)(1130,2007)(1131,2006)(1132,2005)(1133,2004)(1134,2003)(1135,2002)(1136,2001)(1137,2000)(1138,1999)(1139,1998)(1140,1997)(1141,1996)(1142,1995)(1143,1994)(1144,1993)(1145,1992)(1146,1991)(1147,1990)(1148,1989)(1149,1988)(1150,1987)(1151,1986)(1152,1985)(1153,1984)(1154,1983)(1155,1982)(1156,1981)(1157,1980)(1158,1979)(1159,1978)(1160,1977)(1161,1976)(1162,1975)(1163,1974)(1164,1973)(1165,1972)(1166,1971)(1167,1970)(1168,1969)(1169,1968)(1170,1967)(1171,1966)(1172,1965)(1173,1964)(1174,1963)(1175,1962)(1176,1961)(1177,1960)(1178,1959)(1179,1958)(1180,1957)(1181,1956)(1182,1955)(1183,1954)(1184,1953)(1185,1952)(1186,1951)(1187,1950)(1188,1949)(1189,1948)(1190,1947)(1191,1946)(1192,1945)(1193,1944)(1194,1943)(1195,1942)(1196,1941)(1197,1940)(1198,1939)(1199,1938)(1200,1937)(1201,1936)(1202,1935)(1203,1934)(1204,1933)(1205,1932)(1206,1931)(1207,1930)(1208,1929)(1209,1928)(1210,1927)(1211,1926)(1212,1925)(1213,1924)(1214,1923)(1215,1922)(1216,1921)(1217,1920)(1218,1919)(1219,1918)(1220,1917)(1221,1916)(1222,1915)(1223,1914)(1224,1913)(1225,1912)(1226,1911)(1227,1910)(1228,1909)(1229,1908)(1230,1907)(1231,1906)(1232,1905)(1233,1904)(1234,1903)(1235,1902)(1236,1901)(1237,1900)(1238,1899)(1239,1898)(1240,1897)(1241,1896)(1242,1895)(1243,1894)(1244,1893)(1245,1892)(1246,1891)(1247,1890)(1248,1889)(1249,1888)(1250,1887)(1251,1886)(1252,1885)(1253,1884)(1254,1883)(1255,1882)(1256,1881)(1257,1880)(1258,1879)(1259,1878)(1260,1877)(1261,1876)(1262,1875)(1263,1874)(1264,1873)(1265,1872)(1266,1871)(1267,1870)(1268,1869)(1269,1868)(1270,1867)(1271,1866)(1272,1865)(1273,1864)(1274,1863)(1275,1862)(1276,1861)(1277,1860)(1278,1859)(1279,1858)(1280,1857)(1281,1856)(1282,1855)(1283,1854)(1284,1853)(1285,1852)(1286,1851)(1287,1850)(1288,1849)(1289,1848)(1290,1847)(1291,1846)(1292,1845)(1293,1844)(1294,1843)(1295,1842)(1296,1841)(1297,1840)(1298,1839)(1299,1838)(1300,1837)(1301,1836)(1302,1835)(1303,1834)(1304,1833)(1305,1832)(1306,1831)(1307,1830)(1308,1829)(1309,1828)(1310,1827)(1311,1826)(1312,1825)(1313,1824)(1314,1823)(1315,1822)(1316,1821)(1317,1820)(1318,1819)(1319,1818)(1320,1817)(1321,1816)(1322,1815)(1323,1814)(1324,1813)(1325,1812)(1326,1811)(1327,1810)(1328,1809)(1329,1808)(1330,1807)(1331,1806)(1332,1805)(1333,1804)(1334,1803)(1335,1802)(1336,1801)(1337,1800)(1338,1799)(1339,1798)(1340,1797)(1341,1796)(1342,1795)(1343,1794)(1344,1793)(1345,1792)(1346,1791)(1347,1790)(1348,1789)(1349,1788)(1350,1787)(1351,1786)(1352,1785)(1353,1784)(1354,1783)(1355,1782)(1356,1781)(1357,1780)(1358,1779)(1359,1778)(1360,1777)(1361,1776)(1362,1775)(1363,1774)(1364,1773)(1365,1772)(1366,1771)(1367,1770)(1368,1769)(1369,1768)(1370,1767)(1371,1766)(1372,1765)(1373,1764)(1374,1763)(1375,1762)(1376,1761)(1377,1760)(1378,1759)(1379,1758)(1380,1757)(1381,1756)(1382,1755)(1383,1754)(1384,1753)(1385,1752)(1386,1751)(1387,1750)(1388,1749)(1389,1748)(1390,1747)(1391,1746)(1392,1745)(1393,1744)(1394,1743)(1395,1742)(1396,1741)(1397,1740)(1398,1739)(1399,1738)(1400,1737)(1401,1736)(1402,1735)(1403,1734)(1404,1733)(1405,1732)(1406,1731)(1407,1730)(1408,1729)(1409,1728)(1410,1727)(1411,1726)(1412,1725)(1413,1724)(1414,1723)(1415,1722)(1416,1721)(1417,1720)(1418,1719)(1419,1718)(1420,1717)(1421,1716)(1422,1715)(1423,1714)(1424,1713)(1425,1712)(1426,1711)(1427,1710)(1428,1709)(1429,1708)(1430,1707)(1431,1706)(1432,1705)(1433,1704)(1434,1703)(1435,1702)(1436,1701)(1437,1700)(1438,1699)(1439,1698)(1440,1697)(1441,1696)(1442,1695)(1443,1694)(1444,1693)(1445,1692)(1446,1691)(1447,1690)(1448,1689)(1449,1688)(1450,1687)(1451,1686)(1452,1685)(1453,1684)(1454,1683)(1455,1682)(1456,1681)(1457,1680)(1458,1679)(1459,1678)(1460,1677)(1461,1676)(1462,1675)(1463,1674)(1464,1673)(1465,1672)(1466,1671)(1467,1670)(1468,1669)(1469,1668)(1470,1667)(1471,1666)(1472,1665)(1473,1664)(1474,1663)(1475,1662)(1476,1661)(1477,1660)(1478,1659)(1479,1658)(1480,1657)(1481,1656)(1482,1655)(1483,1654)(1484,1653)(1485,1652)(1486,1651)(1487,1650)(1488,1649)(1489,1648)(1490,1647)(1491,1646)(1492,1645)(1493,1644)(1494,1643)(1495,1642)(1496,1641)(1497,1640)(1498,1639)(1499,1638)(1500,1637)(1501,1636)(1502,1635)(1503,1634)(1504,1633)(1505,1632)(1506,1631)(1507,1630)(1508,1629)(1509,1628)(1510,1627)(1511,1626)(1512,1625)(1513,1624)(1514,1623)(1515,1622)(1516,1621)(1517,1620)(1518,1619)(1519,1618)(1520,1617)(1521,1616)(1522,1615)(1523,1614)(1524,1613)(1525,1612)(1526,1611)(1527,1610)(1528,1609)(1529,1608)(1530,1607)(1531,1606)(1532,1605)(1533,1604)(1534,1603)(1535,1602)(1536,1601)(1537,1600)(1538,1599)(1539,1598)(1540,1597)(1541,1596)(1542,1595)(1543,1594)(1544,1593)(1545,1592)(1546,1591)(1547,1590)(1548,1589)(1549,1588)(1550,1587)(1551,1586)(1552,1585)(1553,1584)(1554,1583)(1555,1582)(1556,1581)(1557,1580)(1558,1579)(1559,1578)(1560,1577)(1561,1576)(1562,1575)(1563,1574)(1564,1573)(1565,1572)(1566,1571)(1567,1570)(1568,1569)

Polycyclic presentation:

2^3,3119|a^2=c,b^2=c,b^a=bc,d^b=d^3118

Conjugacy classes & character table

6241 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24952, 11);