Finite Group Databasebeta

?

← Prev (#45657155) Next (#45657157) →

D₁₆₃₁₂ #45657156

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

Aliases

Splittings

Subgroups

22 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 2047 points:

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

Polycyclic presentation:

2^4,2039|c^2=d,b^a=bc,c^a=cd,e^a=e^2038,c^b=cd,e^b=e^2038

Conjugacy classes & character table

8159 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32624, 26);