Finite Group Databasebeta

?

← Prev (#44545305) Next (#44545307) →

Dic₈₀₁₂ #44545306

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

Aliases

Splittings

Subgroups

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 2019 points:

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

Polycyclic presentation:

2^4,2003|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2002,c^b=cd,e^b=e^2002

Conjugacy classes & character table

8015 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32048, 31);