Finite Group Databasebeta

?

← Prev (#36345434) Next (#36345436) →

D₁₀₈₉₅ #36345435

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

Aliases

Splittings

Subgroups

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 2184 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184);(2,5)(3,4)(7,2184)(8,2183)(9,2182)(10,2181)(11,2180)(12,2179)(13,2178)(14,2177)(15,2176)(16,2175)(17,2174)(18,2173)(19,2172)(20,2171)(21,2170)(22,2169)(23,2168)(24,2167)(25,2166)(26,2165)(27,2164)(28,2163)(29,2162)(30,2161)(31,2160)(32,2159)(33,2158)(34,2157)(35,2156)(36,2155)(37,2154)(38,2153)(39,2152)(40,2151)(41,2150)(42,2149)(43,2148)(44,2147)(45,2146)(46,2145)(47,2144)(48,2143)(49,2142)(50,2141)(51,2140)(52,2139)(53,2138)(54,2137)(55,2136)(56,2135)(57,2134)(58,2133)(59,2132)(60,2131)(61,2130)(62,2129)(63,2128)(64,2127)(65,2126)(66,2125)(67,2124)(68,2123)(69,2122)(70,2121)(71,2120)(72,2119)(73,2118)(74,2117)(75,2116)(76,2115)(77,2114)(78,2113)(79,2112)(80,2111)(81,2110)(82,2109)(83,2108)(84,2107)(85,2106)(86,2105)(87,2104)(88,2103)(89,2102)(90,2101)(91,2100)(92,2099)(93,2098)(94,2097)(95,2096)(96,2095)(97,2094)(98,2093)(99,2092)(100,2091)(101,2090)(102,2089)(103,2088)(104,2087)(105,2086)(106,2085)(107,2084)(108,2083)(109,2082)(110,2081)(111,2080)(112,2079)(113,2078)(114,2077)(115,2076)(116,2075)(117,2074)(118,2073)(119,2072)(120,2071)(121,2070)(122,2069)(123,2068)(124,2067)(125,2066)(126,2065)(127,2064)(128,2063)(129,2062)(130,2061)(131,2060)(132,2059)(133,2058)(134,2057)(135,2056)(136,2055)(137,2054)(138,2053)(139,2052)(140,2051)(141,2050)(142,2049)(143,2048)(144,2047)(145,2046)(146,2045)(147,2044)(148,2043)(149,2042)(150,2041)(151,2040)(152,2039)(153,2038)(154,2037)(155,2036)(156,2035)(157,2034)(158,2033)(159,2032)(160,2031)(161,2030)(162,2029)(163,2028)(164,2027)(165,2026)(166,2025)(167,2024)(168,2023)(169,2022)(170,2021)(171,2020)(172,2019)(173,2018)(174,2017)(175,2016)(176,2015)(177,2014)(178,2013)(179,2012)(180,2011)(181,2010)(182,2009)(183,2008)(184,2007)(185,2006)(186,2005)(187,2004)(188,2003)(189,2002)(190,2001)(191,2000)(192,1999)(193,1998)(194,1997)(195,1996)(196,1995)(197,1994)(198,1993)(199,1992)(200,1991)(201,1990)(202,1989)(203,1988)(204,1987)(205,1986)(206,1985)(207,1984)(208,1983)(209,1982)(210,1981)(211,1980)(212,1979)(213,1978)(214,1977)(215,1976)(216,1975)(217,1974)(218,1973)(219,1972)(220,1971)(221,1970)(222,1969)(223,1968)(224,1967)(225,1966)(226,1965)(227,1964)(228,1963)(229,1962)(230,1961)(231,1960)(232,1959)(233,1958)(234,1957)(235,1956)(236,1955)(237,1954)(238,1953)(239,1952)(240,1951)(241,1950)(242,1949)(243,1948)(244,1947)(245,1946)(246,1945)(247,1944)(248,1943)(249,1942)(250,1941)(251,1940)(252,1939)(253,1938)(254,1937)(255,1936)(256,1935)(257,1934)(258,1933)(259,1932)(260,1931)(261,1930)(262,1929)(263,1928)(264,1927)(265,1926)(266,1925)(267,1924)(268,1923)(269,1922)(270,1921)(271,1920)(272,1919)(273,1918)(274,1917)(275,1916)(276,1915)(277,1914)(278,1913)(279,1912)(280,1911)(281,1910)(282,1909)(283,1908)(284,1907)(285,1906)(286,1905)(287,1904)(288,1903)(289,1902)(290,1901)(291,1900)(292,1899)(293,1898)(294,1897)(295,1896)(296,1895)(297,1894)(298,1893)(299,1892)(300,1891)(301,1890)(302,1889)(303,1888)(304,1887)(305,1886)(306,1885)(307,1884)(308,1883)(309,1882)(310,1881)(311,1880)(312,1879)(313,1878)(314,1877)(315,1876)(316,1875)(317,1874)(318,1873)(319,1872)(320,1871)(321,1870)(322,1869)(323,1868)(324,1867)(325,1866)(326,1865)(327,1864)(328,1863)(329,1862)(330,1861)(331,1860)(332,1859)(333,1858)(334,1857)(335,1856)(336,1855)(337,1854)(338,1853)(339,1852)(340,1851)(341,1850)(342,1849)(343,1848)(344,1847)(345,1846)(346,1845)(347,1844)(348,1843)(349,1842)(350,1841)(351,1840)(352,1839)(353,1838)(354,1837)(355,1836)(356,1835)(357,1834)(358,1833)(359,1832)(360,1831)(361,1830)(362,1829)(363,1828)(364,1827)(365,1826)(366,1825)(367,1824)(368,1823)(369,1822)(370,1821)(371,1820)(372,1819)(373,1818)(374,1817)(375,1816)(376,1815)(377,1814)(378,1813)(379,1812)(380,1811)(381,1810)(382,1809)(383,1808)(384,1807)(385,1806)(386,1805)(387,1804)(388,1803)(389,1802)(390,1801)(391,1800)(392,1799)(393,1798)(394,1797)(395,1796)(396,1795)(397,1794)(398,1793)(399,1792)(400,1791)(401,1790)(402,1789)(403,1788)(404,1787)(405,1786)(406,1785)(407,1784)(408,1783)(409,1782)(410,1781)(411,1780)(412,1779)(413,1778)(414,1777)(415,1776)(416,1775)(417,1774)(418,1773)(419,1772)(420,1771)(421,1770)(422,1769)(423,1768)(424,1767)(425,1766)(426,1765)(427,1764)(428,1763)(429,1762)(430,1761)(431,1760)(432,1759)(433,1758)(434,1757)(435,1756)(436,1755)(437,1754)(438,1753)(439,1752)(440,1751)(441,1750)(442,1749)(443,1748)(444,1747)(445,1746)(446,1745)(447,1744)(448,1743)(449,1742)(450,1741)(451,1740)(452,1739)(453,1738)(454,1737)(455,1736)(456,1735)(457,1734)(458,1733)(459,1732)(460,1731)(461,1730)(462,1729)(463,1728)(464,1727)(465,1726)(466,1725)(467,1724)(468,1723)(469,1722)(470,1721)(471,1720)(472,1719)(473,1718)(474,1717)(475,1716)(476,1715)(477,1714)(478,1713)(479,1712)(480,1711)(481,1710)(482,1709)(483,1708)(484,1707)(485,1706)(486,1705)(487,1704)(488,1703)(489,1702)(490,1701)(491,1700)(492,1699)(493,1698)(494,1697)(495,1696)(496,1695)(497,1694)(498,1693)(499,1692)(500,1691)(501,1690)(502,1689)(503,1688)(504,1687)(505,1686)(506,1685)(507,1684)(508,1683)(509,1682)(510,1681)(511,1680)(512,1679)(513,1678)(514,1677)(515,1676)(516,1675)(517,1674)(518,1673)(519,1672)(520,1671)(521,1670)(522,1669)(523,1668)(524,1667)(525,1666)(526,1665)(527,1664)(528,1663)(529,1662)(530,1661)(531,1660)(532,1659)(533,1658)(534,1657)(535,1656)(536,1655)(537,1654)(538,1653)(539,1652)(540,1651)(541,1650)(542,1649)(543,1648)(544,1647)(545,1646)(546,1645)(547,1644)(548,1643)(549,1642)(550,1641)(551,1640)(552,1639)(553,1638)(554,1637)(555,1636)(556,1635)(557,1634)(558,1633)(559,1632)(560,1631)(561,1630)(562,1629)(563,1628)(564,1627)(565,1626)(566,1625)(567,1624)(568,1623)(569,1622)(570,1621)(571,1620)(572,1619)(573,1618)(574,1617)(575,1616)(576,1615)(577,1614)(578,1613)(579,1612)(580,1611)(581,1610)(582,1609)(583,1608)(584,1607)(585,1606)(586,1605)(587,1604)(588,1603)(589,1602)(590,1601)(591,1600)(592,1599)(593,1598)(594,1597)(595,1596)(596,1595)(597,1594)(598,1593)(599,1592)(600,1591)(601,1590)(602,1589)(603,1588)(604,1587)(605,1586)(606,1585)(607,1584)(608,1583)(609,1582)(610,1581)(611,1580)(612,1579)(613,1578)(614,1577)(615,1576)(616,1575)(617,1574)(618,1573)(619,1572)(620,1571)(621,1570)(622,1569)(623,1568)(624,1567)(625,1566)(626,1565)(627,1564)(628,1563)(629,1562)(630,1561)(631,1560)(632,1559)(633,1558)(634,1557)(635,1556)(636,1555)(637,1554)(638,1553)(639,1552)(640,1551)(641,1550)(642,1549)(643,1548)(644,1547)(645,1546)(646,1545)(647,1544)(648,1543)(649,1542)(650,1541)(651,1540)(652,1539)(653,1538)(654,1537)(655,1536)(656,1535)(657,1534)(658,1533)(659,1532)(660,1531)(661,1530)(662,1529)(663,1528)(664,1527)(665,1526)(666,1525)(667,1524)(668,1523)(669,1522)(670,1521)(671,1520)(672,1519)(673,1518)(674,1517)(675,1516)(676,1515)(677,1514)(678,1513)(679,1512)(680,1511)(681,1510)(682,1509)(683,1508)(684,1507)(685,1506)(686,1505)(687,1504)(688,1503)(689,1502)(690,1501)(691,1500)(692,1499)(693,1498)(694,1497)(695,1496)(696,1495)(697,1494)(698,1493)(699,1492)(700,1491)(701,1490)(702,1489)(703,1488)(704,1487)(705,1486)(706,1485)(707,1484)(708,1483)(709,1482)(710,1481)(711,1480)(712,1479)(713,1478)(714,1477)(715,1476)(716,1475)(717,1474)(718,1473)(719,1472)(720,1471)(721,1470)(722,1469)(723,1468)(724,1467)(725,1466)(726,1465)(727,1464)(728,1463)(729,1462)(730,1461)(731,1460)(732,1459)(733,1458)(734,1457)(735,1456)(736,1455)(737,1454)(738,1453)(739,1452)(740,1451)(741,1450)(742,1449)(743,1448)(744,1447)(745,1446)(746,1445)(747,1444)(748,1443)(749,1442)(750,1441)(751,1440)(752,1439)(753,1438)(754,1437)(755,1436)(756,1435)(757,1434)(758,1433)(759,1432)(760,1431)(761,1430)(762,1429)(763,1428)(764,1427)(765,1426)(766,1425)(767,1424)(768,1423)(769,1422)(770,1421)(771,1420)(772,1419)(773,1418)(774,1417)(775,1416)(776,1415)(777,1414)(778,1413)(779,1412)(780,1411)(781,1410)(782,1409)(783,1408)(784,1407)(785,1406)(786,1405)(787,1404)(788,1403)(789,1402)(790,1401)(791,1400)(792,1399)(793,1398)(794,1397)(795,1396)(796,1395)(797,1394)(798,1393)(799,1392)(800,1391)(801,1390)(802,1389)(803,1388)(804,1387)(805,1386)(806,1385)(807,1384)(808,1383)(809,1382)(810,1381)(811,1380)(812,1379)(813,1378)(814,1377)(815,1376)(816,1375)(817,1374)(818,1373)(819,1372)(820,1371)(821,1370)(822,1369)(823,1368)(824,1367)(825,1366)(826,1365)(827,1364)(828,1363)(829,1362)(830,1361)(831,1360)(832,1359)(833,1358)(834,1357)(835,1356)(836,1355)(837,1354)(838,1353)(839,1352)(840,1351)(841,1350)(842,1349)(843,1348)(844,1347)(845,1346)(846,1345)(847,1344)(848,1343)(849,1342)(850,1341)(851,1340)(852,1339)(853,1338)(854,1337)(855,1336)(856,1335)(857,1334)(858,1333)(859,1332)(860,1331)(861,1330)(862,1329)(863,1328)(864,1327)(865,1326)(866,1325)(867,1324)(868,1323)(869,1322)(870,1321)(871,1320)(872,1319)(873,1318)(874,1317)(875,1316)(876,1315)(877,1314)(878,1313)(879,1312)(880,1311)(881,1310)(882,1309)(883,1308)(884,1307)(885,1306)(886,1305)(887,1304)(888,1303)(889,1302)(890,1301)(891,1300)(892,1299)(893,1298)(894,1297)(895,1296)(896,1295)(897,1294)(898,1293)(899,1292)(900,1291)(901,1290)(902,1289)(903,1288)(904,1287)(905,1286)(906,1285)(907,1284)(908,1283)(909,1282)(910,1281)(911,1280)(912,1279)(913,1278)(914,1277)(915,1276)(916,1275)(917,1274)(918,1273)(919,1272)(920,1271)(921,1270)(922,1269)(923,1268)(924,1267)(925,1266)(926,1265)(927,1264)(928,1263)(929,1262)(930,1261)(931,1260)(932,1259)(933,1258)(934,1257)(935,1256)(936,1255)(937,1254)(938,1253)(939,1252)(940,1251)(941,1250)(942,1249)(943,1248)(944,1247)(945,1246)(946,1245)(947,1244)(948,1243)(949,1242)(950,1241)(951,1240)(952,1239)(953,1238)(954,1237)(955,1236)(956,1235)(957,1234)(958,1233)(959,1232)(960,1231)(961,1230)(962,1229)(963,1228)(964,1227)(965,1226)(966,1225)(967,1224)(968,1223)(969,1222)(970,1221)(971,1220)(972,1219)(973,1218)(974,1217)(975,1216)(976,1215)(977,1214)(978,1213)(979,1212)(980,1211)(981,1210)(982,1209)(983,1208)(984,1207)(985,1206)(986,1205)(987,1204)(988,1203)(989,1202)(990,1201)(991,1200)(992,1199)(993,1198)(994,1197)(995,1196)(996,1195)(997,1194)(998,1193)(999,1192)(1000,1191)(1001,1190)(1002,1189)(1003,1188)(1004,1187)(1005,1186)(1006,1185)(1007,1184)(1008,1183)(1009,1182)(1010,1181)(1011,1180)(1012,1179)(1013,1178)(1014,1177)(1015,1176)(1016,1175)(1017,1174)(1018,1173)(1019,1172)(1020,1171)(1021,1170)(1022,1169)(1023,1168)(1024,1167)(1025,1166)(1026,1165)(1027,1164)(1028,1163)(1029,1162)(1030,1161)(1031,1160)(1032,1159)(1033,1158)(1034,1157)(1035,1156)(1036,1155)(1037,1154)(1038,1153)(1039,1152)(1040,1151)(1041,1150)(1042,1149)(1043,1148)(1044,1147)(1045,1146)(1046,1145)(1047,1144)(1048,1143)(1049,1142)(1050,1141)(1051,1140)(1052,1139)(1053,1138)(1054,1137)(1055,1136)(1056,1135)(1057,1134)(1058,1133)(1059,1132)(1060,1131)(1061,1130)(1062,1129)(1063,1128)(1064,1127)(1065,1126)(1066,1125)(1067,1124)(1068,1123)(1069,1122)(1070,1121)(1071,1120)(1072,1119)(1073,1118)(1074,1117)(1075,1116)(1076,1115)(1077,1114)(1078,1113)(1079,1112)(1080,1111)(1081,1110)(1082,1109)(1083,1108)(1084,1107)(1085,1106)(1086,1105)(1087,1104)(1088,1103)(1089,1102)(1090,1101)(1091,1100)(1092,1099)(1093,1098)(1094,1097)(1095,1096)

Polycyclic presentation:

2,5,2179|b^a=b^4,c^a=c^2178

Conjugacy classes & character table

5449 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21790, 3);