Finite Group Databasebeta

?

← Prev (#37557760) Next (#37557762) →

D₁₁₈₈₅ #37557761

• 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 2382 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199,2200,2201,2202,2203,2204,2205,2206,2207,2208,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219,2220,2221,2222,2223,2224,2225,2226,2227,2228,2229,2230,2231,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2302,2303,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382);(2,5)(3,4)(7,2382)(8,2381)(9,2380)(10,2379)(11,2378)(12,2377)(13,2376)(14,2375)(15,2374)(16,2373)(17,2372)(18,2371)(19,2370)(20,2369)(21,2368)(22,2367)(23,2366)(24,2365)(25,2364)(26,2363)(27,2362)(28,2361)(29,2360)(30,2359)(31,2358)(32,2357)(33,2356)(34,2355)(35,2354)(36,2353)(37,2352)(38,2351)(39,2350)(40,2349)(41,2348)(42,2347)(43,2346)(44,2345)(45,2344)(46,2343)(47,2342)(48,2341)(49,2340)(50,2339)(51,2338)(52,2337)(53,2336)(54,2335)(55,2334)(56,2333)(57,2332)(58,2331)(59,2330)(60,2329)(61,2328)(62,2327)(63,2326)(64,2325)(65,2324)(66,2323)(67,2322)(68,2321)(69,2320)(70,2319)(71,2318)(72,2317)(73,2316)(74,2315)(75,2314)(76,2313)(77,2312)(78,2311)(79,2310)(80,2309)(81,2308)(82,2307)(83,2306)(84,2305)(85,2304)(86,2303)(87,2302)(88,2301)(89,2300)(90,2299)(91,2298)(92,2297)(93,2296)(94,2295)(95,2294)(96,2293)(97,2292)(98,2291)(99,2290)(100,2289)(101,2288)(102,2287)(103,2286)(104,2285)(105,2284)(106,2283)(107,2282)(108,2281)(109,2280)(110,2279)(111,2278)(112,2277)(113,2276)(114,2275)(115,2274)(116,2273)(117,2272)(118,2271)(119,2270)(120,2269)(121,2268)(122,2267)(123,2266)(124,2265)(125,2264)(126,2263)(127,2262)(128,2261)(129,2260)(130,2259)(131,2258)(132,2257)(133,2256)(134,2255)(135,2254)(136,2253)(137,2252)(138,2251)(139,2250)(140,2249)(141,2248)(142,2247)(143,2246)(144,2245)(145,2244)(146,2243)(147,2242)(148,2241)(149,2240)(150,2239)(151,2238)(152,2237)(153,2236)(154,2235)(155,2234)(156,2233)(157,2232)(158,2231)(159,2230)(160,2229)(161,2228)(162,2227)(163,2226)(164,2225)(165,2224)(166,2223)(167,2222)(168,2221)(169,2220)(170,2219)(171,2218)(172,2217)(173,2216)(174,2215)(175,2214)(176,2213)(177,2212)(178,2211)(179,2210)(180,2209)(181,2208)(182,2207)(183,2206)(184,2205)(185,2204)(186,2203)(187,2202)(188,2201)(189,2200)(190,2199)(191,2198)(192,2197)(193,2196)(194,2195)(195,2194)(196,2193)(197,2192)(198,2191)(199,2190)(200,2189)(201,2188)(202,2187)(203,2186)(204,2185)(205,2184)(206,2183)(207,2182)(208,2181)(209,2180)(210,2179)(211,2178)(212,2177)(213,2176)(214,2175)(215,2174)(216,2173)(217,2172)(218,2171)(219,2170)(220,2169)(221,2168)(222,2167)(223,2166)(224,2165)(225,2164)(226,2163)(227,2162)(228,2161)(229,2160)(230,2159)(231,2158)(232,2157)(233,2156)(234,2155)(235,2154)(236,2153)(237,2152)(238,2151)(239,2150)(240,2149)(241,2148)(242,2147)(243,2146)(244,2145)(245,2144)(246,2143)(247,2142)(248,2141)(249,2140)(250,2139)(251,2138)(252,2137)(253,2136)(254,2135)(255,2134)(256,2133)(257,2132)(258,2131)(259,2130)(260,2129)(261,2128)(262,2127)(263,2126)(264,2125)(265,2124)(266,2123)(267,2122)(268,2121)(269,2120)(270,2119)(271,2118)(272,2117)(273,2116)(274,2115)(275,2114)(276,2113)(277,2112)(278,2111)(279,2110)(280,2109)(281,2108)(282,2107)(283,2106)(284,2105)(285,2104)(286,2103)(287,2102)(288,2101)(289,2100)(290,2099)(291,2098)(292,2097)(293,2096)(294,2095)(295,2094)(296,2093)(297,2092)(298,2091)(299,2090)(300,2089)(301,2088)(302,2087)(303,2086)(304,2085)(305,2084)(306,2083)(307,2082)(308,2081)(309,2080)(310,2079)(311,2078)(312,2077)(313,2076)(314,2075)(315,2074)(316,2073)(317,2072)(318,2071)(319,2070)(320,2069)(321,2068)(322,2067)(323,2066)(324,2065)(325,2064)(326,2063)(327,2062)(328,2061)(329,2060)(330,2059)(331,2058)(332,2057)(333,2056)(334,2055)(335,2054)(336,2053)(337,2052)(338,2051)(339,2050)(340,2049)(341,2048)(342,2047)(343,2046)(344,2045)(345,2044)(346,2043)(347,2042)(348,2041)(349,2040)(350,2039)(351,2038)(352,2037)(353,2036)(354,2035)(355,2034)(356,2033)(357,2032)(358,2031)(359,2030)(360,2029)(361,2028)(362,2027)(363,2026)(364,2025)(365,2024)(366,2023)(367,2022)(368,2021)(369,2020)(370,2019)(371,2018)(372,2017)(373,2016)(374,2015)(375,2014)(376,2013)(377,2012)(378,2011)(379,2010)(380,2009)(381,2008)(382,2007)(383,2006)(384,2005)(385,2004)(386,2003)(387,2002)(388,2001)(389,2000)(390,1999)(391,1998)(392,1997)(393,1996)(394,1995)(395,1994)(396,1993)(397,1992)(398,1991)(399,1990)(400,1989)(401,1988)(402,1987)(403,1986)(404,1985)(405,1984)(406,1983)(407,1982)(408,1981)(409,1980)(410,1979)(411,1978)(412,1977)(413,1976)(414,1975)(415,1974)(416,1973)(417,1972)(418,1971)(419,1970)(420,1969)(421,1968)(422,1967)(423,1966)(424,1965)(425,1964)(426,1963)(427,1962)(428,1961)(429,1960)(430,1959)(431,1958)(432,1957)(433,1956)(434,1955)(435,1954)(436,1953)(437,1952)(438,1951)(439,1950)(440,1949)(441,1948)(442,1947)(443,1946)(444,1945)(445,1944)(446,1943)(447,1942)(448,1941)(449,1940)(450,1939)(451,1938)(452,1937)(453,1936)(454,1935)(455,1934)(456,1933)(457,1932)(458,1931)(459,1930)(460,1929)(461,1928)(462,1927)(463,1926)(464,1925)(465,1924)(466,1923)(467,1922)(468,1921)(469,1920)(470,1919)(471,1918)(472,1917)(473,1916)(474,1915)(475,1914)(476,1913)(477,1912)(478,1911)(479,1910)(480,1909)(481,1908)(482,1907)(483,1906)(484,1905)(485,1904)(486,1903)(487,1902)(488,1901)(489,1900)(490,1899)(491,1898)(492,1897)(493,1896)(494,1895)(495,1894)(496,1893)(497,1892)(498,1891)(499,1890)(500,1889)(501,1888)(502,1887)(503,1886)(504,1885)(505,1884)(506,1883)(507,1882)(508,1881)(509,1880)(510,1879)(511,1878)(512,1877)(513,1876)(514,1875)(515,1874)(516,1873)(517,1872)(518,1871)(519,1870)(520,1869)(521,1868)(522,1867)(523,1866)(524,1865)(525,1864)(526,1863)(527,1862)(528,1861)(529,1860)(530,1859)(531,1858)(532,1857)(533,1856)(534,1855)(535,1854)(536,1853)(537,1852)(538,1851)(539,1850)(540,1849)(541,1848)(542,1847)(543,1846)(544,1845)(545,1844)(546,1843)(547,1842)(548,1841)(549,1840)(550,1839)(551,1838)(552,1837)(553,1836)(554,1835)(555,1834)(556,1833)(557,1832)(558,1831)(559,1830)(560,1829)(561,1828)(562,1827)(563,1826)(564,1825)(565,1824)(566,1823)(567,1822)(568,1821)(569,1820)(570,1819)(571,1818)(572,1817)(573,1816)(574,1815)(575,1814)(576,1813)(577,1812)(578,1811)(579,1810)(580,1809)(581,1808)(582,1807)(583,1806)(584,1805)(585,1804)(586,1803)(587,1802)(588,1801)(589,1800)(590,1799)(591,1798)(592,1797)(593,1796)(594,1795)(595,1794)(596,1793)(597,1792)(598,1791)(599,1790)(600,1789)(601,1788)(602,1787)(603,1786)(604,1785)(605,1784)(606,1783)(607,1782)(608,1781)(609,1780)(610,1779)(611,1778)(612,1777)(613,1776)(614,1775)(615,1774)(616,1773)(617,1772)(618,1771)(619,1770)(620,1769)(621,1768)(622,1767)(623,1766)(624,1765)(625,1764)(626,1763)(627,1762)(628,1761)(629,1760)(630,1759)(631,1758)(632,1757)(633,1756)(634,1755)(635,1754)(636,1753)(637,1752)(638,1751)(639,1750)(640,1749)(641,1748)(642,1747)(643,1746)(644,1745)(645,1744)(646,1743)(647,1742)(648,1741)(649,1740)(650,1739)(651,1738)(652,1737)(653,1736)(654,1735)(655,1734)(656,1733)(657,1732)(658,1731)(659,1730)(660,1729)(661,1728)(662,1727)(663,1726)(664,1725)(665,1724)(666,1723)(667,1722)(668,1721)(669,1720)(670,1719)(671,1718)(672,1717)(673,1716)(674,1715)(675,1714)(676,1713)(677,1712)(678,1711)(679,1710)(680,1709)(681,1708)(682,1707)(683,1706)(684,1705)(685,1704)(686,1703)(687,1702)(688,1701)(689,1700)(690,1699)(691,1698)(692,1697)(693,1696)(694,1695)(695,1694)(696,1693)(697,1692)(698,1691)(699,1690)(700,1689)(701,1688)(702,1687)(703,1686)(704,1685)(705,1684)(706,1683)(707,1682)(708,1681)(709,1680)(710,1679)(711,1678)(712,1677)(713,1676)(714,1675)(715,1674)(716,1673)(717,1672)(718,1671)(719,1670)(720,1669)(721,1668)(722,1667)(723,1666)(724,1665)(725,1664)(726,1663)(727,1662)(728,1661)(729,1660)(730,1659)(731,1658)(732,1657)(733,1656)(734,1655)(735,1654)(736,1653)(737,1652)(738,1651)(739,1650)(740,1649)(741,1648)(742,1647)(743,1646)(744,1645)(745,1644)(746,1643)(747,1642)(748,1641)(749,1640)(750,1639)(751,1638)(752,1637)(753,1636)(754,1635)(755,1634)(756,1633)(757,1632)(758,1631)(759,1630)(760,1629)(761,1628)(762,1627)(763,1626)(764,1625)(765,1624)(766,1623)(767,1622)(768,1621)(769,1620)(770,1619)(771,1618)(772,1617)(773,1616)(774,1615)(775,1614)(776,1613)(777,1612)(778,1611)(779,1610)(780,1609)(781,1608)(782,1607)(783,1606)(784,1605)(785,1604)(786,1603)(787,1602)(788,1601)(789,1600)(790,1599)(791,1598)(792,1597)(793,1596)(794,1595)(795,1594)(796,1593)(797,1592)(798,1591)(799,1590)(800,1589)(801,1588)(802,1587)(803,1586)(804,1585)(805,1584)(806,1583)(807,1582)(808,1581)(809,1580)(810,1579)(811,1578)(812,1577)(813,1576)(814,1575)(815,1574)(816,1573)(817,1572)(818,1571)(819,1570)(820,1569)(821,1568)(822,1567)(823,1566)(824,1565)(825,1564)(826,1563)(827,1562)(828,1561)(829,1560)(830,1559)(831,1558)(832,1557)(833,1556)(834,1555)(835,1554)(836,1553)(837,1552)(838,1551)(839,1550)(840,1549)(841,1548)(842,1547)(843,1546)(844,1545)(845,1544)(846,1543)(847,1542)(848,1541)(849,1540)(850,1539)(851,1538)(852,1537)(853,1536)(854,1535)(855,1534)(856,1533)(857,1532)(858,1531)(859,1530)(860,1529)(861,1528)(862,1527)(863,1526)(864,1525)(865,1524)(866,1523)(867,1522)(868,1521)(869,1520)(870,1519)(871,1518)(872,1517)(873,1516)(874,1515)(875,1514)(876,1513)(877,1512)(878,1511)(879,1510)(880,1509)(881,1508)(882,1507)(883,1506)(884,1505)(885,1504)(886,1503)(887,1502)(888,1501)(889,1500)(890,1499)(891,1498)(892,1497)(893,1496)(894,1495)(895,1494)(896,1493)(897,1492)(898,1491)(899,1490)(900,1489)(901,1488)(902,1487)(903,1486)(904,1485)(905,1484)(906,1483)(907,1482)(908,1481)(909,1480)(910,1479)(911,1478)(912,1477)(913,1476)(914,1475)(915,1474)(916,1473)(917,1472)(918,1471)(919,1470)(920,1469)(921,1468)(922,1467)(923,1466)(924,1465)(925,1464)(926,1463)(927,1462)(928,1461)(929,1460)(930,1459)(931,1458)(932,1457)(933,1456)(934,1455)(935,1454)(936,1453)(937,1452)(938,1451)(939,1450)(940,1449)(941,1448)(942,1447)(943,1446)(944,1445)(945,1444)(946,1443)(947,1442)(948,1441)(949,1440)(950,1439)(951,1438)(952,1437)(953,1436)(954,1435)(955,1434)(956,1433)(957,1432)(958,1431)(959,1430)(960,1429)(961,1428)(962,1427)(963,1426)(964,1425)(965,1424)(966,1423)(967,1422)(968,1421)(969,1420)(970,1419)(971,1418)(972,1417)(973,1416)(974,1415)(975,1414)(976,1413)(977,1412)(978,1411)(979,1410)(980,1409)(981,1408)(982,1407)(983,1406)(984,1405)(985,1404)(986,1403)(987,1402)(988,1401)(989,1400)(990,1399)(991,1398)(992,1397)(993,1396)(994,1395)(995,1394)(996,1393)(997,1392)(998,1391)(999,1390)(1000,1389)(1001,1388)(1002,1387)(1003,1386)(1004,1385)(1005,1384)(1006,1383)(1007,1382)(1008,1381)(1009,1380)(1010,1379)(1011,1378)(1012,1377)(1013,1376)(1014,1375)(1015,1374)(1016,1373)(1017,1372)(1018,1371)(1019,1370)(1020,1369)(1021,1368)(1022,1367)(1023,1366)(1024,1365)(1025,1364)(1026,1363)(1027,1362)(1028,1361)(1029,1360)(1030,1359)(1031,1358)(1032,1357)(1033,1356)(1034,1355)(1035,1354)(1036,1353)(1037,1352)(1038,1351)(1039,1350)(1040,1349)(1041,1348)(1042,1347)(1043,1346)(1044,1345)(1045,1344)(1046,1343)(1047,1342)(1048,1341)(1049,1340)(1050,1339)(1051,1338)(1052,1337)(1053,1336)(1054,1335)(1055,1334)(1056,1333)(1057,1332)(1058,1331)(1059,1330)(1060,1329)(1061,1328)(1062,1327)(1063,1326)(1064,1325)(1065,1324)(1066,1323)(1067,1322)(1068,1321)(1069,1320)(1070,1319)(1071,1318)(1072,1317)(1073,1316)(1074,1315)(1075,1314)(1076,1313)(1077,1312)(1078,1311)(1079,1310)(1080,1309)(1081,1308)(1082,1307)(1083,1306)(1084,1305)(1085,1304)(1086,1303)(1087,1302)(1088,1301)(1089,1300)(1090,1299)(1091,1298)(1092,1297)(1093,1296)(1094,1295)(1095,1294)(1096,1293)(1097,1292)(1098,1291)(1099,1290)(1100,1289)(1101,1288)(1102,1287)(1103,1286)(1104,1285)(1105,1284)(1106,1283)(1107,1282)(1108,1281)(1109,1280)(1110,1279)(1111,1278)(1112,1277)(1113,1276)(1114,1275)(1115,1274)(1116,1273)(1117,1272)(1118,1271)(1119,1270)(1120,1269)(1121,1268)(1122,1267)(1123,1266)(1124,1265)(1125,1264)(1126,1263)(1127,1262)(1128,1261)(1129,1260)(1130,1259)(1131,1258)(1132,1257)(1133,1256)(1134,1255)(1135,1254)(1136,1253)(1137,1252)(1138,1251)(1139,1250)(1140,1249)(1141,1248)(1142,1247)(1143,1246)(1144,1245)(1145,1244)(1146,1243)(1147,1242)(1148,1241)(1149,1240)(1150,1239)(1151,1238)(1152,1237)(1153,1236)(1154,1235)(1155,1234)(1156,1233)(1157,1232)(1158,1231)(1159,1230)(1160,1229)(1161,1228)(1162,1227)(1163,1226)(1164,1225)(1165,1224)(1166,1223)(1167,1222)(1168,1221)(1169,1220)(1170,1219)(1171,1218)(1172,1217)(1173,1216)(1174,1215)(1175,1214)(1176,1213)(1177,1212)(1178,1211)(1179,1210)(1180,1209)(1181,1208)(1182,1207)(1183,1206)(1184,1205)(1185,1204)(1186,1203)(1187,1202)(1188,1201)(1189,1200)(1190,1199)(1191,1198)(1192,1197)(1193,1196)(1194,1195)

Polycyclic presentation:

2,5,2377|b^a=b^4,c^a=c^2376

Conjugacy classes & character table

5944 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23770, 3);