Finite Group Databasebeta

?

← Prev (#37552680) Next (#37552682) →

D₁₁₆₉₅ #37552681

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

Polycyclic presentation:

2,5,2339|b^a=b^4,c^a=c^2338

Conjugacy classes & character table

5849 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23390, 3);