Finite Group Databasebeta

?

← Prev (#49145157) Next (#49145159) →

Dic₉₁₈₈ #49145158

• 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 2313 points:

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

Polycyclic presentation:

2^4,2297|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2296,c^b=cd,e^b=e^2296

Conjugacy classes & character table

9191 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36752, 31);