← Prev (#31822651) Next (#31822653) →
D8972 #31822652
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 2247 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);(2,4)(6,2247)(7,2246)(8,2245)(9,2244)(10,2243)(11,2242)(12,2241)(13,2240)(14,2239)(15,2238)(16,2237)(17,2236)(18,2235)(19,2234)(20,2233)(21,2232)(22,2231)(23,2230)(24,2229)(25,2228)(26,2227)(27,2226)(28,2225)(29,2224)(30,2223)(31,2222)(32,2221)(33,2220)(34,2219)(35,2218)(36,2217)(37,2216)(38,2215)(39,2214)(40,2213)(41,2212)(42,2211)(43,2210)(44,2209)(45,2208)(46,2207)(47,2206)(48,2205)(49,2204)(50,2203)(51,2202)(52,2201)(53,2200)(54,2199)(55,2198)(56,2197)(57,2196)(58,2195)(59,2194)(60,2193)(61,2192)(62,2191)(63,2190)(64,2189)(65,2188)(66,2187)(67,2186)(68,2185)(69,2184)(70,2183)(71,2182)(72,2181)(73,2180)(74,2179)(75,2178)(76,2177)(77,2176)(78,2175)(79,2174)(80,2173)(81,2172)(82,2171)(83,2170)(84,2169)(85,2168)(86,2167)(87,2166)(88,2165)(89,2164)(90,2163)(91,2162)(92,2161)(93,2160)(94,2159)(95,2158)(96,2157)(97,2156)(98,2155)(99,2154)(100,2153)(101,2152)(102,2151)(103,2150)(104,2149)(105,2148)(106,2147)(107,2146)(108,2145)(109,2144)(110,2143)(111,2142)(112,2141)(113,2140)(114,2139)(115,2138)(116,2137)(117,2136)(118,2135)(119,2134)(120,2133)(121,2132)(122,2131)(123,2130)(124,2129)(125,2128)(126,2127)(127,2126)(128,2125)(129,2124)(130,2123)(131,2122)(132,2121)(133,2120)(134,2119)(135,2118)(136,2117)(137,2116)(138,2115)(139,2114)(140,2113)(141,2112)(142,2111)(143,2110)(144,2109)(145,2108)(146,2107)(147,2106)(148,2105)(149,2104)(150,2103)(151,2102)(152,2101)(153,2100)(154,2099)(155,2098)(156,2097)(157,2096)(158,2095)(159,2094)(160,2093)(161,2092)(162,2091)(163,2090)(164,2089)(165,2088)(166,2087)(167,2086)(168,2085)(169,2084)(170,2083)(171,2082)(172,2081)(173,2080)(174,2079)(175,2078)(176,2077)(177,2076)(178,2075)(179,2074)(180,2073)(181,2072)(182,2071)(183,2070)(184,2069)(185,2068)(186,2067)(187,2066)(188,2065)(189,2064)(190,2063)(191,2062)(192,2061)(193,2060)(194,2059)(195,2058)(196,2057)(197,2056)(198,2055)(199,2054)(200,2053)(201,2052)(202,2051)(203,2050)(204,2049)(205,2048)(206,2047)(207,2046)(208,2045)(209,2044)(210,2043)(211,2042)(212,2041)(213,2040)(214,2039)(215,2038)(216,2037)(217,2036)(218,2035)(219,2034)(220,2033)(221,2032)(222,2031)(223,2030)(224,2029)(225,2028)(226,2027)(227,2026)(228,2025)(229,2024)(230,2023)(231,2022)(232,2021)(233,2020)(234,2019)(235,2018)(236,2017)(237,2016)(238,2015)(239,2014)(240,2013)(241,2012)(242,2011)(243,2010)(244,2009)(245,2008)(246,2007)(247,2006)(248,2005)(249,2004)(250,2003)(251,2002)(252,2001)(253,2000)(254,1999)(255,1998)(256,1997)(257,1996)(258,1995)(259,1994)(260,1993)(261,1992)(262,1991)(263,1990)(264,1989)(265,1988)(266,1987)(267,1986)(268,1985)(269,1984)(270,1983)(271,1982)(272,1981)(273,1980)(274,1979)(275,1978)(276,1977)(277,1976)(278,1975)(279,1974)(280,1973)(281,1972)(282,1971)(283,1970)(284,1969)(285,1968)(286,1967)(287,1966)(288,1965)(289,1964)(290,1963)(291,1962)(292,1961)(293,1960)(294,1959)(295,1958)(296,1957)(297,1956)(298,1955)(299,1954)(300,1953)(301,1952)(302,1951)(303,1950)(304,1949)(305,1948)(306,1947)(307,1946)(308,1945)(309,1944)(310,1943)(311,1942)(312,1941)(313,1940)(314,1939)(315,1938)(316,1937)(317,1936)(318,1935)(319,1934)(320,1933)(321,1932)(322,1931)(323,1930)(324,1929)(325,1928)(326,1927)(327,1926)(328,1925)(329,1924)(330,1923)(331,1922)(332,1921)(333,1920)(334,1919)(335,1918)(336,1917)(337,1916)(338,1915)(339,1914)(340,1913)(341,1912)(342,1911)(343,1910)(344,1909)(345,1908)(346,1907)(347,1906)(348,1905)(349,1904)(350,1903)(351,1902)(352,1901)(353,1900)(354,1899)(355,1898)(356,1897)(357,1896)(358,1895)(359,1894)(360,1893)(361,1892)(362,1891)(363,1890)(364,1889)(365,1888)(366,1887)(367,1886)(368,1885)(369,1884)(370,1883)(371,1882)(372,1881)(373,1880)(374,1879)(375,1878)(376,1877)(377,1876)(378,1875)(379,1874)(380,1873)(381,1872)(382,1871)(383,1870)(384,1869)(385,1868)(386,1867)(387,1866)(388,1865)(389,1864)(390,1863)(391,1862)(392,1861)(393,1860)(394,1859)(395,1858)(396,1857)(397,1856)(398,1855)(399,1854)(400,1853)(401,1852)(402,1851)(403,1850)(404,1849)(405,1848)(406,1847)(407,1846)(408,1845)(409,1844)(410,1843)(411,1842)(412,1841)(413,1840)(414,1839)(415,1838)(416,1837)(417,1836)(418,1835)(419,1834)(420,1833)(421,1832)(422,1831)(423,1830)(424,1829)(425,1828)(426,1827)(427,1826)(428,1825)(429,1824)(430,1823)(431,1822)(432,1821)(433,1820)(434,1819)(435,1818)(436,1817)(437,1816)(438,1815)(439,1814)(440,1813)(441,1812)(442,1811)(443,1810)(444,1809)(445,1808)(446,1807)(447,1806)(448,1805)(449,1804)(450,1803)(451,1802)(452,1801)(453,1800)(454,1799)(455,1798)(456,1797)(457,1796)(458,1795)(459,1794)(460,1793)(461,1792)(462,1791)(463,1790)(464,1789)(465,1788)(466,1787)(467,1786)(468,1785)(469,1784)(470,1783)(471,1782)(472,1781)(473,1780)(474,1779)(475,1778)(476,1777)(477,1776)(478,1775)(479,1774)(480,1773)(481,1772)(482,1771)(483,1770)(484,1769)(485,1768)(486,1767)(487,1766)(488,1765)(489,1764)(490,1763)(491,1762)(492,1761)(493,1760)(494,1759)(495,1758)(496,1757)(497,1756)(498,1755)(499,1754)(500,1753)(501,1752)(502,1751)(503,1750)(504,1749)(505,1748)(506,1747)(507,1746)(508,1745)(509,1744)(510,1743)(511,1742)(512,1741)(513,1740)(514,1739)(515,1738)(516,1737)(517,1736)(518,1735)(519,1734)(520,1733)(521,1732)(522,1731)(523,1730)(524,1729)(525,1728)(526,1727)(527,1726)(528,1725)(529,1724)(530,1723)(531,1722)(532,1721)(533,1720)(534,1719)(535,1718)(536,1717)(537,1716)(538,1715)(539,1714)(540,1713)(541,1712)(542,1711)(543,1710)(544,1709)(545,1708)(546,1707)(547,1706)(548,1705)(549,1704)(550,1703)(551,1702)(552,1701)(553,1700)(554,1699)(555,1698)(556,1697)(557,1696)(558,1695)(559,1694)(560,1693)(561,1692)(562,1691)(563,1690)(564,1689)(565,1688)(566,1687)(567,1686)(568,1685)(569,1684)(570,1683)(571,1682)(572,1681)(573,1680)(574,1679)(575,1678)(576,1677)(577,1676)(578,1675)(579,1674)(580,1673)(581,1672)(582,1671)(583,1670)(584,1669)(585,1668)(586,1667)(587,1666)(588,1665)(589,1664)(590,1663)(591,1662)(592,1661)(593,1660)(594,1659)(595,1658)(596,1657)(597,1656)(598,1655)(599,1654)(600,1653)(601,1652)(602,1651)(603,1650)(604,1649)(605,1648)(606,1647)(607,1646)(608,1645)(609,1644)(610,1643)(611,1642)(612,1641)(613,1640)(614,1639)(615,1638)(616,1637)(617,1636)(618,1635)(619,1634)(620,1633)(621,1632)(622,1631)(623,1630)(624,1629)(625,1628)(626,1627)(627,1626)(628,1625)(629,1624)(630,1623)(631,1622)(632,1621)(633,1620)(634,1619)(635,1618)(636,1617)(637,1616)(638,1615)(639,1614)(640,1613)(641,1612)(642,1611)(643,1610)(644,1609)(645,1608)(646,1607)(647,1606)(648,1605)(649,1604)(650,1603)(651,1602)(652,1601)(653,1600)(654,1599)(655,1598)(656,1597)(657,1596)(658,1595)(659,1594)(660,1593)(661,1592)(662,1591)(663,1590)(664,1589)(665,1588)(666,1587)(667,1586)(668,1585)(669,1584)(670,1583)(671,1582)(672,1581)(673,1580)(674,1579)(675,1578)(676,1577)(677,1576)(678,1575)(679,1574)(680,1573)(681,1572)(682,1571)(683,1570)(684,1569)(685,1568)(686,1567)(687,1566)(688,1565)(689,1564)(690,1563)(691,1562)(692,1561)(693,1560)(694,1559)(695,1558)(696,1557)(697,1556)(698,1555)(699,1554)(700,1553)(701,1552)(702,1551)(703,1550)(704,1549)(705,1548)(706,1547)(707,1546)(708,1545)(709,1544)(710,1543)(711,1542)(712,1541)(713,1540)(714,1539)(715,1538)(716,1537)(717,1536)(718,1535)(719,1534)(720,1533)(721,1532)(722,1531)(723,1530)(724,1529)(725,1528)(726,1527)(727,1526)(728,1525)(729,1524)(730,1523)(731,1522)(732,1521)(733,1520)(734,1519)(735,1518)(736,1517)(737,1516)(738,1515)(739,1514)(740,1513)(741,1512)(742,1511)(743,1510)(744,1509)(745,1508)(746,1507)(747,1506)(748,1505)(749,1504)(750,1503)(751,1502)(752,1501)(753,1500)(754,1499)(755,1498)(756,1497)(757,1496)(758,1495)(759,1494)(760,1493)(761,1492)(762,1491)(763,1490)(764,1489)(765,1488)(766,1487)(767,1486)(768,1485)(769,1484)(770,1483)(771,1482)(772,1481)(773,1480)(774,1479)(775,1478)(776,1477)(777,1476)(778,1475)(779,1474)(780,1473)(781,1472)(782,1471)(783,1470)(784,1469)(785,1468)(786,1467)(787,1466)(788,1465)(789,1464)(790,1463)(791,1462)(792,1461)(793,1460)(794,1459)(795,1458)(796,1457)(797,1456)(798,1455)(799,1454)(800,1453)(801,1452)(802,1451)(803,1450)(804,1449)(805,1448)(806,1447)(807,1446)(808,1445)(809,1444)(810,1443)(811,1442)(812,1441)(813,1440)(814,1439)(815,1438)(816,1437)(817,1436)(818,1435)(819,1434)(820,1433)(821,1432)(822,1431)(823,1430)(824,1429)(825,1428)(826,1427)(827,1426)(828,1425)(829,1424)(830,1423)(831,1422)(832,1421)(833,1420)(834,1419)(835,1418)(836,1417)(837,1416)(838,1415)(839,1414)(840,1413)(841,1412)(842,1411)(843,1410)(844,1409)(845,1408)(846,1407)(847,1406)(848,1405)(849,1404)(850,1403)(851,1402)(852,1401)(853,1400)(854,1399)(855,1398)(856,1397)(857,1396)(858,1395)(859,1394)(860,1393)(861,1392)(862,1391)(863,1390)(864,1389)(865,1388)(866,1387)(867,1386)(868,1385)(869,1384)(870,1383)(871,1382)(872,1381)(873,1380)(874,1379)(875,1378)(876,1377)(877,1376)(878,1375)(879,1374)(880,1373)(881,1372)(882,1371)(883,1370)(884,1369)(885,1368)(886,1367)(887,1366)(888,1365)(889,1364)(890,1363)(891,1362)(892,1361)(893,1360)(894,1359)(895,1358)(896,1357)(897,1356)(898,1355)(899,1354)(900,1353)(901,1352)(902,1351)(903,1350)(904,1349)(905,1348)(906,1347)(907,1346)(908,1345)(909,1344)(910,1343)(911,1342)(912,1341)(913,1340)(914,1339)(915,1338)(916,1337)(917,1336)(918,1335)(919,1334)(920,1333)(921,1332)(922,1331)(923,1330)(924,1329)(925,1328)(926,1327)(927,1326)(928,1325)(929,1324)(930,1323)(931,1322)(932,1321)(933,1320)(934,1319)(935,1318)(936,1317)(937,1316)(938,1315)(939,1314)(940,1313)(941,1312)(942,1311)(943,1310)(944,1309)(945,1308)(946,1307)(947,1306)(948,1305)(949,1304)(950,1303)(951,1302)(952,1301)(953,1300)(954,1299)(955,1298)(956,1297)(957,1296)(958,1295)(959,1294)(960,1293)(961,1292)(962,1291)(963,1290)(964,1289)(965,1288)(966,1287)(967,1286)(968,1285)(969,1284)(970,1283)(971,1282)(972,1281)(973,1280)(974,1279)(975,1278)(976,1277)(977,1276)(978,1275)(979,1274)(980,1273)(981,1272)(982,1271)(983,1270)(984,1269)(985,1268)(986,1267)(987,1266)(988,1265)(989,1264)(990,1263)(991,1262)(992,1261)(993,1260)(994,1259)(995,1258)(996,1257)(997,1256)(998,1255)(999,1254)(1000,1253)(1001,1252)(1002,1251)(1003,1250)(1004,1249)(1005,1248)(1006,1247)(1007,1246)(1008,1245)(1009,1244)(1010,1243)(1011,1242)(1012,1241)(1013,1240)(1014,1239)(1015,1238)(1016,1237)(1017,1236)(1018,1235)(1019,1234)(1020,1233)(1021,1232)(1022,1231)(1023,1230)(1024,1229)(1025,1228)(1026,1227)(1027,1226)(1028,1225)(1029,1224)(1030,1223)(1031,1222)(1032,1221)(1033,1220)(1034,1219)(1035,1218)(1036,1217)(1037,1216)(1038,1215)(1039,1214)(1040,1213)(1041,1212)(1042,1211)(1043,1210)(1044,1209)(1045,1208)(1046,1207)(1047,1206)(1048,1205)(1049,1204)(1050,1203)(1051,1202)(1052,1201)(1053,1200)(1054,1199)(1055,1198)(1056,1197)(1057,1196)(1058,1195)(1059,1194)(1060,1193)(1061,1192)(1062,1191)(1063,1190)(1064,1189)(1065,1188)(1066,1187)(1067,1186)(1068,1185)(1069,1184)(1070,1183)(1071,1182)(1072,1181)(1073,1180)(1074,1179)(1075,1178)(1076,1177)(1077,1176)(1078,1175)(1079,1174)(1080,1173)(1081,1172)(1082,1171)(1083,1170)(1084,1169)(1085,1168)(1086,1167)(1087,1166)(1088,1165)(1089,1164)(1090,1163)(1091,1162)(1092,1161)(1093,1160)(1094,1159)(1095,1158)(1096,1157)(1097,1156)(1098,1155)(1099,1154)(1100,1153)(1101,1152)(1102,1151)(1103,1150)(1104,1149)(1105,1148)(1106,1147)(1107,1146)(1108,1145)(1109,1144)(1110,1143)(1111,1142)(1112,1141)(1113,1140)(1114,1139)(1115,1138)(1116,1137)(1117,1136)(1118,1135)(1119,1134)(1120,1133)(1121,1132)(1122,1131)(1123,1130)(1124,1129)(1125,1128)(1126,1127)
Polycyclic presentation:
2^3,2243|b^a=bc,d^a=d^2242,d^b=d^2242
Conjugacy classes & character table
4489 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17944, 10);
Finite Group Databasebeta