← Prev (#30658125) Next (#30658127) →
D8247 #30658126
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 2752 points:
(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199,2200,2201,2202,2203,2204,2205,2206,2207,2208,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219,2220,2221,2222,2223,2224,2225,2226,2227,2228,2229,2230,2231,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2302,2303,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431,2432,2433,2434,2435,2436,2437,2438,2439,2440,2441,2442,2443,2444,2445,2446,2447,2448,2449,2450,2451,2452,2453,2454,2455,2456,2457,2458,2459,2460,2461,2462,2463,2464,2465,2466,2467,2468,2469,2470,2471,2472,2473,2474,2475,2476,2477,2478,2479,2480,2481,2482,2483,2484,2485,2486,2487,2488,2489,2490,2491,2492,2493,2494,2495,2496,2497,2498,2499,2500,2501,2502,2503,2504,2505,2506,2507,2508,2509,2510,2511,2512,2513,2514,2515,2516,2517,2518,2519,2520,2521,2522,2523,2524,2525,2526,2527,2528,2529,2530,2531,2532,2533,2534,2535,2536,2537,2538,2539,2540,2541,2542,2543,2544,2545,2546,2547,2548,2549,2550,2551,2552,2553,2554,2555,2556,2557,2558,2559,2560,2561,2562,2563,2564,2565,2566,2567,2568,2569,2570,2571,2572,2573,2574,2575,2576,2577,2578,2579,2580,2581,2582,2583,2584,2585,2586,2587,2588,2589,2590,2591,2592,2593,2594,2595,2596,2597,2598,2599,2600,2601,2602,2603,2604,2605,2606,2607,2608,2609,2610,2611,2612,2613,2614,2615,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2626,2627,2628,2629,2630,2631,2632,2633,2634,2635,2636,2637,2638,2639,2640,2641,2642,2643,2644,2645,2646,2647,2648,2649,2650,2651,2652,2653,2654,2655,2656,2657,2658,2659,2660,2661,2662,2663,2664,2665,2666,2667,2668,2669,2670,2671,2672,2673,2674,2675,2676,2677,2678,2679,2680,2681,2682,2683,2684,2685,2686,2687,2688,2689,2690,2691,2692,2693,2694,2695,2696,2697,2698,2699,2700,2701,2702,2703,2704,2705,2706,2707,2708,2709,2710,2711,2712,2713,2714,2715,2716,2717,2718,2719,2720,2721,2722,2723,2724,2725,2726,2727,2728,2729,2730,2731,2732,2733,2734,2735,2736,2737,2738,2739,2740,2741,2742,2743,2744,2745,2746,2747,2748,2749,2750,2751,2752);(2,3)(5,2752)(6,2751)(7,2750)(8,2749)(9,2748)(10,2747)(11,2746)(12,2745)(13,2744)(14,2743)(15,2742)(16,2741)(17,2740)(18,2739)(19,2738)(20,2737)(21,2736)(22,2735)(23,2734)(24,2733)(25,2732)(26,2731)(27,2730)(28,2729)(29,2728)(30,2727)(31,2726)(32,2725)(33,2724)(34,2723)(35,2722)(36,2721)(37,2720)(38,2719)(39,2718)(40,2717)(41,2716)(42,2715)(43,2714)(44,2713)(45,2712)(46,2711)(47,2710)(48,2709)(49,2708)(50,2707)(51,2706)(52,2705)(53,2704)(54,2703)(55,2702)(56,2701)(57,2700)(58,2699)(59,2698)(60,2697)(61,2696)(62,2695)(63,2694)(64,2693)(65,2692)(66,2691)(67,2690)(68,2689)(69,2688)(70,2687)(71,2686)(72,2685)(73,2684)(74,2683)(75,2682)(76,2681)(77,2680)(78,2679)(79,2678)(80,2677)(81,2676)(82,2675)(83,2674)(84,2673)(85,2672)(86,2671)(87,2670)(88,2669)(89,2668)(90,2667)(91,2666)(92,2665)(93,2664)(94,2663)(95,2662)(96,2661)(97,2660)(98,2659)(99,2658)(100,2657)(101,2656)(102,2655)(103,2654)(104,2653)(105,2652)(106,2651)(107,2650)(108,2649)(109,2648)(110,2647)(111,2646)(112,2645)(113,2644)(114,2643)(115,2642)(116,2641)(117,2640)(118,2639)(119,2638)(120,2637)(121,2636)(122,2635)(123,2634)(124,2633)(125,2632)(126,2631)(127,2630)(128,2629)(129,2628)(130,2627)(131,2626)(132,2625)(133,2624)(134,2623)(135,2622)(136,2621)(137,2620)(138,2619)(139,2618)(140,2617)(141,2616)(142,2615)(143,2614)(144,2613)(145,2612)(146,2611)(147,2610)(148,2609)(149,2608)(150,2607)(151,2606)(152,2605)(153,2604)(154,2603)(155,2602)(156,2601)(157,2600)(158,2599)(159,2598)(160,2597)(161,2596)(162,2595)(163,2594)(164,2593)(165,2592)(166,2591)(167,2590)(168,2589)(169,2588)(170,2587)(171,2586)(172,2585)(173,2584)(174,2583)(175,2582)(176,2581)(177,2580)(178,2579)(179,2578)(180,2577)(181,2576)(182,2575)(183,2574)(184,2573)(185,2572)(186,2571)(187,2570)(188,2569)(189,2568)(190,2567)(191,2566)(192,2565)(193,2564)(194,2563)(195,2562)(196,2561)(197,2560)(198,2559)(199,2558)(200,2557)(201,2556)(202,2555)(203,2554)(204,2553)(205,2552)(206,2551)(207,2550)(208,2549)(209,2548)(210,2547)(211,2546)(212,2545)(213,2544)(214,2543)(215,2542)(216,2541)(217,2540)(218,2539)(219,2538)(220,2537)(221,2536)(222,2535)(223,2534)(224,2533)(225,2532)(226,2531)(227,2530)(228,2529)(229,2528)(230,2527)(231,2526)(232,2525)(233,2524)(234,2523)(235,2522)(236,2521)(237,2520)(238,2519)(239,2518)(240,2517)(241,2516)(242,2515)(243,2514)(244,2513)(245,2512)(246,2511)(247,2510)(248,2509)(249,2508)(250,2507)(251,2506)(252,2505)(253,2504)(254,2503)(255,2502)(256,2501)(257,2500)(258,2499)(259,2498)(260,2497)(261,2496)(262,2495)(263,2494)(264,2493)(265,2492)(266,2491)(267,2490)(268,2489)(269,2488)(270,2487)(271,2486)(272,2485)(273,2484)(274,2483)(275,2482)(276,2481)(277,2480)(278,2479)(279,2478)(280,2477)(281,2476)(282,2475)(283,2474)(284,2473)(285,2472)(286,2471)(287,2470)(288,2469)(289,2468)(290,2467)(291,2466)(292,2465)(293,2464)(294,2463)(295,2462)(296,2461)(297,2460)(298,2459)(299,2458)(300,2457)(301,2456)(302,2455)(303,2454)(304,2453)(305,2452)(306,2451)(307,2450)(308,2449)(309,2448)(310,2447)(311,2446)(312,2445)(313,2444)(314,2443)(315,2442)(316,2441)(317,2440)(318,2439)(319,2438)(320,2437)(321,2436)(322,2435)(323,2434)(324,2433)(325,2432)(326,2431)(327,2430)(328,2429)(329,2428)(330,2427)(331,2426)(332,2425)(333,2424)(334,2423)(335,2422)(336,2421)(337,2420)(338,2419)(339,2418)(340,2417)(341,2416)(342,2415)(343,2414)(344,2413)(345,2412)(346,2411)(347,2410)(348,2409)(349,2408)(350,2407)(351,2406)(352,2405)(353,2404)(354,2403)(355,2402)(356,2401)(357,2400)(358,2399)(359,2398)(360,2397)(361,2396)(362,2395)(363,2394)(364,2393)(365,2392)(366,2391)(367,2390)(368,2389)(369,2388)(370,2387)(371,2386)(372,2385)(373,2384)(374,2383)(375,2382)(376,2381)(377,2380)(378,2379)(379,2378)(380,2377)(381,2376)(382,2375)(383,2374)(384,2373)(385,2372)(386,2371)(387,2370)(388,2369)(389,2368)(390,2367)(391,2366)(392,2365)(393,2364)(394,2363)(395,2362)(396,2361)(397,2360)(398,2359)(399,2358)(400,2357)(401,2356)(402,2355)(403,2354)(404,2353)(405,2352)(406,2351)(407,2350)(408,2349)(409,2348)(410,2347)(411,2346)(412,2345)(413,2344)(414,2343)(415,2342)(416,2341)(417,2340)(418,2339)(419,2338)(420,2337)(421,2336)(422,2335)(423,2334)(424,2333)(425,2332)(426,2331)(427,2330)(428,2329)(429,2328)(430,2327)(431,2326)(432,2325)(433,2324)(434,2323)(435,2322)(436,2321)(437,2320)(438,2319)(439,2318)(440,2317)(441,2316)(442,2315)(443,2314)(444,2313)(445,2312)(446,2311)(447,2310)(448,2309)(449,2308)(450,2307)(451,2306)(452,2305)(453,2304)(454,2303)(455,2302)(456,2301)(457,2300)(458,2299)(459,2298)(460,2297)(461,2296)(462,2295)(463,2294)(464,2293)(465,2292)(466,2291)(467,2290)(468,2289)(469,2288)(470,2287)(471,2286)(472,2285)(473,2284)(474,2283)(475,2282)(476,2281)(477,2280)(478,2279)(479,2278)(480,2277)(481,2276)(482,2275)(483,2274)(484,2273)(485,2272)(486,2271)(487,2270)(488,2269)(489,2268)(490,2267)(491,2266)(492,2265)(493,2264)(494,2263)(495,2262)(496,2261)(497,2260)(498,2259)(499,2258)(500,2257)(501,2256)(502,2255)(503,2254)(504,2253)(505,2252)(506,2251)(507,2250)(508,2249)(509,2248)(510,2247)(511,2246)(512,2245)(513,2244)(514,2243)(515,2242)(516,2241)(517,2240)(518,2239)(519,2238)(520,2237)(521,2236)(522,2235)(523,2234)(524,2233)(525,2232)(526,2231)(527,2230)(528,2229)(529,2228)(530,2227)(531,2226)(532,2225)(533,2224)(534,2223)(535,2222)(536,2221)(537,2220)(538,2219)(539,2218)(540,2217)(541,2216)(542,2215)(543,2214)(544,2213)(545,2212)(546,2211)(547,2210)(548,2209)(549,2208)(550,2207)(551,2206)(552,2205)(553,2204)(554,2203)(555,2202)(556,2201)(557,2200)(558,2199)(559,2198)(560,2197)(561,2196)(562,2195)(563,2194)(564,2193)(565,2192)(566,2191)(567,2190)(568,2189)(569,2188)(570,2187)(571,2186)(572,2185)(573,2184)(574,2183)(575,2182)(576,2181)(577,2180)(578,2179)(579,2178)(580,2177)(581,2176)(582,2175)(583,2174)(584,2173)(585,2172)(586,2171)(587,2170)(588,2169)(589,2168)(590,2167)(591,2166)(592,2165)(593,2164)(594,2163)(595,2162)(596,2161)(597,2160)(598,2159)(599,2158)(600,2157)(601,2156)(602,2155)(603,2154)(604,2153)(605,2152)(606,2151)(607,2150)(608,2149)(609,2148)(610,2147)(611,2146)(612,2145)(613,2144)(614,2143)(615,2142)(616,2141)(617,2140)(618,2139)(619,2138)(620,2137)(621,2136)(622,2135)(623,2134)(624,2133)(625,2132)(626,2131)(627,2130)(628,2129)(629,2128)(630,2127)(631,2126)(632,2125)(633,2124)(634,2123)(635,2122)(636,2121)(637,2120)(638,2119)(639,2118)(640,2117)(641,2116)(642,2115)(643,2114)(644,2113)(645,2112)(646,2111)(647,2110)(648,2109)(649,2108)(650,2107)(651,2106)(652,2105)(653,2104)(654,2103)(655,2102)(656,2101)(657,2100)(658,2099)(659,2098)(660,2097)(661,2096)(662,2095)(663,2094)(664,2093)(665,2092)(666,2091)(667,2090)(668,2089)(669,2088)(670,2087)(671,2086)(672,2085)(673,2084)(674,2083)(675,2082)(676,2081)(677,2080)(678,2079)(679,2078)(680,2077)(681,2076)(682,2075)(683,2074)(684,2073)(685,2072)(686,2071)(687,2070)(688,2069)(689,2068)(690,2067)(691,2066)(692,2065)(693,2064)(694,2063)(695,2062)(696,2061)(697,2060)(698,2059)(699,2058)(700,2057)(701,2056)(702,2055)(703,2054)(704,2053)(705,2052)(706,2051)(707,2050)(708,2049)(709,2048)(710,2047)(711,2046)(712,2045)(713,2044)(714,2043)(715,2042)(716,2041)(717,2040)(718,2039)(719,2038)(720,2037)(721,2036)(722,2035)(723,2034)(724,2033)(725,2032)(726,2031)(727,2030)(728,2029)(729,2028)(730,2027)(731,2026)(732,2025)(733,2024)(734,2023)(735,2022)(736,2021)(737,2020)(738,2019)(739,2018)(740,2017)(741,2016)(742,2015)(743,2014)(744,2013)(745,2012)(746,2011)(747,2010)(748,2009)(749,2008)(750,2007)(751,2006)(752,2005)(753,2004)(754,2003)(755,2002)(756,2001)(757,2000)(758,1999)(759,1998)(760,1997)(761,1996)(762,1995)(763,1994)(764,1993)(765,1992)(766,1991)(767,1990)(768,1989)(769,1988)(770,1987)(771,1986)(772,1985)(773,1984)(774,1983)(775,1982)(776,1981)(777,1980)(778,1979)(779,1978)(780,1977)(781,1976)(782,1975)(783,1974)(784,1973)(785,1972)(786,1971)(787,1970)(788,1969)(789,1968)(790,1967)(791,1966)(792,1965)(793,1964)(794,1963)(795,1962)(796,1961)(797,1960)(798,1959)(799,1958)(800,1957)(801,1956)(802,1955)(803,1954)(804,1953)(805,1952)(806,1951)(807,1950)(808,1949)(809,1948)(810,1947)(811,1946)(812,1945)(813,1944)(814,1943)(815,1942)(816,1941)(817,1940)(818,1939)(819,1938)(820,1937)(821,1936)(822,1935)(823,1934)(824,1933)(825,1932)(826,1931)(827,1930)(828,1929)(829,1928)(830,1927)(831,1926)(832,1925)(833,1924)(834,1923)(835,1922)(836,1921)(837,1920)(838,1919)(839,1918)(840,1917)(841,1916)(842,1915)(843,1914)(844,1913)(845,1912)(846,1911)(847,1910)(848,1909)(849,1908)(850,1907)(851,1906)(852,1905)(853,1904)(854,1903)(855,1902)(856,1901)(857,1900)(858,1899)(859,1898)(860,1897)(861,1896)(862,1895)(863,1894)(864,1893)(865,1892)(866,1891)(867,1890)(868,1889)(869,1888)(870,1887)(871,1886)(872,1885)(873,1884)(874,1883)(875,1882)(876,1881)(877,1880)(878,1879)(879,1878)(880,1877)(881,1876)(882,1875)(883,1874)(884,1873)(885,1872)(886,1871)(887,1870)(888,1869)(889,1868)(890,1867)(891,1866)(892,1865)(893,1864)(894,1863)(895,1862)(896,1861)(897,1860)(898,1859)(899,1858)(900,1857)(901,1856)(902,1855)(903,1854)(904,1853)(905,1852)(906,1851)(907,1850)(908,1849)(909,1848)(910,1847)(911,1846)(912,1845)(913,1844)(914,1843)(915,1842)(916,1841)(917,1840)(918,1839)(919,1838)(920,1837)(921,1836)(922,1835)(923,1834)(924,1833)(925,1832)(926,1831)(927,1830)(928,1829)(929,1828)(930,1827)(931,1826)(932,1825)(933,1824)(934,1823)(935,1822)(936,1821)(937,1820)(938,1819)(939,1818)(940,1817)(941,1816)(942,1815)(943,1814)(944,1813)(945,1812)(946,1811)(947,1810)(948,1809)(949,1808)(950,1807)(951,1806)(952,1805)(953,1804)(954,1803)(955,1802)(956,1801)(957,1800)(958,1799)(959,1798)(960,1797)(961,1796)(962,1795)(963,1794)(964,1793)(965,1792)(966,1791)(967,1790)(968,1789)(969,1788)(970,1787)(971,1786)(972,1785)(973,1784)(974,1783)(975,1782)(976,1781)(977,1780)(978,1779)(979,1778)(980,1777)(981,1776)(982,1775)(983,1774)(984,1773)(985,1772)(986,1771)(987,1770)(988,1769)(989,1768)(990,1767)(991,1766)(992,1765)(993,1764)(994,1763)(995,1762)(996,1761)(997,1760)(998,1759)(999,1758)(1000,1757)(1001,1756)(1002,1755)(1003,1754)(1004,1753)(1005,1752)(1006,1751)(1007,1750)(1008,1749)(1009,1748)(1010,1747)(1011,1746)(1012,1745)(1013,1744)(1014,1743)(1015,1742)(1016,1741)(1017,1740)(1018,1739)(1019,1738)(1020,1737)(1021,1736)(1022,1735)(1023,1734)(1024,1733)(1025,1732)(1026,1731)(1027,1730)(1028,1729)(1029,1728)(1030,1727)(1031,1726)(1032,1725)(1033,1724)(1034,1723)(1035,1722)(1036,1721)(1037,1720)(1038,1719)(1039,1718)(1040,1717)(1041,1716)(1042,1715)(1043,1714)(1044,1713)(1045,1712)(1046,1711)(1047,1710)(1048,1709)(1049,1708)(1050,1707)(1051,1706)(1052,1705)(1053,1704)(1054,1703)(1055,1702)(1056,1701)(1057,1700)(1058,1699)(1059,1698)(1060,1697)(1061,1696)(1062,1695)(1063,1694)(1064,1693)(1065,1692)(1066,1691)(1067,1690)(1068,1689)(1069,1688)(1070,1687)(1071,1686)(1072,1685)(1073,1684)(1074,1683)(1075,1682)(1076,1681)(1077,1680)(1078,1679)(1079,1678)(1080,1677)(1081,1676)(1082,1675)(1083,1674)(1084,1673)(1085,1672)(1086,1671)(1087,1670)(1088,1669)(1089,1668)(1090,1667)(1091,1666)(1092,1665)(1093,1664)(1094,1663)(1095,1662)(1096,1661)(1097,1660)(1098,1659)(1099,1658)(1100,1657)(1101,1656)(1102,1655)(1103,1654)(1104,1653)(1105,1652)(1106,1651)(1107,1650)(1108,1649)(1109,1648)(1110,1647)(1111,1646)(1112,1645)(1113,1644)(1114,1643)(1115,1642)(1116,1641)(1117,1640)(1118,1639)(1119,1638)(1120,1637)(1121,1636)(1122,1635)(1123,1634)(1124,1633)(1125,1632)(1126,1631)(1127,1630)(1128,1629)(1129,1628)(1130,1627)(1131,1626)(1132,1625)(1133,1624)(1134,1623)(1135,1622)(1136,1621)(1137,1620)(1138,1619)(1139,1618)(1140,1617)(1141,1616)(1142,1615)(1143,1614)(1144,1613)(1145,1612)(1146,1611)(1147,1610)(1148,1609)(1149,1608)(1150,1607)(1151,1606)(1152,1605)(1153,1604)(1154,1603)(1155,1602)(1156,1601)(1157,1600)(1158,1599)(1159,1598)(1160,1597)(1161,1596)(1162,1595)(1163,1594)(1164,1593)(1165,1592)(1166,1591)(1167,1590)(1168,1589)(1169,1588)(1170,1587)(1171,1586)(1172,1585)(1173,1584)(1174,1583)(1175,1582)(1176,1581)(1177,1580)(1178,1579)(1179,1578)(1180,1577)(1181,1576)(1182,1575)(1183,1574)(1184,1573)(1185,1572)(1186,1571)(1187,1570)(1188,1569)(1189,1568)(1190,1567)(1191,1566)(1192,1565)(1193,1564)(1194,1563)(1195,1562)(1196,1561)(1197,1560)(1198,1559)(1199,1558)(1200,1557)(1201,1556)(1202,1555)(1203,1554)(1204,1553)(1205,1552)(1206,1551)(1207,1550)(1208,1549)(1209,1548)(1210,1547)(1211,1546)(1212,1545)(1213,1544)(1214,1543)(1215,1542)(1216,1541)(1217,1540)(1218,1539)(1219,1538)(1220,1537)(1221,1536)(1222,1535)(1223,1534)(1224,1533)(1225,1532)(1226,1531)(1227,1530)(1228,1529)(1229,1528)(1230,1527)(1231,1526)(1232,1525)(1233,1524)(1234,1523)(1235,1522)(1236,1521)(1237,1520)(1238,1519)(1239,1518)(1240,1517)(1241,1516)(1242,1515)(1243,1514)(1244,1513)(1245,1512)(1246,1511)(1247,1510)(1248,1509)(1249,1508)(1250,1507)(1251,1506)(1252,1505)(1253,1504)(1254,1503)(1255,1502)(1256,1501)(1257,1500)(1258,1499)(1259,1498)(1260,1497)(1261,1496)(1262,1495)(1263,1494)(1264,1493)(1265,1492)(1266,1491)(1267,1490)(1268,1489)(1269,1488)(1270,1487)(1271,1486)(1272,1485)(1273,1484)(1274,1483)(1275,1482)(1276,1481)(1277,1480)(1278,1479)(1279,1478)(1280,1477)(1281,1476)(1282,1475)(1283,1474)(1284,1473)(1285,1472)(1286,1471)(1287,1470)(1288,1469)(1289,1468)(1290,1467)(1291,1466)(1292,1465)(1293,1464)(1294,1463)(1295,1462)(1296,1461)(1297,1460)(1298,1459)(1299,1458)(1300,1457)(1301,1456)(1302,1455)(1303,1454)(1304,1453)(1305,1452)(1306,1451)(1307,1450)(1308,1449)(1309,1448)(1310,1447)(1311,1446)(1312,1445)(1313,1444)(1314,1443)(1315,1442)(1316,1441)(1317,1440)(1318,1439)(1319,1438)(1320,1437)(1321,1436)(1322,1435)(1323,1434)(1324,1433)(1325,1432)(1326,1431)(1327,1430)(1328,1429)(1329,1428)(1330,1427)(1331,1426)(1332,1425)(1333,1424)(1334,1423)(1335,1422)(1336,1421)(1337,1420)(1338,1419)(1339,1418)(1340,1417)(1341,1416)(1342,1415)(1343,1414)(1344,1413)(1345,1412)(1346,1411)(1347,1410)(1348,1409)(1349,1408)(1350,1407)(1351,1406)(1352,1405)(1353,1404)(1354,1403)(1355,1402)(1356,1401)(1357,1400)(1358,1399)(1359,1398)(1360,1397)(1361,1396)(1362,1395)(1363,1394)(1364,1393)(1365,1392)(1366,1391)(1367,1390)(1368,1389)(1369,1388)(1370,1387)(1371,1386)(1372,1385)(1373,1384)(1374,1383)(1375,1382)(1376,1381)(1377,1380)(1378,1379)
Polycyclic presentation:
2,3,2749|b^a=b^2,c^a=c^2748
Conjugacy classes & character table
4125 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16494, 5);
Finite Group Databasebeta