← Prev (#43249451) Next (#43249453) →
D14215 #43249452
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 2848 points:
(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199,2200,2201,2202,2203,2204,2205,2206,2207,2208,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219,2220,2221,2222,2223,2224,2225,2226,2227,2228,2229,2230,2231,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2302,2303,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431,2432,2433,2434,2435,2436,2437,2438,2439,2440,2441,2442,2443,2444,2445,2446,2447,2448,2449,2450,2451,2452,2453,2454,2455,2456,2457,2458,2459,2460,2461,2462,2463,2464,2465,2466,2467,2468,2469,2470,2471,2472,2473,2474,2475,2476,2477,2478,2479,2480,2481,2482,2483,2484,2485,2486,2487,2488,2489,2490,2491,2492,2493,2494,2495,2496,2497,2498,2499,2500,2501,2502,2503,2504,2505,2506,2507,2508,2509,2510,2511,2512,2513,2514,2515,2516,2517,2518,2519,2520,2521,2522,2523,2524,2525,2526,2527,2528,2529,2530,2531,2532,2533,2534,2535,2536,2537,2538,2539,2540,2541,2542,2543,2544,2545,2546,2547,2548,2549,2550,2551,2552,2553,2554,2555,2556,2557,2558,2559,2560,2561,2562,2563,2564,2565,2566,2567,2568,2569,2570,2571,2572,2573,2574,2575,2576,2577,2578,2579,2580,2581,2582,2583,2584,2585,2586,2587,2588,2589,2590,2591,2592,2593,2594,2595,2596,2597,2598,2599,2600,2601,2602,2603,2604,2605,2606,2607,2608,2609,2610,2611,2612,2613,2614,2615,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2626,2627,2628,2629,2630,2631,2632,2633,2634,2635,2636,2637,2638,2639,2640,2641,2642,2643,2644,2645,2646,2647,2648,2649,2650,2651,2652,2653,2654,2655,2656,2657,2658,2659,2660,2661,2662,2663,2664,2665,2666,2667,2668,2669,2670,2671,2672,2673,2674,2675,2676,2677,2678,2679,2680,2681,2682,2683,2684,2685,2686,2687,2688,2689,2690,2691,2692,2693,2694,2695,2696,2697,2698,2699,2700,2701,2702,2703,2704,2705,2706,2707,2708,2709,2710,2711,2712,2713,2714,2715,2716,2717,2718,2719,2720,2721,2722,2723,2724,2725,2726,2727,2728,2729,2730,2731,2732,2733,2734,2735,2736,2737,2738,2739,2740,2741,2742,2743,2744,2745,2746,2747,2748,2749,2750,2751,2752,2753,2754,2755,2756,2757,2758,2759,2760,2761,2762,2763,2764,2765,2766,2767,2768,2769,2770,2771,2772,2773,2774,2775,2776,2777,2778,2779,2780,2781,2782,2783,2784,2785,2786,2787,2788,2789,2790,2791,2792,2793,2794,2795,2796,2797,2798,2799,2800,2801,2802,2803,2804,2805,2806,2807,2808,2809,2810,2811,2812,2813,2814,2815,2816,2817,2818,2819,2820,2821,2822,2823,2824,2825,2826,2827,2828,2829,2830,2831,2832,2833,2834,2835,2836,2837,2838,2839,2840,2841,2842,2843,2844,2845,2846,2847,2848);(2,5)(3,4)(7,2848)(8,2847)(9,2846)(10,2845)(11,2844)(12,2843)(13,2842)(14,2841)(15,2840)(16,2839)(17,2838)(18,2837)(19,2836)(20,2835)(21,2834)(22,2833)(23,2832)(24,2831)(25,2830)(26,2829)(27,2828)(28,2827)(29,2826)(30,2825)(31,2824)(32,2823)(33,2822)(34,2821)(35,2820)(36,2819)(37,2818)(38,2817)(39,2816)(40,2815)(41,2814)(42,2813)(43,2812)(44,2811)(45,2810)(46,2809)(47,2808)(48,2807)(49,2806)(50,2805)(51,2804)(52,2803)(53,2802)(54,2801)(55,2800)(56,2799)(57,2798)(58,2797)(59,2796)(60,2795)(61,2794)(62,2793)(63,2792)(64,2791)(65,2790)(66,2789)(67,2788)(68,2787)(69,2786)(70,2785)(71,2784)(72,2783)(73,2782)(74,2781)(75,2780)(76,2779)(77,2778)(78,2777)(79,2776)(80,2775)(81,2774)(82,2773)(83,2772)(84,2771)(85,2770)(86,2769)(87,2768)(88,2767)(89,2766)(90,2765)(91,2764)(92,2763)(93,2762)(94,2761)(95,2760)(96,2759)(97,2758)(98,2757)(99,2756)(100,2755)(101,2754)(102,2753)(103,2752)(104,2751)(105,2750)(106,2749)(107,2748)(108,2747)(109,2746)(110,2745)(111,2744)(112,2743)(113,2742)(114,2741)(115,2740)(116,2739)(117,2738)(118,2737)(119,2736)(120,2735)(121,2734)(122,2733)(123,2732)(124,2731)(125,2730)(126,2729)(127,2728)(128,2727)(129,2726)(130,2725)(131,2724)(132,2723)(133,2722)(134,2721)(135,2720)(136,2719)(137,2718)(138,2717)(139,2716)(140,2715)(141,2714)(142,2713)(143,2712)(144,2711)(145,2710)(146,2709)(147,2708)(148,2707)(149,2706)(150,2705)(151,2704)(152,2703)(153,2702)(154,2701)(155,2700)(156,2699)(157,2698)(158,2697)(159,2696)(160,2695)(161,2694)(162,2693)(163,2692)(164,2691)(165,2690)(166,2689)(167,2688)(168,2687)(169,2686)(170,2685)(171,2684)(172,2683)(173,2682)(174,2681)(175,2680)(176,2679)(177,2678)(178,2677)(179,2676)(180,2675)(181,2674)(182,2673)(183,2672)(184,2671)(185,2670)(186,2669)(187,2668)(188,2667)(189,2666)(190,2665)(191,2664)(192,2663)(193,2662)(194,2661)(195,2660)(196,2659)(197,2658)(198,2657)(199,2656)(200,2655)(201,2654)(202,2653)(203,2652)(204,2651)(205,2650)(206,2649)(207,2648)(208,2647)(209,2646)(210,2645)(211,2644)(212,2643)(213,2642)(214,2641)(215,2640)(216,2639)(217,2638)(218,2637)(219,2636)(220,2635)(221,2634)(222,2633)(223,2632)(224,2631)(225,2630)(226,2629)(227,2628)(228,2627)(229,2626)(230,2625)(231,2624)(232,2623)(233,2622)(234,2621)(235,2620)(236,2619)(237,2618)(238,2617)(239,2616)(240,2615)(241,2614)(242,2613)(243,2612)(244,2611)(245,2610)(246,2609)(247,2608)(248,2607)(249,2606)(250,2605)(251,2604)(252,2603)(253,2602)(254,2601)(255,2600)(256,2599)(257,2598)(258,2597)(259,2596)(260,2595)(261,2594)(262,2593)(263,2592)(264,2591)(265,2590)(266,2589)(267,2588)(268,2587)(269,2586)(270,2585)(271,2584)(272,2583)(273,2582)(274,2581)(275,2580)(276,2579)(277,2578)(278,2577)(279,2576)(280,2575)(281,2574)(282,2573)(283,2572)(284,2571)(285,2570)(286,2569)(287,2568)(288,2567)(289,2566)(290,2565)(291,2564)(292,2563)(293,2562)(294,2561)(295,2560)(296,2559)(297,2558)(298,2557)(299,2556)(300,2555)(301,2554)(302,2553)(303,2552)(304,2551)(305,2550)(306,2549)(307,2548)(308,2547)(309,2546)(310,2545)(311,2544)(312,2543)(313,2542)(314,2541)(315,2540)(316,2539)(317,2538)(318,2537)(319,2536)(320,2535)(321,2534)(322,2533)(323,2532)(324,2531)(325,2530)(326,2529)(327,2528)(328,2527)(329,2526)(330,2525)(331,2524)(332,2523)(333,2522)(334,2521)(335,2520)(336,2519)(337,2518)(338,2517)(339,2516)(340,2515)(341,2514)(342,2513)(343,2512)(344,2511)(345,2510)(346,2509)(347,2508)(348,2507)(349,2506)(350,2505)(351,2504)(352,2503)(353,2502)(354,2501)(355,2500)(356,2499)(357,2498)(358,2497)(359,2496)(360,2495)(361,2494)(362,2493)(363,2492)(364,2491)(365,2490)(366,2489)(367,2488)(368,2487)(369,2486)(370,2485)(371,2484)(372,2483)(373,2482)(374,2481)(375,2480)(376,2479)(377,2478)(378,2477)(379,2476)(380,2475)(381,2474)(382,2473)(383,2472)(384,2471)(385,2470)(386,2469)(387,2468)(388,2467)(389,2466)(390,2465)(391,2464)(392,2463)(393,2462)(394,2461)(395,2460)(396,2459)(397,2458)(398,2457)(399,2456)(400,2455)(401,2454)(402,2453)(403,2452)(404,2451)(405,2450)(406,2449)(407,2448)(408,2447)(409,2446)(410,2445)(411,2444)(412,2443)(413,2442)(414,2441)(415,2440)(416,2439)(417,2438)(418,2437)(419,2436)(420,2435)(421,2434)(422,2433)(423,2432)(424,2431)(425,2430)(426,2429)(427,2428)(428,2427)(429,2426)(430,2425)(431,2424)(432,2423)(433,2422)(434,2421)(435,2420)(436,2419)(437,2418)(438,2417)(439,2416)(440,2415)(441,2414)(442,2413)(443,2412)(444,2411)(445,2410)(446,2409)(447,2408)(448,2407)(449,2406)(450,2405)(451,2404)(452,2403)(453,2402)(454,2401)(455,2400)(456,2399)(457,2398)(458,2397)(459,2396)(460,2395)(461,2394)(462,2393)(463,2392)(464,2391)(465,2390)(466,2389)(467,2388)(468,2387)(469,2386)(470,2385)(471,2384)(472,2383)(473,2382)(474,2381)(475,2380)(476,2379)(477,2378)(478,2377)(479,2376)(480,2375)(481,2374)(482,2373)(483,2372)(484,2371)(485,2370)(486,2369)(487,2368)(488,2367)(489,2366)(490,2365)(491,2364)(492,2363)(493,2362)(494,2361)(495,2360)(496,2359)(497,2358)(498,2357)(499,2356)(500,2355)(501,2354)(502,2353)(503,2352)(504,2351)(505,2350)(506,2349)(507,2348)(508,2347)(509,2346)(510,2345)(511,2344)(512,2343)(513,2342)(514,2341)(515,2340)(516,2339)(517,2338)(518,2337)(519,2336)(520,2335)(521,2334)(522,2333)(523,2332)(524,2331)(525,2330)(526,2329)(527,2328)(528,2327)(529,2326)(530,2325)(531,2324)(532,2323)(533,2322)(534,2321)(535,2320)(536,2319)(537,2318)(538,2317)(539,2316)(540,2315)(541,2314)(542,2313)(543,2312)(544,2311)(545,2310)(546,2309)(547,2308)(548,2307)(549,2306)(550,2305)(551,2304)(552,2303)(553,2302)(554,2301)(555,2300)(556,2299)(557,2298)(558,2297)(559,2296)(560,2295)(561,2294)(562,2293)(563,2292)(564,2291)(565,2290)(566,2289)(567,2288)(568,2287)(569,2286)(570,2285)(571,2284)(572,2283)(573,2282)(574,2281)(575,2280)(576,2279)(577,2278)(578,2277)(579,2276)(580,2275)(581,2274)(582,2273)(583,2272)(584,2271)(585,2270)(586,2269)(587,2268)(588,2267)(589,2266)(590,2265)(591,2264)(592,2263)(593,2262)(594,2261)(595,2260)(596,2259)(597,2258)(598,2257)(599,2256)(600,2255)(601,2254)(602,2253)(603,2252)(604,2251)(605,2250)(606,2249)(607,2248)(608,2247)(609,2246)(610,2245)(611,2244)(612,2243)(613,2242)(614,2241)(615,2240)(616,2239)(617,2238)(618,2237)(619,2236)(620,2235)(621,2234)(622,2233)(623,2232)(624,2231)(625,2230)(626,2229)(627,2228)(628,2227)(629,2226)(630,2225)(631,2224)(632,2223)(633,2222)(634,2221)(635,2220)(636,2219)(637,2218)(638,2217)(639,2216)(640,2215)(641,2214)(642,2213)(643,2212)(644,2211)(645,2210)(646,2209)(647,2208)(648,2207)(649,2206)(650,2205)(651,2204)(652,2203)(653,2202)(654,2201)(655,2200)(656,2199)(657,2198)(658,2197)(659,2196)(660,2195)(661,2194)(662,2193)(663,2192)(664,2191)(665,2190)(666,2189)(667,2188)(668,2187)(669,2186)(670,2185)(671,2184)(672,2183)(673,2182)(674,2181)(675,2180)(676,2179)(677,2178)(678,2177)(679,2176)(680,2175)(681,2174)(682,2173)(683,2172)(684,2171)(685,2170)(686,2169)(687,2168)(688,2167)(689,2166)(690,2165)(691,2164)(692,2163)(693,2162)(694,2161)(695,2160)(696,2159)(697,2158)(698,2157)(699,2156)(700,2155)(701,2154)(702,2153)(703,2152)(704,2151)(705,2150)(706,2149)(707,2148)(708,2147)(709,2146)(710,2145)(711,2144)(712,2143)(713,2142)(714,2141)(715,2140)(716,2139)(717,2138)(718,2137)(719,2136)(720,2135)(721,2134)(722,2133)(723,2132)(724,2131)(725,2130)(726,2129)(727,2128)(728,2127)(729,2126)(730,2125)(731,2124)(732,2123)(733,2122)(734,2121)(735,2120)(736,2119)(737,2118)(738,2117)(739,2116)(740,2115)(741,2114)(742,2113)(743,2112)(744,2111)(745,2110)(746,2109)(747,2108)(748,2107)(749,2106)(750,2105)(751,2104)(752,2103)(753,2102)(754,2101)(755,2100)(756,2099)(757,2098)(758,2097)(759,2096)(760,2095)(761,2094)(762,2093)(763,2092)(764,2091)(765,2090)(766,2089)(767,2088)(768,2087)(769,2086)(770,2085)(771,2084)(772,2083)(773,2082)(774,2081)(775,2080)(776,2079)(777,2078)(778,2077)(779,2076)(780,2075)(781,2074)(782,2073)(783,2072)(784,2071)(785,2070)(786,2069)(787,2068)(788,2067)(789,2066)(790,2065)(791,2064)(792,2063)(793,2062)(794,2061)(795,2060)(796,2059)(797,2058)(798,2057)(799,2056)(800,2055)(801,2054)(802,2053)(803,2052)(804,2051)(805,2050)(806,2049)(807,2048)(808,2047)(809,2046)(810,2045)(811,2044)(812,2043)(813,2042)(814,2041)(815,2040)(816,2039)(817,2038)(818,2037)(819,2036)(820,2035)(821,2034)(822,2033)(823,2032)(824,2031)(825,2030)(826,2029)(827,2028)(828,2027)(829,2026)(830,2025)(831,2024)(832,2023)(833,2022)(834,2021)(835,2020)(836,2019)(837,2018)(838,2017)(839,2016)(840,2015)(841,2014)(842,2013)(843,2012)(844,2011)(845,2010)(846,2009)(847,2008)(848,2007)(849,2006)(850,2005)(851,2004)(852,2003)(853,2002)(854,2001)(855,2000)(856,1999)(857,1998)(858,1997)(859,1996)(860,1995)(861,1994)(862,1993)(863,1992)(864,1991)(865,1990)(866,1989)(867,1988)(868,1987)(869,1986)(870,1985)(871,1984)(872,1983)(873,1982)(874,1981)(875,1980)(876,1979)(877,1978)(878,1977)(879,1976)(880,1975)(881,1974)(882,1973)(883,1972)(884,1971)(885,1970)(886,1969)(887,1968)(888,1967)(889,1966)(890,1965)(891,1964)(892,1963)(893,1962)(894,1961)(895,1960)(896,1959)(897,1958)(898,1957)(899,1956)(900,1955)(901,1954)(902,1953)(903,1952)(904,1951)(905,1950)(906,1949)(907,1948)(908,1947)(909,1946)(910,1945)(911,1944)(912,1943)(913,1942)(914,1941)(915,1940)(916,1939)(917,1938)(918,1937)(919,1936)(920,1935)(921,1934)(922,1933)(923,1932)(924,1931)(925,1930)(926,1929)(927,1928)(928,1927)(929,1926)(930,1925)(931,1924)(932,1923)(933,1922)(934,1921)(935,1920)(936,1919)(937,1918)(938,1917)(939,1916)(940,1915)(941,1914)(942,1913)(943,1912)(944,1911)(945,1910)(946,1909)(947,1908)(948,1907)(949,1906)(950,1905)(951,1904)(952,1903)(953,1902)(954,1901)(955,1900)(956,1899)(957,1898)(958,1897)(959,1896)(960,1895)(961,1894)(962,1893)(963,1892)(964,1891)(965,1890)(966,1889)(967,1888)(968,1887)(969,1886)(970,1885)(971,1884)(972,1883)(973,1882)(974,1881)(975,1880)(976,1879)(977,1878)(978,1877)(979,1876)(980,1875)(981,1874)(982,1873)(983,1872)(984,1871)(985,1870)(986,1869)(987,1868)(988,1867)(989,1866)(990,1865)(991,1864)(992,1863)(993,1862)(994,1861)(995,1860)(996,1859)(997,1858)(998,1857)(999,1856)(1000,1855)(1001,1854)(1002,1853)(1003,1852)(1004,1851)(1005,1850)(1006,1849)(1007,1848)(1008,1847)(1009,1846)(1010,1845)(1011,1844)(1012,1843)(1013,1842)(1014,1841)(1015,1840)(1016,1839)(1017,1838)(1018,1837)(1019,1836)(1020,1835)(1021,1834)(1022,1833)(1023,1832)(1024,1831)(1025,1830)(1026,1829)(1027,1828)(1028,1827)(1029,1826)(1030,1825)(1031,1824)(1032,1823)(1033,1822)(1034,1821)(1035,1820)(1036,1819)(1037,1818)(1038,1817)(1039,1816)(1040,1815)(1041,1814)(1042,1813)(1043,1812)(1044,1811)(1045,1810)(1046,1809)(1047,1808)(1048,1807)(1049,1806)(1050,1805)(1051,1804)(1052,1803)(1053,1802)(1054,1801)(1055,1800)(1056,1799)(1057,1798)(1058,1797)(1059,1796)(1060,1795)(1061,1794)(1062,1793)(1063,1792)(1064,1791)(1065,1790)(1066,1789)(1067,1788)(1068,1787)(1069,1786)(1070,1785)(1071,1784)(1072,1783)(1073,1782)(1074,1781)(1075,1780)(1076,1779)(1077,1778)(1078,1777)(1079,1776)(1080,1775)(1081,1774)(1082,1773)(1083,1772)(1084,1771)(1085,1770)(1086,1769)(1087,1768)(1088,1767)(1089,1766)(1090,1765)(1091,1764)(1092,1763)(1093,1762)(1094,1761)(1095,1760)(1096,1759)(1097,1758)(1098,1757)(1099,1756)(1100,1755)(1101,1754)(1102,1753)(1103,1752)(1104,1751)(1105,1750)(1106,1749)(1107,1748)(1108,1747)(1109,1746)(1110,1745)(1111,1744)(1112,1743)(1113,1742)(1114,1741)(1115,1740)(1116,1739)(1117,1738)(1118,1737)(1119,1736)(1120,1735)(1121,1734)(1122,1733)(1123,1732)(1124,1731)(1125,1730)(1126,1729)(1127,1728)(1128,1727)(1129,1726)(1130,1725)(1131,1724)(1132,1723)(1133,1722)(1134,1721)(1135,1720)(1136,1719)(1137,1718)(1138,1717)(1139,1716)(1140,1715)(1141,1714)(1142,1713)(1143,1712)(1144,1711)(1145,1710)(1146,1709)(1147,1708)(1148,1707)(1149,1706)(1150,1705)(1151,1704)(1152,1703)(1153,1702)(1154,1701)(1155,1700)(1156,1699)(1157,1698)(1158,1697)(1159,1696)(1160,1695)(1161,1694)(1162,1693)(1163,1692)(1164,1691)(1165,1690)(1166,1689)(1167,1688)(1168,1687)(1169,1686)(1170,1685)(1171,1684)(1172,1683)(1173,1682)(1174,1681)(1175,1680)(1176,1679)(1177,1678)(1178,1677)(1179,1676)(1180,1675)(1181,1674)(1182,1673)(1183,1672)(1184,1671)(1185,1670)(1186,1669)(1187,1668)(1188,1667)(1189,1666)(1190,1665)(1191,1664)(1192,1663)(1193,1662)(1194,1661)(1195,1660)(1196,1659)(1197,1658)(1198,1657)(1199,1656)(1200,1655)(1201,1654)(1202,1653)(1203,1652)(1204,1651)(1205,1650)(1206,1649)(1207,1648)(1208,1647)(1209,1646)(1210,1645)(1211,1644)(1212,1643)(1213,1642)(1214,1641)(1215,1640)(1216,1639)(1217,1638)(1218,1637)(1219,1636)(1220,1635)(1221,1634)(1222,1633)(1223,1632)(1224,1631)(1225,1630)(1226,1629)(1227,1628)(1228,1627)(1229,1626)(1230,1625)(1231,1624)(1232,1623)(1233,1622)(1234,1621)(1235,1620)(1236,1619)(1237,1618)(1238,1617)(1239,1616)(1240,1615)(1241,1614)(1242,1613)(1243,1612)(1244,1611)(1245,1610)(1246,1609)(1247,1608)(1248,1607)(1249,1606)(1250,1605)(1251,1604)(1252,1603)(1253,1602)(1254,1601)(1255,1600)(1256,1599)(1257,1598)(1258,1597)(1259,1596)(1260,1595)(1261,1594)(1262,1593)(1263,1592)(1264,1591)(1265,1590)(1266,1589)(1267,1588)(1268,1587)(1269,1586)(1270,1585)(1271,1584)(1272,1583)(1273,1582)(1274,1581)(1275,1580)(1276,1579)(1277,1578)(1278,1577)(1279,1576)(1280,1575)(1281,1574)(1282,1573)(1283,1572)(1284,1571)(1285,1570)(1286,1569)(1287,1568)(1288,1567)(1289,1566)(1290,1565)(1291,1564)(1292,1563)(1293,1562)(1294,1561)(1295,1560)(1296,1559)(1297,1558)(1298,1557)(1299,1556)(1300,1555)(1301,1554)(1302,1553)(1303,1552)(1304,1551)(1305,1550)(1306,1549)(1307,1548)(1308,1547)(1309,1546)(1310,1545)(1311,1544)(1312,1543)(1313,1542)(1314,1541)(1315,1540)(1316,1539)(1317,1538)(1318,1537)(1319,1536)(1320,1535)(1321,1534)(1322,1533)(1323,1532)(1324,1531)(1325,1530)(1326,1529)(1327,1528)(1328,1527)(1329,1526)(1330,1525)(1331,1524)(1332,1523)(1333,1522)(1334,1521)(1335,1520)(1336,1519)(1337,1518)(1338,1517)(1339,1516)(1340,1515)(1341,1514)(1342,1513)(1343,1512)(1344,1511)(1345,1510)(1346,1509)(1347,1508)(1348,1507)(1349,1506)(1350,1505)(1351,1504)(1352,1503)(1353,1502)(1354,1501)(1355,1500)(1356,1499)(1357,1498)(1358,1497)(1359,1496)(1360,1495)(1361,1494)(1362,1493)(1363,1492)(1364,1491)(1365,1490)(1366,1489)(1367,1488)(1368,1487)(1369,1486)(1370,1485)(1371,1484)(1372,1483)(1373,1482)(1374,1481)(1375,1480)(1376,1479)(1377,1478)(1378,1477)(1379,1476)(1380,1475)(1381,1474)(1382,1473)(1383,1472)(1384,1471)(1385,1470)(1386,1469)(1387,1468)(1388,1467)(1389,1466)(1390,1465)(1391,1464)(1392,1463)(1393,1462)(1394,1461)(1395,1460)(1396,1459)(1397,1458)(1398,1457)(1399,1456)(1400,1455)(1401,1454)(1402,1453)(1403,1452)(1404,1451)(1405,1450)(1406,1449)(1407,1448)(1408,1447)(1409,1446)(1410,1445)(1411,1444)(1412,1443)(1413,1442)(1414,1441)(1415,1440)(1416,1439)(1417,1438)(1418,1437)(1419,1436)(1420,1435)(1421,1434)(1422,1433)(1423,1432)(1424,1431)(1425,1430)(1426,1429)(1427,1428)
Polycyclic presentation:
2,5,2843|b^a=b^4,c^a=c^2842
Conjugacy classes & character table
7109 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28430, 3);
Finite Group Databasebeta