Finite Group Databasebeta

?

← Prev (#72288459) Next (#72288461) →

D₂₅₂₈₁ #72288460

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem
• Frobenius

Aliases

Splittings

Subgroups

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Polycyclic presentation:

2,3,53,3,53|b^3=d,c^53=e,b^a=b^2d^2,c^a=c^52e^52,d^a=d^2,e^a=e^52

Conjugacy classes & character table

12642 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:

gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e");;
gap> coll := SingleCollector(F, [2, 3, 53, 3, 53]);;
gap> SetPower(coll, 2, F.4);;
gap> SetPower(coll, 3, F.5);;
gap> SetConjugate(coll, 2, 1, F.2^2*F.4^2);;
gap> SetConjugate(coll, 3, 1, F.3^52*F.5^52);;
gap> SetConjugate(coll, 4, 1, F.4^2);;
gap> SetConjugate(coll, 5, 1, F.5^52);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);