Finite Group Databasebeta

?

← Prev (#38733380) Next (#38733382) →

D₁₂₄₃₆ #38733381

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

Aliases

Splittings

Subgroups

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 3113 points:

(1,2,3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199,2200,2201,2202,2203,2204,2205,2206,2207,2208,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219,2220,2221,2222,2223,2224,2225,2226,2227,2228,2229,2230,2231,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2302,2303,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431,2432,2433,2434,2435,2436,2437,2438,2439,2440,2441,2442,2443,2444,2445,2446,2447,2448,2449,2450,2451,2452,2453,2454,2455,2456,2457,2458,2459,2460,2461,2462,2463,2464,2465,2466,2467,2468,2469,2470,2471,2472,2473,2474,2475,2476,2477,2478,2479,2480,2481,2482,2483,2484,2485,2486,2487,2488,2489,2490,2491,2492,2493,2494,2495,2496,2497,2498,2499,2500,2501,2502,2503,2504,2505,2506,2507,2508,2509,2510,2511,2512,2513,2514,2515,2516,2517,2518,2519,2520,2521,2522,2523,2524,2525,2526,2527,2528,2529,2530,2531,2532,2533,2534,2535,2536,2537,2538,2539,2540,2541,2542,2543,2544,2545,2546,2547,2548,2549,2550,2551,2552,2553,2554,2555,2556,2557,2558,2559,2560,2561,2562,2563,2564,2565,2566,2567,2568,2569,2570,2571,2572,2573,2574,2575,2576,2577,2578,2579,2580,2581,2582,2583,2584,2585,2586,2587,2588,2589,2590,2591,2592,2593,2594,2595,2596,2597,2598,2599,2600,2601,2602,2603,2604,2605,2606,2607,2608,2609,2610,2611,2612,2613,2614,2615,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2626,2627,2628,2629,2630,2631,2632,2633,2634,2635,2636,2637,2638,2639,2640,2641,2642,2643,2644,2645,2646,2647,2648,2649,2650,2651,2652,2653,2654,2655,2656,2657,2658,2659,2660,2661,2662,2663,2664,2665,2666,2667,2668,2669,2670,2671,2672,2673,2674,2675,2676,2677,2678,2679,2680,2681,2682,2683,2684,2685,2686,2687,2688,2689,2690,2691,2692,2693,2694,2695,2696,2697,2698,2699,2700,2701,2702,2703,2704,2705,2706,2707,2708,2709,2710,2711,2712,2713,2714,2715,2716,2717,2718,2719,2720,2721,2722,2723,2724,2725,2726,2727,2728,2729,2730,2731,2732,2733,2734,2735,2736,2737,2738,2739,2740,2741,2742,2743,2744,2745,2746,2747,2748,2749,2750,2751,2752,2753,2754,2755,2756,2757,2758,2759,2760,2761,2762,2763,2764,2765,2766,2767,2768,2769,2770,2771,2772,2773,2774,2775,2776,2777,2778,2779,2780,2781,2782,2783,2784,2785,2786,2787,2788,2789,2790,2791,2792,2793,2794,2795,2796,2797,2798,2799,2800,2801,2802,2803,2804,2805,2806,2807,2808,2809,2810,2811,2812,2813,2814,2815,2816,2817,2818,2819,2820,2821,2822,2823,2824,2825,2826,2827,2828,2829,2830,2831,2832,2833,2834,2835,2836,2837,2838,2839,2840,2841,2842,2843,2844,2845,2846,2847,2848,2849,2850,2851,2852,2853,2854,2855,2856,2857,2858,2859,2860,2861,2862,2863,2864,2865,2866,2867,2868,2869,2870,2871,2872,2873,2874,2875,2876,2877,2878,2879,2880,2881,2882,2883,2884,2885,2886,2887,2888,2889,2890,2891,2892,2893,2894,2895,2896,2897,2898,2899,2900,2901,2902,2903,2904,2905,2906,2907,2908,2909,2910,2911,2912,2913,2914,2915,2916,2917,2918,2919,2920,2921,2922,2923,2924,2925,2926,2927,2928,2929,2930,2931,2932,2933,2934,2935,2936,2937,2938,2939,2940,2941,2942,2943,2944,2945,2946,2947,2948,2949,2950,2951,2952,2953,2954,2955,2956,2957,2958,2959,2960,2961,2962,2963,2964,2965,2966,2967,2968,2969,2970,2971,2972,2973,2974,2975,2976,2977,2978,2979,2980,2981,2982,2983,2984,2985,2986,2987,2988,2989,2990,2991,2992,2993,2994,2995,2996,2997,2998,2999,3000,3001,3002,3003,3004,3005,3006,3007,3008,3009,3010,3011,3012,3013,3014,3015,3016,3017,3018,3019,3020,3021,3022,3023,3024,3025,3026,3027,3028,3029,3030,3031,3032,3033,3034,3035,3036,3037,3038,3039,3040,3041,3042,3043,3044,3045,3046,3047,3048,3049,3050,3051,3052,3053,3054,3055,3056,3057,3058,3059,3060,3061,3062,3063,3064,3065,3066,3067,3068,3069,3070,3071,3072,3073,3074,3075,3076,3077,3078,3079,3080,3081,3082,3083,3084,3085,3086,3087,3088,3089,3090,3091,3092,3093,3094,3095,3096,3097,3098,3099,3100,3101,3102,3103,3104,3105,3106,3107,3108,3109,3110,3111,3112,3113);(2,4)(6,3113)(7,3112)(8,3111)(9,3110)(10,3109)(11,3108)(12,3107)(13,3106)(14,3105)(15,3104)(16,3103)(17,3102)(18,3101)(19,3100)(20,3099)(21,3098)(22,3097)(23,3096)(24,3095)(25,3094)(26,3093)(27,3092)(28,3091)(29,3090)(30,3089)(31,3088)(32,3087)(33,3086)(34,3085)(35,3084)(36,3083)(37,3082)(38,3081)(39,3080)(40,3079)(41,3078)(42,3077)(43,3076)(44,3075)(45,3074)(46,3073)(47,3072)(48,3071)(49,3070)(50,3069)(51,3068)(52,3067)(53,3066)(54,3065)(55,3064)(56,3063)(57,3062)(58,3061)(59,3060)(60,3059)(61,3058)(62,3057)(63,3056)(64,3055)(65,3054)(66,3053)(67,3052)(68,3051)(69,3050)(70,3049)(71,3048)(72,3047)(73,3046)(74,3045)(75,3044)(76,3043)(77,3042)(78,3041)(79,3040)(80,3039)(81,3038)(82,3037)(83,3036)(84,3035)(85,3034)(86,3033)(87,3032)(88,3031)(89,3030)(90,3029)(91,3028)(92,3027)(93,3026)(94,3025)(95,3024)(96,3023)(97,3022)(98,3021)(99,3020)(100,3019)(101,3018)(102,3017)(103,3016)(104,3015)(105,3014)(106,3013)(107,3012)(108,3011)(109,3010)(110,3009)(111,3008)(112,3007)(113,3006)(114,3005)(115,3004)(116,3003)(117,3002)(118,3001)(119,3000)(120,2999)(121,2998)(122,2997)(123,2996)(124,2995)(125,2994)(126,2993)(127,2992)(128,2991)(129,2990)(130,2989)(131,2988)(132,2987)(133,2986)(134,2985)(135,2984)(136,2983)(137,2982)(138,2981)(139,2980)(140,2979)(141,2978)(142,2977)(143,2976)(144,2975)(145,2974)(146,2973)(147,2972)(148,2971)(149,2970)(150,2969)(151,2968)(152,2967)(153,2966)(154,2965)(155,2964)(156,2963)(157,2962)(158,2961)(159,2960)(160,2959)(161,2958)(162,2957)(163,2956)(164,2955)(165,2954)(166,2953)(167,2952)(168,2951)(169,2950)(170,2949)(171,2948)(172,2947)(173,2946)(174,2945)(175,2944)(176,2943)(177,2942)(178,2941)(179,2940)(180,2939)(181,2938)(182,2937)(183,2936)(184,2935)(185,2934)(186,2933)(187,2932)(188,2931)(189,2930)(190,2929)(191,2928)(192,2927)(193,2926)(194,2925)(195,2924)(196,2923)(197,2922)(198,2921)(199,2920)(200,2919)(201,2918)(202,2917)(203,2916)(204,2915)(205,2914)(206,2913)(207,2912)(208,2911)(209,2910)(210,2909)(211,2908)(212,2907)(213,2906)(214,2905)(215,2904)(216,2903)(217,2902)(218,2901)(219,2900)(220,2899)(221,2898)(222,2897)(223,2896)(224,2895)(225,2894)(226,2893)(227,2892)(228,2891)(229,2890)(230,2889)(231,2888)(232,2887)(233,2886)(234,2885)(235,2884)(236,2883)(237,2882)(238,2881)(239,2880)(240,2879)(241,2878)(242,2877)(243,2876)(244,2875)(245,2874)(246,2873)(247,2872)(248,2871)(249,2870)(250,2869)(251,2868)(252,2867)(253,2866)(254,2865)(255,2864)(256,2863)(257,2862)(258,2861)(259,2860)(260,2859)(261,2858)(262,2857)(263,2856)(264,2855)(265,2854)(266,2853)(267,2852)(268,2851)(269,2850)(270,2849)(271,2848)(272,2847)(273,2846)(274,2845)(275,2844)(276,2843)(277,2842)(278,2841)(279,2840)(280,2839)(281,2838)(282,2837)(283,2836)(284,2835)(285,2834)(286,2833)(287,2832)(288,2831)(289,2830)(290,2829)(291,2828)(292,2827)(293,2826)(294,2825)(295,2824)(296,2823)(297,2822)(298,2821)(299,2820)(300,2819)(301,2818)(302,2817)(303,2816)(304,2815)(305,2814)(306,2813)(307,2812)(308,2811)(309,2810)(310,2809)(311,2808)(312,2807)(313,2806)(314,2805)(315,2804)(316,2803)(317,2802)(318,2801)(319,2800)(320,2799)(321,2798)(322,2797)(323,2796)(324,2795)(325,2794)(326,2793)(327,2792)(328,2791)(329,2790)(330,2789)(331,2788)(332,2787)(333,2786)(334,2785)(335,2784)(336,2783)(337,2782)(338,2781)(339,2780)(340,2779)(341,2778)(342,2777)(343,2776)(344,2775)(345,2774)(346,2773)(347,2772)(348,2771)(349,2770)(350,2769)(351,2768)(352,2767)(353,2766)(354,2765)(355,2764)(356,2763)(357,2762)(358,2761)(359,2760)(360,2759)(361,2758)(362,2757)(363,2756)(364,2755)(365,2754)(366,2753)(367,2752)(368,2751)(369,2750)(370,2749)(371,2748)(372,2747)(373,2746)(374,2745)(375,2744)(376,2743)(377,2742)(378,2741)(379,2740)(380,2739)(381,2738)(382,2737)(383,2736)(384,2735)(385,2734)(386,2733)(387,2732)(388,2731)(389,2730)(390,2729)(391,2728)(392,2727)(393,2726)(394,2725)(395,2724)(396,2723)(397,2722)(398,2721)(399,2720)(400,2719)(401,2718)(402,2717)(403,2716)(404,2715)(405,2714)(406,2713)(407,2712)(408,2711)(409,2710)(410,2709)(411,2708)(412,2707)(413,2706)(414,2705)(415,2704)(416,2703)(417,2702)(418,2701)(419,2700)(420,2699)(421,2698)(422,2697)(423,2696)(424,2695)(425,2694)(426,2693)(427,2692)(428,2691)(429,2690)(430,2689)(431,2688)(432,2687)(433,2686)(434,2685)(435,2684)(436,2683)(437,2682)(438,2681)(439,2680)(440,2679)(441,2678)(442,2677)(443,2676)(444,2675)(445,2674)(446,2673)(447,2672)(448,2671)(449,2670)(450,2669)(451,2668)(452,2667)(453,2666)(454,2665)(455,2664)(456,2663)(457,2662)(458,2661)(459,2660)(460,2659)(461,2658)(462,2657)(463,2656)(464,2655)(465,2654)(466,2653)(467,2652)(468,2651)(469,2650)(470,2649)(471,2648)(472,2647)(473,2646)(474,2645)(475,2644)(476,2643)(477,2642)(478,2641)(479,2640)(480,2639)(481,2638)(482,2637)(483,2636)(484,2635)(485,2634)(486,2633)(487,2632)(488,2631)(489,2630)(490,2629)(491,2628)(492,2627)(493,2626)(494,2625)(495,2624)(496,2623)(497,2622)(498,2621)(499,2620)(500,2619)(501,2618)(502,2617)(503,2616)(504,2615)(505,2614)(506,2613)(507,2612)(508,2611)(509,2610)(510,2609)(511,2608)(512,2607)(513,2606)(514,2605)(515,2604)(516,2603)(517,2602)(518,2601)(519,2600)(520,2599)(521,2598)(522,2597)(523,2596)(524,2595)(525,2594)(526,2593)(527,2592)(528,2591)(529,2590)(530,2589)(531,2588)(532,2587)(533,2586)(534,2585)(535,2584)(536,2583)(537,2582)(538,2581)(539,2580)(540,2579)(541,2578)(542,2577)(543,2576)(544,2575)(545,2574)(546,2573)(547,2572)(548,2571)(549,2570)(550,2569)(551,2568)(552,2567)(553,2566)(554,2565)(555,2564)(556,2563)(557,2562)(558,2561)(559,2560)(560,2559)(561,2558)(562,2557)(563,2556)(564,2555)(565,2554)(566,2553)(567,2552)(568,2551)(569,2550)(570,2549)(571,2548)(572,2547)(573,2546)(574,2545)(575,2544)(576,2543)(577,2542)(578,2541)(579,2540)(580,2539)(581,2538)(582,2537)(583,2536)(584,2535)(585,2534)(586,2533)(587,2532)(588,2531)(589,2530)(590,2529)(591,2528)(592,2527)(593,2526)(594,2525)(595,2524)(596,2523)(597,2522)(598,2521)(599,2520)(600,2519)(601,2518)(602,2517)(603,2516)(604,2515)(605,2514)(606,2513)(607,2512)(608,2511)(609,2510)(610,2509)(611,2508)(612,2507)(613,2506)(614,2505)(615,2504)(616,2503)(617,2502)(618,2501)(619,2500)(620,2499)(621,2498)(622,2497)(623,2496)(624,2495)(625,2494)(626,2493)(627,2492)(628,2491)(629,2490)(630,2489)(631,2488)(632,2487)(633,2486)(634,2485)(635,2484)(636,2483)(637,2482)(638,2481)(639,2480)(640,2479)(641,2478)(642,2477)(643,2476)(644,2475)(645,2474)(646,2473)(647,2472)(648,2471)(649,2470)(650,2469)(651,2468)(652,2467)(653,2466)(654,2465)(655,2464)(656,2463)(657,2462)(658,2461)(659,2460)(660,2459)(661,2458)(662,2457)(663,2456)(664,2455)(665,2454)(666,2453)(667,2452)(668,2451)(669,2450)(670,2449)(671,2448)(672,2447)(673,2446)(674,2445)(675,2444)(676,2443)(677,2442)(678,2441)(679,2440)(680,2439)(681,2438)(682,2437)(683,2436)(684,2435)(685,2434)(686,2433)(687,2432)(688,2431)(689,2430)(690,2429)(691,2428)(692,2427)(693,2426)(694,2425)(695,2424)(696,2423)(697,2422)(698,2421)(699,2420)(700,2419)(701,2418)(702,2417)(703,2416)(704,2415)(705,2414)(706,2413)(707,2412)(708,2411)(709,2410)(710,2409)(711,2408)(712,2407)(713,2406)(714,2405)(715,2404)(716,2403)(717,2402)(718,2401)(719,2400)(720,2399)(721,2398)(722,2397)(723,2396)(724,2395)(725,2394)(726,2393)(727,2392)(728,2391)(729,2390)(730,2389)(731,2388)(732,2387)(733,2386)(734,2385)(735,2384)(736,2383)(737,2382)(738,2381)(739,2380)(740,2379)(741,2378)(742,2377)(743,2376)(744,2375)(745,2374)(746,2373)(747,2372)(748,2371)(749,2370)(750,2369)(751,2368)(752,2367)(753,2366)(754,2365)(755,2364)(756,2363)(757,2362)(758,2361)(759,2360)(760,2359)(761,2358)(762,2357)(763,2356)(764,2355)(765,2354)(766,2353)(767,2352)(768,2351)(769,2350)(770,2349)(771,2348)(772,2347)(773,2346)(774,2345)(775,2344)(776,2343)(777,2342)(778,2341)(779,2340)(780,2339)(781,2338)(782,2337)(783,2336)(784,2335)(785,2334)(786,2333)(787,2332)(788,2331)(789,2330)(790,2329)(791,2328)(792,2327)(793,2326)(794,2325)(795,2324)(796,2323)(797,2322)(798,2321)(799,2320)(800,2319)(801,2318)(802,2317)(803,2316)(804,2315)(805,2314)(806,2313)(807,2312)(808,2311)(809,2310)(810,2309)(811,2308)(812,2307)(813,2306)(814,2305)(815,2304)(816,2303)(817,2302)(818,2301)(819,2300)(820,2299)(821,2298)(822,2297)(823,2296)(824,2295)(825,2294)(826,2293)(827,2292)(828,2291)(829,2290)(830,2289)(831,2288)(832,2287)(833,2286)(834,2285)(835,2284)(836,2283)(837,2282)(838,2281)(839,2280)(840,2279)(841,2278)(842,2277)(843,2276)(844,2275)(845,2274)(846,2273)(847,2272)(848,2271)(849,2270)(850,2269)(851,2268)(852,2267)(853,2266)(854,2265)(855,2264)(856,2263)(857,2262)(858,2261)(859,2260)(860,2259)(861,2258)(862,2257)(863,2256)(864,2255)(865,2254)(866,2253)(867,2252)(868,2251)(869,2250)(870,2249)(871,2248)(872,2247)(873,2246)(874,2245)(875,2244)(876,2243)(877,2242)(878,2241)(879,2240)(880,2239)(881,2238)(882,2237)(883,2236)(884,2235)(885,2234)(886,2233)(887,2232)(888,2231)(889,2230)(890,2229)(891,2228)(892,2227)(893,2226)(894,2225)(895,2224)(896,2223)(897,2222)(898,2221)(899,2220)(900,2219)(901,2218)(902,2217)(903,2216)(904,2215)(905,2214)(906,2213)(907,2212)(908,2211)(909,2210)(910,2209)(911,2208)(912,2207)(913,2206)(914,2205)(915,2204)(916,2203)(917,2202)(918,2201)(919,2200)(920,2199)(921,2198)(922,2197)(923,2196)(924,2195)(925,2194)(926,2193)(927,2192)(928,2191)(929,2190)(930,2189)(931,2188)(932,2187)(933,2186)(934,2185)(935,2184)(936,2183)(937,2182)(938,2181)(939,2180)(940,2179)(941,2178)(942,2177)(943,2176)(944,2175)(945,2174)(946,2173)(947,2172)(948,2171)(949,2170)(950,2169)(951,2168)(952,2167)(953,2166)(954,2165)(955,2164)(956,2163)(957,2162)(958,2161)(959,2160)(960,2159)(961,2158)(962,2157)(963,2156)(964,2155)(965,2154)(966,2153)(967,2152)(968,2151)(969,2150)(970,2149)(971,2148)(972,2147)(973,2146)(974,2145)(975,2144)(976,2143)(977,2142)(978,2141)(979,2140)(980,2139)(981,2138)(982,2137)(983,2136)(984,2135)(985,2134)(986,2133)(987,2132)(988,2131)(989,2130)(990,2129)(991,2128)(992,2127)(993,2126)(994,2125)(995,2124)(996,2123)(997,2122)(998,2121)(999,2120)(1000,2119)(1001,2118)(1002,2117)(1003,2116)(1004,2115)(1005,2114)(1006,2113)(1007,2112)(1008,2111)(1009,2110)(1010,2109)(1011,2108)(1012,2107)(1013,2106)(1014,2105)(1015,2104)(1016,2103)(1017,2102)(1018,2101)(1019,2100)(1020,2099)(1021,2098)(1022,2097)(1023,2096)(1024,2095)(1025,2094)(1026,2093)(1027,2092)(1028,2091)(1029,2090)(1030,2089)(1031,2088)(1032,2087)(1033,2086)(1034,2085)(1035,2084)(1036,2083)(1037,2082)(1038,2081)(1039,2080)(1040,2079)(1041,2078)(1042,2077)(1043,2076)(1044,2075)(1045,2074)(1046,2073)(1047,2072)(1048,2071)(1049,2070)(1050,2069)(1051,2068)(1052,2067)(1053,2066)(1054,2065)(1055,2064)(1056,2063)(1057,2062)(1058,2061)(1059,2060)(1060,2059)(1061,2058)(1062,2057)(1063,2056)(1064,2055)(1065,2054)(1066,2053)(1067,2052)(1068,2051)(1069,2050)(1070,2049)(1071,2048)(1072,2047)(1073,2046)(1074,2045)(1075,2044)(1076,2043)(1077,2042)(1078,2041)(1079,2040)(1080,2039)(1081,2038)(1082,2037)(1083,2036)(1084,2035)(1085,2034)(1086,2033)(1087,2032)(1088,2031)(1089,2030)(1090,2029)(1091,2028)(1092,2027)(1093,2026)(1094,2025)(1095,2024)(1096,2023)(1097,2022)(1098,2021)(1099,2020)(1100,2019)(1101,2018)(1102,2017)(1103,2016)(1104,2015)(1105,2014)(1106,2013)(1107,2012)(1108,2011)(1109,2010)(1110,2009)(1111,2008)(1112,2007)(1113,2006)(1114,2005)(1115,2004)(1116,2003)(1117,2002)(1118,2001)(1119,2000)(1120,1999)(1121,1998)(1122,1997)(1123,1996)(1124,1995)(1125,1994)(1126,1993)(1127,1992)(1128,1991)(1129,1990)(1130,1989)(1131,1988)(1132,1987)(1133,1986)(1134,1985)(1135,1984)(1136,1983)(1137,1982)(1138,1981)(1139,1980)(1140,1979)(1141,1978)(1142,1977)(1143,1976)(1144,1975)(1145,1974)(1146,1973)(1147,1972)(1148,1971)(1149,1970)(1150,1969)(1151,1968)(1152,1967)(1153,1966)(1154,1965)(1155,1964)(1156,1963)(1157,1962)(1158,1961)(1159,1960)(1160,1959)(1161,1958)(1162,1957)(1163,1956)(1164,1955)(1165,1954)(1166,1953)(1167,1952)(1168,1951)(1169,1950)(1170,1949)(1171,1948)(1172,1947)(1173,1946)(1174,1945)(1175,1944)(1176,1943)(1177,1942)(1178,1941)(1179,1940)(1180,1939)(1181,1938)(1182,1937)(1183,1936)(1184,1935)(1185,1934)(1186,1933)(1187,1932)(1188,1931)(1189,1930)(1190,1929)(1191,1928)(1192,1927)(1193,1926)(1194,1925)(1195,1924)(1196,1923)(1197,1922)(1198,1921)(1199,1920)(1200,1919)(1201,1918)(1202,1917)(1203,1916)(1204,1915)(1205,1914)(1206,1913)(1207,1912)(1208,1911)(1209,1910)(1210,1909)(1211,1908)(1212,1907)(1213,1906)(1214,1905)(1215,1904)(1216,1903)(1217,1902)(1218,1901)(1219,1900)(1220,1899)(1221,1898)(1222,1897)(1223,1896)(1224,1895)(1225,1894)(1226,1893)(1227,1892)(1228,1891)(1229,1890)(1230,1889)(1231,1888)(1232,1887)(1233,1886)(1234,1885)(1235,1884)(1236,1883)(1237,1882)(1238,1881)(1239,1880)(1240,1879)(1241,1878)(1242,1877)(1243,1876)(1244,1875)(1245,1874)(1246,1873)(1247,1872)(1248,1871)(1249,1870)(1250,1869)(1251,1868)(1252,1867)(1253,1866)(1254,1865)(1255,1864)(1256,1863)(1257,1862)(1258,1861)(1259,1860)(1260,1859)(1261,1858)(1262,1857)(1263,1856)(1264,1855)(1265,1854)(1266,1853)(1267,1852)(1268,1851)(1269,1850)(1270,1849)(1271,1848)(1272,1847)(1273,1846)(1274,1845)(1275,1844)(1276,1843)(1277,1842)(1278,1841)(1279,1840)(1280,1839)(1281,1838)(1282,1837)(1283,1836)(1284,1835)(1285,1834)(1286,1833)(1287,1832)(1288,1831)(1289,1830)(1290,1829)(1291,1828)(1292,1827)(1293,1826)(1294,1825)(1295,1824)(1296,1823)(1297,1822)(1298,1821)(1299,1820)(1300,1819)(1301,1818)(1302,1817)(1303,1816)(1304,1815)(1305,1814)(1306,1813)(1307,1812)(1308,1811)(1309,1810)(1310,1809)(1311,1808)(1312,1807)(1313,1806)(1314,1805)(1315,1804)(1316,1803)(1317,1802)(1318,1801)(1319,1800)(1320,1799)(1321,1798)(1322,1797)(1323,1796)(1324,1795)(1325,1794)(1326,1793)(1327,1792)(1328,1791)(1329,1790)(1330,1789)(1331,1788)(1332,1787)(1333,1786)(1334,1785)(1335,1784)(1336,1783)(1337,1782)(1338,1781)(1339,1780)(1340,1779)(1341,1778)(1342,1777)(1343,1776)(1344,1775)(1345,1774)(1346,1773)(1347,1772)(1348,1771)(1349,1770)(1350,1769)(1351,1768)(1352,1767)(1353,1766)(1354,1765)(1355,1764)(1356,1763)(1357,1762)(1358,1761)(1359,1760)(1360,1759)(1361,1758)(1362,1757)(1363,1756)(1364,1755)(1365,1754)(1366,1753)(1367,1752)(1368,1751)(1369,1750)(1370,1749)(1371,1748)(1372,1747)(1373,1746)(1374,1745)(1375,1744)(1376,1743)(1377,1742)(1378,1741)(1379,1740)(1380,1739)(1381,1738)(1382,1737)(1383,1736)(1384,1735)(1385,1734)(1386,1733)(1387,1732)(1388,1731)(1389,1730)(1390,1729)(1391,1728)(1392,1727)(1393,1726)(1394,1725)(1395,1724)(1396,1723)(1397,1722)(1398,1721)(1399,1720)(1400,1719)(1401,1718)(1402,1717)(1403,1716)(1404,1715)(1405,1714)(1406,1713)(1407,1712)(1408,1711)(1409,1710)(1410,1709)(1411,1708)(1412,1707)(1413,1706)(1414,1705)(1415,1704)(1416,1703)(1417,1702)(1418,1701)(1419,1700)(1420,1699)(1421,1698)(1422,1697)(1423,1696)(1424,1695)(1425,1694)(1426,1693)(1427,1692)(1428,1691)(1429,1690)(1430,1689)(1431,1688)(1432,1687)(1433,1686)(1434,1685)(1435,1684)(1436,1683)(1437,1682)(1438,1681)(1439,1680)(1440,1679)(1441,1678)(1442,1677)(1443,1676)(1444,1675)(1445,1674)(1446,1673)(1447,1672)(1448,1671)(1449,1670)(1450,1669)(1451,1668)(1452,1667)(1453,1666)(1454,1665)(1455,1664)(1456,1663)(1457,1662)(1458,1661)(1459,1660)(1460,1659)(1461,1658)(1462,1657)(1463,1656)(1464,1655)(1465,1654)(1466,1653)(1467,1652)(1468,1651)(1469,1650)(1470,1649)(1471,1648)(1472,1647)(1473,1646)(1474,1645)(1475,1644)(1476,1643)(1477,1642)(1478,1641)(1479,1640)(1480,1639)(1481,1638)(1482,1637)(1483,1636)(1484,1635)(1485,1634)(1486,1633)(1487,1632)(1488,1631)(1489,1630)(1490,1629)(1491,1628)(1492,1627)(1493,1626)(1494,1625)(1495,1624)(1496,1623)(1497,1622)(1498,1621)(1499,1620)(1500,1619)(1501,1618)(1502,1617)(1503,1616)(1504,1615)(1505,1614)(1506,1613)(1507,1612)(1508,1611)(1509,1610)(1510,1609)(1511,1608)(1512,1607)(1513,1606)(1514,1605)(1515,1604)(1516,1603)(1517,1602)(1518,1601)(1519,1600)(1520,1599)(1521,1598)(1522,1597)(1523,1596)(1524,1595)(1525,1594)(1526,1593)(1527,1592)(1528,1591)(1529,1590)(1530,1589)(1531,1588)(1532,1587)(1533,1586)(1534,1585)(1535,1584)(1536,1583)(1537,1582)(1538,1581)(1539,1580)(1540,1579)(1541,1578)(1542,1577)(1543,1576)(1544,1575)(1545,1574)(1546,1573)(1547,1572)(1548,1571)(1549,1570)(1550,1569)(1551,1568)(1552,1567)(1553,1566)(1554,1565)(1555,1564)(1556,1563)(1557,1562)(1558,1561)(1559,1560)

Polycyclic presentation:

2^3,3109|b^a=bc,d^a=d^3108,d^b=d^3108

Conjugacy classes & character table

6221 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24872, 10);