Finite Group Databasebeta

?

← Prev (#37567306) Next (#37567308) →

Dic₆₀₉₈ #37567307

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

Aliases

Splittings

Subgroups

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 3057 points:

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

Polycyclic presentation:

2^3,3049|a^2=c,b^2=c,b^a=bc,d^b=d^3048

Conjugacy classes & character table

6101 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24392, 11);