Finite Group Databasebeta

?

← Prev (#37587519) Next (#37587521) →

Dic₆₁₂₂ #37587520

• 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 3069 points:

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

Polycyclic presentation:

2^3,3061|a^2=c,b^2=c,b^a=bc,d^b=d^3060

Conjugacy classes & character table

6125 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24488, 11);