Finite Group Databasebeta

?

← Prev (#37564030) Next (#37564032) →

D₁₂₀₉₂ #37564031

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

Polycyclic presentation:

2^3,3023|b^a=bc,d^a=d^3022,d^b=d^3022

Conjugacy classes & character table

6049 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24184, 10);