D₂₈₂₃₃ #72291597

order	56466
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₂₈₂₃₃

Splittings

Fitting, derived, Hall	C₉×C₃₁₃₇ ⋊ C₂
Sylow	C₃₁₃₇ ⋊ D₉
Sylow	C₉ ⋊ D₃₁₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₃₁₃₇	C₂
Frattini	C₃	D₉₄₁₁
socle	C₃×C₃₁₃₇	D₃
LCS	G ▷ C₉×C₃₁₃₇
UCS	C₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 3146
transitive degree	μ_t(G) = 28233

A minimal faithful permutation representation — 2 generators on 3146 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199,2200,2201,2202,2203,2204,2205,2206,2207,2208,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219,2220,2221,2222,2223,2224,2225,2226,2227,2228,2229,2230,2231,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2302,2303,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431,2432,2433,2434,2435,2436,2437,2438,2439,2440,2441,2442,2443,2444,2445,2446,2447,2448,2449,2450,2451,2452,2453,2454,2455,2456,2457,2458,2459,2460,2461,2462,2463,2464,2465,2466,2467,2468,2469,2470,2471,2472,2473,2474,2475,2476,2477,2478,2479,2480,2481,2482,2483,2484,2485,2486,2487,2488,2489,2490,2491,2492,2493,2494,2495,2496,2497,2498,2499,2500,2501,2502,2503,2504,2505,2506,2507,2508,2509,2510,2511,2512,2513,2514,2515,2516,2517,2518,2519,2520,2521,2522,2523,2524,2525,2526,2527,2528,2529,2530,2531,2532,2533,2534,2535,2536,2537,2538,2539,2540,2541,2542,2543,2544,2545,2546,2547,2548,2549,2550,2551,2552,2553,2554,2555,2556,2557,2558,2559,2560,2561,2562,2563,2564,2565,2566,2567,2568,2569,2570,2571,2572,2573,2574,2575,2576,2577,2578,2579,2580,2581,2582,2583,2584,2585,2586,2587,2588,2589,2590,2591,2592,2593,2594,2595,2596,2597,2598,2599,2600,2601,2602,2603,2604,2605,2606,2607,2608,2609,2610,2611,2612,2613,2614,2615,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2626,2627,2628,2629,2630,2631,2632,2633,2634,2635,2636,2637,2638,2639,2640,2641,2642,2643,2644,2645,2646,2647,2648,2649,2650,2651,2652,2653,2654,2655,2656,2657,2658,2659,2660,2661,2662,2663,2664,2665,2666,2667,2668,2669,2670,2671,2672,2673,2674,2675,2676,2677,2678,2679,2680,2681,2682,2683,2684,2685,2686,2687,2688,2689,2690,2691,2692,2693,2694,2695,2696,2697,2698,2699,2700,2701,2702,2703,2704,2705,2706,2707,2708,2709,2710,2711,2712,2713,2714,2715,2716,2717,2718,2719,2720,2721,2722,2723,2724,2725,2726,2727,2728,2729,2730,2731,2732,2733,2734,2735,2736,2737,2738,2739,2740,2741,2742,2743,2744,2745,2746,2747,2748,2749,2750,2751,2752,2753,2754,2755,2756,2757,2758,2759,2760,2761,2762,2763,2764,2765,2766,2767,2768,2769,2770,2771,2772,2773,2774,2775,2776,2777,2778,2779,2780,2781,2782,2783,2784,2785,2786,2787,2788,2789,2790,2791,2792,2793,2794,2795,2796,2797,2798,2799,2800,2801,2802,2803,2804,2805,2806,2807,2808,2809,2810,2811,2812,2813,2814,2815,2816,2817,2818,2819,2820,2821,2822,2823,2824,2825,2826,2827,2828,2829,2830,2831,2832,2833,2834,2835,2836,2837,2838,2839,2840,2841,2842,2843,2844,2845,2846,2847,2848,2849,2850,2851,2852,2853,2854,2855,2856,2857,2858,2859,2860,2861,2862,2863,2864,2865,2866,2867,2868,2869,2870,2871,2872,2873,2874,2875,2876,2877,2878,2879,2880,2881,2882,2883,2884,2885,2886,2887,2888,2889,2890,2891,2892,2893,2894,2895,2896,2897,2898,2899,2900,2901,2902,2903,2904,2905,2906,2907,2908,2909,2910,2911,2912,2913,2914,2915,2916,2917,2918,2919,2920,2921,2922,2923,2924,2925,2926,2927,2928,2929,2930,2931,2932,2933,2934,2935,2936,2937,2938,2939,2940,2941,2942,2943,2944,2945,2946,2947,2948,2949,2950,2951,2952,2953,2954,2955,2956,2957,2958,2959,2960,2961,2962,2963,2964,2965,2966,2967,2968,2969,2970,2971,2972,2973,2974,2975,2976,2977,2978,2979,2980,2981,2982,2983,2984,2985,2986,2987,2988,2989,2990,2991,2992,2993,2994,2995,2996,2997,2998,2999,3000,3001,3002,3003,3004,3005,3006,3007,3008,3009,3010,3011,3012,3013,3014,3015,3016,3017,3018,3019,3020,3021,3022,3023,3024,3025,3026,3027,3028,3029,3030,3031,3032,3033,3034,3035,3036,3037,3038,3039,3040,3041,3042,3043,3044,3045,3046,3047,3048,3049,3050,3051,3052,3053,3054,3055,3056,3057,3058,3059,3060,3061,3062,3063,3064,3065,3066,3067,3068,3069,3070,3071,3072,3073,3074,3075,3076,3077,3078,3079,3080,3081,3082,3083,3084,3085,3086,3087,3088,3089,3090,3091,3092,3093,3094,3095,3096,3097,3098,3099,3100,3101,3102,3103,3104,3105,3106,3107,3108,3109,3110,3111,3112,3113,3114,3115,3116,3117,3118,3119,3120,3121,3122,3123,3124,3125,3126,3127,3128,3129,3130,3131,3132,3133,3134,3135,3136,3137,3138,3139,3140,3141,3142,3143,3144,3145,3146);(2,9)(3,8)(4,7)(5,6)(11,3146)(12,3145)(13,3144)(14,3143)(15,3142)(16,3141)(17,3140)(18,3139)(19,3138)(20,3137)(21,3136)(22,3135)(23,3134)(24,3133)(25,3132)(26,3131)(27,3130)(28,3129)(29,3128)(30,3127)(31,3126)(32,3125)(33,3124)(34,3123)(35,3122)(36,3121)(37,3120)(38,3119)(39,3118)(40,3117)(41,3116)(42,3115)(43,3114)(44,3113)(45,3112)(46,3111)(47,3110)(48,3109)(49,3108)(50,3107)(51,3106)(52,3105)(53,3104)(54,3103)(55,3102)(56,3101)(57,3100)(58,3099)(59,3098)(60,3097)(61,3096)(62,3095)(63,3094)(64,3093)(65,3092)(66,3091)(67,3090)(68,3089)(69,3088)(70,3087)(71,3086)(72,3085)(73,3084)(74,3083)(75,3082)(76,3081)(77,3080)(78,3079)(79,3078)(80,3077)(81,3076)(82,3075)(83,3074)(84,3073)(85,3072)(86,3071)(87,3070)(88,3069)(89,3068)(90,3067)(91,3066)(92,3065)(93,3064)(94,3063)(95,3062)(96,3061)(97,3060)(98,3059)(99,3058)(100,3057)(101,3056)(102,3055)(103,3054)(104,3053)(105,3052)(106,3051)(107,3050)(108,3049)(109,3048)(110,3047)(111,3046)(112,3045)(113,3044)(114,3043)(115,3042)(116,3041)(117,3040)(118,3039)(119,3038)(120,3037)(121,3036)(122,3035)(123,3034)(124,3033)(125,3032)(126,3031)(127,3030)(128,3029)(129,3028)(130,3027)(131,3026)(132,3025)(133,3024)(134,3023)(135,3022)(136,3021)(137,3020)(138,3019)(139,3018)(140,3017)(141,3016)(142,3015)(143,3014)(144,3013)(145,3012)(146,3011)(147,3010)(148,3009)(149,3008)(150,3007)(151,3006)(152,3005)(153,3004)(154,3003)(155,3002)(156,3001)(157,3000)(158,2999)(159,2998)(160,2997)(161,2996)(162,2995)(163,2994)(164,2993)(165,2992)(166,2991)(167,2990)(168,2989)(169,2988)(170,2987)(171,2986)(172,2985)(173,2984)(174,2983)(175,2982)(176,2981)(177,2980)(178,2979)(179,2978)(180,2977)(181,2976)(182,2975)(183,2974)(184,2973)(185,2972)(186,2971)(187,2970)(188,2969)(189,2968)(190,2967)(191,2966)(192,2965)(193,2964)(194,2963)(195,2962)(196,2961)(197,2960)(198,2959)(199,2958)(200,2957)(201,2956)(202,2955)(203,2954)(204,2953)(205,2952)(206,2951)(207,2950)(208,2949)(209,2948)(210,2947)(211,2946)(212,2945)(213,2944)(214,2943)(215,2942)(216,2941)(217,2940)(218,2939)(219,2938)(220,2937)(221,2936)(222,2935)(223,2934)(224,2933)(225,2932)(226,2931)(227,2930)(228,2929)(229,2928)(230,2927)(231,2926)(232,2925)(233,2924)(234,2923)(235,2922)(236,2921)(237,2920)(238,2919)(239,2918)(240,2917)(241,2916)(242,2915)(243,2914)(244,2913)(245,2912)(246,2911)(247,2910)(248,2909)(249,2908)(250,2907)(251,2906)(252,2905)(253,2904)(254,2903)(255,2902)(256,2901)(257,2900)(258,2899)(259,2898)(260,2897)(261,2896)(262,2895)(263,2894)(264,2893)(265,2892)(266,2891)(267,2890)(268,2889)(269,2888)(270,2887)(271,2886)(272,2885)(273,2884)(274,2883)(275,2882)(276,2881)(277,2880)(278,2879)(279,2878)(280,2877)(281,2876)(282,2875)(283,2874)(284,2873)(285,2872)(286,2871)(287,2870)(288,2869)(289,2868)(290,2867)(291,2866)(292,2865)(293,2864)(294,2863)(295,2862)(296,2861)(297,2860)(298,2859)(299,2858)(300,2857)(301,2856)(302,2855)(303,2854)(304,2853)(305,2852)(306,2851)(307,2850)(308,2849)(309,2848)(310,2847)(311,2846)(312,2845)(313,2844)(314,2843)(315,2842)(316,2841)(317,2840)(318,2839)(319,2838)(320,2837)(321,2836)(322,2835)(323,2834)(324,2833)(325,2832)(326,2831)(327,2830)(328,2829)(329,2828)(330,2827)(331,2826)(332,2825)(333,2824)(334,2823)(335,2822)(336,2821)(337,2820)(338,2819)(339,2818)(340,2817)(341,2816)(342,2815)(343,2814)(344,2813)(345,2812)(346,2811)(347,2810)(348,2809)(349,2808)(350,2807)(351,2806)(352,2805)(353,2804)(354,2803)(355,2802)(356,2801)(357,2800)(358,2799)(359,2798)(360,2797)(361,2796)(362,2795)(363,2794)(364,2793)(365,2792)(366,2791)(367,2790)(368,2789)(369,2788)(370,2787)(371,2786)(372,2785)(373,2784)(374,2783)(375,2782)(376,2781)(377,2780)(378,2779)(379,2778)(380,2777)(381,2776)(382,2775)(383,2774)(384,2773)(385,2772)(386,2771)(387,2770)(388,2769)(389,2768)(390,2767)(391,2766)(392,2765)(393,2764)(394,2763)(395,2762)(396,2761)(397,2760)(398,2759)(399,2758)(400,2757)(401,2756)(402,2755)(403,2754)(404,2753)(405,2752)(406,2751)(407,2750)(408,2749)(409,2748)(410,2747)(411,2746)(412,2745)(413,2744)(414,2743)(415,2742)(416,2741)(417,2740)(418,2739)(419,2738)(420,2737)(421,2736)(422,2735)(423,2734)(424,2733)(425,2732)(426,2731)(427,2730)(428,2729)(429,2728)(430,2727)(431,2726)(432,2725)(433,2724)(434,2723)(435,2722)(436,2721)(437,2720)(438,2719)(439,2718)(440,2717)(441,2716)(442,2715)(443,2714)(444,2713)(445,2712)(446,2711)(447,2710)(448,2709)(449,2708)(450,2707)(451,2706)(452,2705)(453,2704)(454,2703)(455,2702)(456,2701)(457,2700)(458,2699)(459,2698)(460,2697)(461,2696)(462,2695)(463,2694)(464,2693)(465,2692)(466,2691)(467,2690)(468,2689)(469,2688)(470,2687)(471,2686)(472,2685)(473,2684)(474,2683)(475,2682)(476,2681)(477,2680)(478,2679)(479,2678)(480,2677)(481,2676)(482,2675)(483,2674)(484,2673)(485,2672)(486,2671)(487,2670)(488,2669)(489,2668)(490,2667)(491,2666)(492,2665)(493,2664)(494,2663)(495,2662)(496,2661)(497,2660)(498,2659)(499,2658)(500,2657)(501,2656)(502,2655)(503,2654)(504,2653)(505,2652)(506,2651)(507,2650)(508,2649)(509,2648)(510,2647)(511,2646)(512,2645)(513,2644)(514,2643)(515,2642)(516,2641)(517,2640)(518,2639)(519,2638)(520,2637)(521,2636)(522,2635)(523,2634)(524,2633)(525,2632)(526,2631)(527,2630)(528,2629)(529,2628)(530,2627)(531,2626)(532,2625)(533,2624)(534,2623)(535,2622)(536,2621)(537,2620)(538,2619)(539,2618)(540,2617)(541,2616)(542,2615)(543,2614)(544,2613)(545,2612)(546,2611)(547,2610)(548,2609)(549,2608)(550,2607)(551,2606)(552,2605)(553,2604)(554,2603)(555,2602)(556,2601)(557,2600)(558,2599)(559,2598)(560,2597)(561,2596)(562,2595)(563,2594)(564,2593)(565,2592)(566,2591)(567,2590)(568,2589)(569,2588)(570,2587)(571,2586)(572,2585)(573,2584)(574,2583)(575,2582)(576,2581)(577,2580)(578,2579)(579,2578)(580,2577)(581,2576)(582,2575)(583,2574)(584,2573)(585,2572)(586,2571)(587,2570)(588,2569)(589,2568)(590,2567)(591,2566)(592,2565)(593,2564)(594,2563)(595,2562)(596,2561)(597,2560)(598,2559)(599,2558)(600,2557)(601,2556)(602,2555)(603,2554)(604,2553)(605,2552)(606,2551)(607,2550)(608,2549)(609,2548)(610,2547)(611,2546)(612,2545)(613,2544)(614,2543)(615,2542)(616,2541)(617,2540)(618,2539)(619,2538)(620,2537)(621,2536)(622,2535)(623,2534)(624,2533)(625,2532)(626,2531)(627,2530)(628,2529)(629,2528)(630,2527)(631,2526)(632,2525)(633,2524)(634,2523)(635,2522)(636,2521)(637,2520)(638,2519)(639,2518)(640,2517)(641,2516)(642,2515)(643,2514)(644,2513)(645,2512)(646,2511)(647,2510)(648,2509)(649,2508)(650,2507)(651,2506)(652,2505)(653,2504)(654,2503)(655,2502)(656,2501)(657,2500)(658,2499)(659,2498)(660,2497)(661,2496)(662,2495)(663,2494)(664,2493)(665,2492)(666,2491)(667,2490)(668,2489)(669,2488)(670,2487)(671,2486)(672,2485)(673,2484)(674,2483)(675,2482)(676,2481)(677,2480)(678,2479)(679,2478)(680,2477)(681,2476)(682,2475)(683,2474)(684,2473)(685,2472)(686,2471)(687,2470)(688,2469)(689,2468)(690,2467)(691,2466)(692,2465)(693,2464)(694,2463)(695,2462)(696,2461)(697,2460)(698,2459)(699,2458)(700,2457)(701,2456)(702,2455)(703,2454)(704,2453)(705,2452)(706,2451)(707,2450)(708,2449)(709,2448)(710,2447)(711,2446)(712,2445)(713,2444)(714,2443)(715,2442)(716,2441)(717,2440)(718,2439)(719,2438)(720,2437)(721,2436)(722,2435)(723,2434)(724,2433)(725,2432)(726,2431)(727,2430)(728,2429)(729,2428)(730,2427)(731,2426)(732,2425)(733,2424)(734,2423)(735,2422)(736,2421)(737,2420)(738,2419)(739,2418)(740,2417)(741,2416)(742,2415)(743,2414)(744,2413)(745,2412)(746,2411)(747,2410)(748,2409)(749,2408)(750,2407)(751,2406)(752,2405)(753,2404)(754,2403)(755,2402)(756,2401)(757,2400)(758,2399)(759,2398)(760,2397)(761,2396)(762,2395)(763,2394)(764,2393)(765,2392)(766,2391)(767,2390)(768,2389)(769,2388)(770,2387)(771,2386)(772,2385)(773,2384)(774,2383)(775,2382)(776,2381)(777,2380)(778,2379)(779,2378)(780,2377)(781,2376)(782,2375)(783,2374)(784,2373)(785,2372)(786,2371)(787,2370)(788,2369)(789,2368)(790,2367)(791,2366)(792,2365)(793,2364)(794,2363)(795,2362)(796,2361)(797,2360)(798,2359)(799,2358)(800,2357)(801,2356)(802,2355)(803,2354)(804,2353)(805,2352)(806,2351)(807,2350)(808,2349)(809,2348)(810,2347)(811,2346)(812,2345)(813,2344)(814,2343)(815,2342)(816,2341)(817,2340)(818,2339)(819,2338)(820,2337)(821,2336)(822,2335)(823,2334)(824,2333)(825,2332)(826,2331)(827,2330)(828,2329)(829,2328)(830,2327)(831,2326)(832,2325)(833,2324)(834,2323)(835,2322)(836,2321)(837,2320)(838,2319)(839,2318)(840,2317)(841,2316)(842,2315)(843,2314)(844,2313)(845,2312)(846,2311)(847,2310)(848,2309)(849,2308)(850,2307)(851,2306)(852,2305)(853,2304)(854,2303)(855,2302)(856,2301)(857,2300)(858,2299)(859,2298)(860,2297)(861,2296)(862,2295)(863,2294)(864,2293)(865,2292)(866,2291)(867,2290)(868,2289)(869,2288)(870,2287)(871,2286)(872,2285)(873,2284)(874,2283)(875,2282)(876,2281)(877,2280)(878,2279)(879,2278)(880,2277)(881,2276)(882,2275)(883,2274)(884,2273)(885,2272)(886,2271)(887,2270)(888,2269)(889,2268)(890,2267)(891,2266)(892,2265)(893,2264)(894,2263)(895,2262)(896,2261)(897,2260)(898,2259)(899,2258)(900,2257)(901,2256)(902,2255)(903,2254)(904,2253)(905,2252)(906,2251)(907,2250)(908,2249)(909,2248)(910,2247)(911,2246)(912,2245)(913,2244)(914,2243)(915,2242)(916,2241)(917,2240)(918,2239)(919,2238)(920,2237)(921,2236)(922,2235)(923,2234)(924,2233)(925,2232)(926,2231)(927,2230)(928,2229)(929,2228)(930,2227)(931,2226)(932,2225)(933,2224)(934,2223)(935,2222)(936,2221)(937,2220)(938,2219)(939,2218)(940,2217)(941,2216)(942,2215)(943,2214)(944,2213)(945,2212)(946,2211)(947,2210)(948,2209)(949,2208)(950,2207)(951,2206)(952,2205)(953,2204)(954,2203)(955,2202)(956,2201)(957,2200)(958,2199)(959,2198)(960,2197)(961,2196)(962,2195)(963,2194)(964,2193)(965,2192)(966,2191)(967,2190)(968,2189)(969,2188)(970,2187)(971,2186)(972,2185)(973,2184)(974,2183)(975,2182)(976,2181)(977,2180)(978,2179)(979,2178)(980,2177)(981,2176)(982,2175)(983,2174)(984,2173)(985,2172)(986,2171)(987,2170)(988,2169)(989,2168)(990,2167)(991,2166)(992,2165)(993,2164)(994,2163)(995,2162)(996,2161)(997,2160)(998,2159)(999,2158)(1000,2157)(1001,2156)(1002,2155)(1003,2154)(1004,2153)(1005,2152)(1006,2151)(1007,2150)(1008,2149)(1009,2148)(1010,2147)(1011,2146)(1012,2145)(1013,2144)(1014,2143)(1015,2142)(1016,2141)(1017,2140)(1018,2139)(1019,2138)(1020,2137)(1021,2136)(1022,2135)(1023,2134)(1024,2133)(1025,2132)(1026,2131)(1027,2130)(1028,2129)(1029,2128)(1030,2127)(1031,2126)(1032,2125)(1033,2124)(1034,2123)(1035,2122)(1036,2121)(1037,2120)(1038,2119)(1039,2118)(1040,2117)(1041,2116)(1042,2115)(1043,2114)(1044,2113)(1045,2112)(1046,2111)(1047,2110)(1048,2109)(1049,2108)(1050,2107)(1051,2106)(1052,2105)(1053,2104)(1054,2103)(1055,2102)(1056,2101)(1057,2100)(1058,2099)(1059,2098)(1060,2097)(1061,2096)(1062,2095)(1063,2094)(1064,2093)(1065,2092)(1066,2091)(1067,2090)(1068,2089)(1069,2088)(1070,2087)(1071,2086)(1072,2085)(1073,2084)(1074,2083)(1075,2082)(1076,2081)(1077,2080)(1078,2079)(1079,2078)(1080,2077)(1081,2076)(1082,2075)(1083,2074)(1084,2073)(1085,2072)(1086,2071)(1087,2070)(1088,2069)(1089,2068)(1090,2067)(1091,2066)(1092,2065)(1093,2064)(1094,2063)(1095,2062)(1096,2061)(1097,2060)(1098,2059)(1099,2058)(1100,2057)(1101,2056)(1102,2055)(1103,2054)(1104,2053)(1105,2052)(1106,2051)(1107,2050)(1108,2049)(1109,2048)(1110,2047)(1111,2046)(1112,2045)(1113,2044)(1114,2043)(1115,2042)(1116,2041)(1117,2040)(1118,2039)(1119,2038)(1120,2037)(1121,2036)(1122,2035)(1123,2034)(1124,2033)(1125,2032)(1126,2031)(1127,2030)(1128,2029)(1129,2028)(1130,2027)(1131,2026)(1132,2025)(1133,2024)(1134,2023)(1135,2022)(1136,2021)(1137,2020)(1138,2019)(1139,2018)(1140,2017)(1141,2016)(1142,2015)(1143,2014)(1144,2013)(1145,2012)(1146,2011)(1147,2010)(1148,2009)(1149,2008)(1150,2007)(1151,2006)(1152,2005)(1153,2004)(1154,2003)(1155,2002)(1156,2001)(1157,2000)(1158,1999)(1159,1998)(1160,1997)(1161,1996)(1162,1995)(1163,1994)(1164,1993)(1165,1992)(1166,1991)(1167,1990)(1168,1989)(1169,1988)(1170,1987)(1171,1986)(1172,1985)(1173,1984)(1174,1983)(1175,1982)(1176,1981)(1177,1980)(1178,1979)(1179,1978)(1180,1977)(1181,1976)(1182,1975)(1183,1974)(1184,1973)(1185,1972)(1186,1971)(1187,1970)(1188,1969)(1189,1968)(1190,1967)(1191,1966)(1192,1965)(1193,1964)(1194,1963)(1195,1962)(1196,1961)(1197,1960)(1198,1959)(1199,1958)(1200,1957)(1201,1956)(1202,1955)(1203,1954)(1204,1953)(1205,1952)(1206,1951)(1207,1950)(1208,1949)(1209,1948)(1210,1947)(1211,1946)(1212,1945)(1213,1944)(1214,1943)(1215,1942)(1216,1941)(1217,1940)(1218,1939)(1219,1938)(1220,1937)(1221,1936)(1222,1935)(1223,1934)(1224,1933)(1225,1932)(1226,1931)(1227,1930)(1228,1929)(1229,1928)(1230,1927)(1231,1926)(1232,1925)(1233,1924)(1234,1923)(1235,1922)(1236,1921)(1237,1920)(1238,1919)(1239,1918)(1240,1917)(1241,1916)(1242,1915)(1243,1914)(1244,1913)(1245,1912)(1246,1911)(1247,1910)(1248,1909)(1249,1908)(1250,1907)(1251,1906)(1252,1905)(1253,1904)(1254,1903)(1255,1902)(1256,1901)(1257,1900)(1258,1899)(1259,1898)(1260,1897)(1261,1896)(1262,1895)(1263,1894)(1264,1893)(1265,1892)(1266,1891)(1267,1890)(1268,1889)(1269,1888)(1270,1887)(1271,1886)(1272,1885)(1273,1884)(1274,1883)(1275,1882)(1276,1881)(1277,1880)(1278,1879)(1279,1878)(1280,1877)(1281,1876)(1282,1875)(1283,1874)(1284,1873)(1285,1872)(1286,1871)(1287,1870)(1288,1869)(1289,1868)(1290,1867)(1291,1866)(1292,1865)(1293,1864)(1294,1863)(1295,1862)(1296,1861)(1297,1860)(1298,1859)(1299,1858)(1300,1857)(1301,1856)(1302,1855)(1303,1854)(1304,1853)(1305,1852)(1306,1851)(1307,1850)(1308,1849)(1309,1848)(1310,1847)(1311,1846)(1312,1845)(1313,1844)(1314,1843)(1315,1842)(1316,1841)(1317,1840)(1318,1839)(1319,1838)(1320,1837)(1321,1836)(1322,1835)(1323,1834)(1324,1833)(1325,1832)(1326,1831)(1327,1830)(1328,1829)(1329,1828)(1330,1827)(1331,1826)(1332,1825)(1333,1824)(1334,1823)(1335,1822)(1336,1821)(1337,1820)(1338,1819)(1339,1818)(1340,1817)(1341,1816)(1342,1815)(1343,1814)(1344,1813)(1345,1812)(1346,1811)(1347,1810)(1348,1809)(1349,1808)(1350,1807)(1351,1806)(1352,1805)(1353,1804)(1354,1803)(1355,1802)(1356,1801)(1357,1800)(1358,1799)(1359,1798)(1360,1797)(1361,1796)(1362,1795)(1363,1794)(1364,1793)(1365,1792)(1366,1791)(1367,1790)(1368,1789)(1369,1788)(1370,1787)(1371,1786)(1372,1785)(1373,1784)(1374,1783)(1375,1782)(1376,1781)(1377,1780)(1378,1779)(1379,1778)(1380,1777)(1381,1776)(1382,1775)(1383,1774)(1384,1773)(1385,1772)(1386,1771)(1387,1770)(1388,1769)(1389,1768)(1390,1767)(1391,1766)(1392,1765)(1393,1764)(1394,1763)(1395,1762)(1396,1761)(1397,1760)(1398,1759)(1399,1758)(1400,1757)(1401,1756)(1402,1755)(1403,1754)(1404,1753)(1405,1752)(1406,1751)(1407,1750)(1408,1749)(1409,1748)(1410,1747)(1411,1746)(1412,1745)(1413,1744)(1414,1743)(1415,1742)(1416,1741)(1417,1740)(1418,1739)(1419,1738)(1420,1737)(1421,1736)(1422,1735)(1423,1734)(1424,1733)(1425,1732)(1426,1731)(1427,1730)(1428,1729)(1429,1728)(1430,1727)(1431,1726)(1432,1725)(1433,1724)(1434,1723)(1435,1722)(1436,1721)(1437,1720)(1438,1719)(1439,1718)(1440,1717)(1441,1716)(1442,1715)(1443,1714)(1444,1713)(1445,1712)(1446,1711)(1447,1710)(1448,1709)(1449,1708)(1450,1707)(1451,1706)(1452,1705)(1453,1704)(1454,1703)(1455,1702)(1456,1701)(1457,1700)(1458,1699)(1459,1698)(1460,1697)(1461,1696)(1462,1695)(1463,1694)(1464,1693)(1465,1692)(1466,1691)(1467,1690)(1468,1689)(1469,1688)(1470,1687)(1471,1686)(1472,1685)(1473,1684)(1474,1683)(1475,1682)(1476,1681)(1477,1680)(1478,1679)(1479,1678)(1480,1677)(1481,1676)(1482,1675)(1483,1674)(1484,1673)(1485,1672)(1486,1671)(1487,1670)(1488,1669)(1489,1668)(1490,1667)(1491,1666)(1492,1665)(1493,1664)(1494,1663)(1495,1662)(1496,1661)(1497,1660)(1498,1659)(1499,1658)(1500,1657)(1501,1656)(1502,1655)(1503,1654)(1504,1653)(1505,1652)(1506,1651)(1507,1650)(1508,1649)(1509,1648)(1510,1647)(1511,1646)(1512,1645)(1513,1644)(1514,1643)(1515,1642)(1516,1641)(1517,1640)(1518,1639)(1519,1638)(1520,1637)(1521,1636)(1522,1635)(1523,1634)(1524,1633)(1525,1632)(1526,1631)(1527,1630)(1528,1629)(1529,1628)(1530,1627)(1531,1626)(1532,1625)(1533,1624)(1534,1623)(1535,1622)(1536,1621)(1537,1620)(1538,1619)(1539,1618)(1540,1617)(1541,1616)(1542,1615)(1543,1614)(1544,1613)(1545,1612)(1546,1611)(1547,1610)(1548,1609)(1549,1608)(1550,1607)(1551,1606)(1552,1605)(1553,1604)(1554,1603)(1555,1602)(1556,1601)(1557,1600)(1558,1599)(1559,1598)(1560,1597)(1561,1596)(1562,1595)(1563,1594)(1564,1593)(1565,1592)(1566,1591)(1567,1590)(1568,1589)(1569,1588)(1570,1587)(1571,1586)(1572,1585)(1573,1584)(1574,1583)(1575,1582)(1576,1581)(1577,1580)(1578,1579)

Polycyclic presentation:

2,3,3137,3|b^3=d,b^a=b^2d^2,c^a=c^3136,d^a=d^2

Conjugacy classes & character table

14118 conjugacy classes. The character table is too large to display.

GAP

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

gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d");;
gap> coll := SingleCollector(F, [2, 3, 3137, 3]);;
gap> SetPower(coll, 2, F.4);;
gap> SetConjugate(coll, 2, 1, F.2^2*F.4^2);;
gap> SetConjugate(coll, 3, 1, F.3^3136);;
gap> SetConjugate(coll, 4, 1, F.4^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);

D28233 #72291597