Dic₇₇₃₇ #44526178

order	30948
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₇₇₃₇
unambiguous semidirect product	C₃⋊Dic₂₅₇₉
unambiguous semidirect product	C₂₅₇₉⋊Dic₃

Splittings

derived, Hall	C₃×C₂₅₇₉ ⋊ C₄
Sylow	C₂₅₇₉ ⋊ Dic₃
Sylow	C₃ ⋊ Dic₂₅₇₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇₇₃₇
commutator, hypocenter	C₃×C₂₅₇₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₂₅₇₉	C₂
LCS	G ▷ C₃×C₂₅₇₉
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 2586
transitive degree	μ_t(G) = 30948

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

Polycyclic presentation:

2,3,2579,2|a^2=d,b^a=b^2,c^a=c^2578

Conjugacy classes & character table

7740 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₅₄₇₄
maximal normal subgroup of	Dic₁₅₄₇₄

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30948, 4);

Dic7737 #44526178