D₇₉₇₁ #30629992

order	15942
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₇₉₇₁
unambiguous semidirect product	C₃⋊D₂₆₅₇
unambiguous semidirect product	C₂₆₅₇⋊D₃

Splittings

Fitting, socle, derived, Hall	C₃×C₂₆₅₇ ⋊ C₂
Sylow	C₂₆₅₇ ⋊ D₃
Sylow	C₃ ⋊ D₂₆₅₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₂₆₅₇	C₂
LCS	G ▷ C₃×C₂₆₅₇
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 2660
transitive degree	μ_t(G) = 7971

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

Polycyclic presentation:

2,3,2657|b^a=b^2,c^a=c^2656

Conjugacy classes & character table

3987 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×D₂₆₅₇, C₂×D₇₉₇₁
maximal normal subgroup of	D₃×D₂₆₅₇, C₂×D₇₉₇₁
maximal quotient of	Dic₇₉₇₁, C₂×D₇₉₇₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15942, 3);

D7971 #30629992