D₁₅₉₆₇ #44542547

order	31934
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₅₉₆₇
unambiguous semidirect product	C₇⋊D₂₂₈₁
unambiguous semidirect product	C₂₂₈₁⋊D₇

Splittings

Fitting, socle, derived, Hall	C₇×C₂₂₈₁ ⋊ C₂
Sylow	C₂₂₈₁ ⋊ D₇
Sylow	C₇ ⋊ D₂₂₈₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₂₂₈₁	C₂
LCS	G ▷ C₇×C₂₂₈₁
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 2288
transitive degree	μ_t(G) = 15967

A minimal faithful permutation representation — 2 generators on 2288 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);(2,7)(3,6)(4,5)(9,2288)(10,2287)(11,2286)(12,2285)(13,2284)(14,2283)(15,2282)(16,2281)(17,2280)(18,2279)(19,2278)(20,2277)(21,2276)(22,2275)(23,2274)(24,2273)(25,2272)(26,2271)(27,2270)(28,2269)(29,2268)(30,2267)(31,2266)(32,2265)(33,2264)(34,2263)(35,2262)(36,2261)(37,2260)(38,2259)(39,2258)(40,2257)(41,2256)(42,2255)(43,2254)(44,2253)(45,2252)(46,2251)(47,2250)(48,2249)(49,2248)(50,2247)(51,2246)(52,2245)(53,2244)(54,2243)(55,2242)(56,2241)(57,2240)(58,2239)(59,2238)(60,2237)(61,2236)(62,2235)(63,2234)(64,2233)(65,2232)(66,2231)(67,2230)(68,2229)(69,2228)(70,2227)(71,2226)(72,2225)(73,2224)(74,2223)(75,2222)(76,2221)(77,2220)(78,2219)(79,2218)(80,2217)(81,2216)(82,2215)(83,2214)(84,2213)(85,2212)(86,2211)(87,2210)(88,2209)(89,2208)(90,2207)(91,2206)(92,2205)(93,2204)(94,2203)(95,2202)(96,2201)(97,2200)(98,2199)(99,2198)(100,2197)(101,2196)(102,2195)(103,2194)(104,2193)(105,2192)(106,2191)(107,2190)(108,2189)(109,2188)(110,2187)(111,2186)(112,2185)(113,2184)(114,2183)(115,2182)(116,2181)(117,2180)(118,2179)(119,2178)(120,2177)(121,2176)(122,2175)(123,2174)(124,2173)(125,2172)(126,2171)(127,2170)(128,2169)(129,2168)(130,2167)(131,2166)(132,2165)(133,2164)(134,2163)(135,2162)(136,2161)(137,2160)(138,2159)(139,2158)(140,2157)(141,2156)(142,2155)(143,2154)(144,2153)(145,2152)(146,2151)(147,2150)(148,2149)(149,2148)(150,2147)(151,2146)(152,2145)(153,2144)(154,2143)(155,2142)(156,2141)(157,2140)(158,2139)(159,2138)(160,2137)(161,2136)(162,2135)(163,2134)(164,2133)(165,2132)(166,2131)(167,2130)(168,2129)(169,2128)(170,2127)(171,2126)(172,2125)(173,2124)(174,2123)(175,2122)(176,2121)(177,2120)(178,2119)(179,2118)(180,2117)(181,2116)(182,2115)(183,2114)(184,2113)(185,2112)(186,2111)(187,2110)(188,2109)(189,2108)(190,2107)(191,2106)(192,2105)(193,2104)(194,2103)(195,2102)(196,2101)(197,2100)(198,2099)(199,2098)(200,2097)(201,2096)(202,2095)(203,2094)(204,2093)(205,2092)(206,2091)(207,2090)(208,2089)(209,2088)(210,2087)(211,2086)(212,2085)(213,2084)(214,2083)(215,2082)(216,2081)(217,2080)(218,2079)(219,2078)(220,2077)(221,2076)(222,2075)(223,2074)(224,2073)(225,2072)(226,2071)(227,2070)(228,2069)(229,2068)(230,2067)(231,2066)(232,2065)(233,2064)(234,2063)(235,2062)(236,2061)(237,2060)(238,2059)(239,2058)(240,2057)(241,2056)(242,2055)(243,2054)(244,2053)(245,2052)(246,2051)(247,2050)(248,2049)(249,2048)(250,2047)(251,2046)(252,2045)(253,2044)(254,2043)(255,2042)(256,2041)(257,2040)(258,2039)(259,2038)(260,2037)(261,2036)(262,2035)(263,2034)(264,2033)(265,2032)(266,2031)(267,2030)(268,2029)(269,2028)(270,2027)(271,2026)(272,2025)(273,2024)(274,2023)(275,2022)(276,2021)(277,2020)(278,2019)(279,2018)(280,2017)(281,2016)(282,2015)(283,2014)(284,2013)(285,2012)(286,2011)(287,2010)(288,2009)(289,2008)(290,2007)(291,2006)(292,2005)(293,2004)(294,2003)(295,2002)(296,2001)(297,2000)(298,1999)(299,1998)(300,1997)(301,1996)(302,1995)(303,1994)(304,1993)(305,1992)(306,1991)(307,1990)(308,1989)(309,1988)(310,1987)(311,1986)(312,1985)(313,1984)(314,1983)(315,1982)(316,1981)(317,1980)(318,1979)(319,1978)(320,1977)(321,1976)(322,1975)(323,1974)(324,1973)(325,1972)(326,1971)(327,1970)(328,1969)(329,1968)(330,1967)(331,1966)(332,1965)(333,1964)(334,1963)(335,1962)(336,1961)(337,1960)(338,1959)(339,1958)(340,1957)(341,1956)(342,1955)(343,1954)(344,1953)(345,1952)(346,1951)(347,1950)(348,1949)(349,1948)(350,1947)(351,1946)(352,1945)(353,1944)(354,1943)(355,1942)(356,1941)(357,1940)(358,1939)(359,1938)(360,1937)(361,1936)(362,1935)(363,1934)(364,1933)(365,1932)(366,1931)(367,1930)(368,1929)(369,1928)(370,1927)(371,1926)(372,1925)(373,1924)(374,1923)(375,1922)(376,1921)(377,1920)(378,1919)(379,1918)(380,1917)(381,1916)(382,1915)(383,1914)(384,1913)(385,1912)(386,1911)(387,1910)(388,1909)(389,1908)(390,1907)(391,1906)(392,1905)(393,1904)(394,1903)(395,1902)(396,1901)(397,1900)(398,1899)(399,1898)(400,1897)(401,1896)(402,1895)(403,1894)(404,1893)(405,1892)(406,1891)(407,1890)(408,1889)(409,1888)(410,1887)(411,1886)(412,1885)(413,1884)(414,1883)(415,1882)(416,1881)(417,1880)(418,1879)(419,1878)(420,1877)(421,1876)(422,1875)(423,1874)(424,1873)(425,1872)(426,1871)(427,1870)(428,1869)(429,1868)(430,1867)(431,1866)(432,1865)(433,1864)(434,1863)(435,1862)(436,1861)(437,1860)(438,1859)(439,1858)(440,1857)(441,1856)(442,1855)(443,1854)(444,1853)(445,1852)(446,1851)(447,1850)(448,1849)(449,1848)(450,1847)(451,1846)(452,1845)(453,1844)(454,1843)(455,1842)(456,1841)(457,1840)(458,1839)(459,1838)(460,1837)(461,1836)(462,1835)(463,1834)(464,1833)(465,1832)(466,1831)(467,1830)(468,1829)(469,1828)(470,1827)(471,1826)(472,1825)(473,1824)(474,1823)(475,1822)(476,1821)(477,1820)(478,1819)(479,1818)(480,1817)(481,1816)(482,1815)(483,1814)(484,1813)(485,1812)(486,1811)(487,1810)(488,1809)(489,1808)(490,1807)(491,1806)(492,1805)(493,1804)(494,1803)(495,1802)(496,1801)(497,1800)(498,1799)(499,1798)(500,1797)(501,1796)(502,1795)(503,1794)(504,1793)(505,1792)(506,1791)(507,1790)(508,1789)(509,1788)(510,1787)(511,1786)(512,1785)(513,1784)(514,1783)(515,1782)(516,1781)(517,1780)(518,1779)(519,1778)(520,1777)(521,1776)(522,1775)(523,1774)(524,1773)(525,1772)(526,1771)(527,1770)(528,1769)(529,1768)(530,1767)(531,1766)(532,1765)(533,1764)(534,1763)(535,1762)(536,1761)(537,1760)(538,1759)(539,1758)(540,1757)(541,1756)(542,1755)(543,1754)(544,1753)(545,1752)(546,1751)(547,1750)(548,1749)(549,1748)(550,1747)(551,1746)(552,1745)(553,1744)(554,1743)(555,1742)(556,1741)(557,1740)(558,1739)(559,1738)(560,1737)(561,1736)(562,1735)(563,1734)(564,1733)(565,1732)(566,1731)(567,1730)(568,1729)(569,1728)(570,1727)(571,1726)(572,1725)(573,1724)(574,1723)(575,1722)(576,1721)(577,1720)(578,1719)(579,1718)(580,1717)(581,1716)(582,1715)(583,1714)(584,1713)(585,1712)(586,1711)(587,1710)(588,1709)(589,1708)(590,1707)(591,1706)(592,1705)(593,1704)(594,1703)(595,1702)(596,1701)(597,1700)(598,1699)(599,1698)(600,1697)(601,1696)(602,1695)(603,1694)(604,1693)(605,1692)(606,1691)(607,1690)(608,1689)(609,1688)(610,1687)(611,1686)(612,1685)(613,1684)(614,1683)(615,1682)(616,1681)(617,1680)(618,1679)(619,1678)(620,1677)(621,1676)(622,1675)(623,1674)(624,1673)(625,1672)(626,1671)(627,1670)(628,1669)(629,1668)(630,1667)(631,1666)(632,1665)(633,1664)(634,1663)(635,1662)(636,1661)(637,1660)(638,1659)(639,1658)(640,1657)(641,1656)(642,1655)(643,1654)(644,1653)(645,1652)(646,1651)(647,1650)(648,1649)(649,1648)(650,1647)(651,1646)(652,1645)(653,1644)(654,1643)(655,1642)(656,1641)(657,1640)(658,1639)(659,1638)(660,1637)(661,1636)(662,1635)(663,1634)(664,1633)(665,1632)(666,1631)(667,1630)(668,1629)(669,1628)(670,1627)(671,1626)(672,1625)(673,1624)(674,1623)(675,1622)(676,1621)(677,1620)(678,1619)(679,1618)(680,1617)(681,1616)(682,1615)(683,1614)(684,1613)(685,1612)(686,1611)(687,1610)(688,1609)(689,1608)(690,1607)(691,1606)(692,1605)(693,1604)(694,1603)(695,1602)(696,1601)(697,1600)(698,1599)(699,1598)(700,1597)(701,1596)(702,1595)(703,1594)(704,1593)(705,1592)(706,1591)(707,1590)(708,1589)(709,1588)(710,1587)(711,1586)(712,1585)(713,1584)(714,1583)(715,1582)(716,1581)(717,1580)(718,1579)(719,1578)(720,1577)(721,1576)(722,1575)(723,1574)(724,1573)(725,1572)(726,1571)(727,1570)(728,1569)(729,1568)(730,1567)(731,1566)(732,1565)(733,1564)(734,1563)(735,1562)(736,1561)(737,1560)(738,1559)(739,1558)(740,1557)(741,1556)(742,1555)(743,1554)(744,1553)(745,1552)(746,1551)(747,1550)(748,1549)(749,1548)(750,1547)(751,1546)(752,1545)(753,1544)(754,1543)(755,1542)(756,1541)(757,1540)(758,1539)(759,1538)(760,1537)(761,1536)(762,1535)(763,1534)(764,1533)(765,1532)(766,1531)(767,1530)(768,1529)(769,1528)(770,1527)(771,1526)(772,1525)(773,1524)(774,1523)(775,1522)(776,1521)(777,1520)(778,1519)(779,1518)(780,1517)(781,1516)(782,1515)(783,1514)(784,1513)(785,1512)(786,1511)(787,1510)(788,1509)(789,1508)(790,1507)(791,1506)(792,1505)(793,1504)(794,1503)(795,1502)(796,1501)(797,1500)(798,1499)(799,1498)(800,1497)(801,1496)(802,1495)(803,1494)(804,1493)(805,1492)(806,1491)(807,1490)(808,1489)(809,1488)(810,1487)(811,1486)(812,1485)(813,1484)(814,1483)(815,1482)(816,1481)(817,1480)(818,1479)(819,1478)(820,1477)(821,1476)(822,1475)(823,1474)(824,1473)(825,1472)(826,1471)(827,1470)(828,1469)(829,1468)(830,1467)(831,1466)(832,1465)(833,1464)(834,1463)(835,1462)(836,1461)(837,1460)(838,1459)(839,1458)(840,1457)(841,1456)(842,1455)(843,1454)(844,1453)(845,1452)(846,1451)(847,1450)(848,1449)(849,1448)(850,1447)(851,1446)(852,1445)(853,1444)(854,1443)(855,1442)(856,1441)(857,1440)(858,1439)(859,1438)(860,1437)(861,1436)(862,1435)(863,1434)(864,1433)(865,1432)(866,1431)(867,1430)(868,1429)(869,1428)(870,1427)(871,1426)(872,1425)(873,1424)(874,1423)(875,1422)(876,1421)(877,1420)(878,1419)(879,1418)(880,1417)(881,1416)(882,1415)(883,1414)(884,1413)(885,1412)(886,1411)(887,1410)(888,1409)(889,1408)(890,1407)(891,1406)(892,1405)(893,1404)(894,1403)(895,1402)(896,1401)(897,1400)(898,1399)(899,1398)(900,1397)(901,1396)(902,1395)(903,1394)(904,1393)(905,1392)(906,1391)(907,1390)(908,1389)(909,1388)(910,1387)(911,1386)(912,1385)(913,1384)(914,1383)(915,1382)(916,1381)(917,1380)(918,1379)(919,1378)(920,1377)(921,1376)(922,1375)(923,1374)(924,1373)(925,1372)(926,1371)(927,1370)(928,1369)(929,1368)(930,1367)(931,1366)(932,1365)(933,1364)(934,1363)(935,1362)(936,1361)(937,1360)(938,1359)(939,1358)(940,1357)(941,1356)(942,1355)(943,1354)(944,1353)(945,1352)(946,1351)(947,1350)(948,1349)(949,1348)(950,1347)(951,1346)(952,1345)(953,1344)(954,1343)(955,1342)(956,1341)(957,1340)(958,1339)(959,1338)(960,1337)(961,1336)(962,1335)(963,1334)(964,1333)(965,1332)(966,1331)(967,1330)(968,1329)(969,1328)(970,1327)(971,1326)(972,1325)(973,1324)(974,1323)(975,1322)(976,1321)(977,1320)(978,1319)(979,1318)(980,1317)(981,1316)(982,1315)(983,1314)(984,1313)(985,1312)(986,1311)(987,1310)(988,1309)(989,1308)(990,1307)(991,1306)(992,1305)(993,1304)(994,1303)(995,1302)(996,1301)(997,1300)(998,1299)(999,1298)(1000,1297)(1001,1296)(1002,1295)(1003,1294)(1004,1293)(1005,1292)(1006,1291)(1007,1290)(1008,1289)(1009,1288)(1010,1287)(1011,1286)(1012,1285)(1013,1284)(1014,1283)(1015,1282)(1016,1281)(1017,1280)(1018,1279)(1019,1278)(1020,1277)(1021,1276)(1022,1275)(1023,1274)(1024,1273)(1025,1272)(1026,1271)(1027,1270)(1028,1269)(1029,1268)(1030,1267)(1031,1266)(1032,1265)(1033,1264)(1034,1263)(1035,1262)(1036,1261)(1037,1260)(1038,1259)(1039,1258)(1040,1257)(1041,1256)(1042,1255)(1043,1254)(1044,1253)(1045,1252)(1046,1251)(1047,1250)(1048,1249)(1049,1248)(1050,1247)(1051,1246)(1052,1245)(1053,1244)(1054,1243)(1055,1242)(1056,1241)(1057,1240)(1058,1239)(1059,1238)(1060,1237)(1061,1236)(1062,1235)(1063,1234)(1064,1233)(1065,1232)(1066,1231)(1067,1230)(1068,1229)(1069,1228)(1070,1227)(1071,1226)(1072,1225)(1073,1224)(1074,1223)(1075,1222)(1076,1221)(1077,1220)(1078,1219)(1079,1218)(1080,1217)(1081,1216)(1082,1215)(1083,1214)(1084,1213)(1085,1212)(1086,1211)(1087,1210)(1088,1209)(1089,1208)(1090,1207)(1091,1206)(1092,1205)(1093,1204)(1094,1203)(1095,1202)(1096,1201)(1097,1200)(1098,1199)(1099,1198)(1100,1197)(1101,1196)(1102,1195)(1103,1194)(1104,1193)(1105,1192)(1106,1191)(1107,1190)(1108,1189)(1109,1188)(1110,1187)(1111,1186)(1112,1185)(1113,1184)(1114,1183)(1115,1182)(1116,1181)(1117,1180)(1118,1179)(1119,1178)(1120,1177)(1121,1176)(1122,1175)(1123,1174)(1124,1173)(1125,1172)(1126,1171)(1127,1170)(1128,1169)(1129,1168)(1130,1167)(1131,1166)(1132,1165)(1133,1164)(1134,1163)(1135,1162)(1136,1161)(1137,1160)(1138,1159)(1139,1158)(1140,1157)(1141,1156)(1142,1155)(1143,1154)(1144,1153)(1145,1152)(1146,1151)(1147,1150)(1148,1149)

Polycyclic presentation:

2,7,2281|b^a=b^6,c^a=c^2280

Conjugacy classes & character table

7985 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₅₉₆₇
maximal normal subgroup of	C₂×D₁₅₉₆₇
maximal quotient of	Dic₁₅₉₆₇, C₂×D₁₅₉₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31934, 3);

D15967 #44542547