D₁₆₀₅₁ #44545721

order	32102
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₀₅₁
unambiguous semidirect product	C₇⋊D₂₂₉₃
unambiguous semidirect product	C₂₂₉₃⋊D₇

Splittings

Fitting, socle, derived, Hall	C₇×C₂₂₉₃ ⋊ C₂
Sylow	C₂₂₉₃ ⋊ D₇
Sylow	C₇ ⋊ D₂₂₉₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₂₂₉₃	C₂
LCS	G ▷ C₇×C₂₂₉₃
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 2300
transitive degree	μ_t(G) = 16051

A minimal faithful permutation representation — 2 generators on 2300 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);(2,7)(3,6)(4,5)(9,2300)(10,2299)(11,2298)(12,2297)(13,2296)(14,2295)(15,2294)(16,2293)(17,2292)(18,2291)(19,2290)(20,2289)(21,2288)(22,2287)(23,2286)(24,2285)(25,2284)(26,2283)(27,2282)(28,2281)(29,2280)(30,2279)(31,2278)(32,2277)(33,2276)(34,2275)(35,2274)(36,2273)(37,2272)(38,2271)(39,2270)(40,2269)(41,2268)(42,2267)(43,2266)(44,2265)(45,2264)(46,2263)(47,2262)(48,2261)(49,2260)(50,2259)(51,2258)(52,2257)(53,2256)(54,2255)(55,2254)(56,2253)(57,2252)(58,2251)(59,2250)(60,2249)(61,2248)(62,2247)(63,2246)(64,2245)(65,2244)(66,2243)(67,2242)(68,2241)(69,2240)(70,2239)(71,2238)(72,2237)(73,2236)(74,2235)(75,2234)(76,2233)(77,2232)(78,2231)(79,2230)(80,2229)(81,2228)(82,2227)(83,2226)(84,2225)(85,2224)(86,2223)(87,2222)(88,2221)(89,2220)(90,2219)(91,2218)(92,2217)(93,2216)(94,2215)(95,2214)(96,2213)(97,2212)(98,2211)(99,2210)(100,2209)(101,2208)(102,2207)(103,2206)(104,2205)(105,2204)(106,2203)(107,2202)(108,2201)(109,2200)(110,2199)(111,2198)(112,2197)(113,2196)(114,2195)(115,2194)(116,2193)(117,2192)(118,2191)(119,2190)(120,2189)(121,2188)(122,2187)(123,2186)(124,2185)(125,2184)(126,2183)(127,2182)(128,2181)(129,2180)(130,2179)(131,2178)(132,2177)(133,2176)(134,2175)(135,2174)(136,2173)(137,2172)(138,2171)(139,2170)(140,2169)(141,2168)(142,2167)(143,2166)(144,2165)(145,2164)(146,2163)(147,2162)(148,2161)(149,2160)(150,2159)(151,2158)(152,2157)(153,2156)(154,2155)(155,2154)(156,2153)(157,2152)(158,2151)(159,2150)(160,2149)(161,2148)(162,2147)(163,2146)(164,2145)(165,2144)(166,2143)(167,2142)(168,2141)(169,2140)(170,2139)(171,2138)(172,2137)(173,2136)(174,2135)(175,2134)(176,2133)(177,2132)(178,2131)(179,2130)(180,2129)(181,2128)(182,2127)(183,2126)(184,2125)(185,2124)(186,2123)(187,2122)(188,2121)(189,2120)(190,2119)(191,2118)(192,2117)(193,2116)(194,2115)(195,2114)(196,2113)(197,2112)(198,2111)(199,2110)(200,2109)(201,2108)(202,2107)(203,2106)(204,2105)(205,2104)(206,2103)(207,2102)(208,2101)(209,2100)(210,2099)(211,2098)(212,2097)(213,2096)(214,2095)(215,2094)(216,2093)(217,2092)(218,2091)(219,2090)(220,2089)(221,2088)(222,2087)(223,2086)(224,2085)(225,2084)(226,2083)(227,2082)(228,2081)(229,2080)(230,2079)(231,2078)(232,2077)(233,2076)(234,2075)(235,2074)(236,2073)(237,2072)(238,2071)(239,2070)(240,2069)(241,2068)(242,2067)(243,2066)(244,2065)(245,2064)(246,2063)(247,2062)(248,2061)(249,2060)(250,2059)(251,2058)(252,2057)(253,2056)(254,2055)(255,2054)(256,2053)(257,2052)(258,2051)(259,2050)(260,2049)(261,2048)(262,2047)(263,2046)(264,2045)(265,2044)(266,2043)(267,2042)(268,2041)(269,2040)(270,2039)(271,2038)(272,2037)(273,2036)(274,2035)(275,2034)(276,2033)(277,2032)(278,2031)(279,2030)(280,2029)(281,2028)(282,2027)(283,2026)(284,2025)(285,2024)(286,2023)(287,2022)(288,2021)(289,2020)(290,2019)(291,2018)(292,2017)(293,2016)(294,2015)(295,2014)(296,2013)(297,2012)(298,2011)(299,2010)(300,2009)(301,2008)(302,2007)(303,2006)(304,2005)(305,2004)(306,2003)(307,2002)(308,2001)(309,2000)(310,1999)(311,1998)(312,1997)(313,1996)(314,1995)(315,1994)(316,1993)(317,1992)(318,1991)(319,1990)(320,1989)(321,1988)(322,1987)(323,1986)(324,1985)(325,1984)(326,1983)(327,1982)(328,1981)(329,1980)(330,1979)(331,1978)(332,1977)(333,1976)(334,1975)(335,1974)(336,1973)(337,1972)(338,1971)(339,1970)(340,1969)(341,1968)(342,1967)(343,1966)(344,1965)(345,1964)(346,1963)(347,1962)(348,1961)(349,1960)(350,1959)(351,1958)(352,1957)(353,1956)(354,1955)(355,1954)(356,1953)(357,1952)(358,1951)(359,1950)(360,1949)(361,1948)(362,1947)(363,1946)(364,1945)(365,1944)(366,1943)(367,1942)(368,1941)(369,1940)(370,1939)(371,1938)(372,1937)(373,1936)(374,1935)(375,1934)(376,1933)(377,1932)(378,1931)(379,1930)(380,1929)(381,1928)(382,1927)(383,1926)(384,1925)(385,1924)(386,1923)(387,1922)(388,1921)(389,1920)(390,1919)(391,1918)(392,1917)(393,1916)(394,1915)(395,1914)(396,1913)(397,1912)(398,1911)(399,1910)(400,1909)(401,1908)(402,1907)(403,1906)(404,1905)(405,1904)(406,1903)(407,1902)(408,1901)(409,1900)(410,1899)(411,1898)(412,1897)(413,1896)(414,1895)(415,1894)(416,1893)(417,1892)(418,1891)(419,1890)(420,1889)(421,1888)(422,1887)(423,1886)(424,1885)(425,1884)(426,1883)(427,1882)(428,1881)(429,1880)(430,1879)(431,1878)(432,1877)(433,1876)(434,1875)(435,1874)(436,1873)(437,1872)(438,1871)(439,1870)(440,1869)(441,1868)(442,1867)(443,1866)(444,1865)(445,1864)(446,1863)(447,1862)(448,1861)(449,1860)(450,1859)(451,1858)(452,1857)(453,1856)(454,1855)(455,1854)(456,1853)(457,1852)(458,1851)(459,1850)(460,1849)(461,1848)(462,1847)(463,1846)(464,1845)(465,1844)(466,1843)(467,1842)(468,1841)(469,1840)(470,1839)(471,1838)(472,1837)(473,1836)(474,1835)(475,1834)(476,1833)(477,1832)(478,1831)(479,1830)(480,1829)(481,1828)(482,1827)(483,1826)(484,1825)(485,1824)(486,1823)(487,1822)(488,1821)(489,1820)(490,1819)(491,1818)(492,1817)(493,1816)(494,1815)(495,1814)(496,1813)(497,1812)(498,1811)(499,1810)(500,1809)(501,1808)(502,1807)(503,1806)(504,1805)(505,1804)(506,1803)(507,1802)(508,1801)(509,1800)(510,1799)(511,1798)(512,1797)(513,1796)(514,1795)(515,1794)(516,1793)(517,1792)(518,1791)(519,1790)(520,1789)(521,1788)(522,1787)(523,1786)(524,1785)(525,1784)(526,1783)(527,1782)(528,1781)(529,1780)(530,1779)(531,1778)(532,1777)(533,1776)(534,1775)(535,1774)(536,1773)(537,1772)(538,1771)(539,1770)(540,1769)(541,1768)(542,1767)(543,1766)(544,1765)(545,1764)(546,1763)(547,1762)(548,1761)(549,1760)(550,1759)(551,1758)(552,1757)(553,1756)(554,1755)(555,1754)(556,1753)(557,1752)(558,1751)(559,1750)(560,1749)(561,1748)(562,1747)(563,1746)(564,1745)(565,1744)(566,1743)(567,1742)(568,1741)(569,1740)(570,1739)(571,1738)(572,1737)(573,1736)(574,1735)(575,1734)(576,1733)(577,1732)(578,1731)(579,1730)(580,1729)(581,1728)(582,1727)(583,1726)(584,1725)(585,1724)(586,1723)(587,1722)(588,1721)(589,1720)(590,1719)(591,1718)(592,1717)(593,1716)(594,1715)(595,1714)(596,1713)(597,1712)(598,1711)(599,1710)(600,1709)(601,1708)(602,1707)(603,1706)(604,1705)(605,1704)(606,1703)(607,1702)(608,1701)(609,1700)(610,1699)(611,1698)(612,1697)(613,1696)(614,1695)(615,1694)(616,1693)(617,1692)(618,1691)(619,1690)(620,1689)(621,1688)(622,1687)(623,1686)(624,1685)(625,1684)(626,1683)(627,1682)(628,1681)(629,1680)(630,1679)(631,1678)(632,1677)(633,1676)(634,1675)(635,1674)(636,1673)(637,1672)(638,1671)(639,1670)(640,1669)(641,1668)(642,1667)(643,1666)(644,1665)(645,1664)(646,1663)(647,1662)(648,1661)(649,1660)(650,1659)(651,1658)(652,1657)(653,1656)(654,1655)(655,1654)(656,1653)(657,1652)(658,1651)(659,1650)(660,1649)(661,1648)(662,1647)(663,1646)(664,1645)(665,1644)(666,1643)(667,1642)(668,1641)(669,1640)(670,1639)(671,1638)(672,1637)(673,1636)(674,1635)(675,1634)(676,1633)(677,1632)(678,1631)(679,1630)(680,1629)(681,1628)(682,1627)(683,1626)(684,1625)(685,1624)(686,1623)(687,1622)(688,1621)(689,1620)(690,1619)(691,1618)(692,1617)(693,1616)(694,1615)(695,1614)(696,1613)(697,1612)(698,1611)(699,1610)(700,1609)(701,1608)(702,1607)(703,1606)(704,1605)(705,1604)(706,1603)(707,1602)(708,1601)(709,1600)(710,1599)(711,1598)(712,1597)(713,1596)(714,1595)(715,1594)(716,1593)(717,1592)(718,1591)(719,1590)(720,1589)(721,1588)(722,1587)(723,1586)(724,1585)(725,1584)(726,1583)(727,1582)(728,1581)(729,1580)(730,1579)(731,1578)(732,1577)(733,1576)(734,1575)(735,1574)(736,1573)(737,1572)(738,1571)(739,1570)(740,1569)(741,1568)(742,1567)(743,1566)(744,1565)(745,1564)(746,1563)(747,1562)(748,1561)(749,1560)(750,1559)(751,1558)(752,1557)(753,1556)(754,1555)(755,1554)(756,1553)(757,1552)(758,1551)(759,1550)(760,1549)(761,1548)(762,1547)(763,1546)(764,1545)(765,1544)(766,1543)(767,1542)(768,1541)(769,1540)(770,1539)(771,1538)(772,1537)(773,1536)(774,1535)(775,1534)(776,1533)(777,1532)(778,1531)(779,1530)(780,1529)(781,1528)(782,1527)(783,1526)(784,1525)(785,1524)(786,1523)(787,1522)(788,1521)(789,1520)(790,1519)(791,1518)(792,1517)(793,1516)(794,1515)(795,1514)(796,1513)(797,1512)(798,1511)(799,1510)(800,1509)(801,1508)(802,1507)(803,1506)(804,1505)(805,1504)(806,1503)(807,1502)(808,1501)(809,1500)(810,1499)(811,1498)(812,1497)(813,1496)(814,1495)(815,1494)(816,1493)(817,1492)(818,1491)(819,1490)(820,1489)(821,1488)(822,1487)(823,1486)(824,1485)(825,1484)(826,1483)(827,1482)(828,1481)(829,1480)(830,1479)(831,1478)(832,1477)(833,1476)(834,1475)(835,1474)(836,1473)(837,1472)(838,1471)(839,1470)(840,1469)(841,1468)(842,1467)(843,1466)(844,1465)(845,1464)(846,1463)(847,1462)(848,1461)(849,1460)(850,1459)(851,1458)(852,1457)(853,1456)(854,1455)(855,1454)(856,1453)(857,1452)(858,1451)(859,1450)(860,1449)(861,1448)(862,1447)(863,1446)(864,1445)(865,1444)(866,1443)(867,1442)(868,1441)(869,1440)(870,1439)(871,1438)(872,1437)(873,1436)(874,1435)(875,1434)(876,1433)(877,1432)(878,1431)(879,1430)(880,1429)(881,1428)(882,1427)(883,1426)(884,1425)(885,1424)(886,1423)(887,1422)(888,1421)(889,1420)(890,1419)(891,1418)(892,1417)(893,1416)(894,1415)(895,1414)(896,1413)(897,1412)(898,1411)(899,1410)(900,1409)(901,1408)(902,1407)(903,1406)(904,1405)(905,1404)(906,1403)(907,1402)(908,1401)(909,1400)(910,1399)(911,1398)(912,1397)(913,1396)(914,1395)(915,1394)(916,1393)(917,1392)(918,1391)(919,1390)(920,1389)(921,1388)(922,1387)(923,1386)(924,1385)(925,1384)(926,1383)(927,1382)(928,1381)(929,1380)(930,1379)(931,1378)(932,1377)(933,1376)(934,1375)(935,1374)(936,1373)(937,1372)(938,1371)(939,1370)(940,1369)(941,1368)(942,1367)(943,1366)(944,1365)(945,1364)(946,1363)(947,1362)(948,1361)(949,1360)(950,1359)(951,1358)(952,1357)(953,1356)(954,1355)(955,1354)(956,1353)(957,1352)(958,1351)(959,1350)(960,1349)(961,1348)(962,1347)(963,1346)(964,1345)(965,1344)(966,1343)(967,1342)(968,1341)(969,1340)(970,1339)(971,1338)(972,1337)(973,1336)(974,1335)(975,1334)(976,1333)(977,1332)(978,1331)(979,1330)(980,1329)(981,1328)(982,1327)(983,1326)(984,1325)(985,1324)(986,1323)(987,1322)(988,1321)(989,1320)(990,1319)(991,1318)(992,1317)(993,1316)(994,1315)(995,1314)(996,1313)(997,1312)(998,1311)(999,1310)(1000,1309)(1001,1308)(1002,1307)(1003,1306)(1004,1305)(1005,1304)(1006,1303)(1007,1302)(1008,1301)(1009,1300)(1010,1299)(1011,1298)(1012,1297)(1013,1296)(1014,1295)(1015,1294)(1016,1293)(1017,1292)(1018,1291)(1019,1290)(1020,1289)(1021,1288)(1022,1287)(1023,1286)(1024,1285)(1025,1284)(1026,1283)(1027,1282)(1028,1281)(1029,1280)(1030,1279)(1031,1278)(1032,1277)(1033,1276)(1034,1275)(1035,1274)(1036,1273)(1037,1272)(1038,1271)(1039,1270)(1040,1269)(1041,1268)(1042,1267)(1043,1266)(1044,1265)(1045,1264)(1046,1263)(1047,1262)(1048,1261)(1049,1260)(1050,1259)(1051,1258)(1052,1257)(1053,1256)(1054,1255)(1055,1254)(1056,1253)(1057,1252)(1058,1251)(1059,1250)(1060,1249)(1061,1248)(1062,1247)(1063,1246)(1064,1245)(1065,1244)(1066,1243)(1067,1242)(1068,1241)(1069,1240)(1070,1239)(1071,1238)(1072,1237)(1073,1236)(1074,1235)(1075,1234)(1076,1233)(1077,1232)(1078,1231)(1079,1230)(1080,1229)(1081,1228)(1082,1227)(1083,1226)(1084,1225)(1085,1224)(1086,1223)(1087,1222)(1088,1221)(1089,1220)(1090,1219)(1091,1218)(1092,1217)(1093,1216)(1094,1215)(1095,1214)(1096,1213)(1097,1212)(1098,1211)(1099,1210)(1100,1209)(1101,1208)(1102,1207)(1103,1206)(1104,1205)(1105,1204)(1106,1203)(1107,1202)(1108,1201)(1109,1200)(1110,1199)(1111,1198)(1112,1197)(1113,1196)(1114,1195)(1115,1194)(1116,1193)(1117,1192)(1118,1191)(1119,1190)(1120,1189)(1121,1188)(1122,1187)(1123,1186)(1124,1185)(1125,1184)(1126,1183)(1127,1182)(1128,1181)(1129,1180)(1130,1179)(1131,1178)(1132,1177)(1133,1176)(1134,1175)(1135,1174)(1136,1173)(1137,1172)(1138,1171)(1139,1170)(1140,1169)(1141,1168)(1142,1167)(1143,1166)(1144,1165)(1145,1164)(1146,1163)(1147,1162)(1148,1161)(1149,1160)(1150,1159)(1151,1158)(1152,1157)(1153,1156)(1154,1155)

Polycyclic presentation:

2,7,2293|b^a=b^6,c^a=c^2292

Conjugacy classes & character table

8027 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₆₀₅₁
maximal normal subgroup of	C₂×D₁₆₀₅₁
maximal quotient of	Dic₁₆₀₅₁, C₂×D₁₆₀₅₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32102, 3);

D16051 #44545721