Dic₄₆₁₈ #32914792

order	18472
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₄₆₁₈
unambiguous semidirect product	C₂₃₀₉⋊Q₈

Splittings

Sylow

C₂₃₀₉ ⋊ Q₈

Subgroups

	subgroup	G/H
center, Frattini	C₂	C₂×D₂₃₀₉
commutator, socle, prime radical, cosocle	C₂×C₂₃₀₉	C₂²
Fitting	C₄×C₂₃₀₉	C₂
hypercenter	C₄	D₂₃₀₉
hypocenter	C₂₃₀₉	Q₈
LCS	G ▷ C₂×C₂₃₀₉ ▷ C₂₃₀₉
UCS	C₁ ◁ C₂ ◁ C₄

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 2317
transitive degree	μ_t(G) = 18472

A minimal faithful permutation representation — 2 generators on 2317 points:

(1,2,3,4)(5,8,7,6)(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);(1,5,3,7)(2,6,4,8)(10,2317)(11,2316)(12,2315)(13,2314)(14,2313)(15,2312)(16,2311)(17,2310)(18,2309)(19,2308)(20,2307)(21,2306)(22,2305)(23,2304)(24,2303)(25,2302)(26,2301)(27,2300)(28,2299)(29,2298)(30,2297)(31,2296)(32,2295)(33,2294)(34,2293)(35,2292)(36,2291)(37,2290)(38,2289)(39,2288)(40,2287)(41,2286)(42,2285)(43,2284)(44,2283)(45,2282)(46,2281)(47,2280)(48,2279)(49,2278)(50,2277)(51,2276)(52,2275)(53,2274)(54,2273)(55,2272)(56,2271)(57,2270)(58,2269)(59,2268)(60,2267)(61,2266)(62,2265)(63,2264)(64,2263)(65,2262)(66,2261)(67,2260)(68,2259)(69,2258)(70,2257)(71,2256)(72,2255)(73,2254)(74,2253)(75,2252)(76,2251)(77,2250)(78,2249)(79,2248)(80,2247)(81,2246)(82,2245)(83,2244)(84,2243)(85,2242)(86,2241)(87,2240)(88,2239)(89,2238)(90,2237)(91,2236)(92,2235)(93,2234)(94,2233)(95,2232)(96,2231)(97,2230)(98,2229)(99,2228)(100,2227)(101,2226)(102,2225)(103,2224)(104,2223)(105,2222)(106,2221)(107,2220)(108,2219)(109,2218)(110,2217)(111,2216)(112,2215)(113,2214)(114,2213)(115,2212)(116,2211)(117,2210)(118,2209)(119,2208)(120,2207)(121,2206)(122,2205)(123,2204)(124,2203)(125,2202)(126,2201)(127,2200)(128,2199)(129,2198)(130,2197)(131,2196)(132,2195)(133,2194)(134,2193)(135,2192)(136,2191)(137,2190)(138,2189)(139,2188)(140,2187)(141,2186)(142,2185)(143,2184)(144,2183)(145,2182)(146,2181)(147,2180)(148,2179)(149,2178)(150,2177)(151,2176)(152,2175)(153,2174)(154,2173)(155,2172)(156,2171)(157,2170)(158,2169)(159,2168)(160,2167)(161,2166)(162,2165)(163,2164)(164,2163)(165,2162)(166,2161)(167,2160)(168,2159)(169,2158)(170,2157)(171,2156)(172,2155)(173,2154)(174,2153)(175,2152)(176,2151)(177,2150)(178,2149)(179,2148)(180,2147)(181,2146)(182,2145)(183,2144)(184,2143)(185,2142)(186,2141)(187,2140)(188,2139)(189,2138)(190,2137)(191,2136)(192,2135)(193,2134)(194,2133)(195,2132)(196,2131)(197,2130)(198,2129)(199,2128)(200,2127)(201,2126)(202,2125)(203,2124)(204,2123)(205,2122)(206,2121)(207,2120)(208,2119)(209,2118)(210,2117)(211,2116)(212,2115)(213,2114)(214,2113)(215,2112)(216,2111)(217,2110)(218,2109)(219,2108)(220,2107)(221,2106)(222,2105)(223,2104)(224,2103)(225,2102)(226,2101)(227,2100)(228,2099)(229,2098)(230,2097)(231,2096)(232,2095)(233,2094)(234,2093)(235,2092)(236,2091)(237,2090)(238,2089)(239,2088)(240,2087)(241,2086)(242,2085)(243,2084)(244,2083)(245,2082)(246,2081)(247,2080)(248,2079)(249,2078)(250,2077)(251,2076)(252,2075)(253,2074)(254,2073)(255,2072)(256,2071)(257,2070)(258,2069)(259,2068)(260,2067)(261,2066)(262,2065)(263,2064)(264,2063)(265,2062)(266,2061)(267,2060)(268,2059)(269,2058)(270,2057)(271,2056)(272,2055)(273,2054)(274,2053)(275,2052)(276,2051)(277,2050)(278,2049)(279,2048)(280,2047)(281,2046)(282,2045)(283,2044)(284,2043)(285,2042)(286,2041)(287,2040)(288,2039)(289,2038)(290,2037)(291,2036)(292,2035)(293,2034)(294,2033)(295,2032)(296,2031)(297,2030)(298,2029)(299,2028)(300,2027)(301,2026)(302,2025)(303,2024)(304,2023)(305,2022)(306,2021)(307,2020)(308,2019)(309,2018)(310,2017)(311,2016)(312,2015)(313,2014)(314,2013)(315,2012)(316,2011)(317,2010)(318,2009)(319,2008)(320,2007)(321,2006)(322,2005)(323,2004)(324,2003)(325,2002)(326,2001)(327,2000)(328,1999)(329,1998)(330,1997)(331,1996)(332,1995)(333,1994)(334,1993)(335,1992)(336,1991)(337,1990)(338,1989)(339,1988)(340,1987)(341,1986)(342,1985)(343,1984)(344,1983)(345,1982)(346,1981)(347,1980)(348,1979)(349,1978)(350,1977)(351,1976)(352,1975)(353,1974)(354,1973)(355,1972)(356,1971)(357,1970)(358,1969)(359,1968)(360,1967)(361,1966)(362,1965)(363,1964)(364,1963)(365,1962)(366,1961)(367,1960)(368,1959)(369,1958)(370,1957)(371,1956)(372,1955)(373,1954)(374,1953)(375,1952)(376,1951)(377,1950)(378,1949)(379,1948)(380,1947)(381,1946)(382,1945)(383,1944)(384,1943)(385,1942)(386,1941)(387,1940)(388,1939)(389,1938)(390,1937)(391,1936)(392,1935)(393,1934)(394,1933)(395,1932)(396,1931)(397,1930)(398,1929)(399,1928)(400,1927)(401,1926)(402,1925)(403,1924)(404,1923)(405,1922)(406,1921)(407,1920)(408,1919)(409,1918)(410,1917)(411,1916)(412,1915)(413,1914)(414,1913)(415,1912)(416,1911)(417,1910)(418,1909)(419,1908)(420,1907)(421,1906)(422,1905)(423,1904)(424,1903)(425,1902)(426,1901)(427,1900)(428,1899)(429,1898)(430,1897)(431,1896)(432,1895)(433,1894)(434,1893)(435,1892)(436,1891)(437,1890)(438,1889)(439,1888)(440,1887)(441,1886)(442,1885)(443,1884)(444,1883)(445,1882)(446,1881)(447,1880)(448,1879)(449,1878)(450,1877)(451,1876)(452,1875)(453,1874)(454,1873)(455,1872)(456,1871)(457,1870)(458,1869)(459,1868)(460,1867)(461,1866)(462,1865)(463,1864)(464,1863)(465,1862)(466,1861)(467,1860)(468,1859)(469,1858)(470,1857)(471,1856)(472,1855)(473,1854)(474,1853)(475,1852)(476,1851)(477,1850)(478,1849)(479,1848)(480,1847)(481,1846)(482,1845)(483,1844)(484,1843)(485,1842)(486,1841)(487,1840)(488,1839)(489,1838)(490,1837)(491,1836)(492,1835)(493,1834)(494,1833)(495,1832)(496,1831)(497,1830)(498,1829)(499,1828)(500,1827)(501,1826)(502,1825)(503,1824)(504,1823)(505,1822)(506,1821)(507,1820)(508,1819)(509,1818)(510,1817)(511,1816)(512,1815)(513,1814)(514,1813)(515,1812)(516,1811)(517,1810)(518,1809)(519,1808)(520,1807)(521,1806)(522,1805)(523,1804)(524,1803)(525,1802)(526,1801)(527,1800)(528,1799)(529,1798)(530,1797)(531,1796)(532,1795)(533,1794)(534,1793)(535,1792)(536,1791)(537,1790)(538,1789)(539,1788)(540,1787)(541,1786)(542,1785)(543,1784)(544,1783)(545,1782)(546,1781)(547,1780)(548,1779)(549,1778)(550,1777)(551,1776)(552,1775)(553,1774)(554,1773)(555,1772)(556,1771)(557,1770)(558,1769)(559,1768)(560,1767)(561,1766)(562,1765)(563,1764)(564,1763)(565,1762)(566,1761)(567,1760)(568,1759)(569,1758)(570,1757)(571,1756)(572,1755)(573,1754)(574,1753)(575,1752)(576,1751)(577,1750)(578,1749)(579,1748)(580,1747)(581,1746)(582,1745)(583,1744)(584,1743)(585,1742)(586,1741)(587,1740)(588,1739)(589,1738)(590,1737)(591,1736)(592,1735)(593,1734)(594,1733)(595,1732)(596,1731)(597,1730)(598,1729)(599,1728)(600,1727)(601,1726)(602,1725)(603,1724)(604,1723)(605,1722)(606,1721)(607,1720)(608,1719)(609,1718)(610,1717)(611,1716)(612,1715)(613,1714)(614,1713)(615,1712)(616,1711)(617,1710)(618,1709)(619,1708)(620,1707)(621,1706)(622,1705)(623,1704)(624,1703)(625,1702)(626,1701)(627,1700)(628,1699)(629,1698)(630,1697)(631,1696)(632,1695)(633,1694)(634,1693)(635,1692)(636,1691)(637,1690)(638,1689)(639,1688)(640,1687)(641,1686)(642,1685)(643,1684)(644,1683)(645,1682)(646,1681)(647,1680)(648,1679)(649,1678)(650,1677)(651,1676)(652,1675)(653,1674)(654,1673)(655,1672)(656,1671)(657,1670)(658,1669)(659,1668)(660,1667)(661,1666)(662,1665)(663,1664)(664,1663)(665,1662)(666,1661)(667,1660)(668,1659)(669,1658)(670,1657)(671,1656)(672,1655)(673,1654)(674,1653)(675,1652)(676,1651)(677,1650)(678,1649)(679,1648)(680,1647)(681,1646)(682,1645)(683,1644)(684,1643)(685,1642)(686,1641)(687,1640)(688,1639)(689,1638)(690,1637)(691,1636)(692,1635)(693,1634)(694,1633)(695,1632)(696,1631)(697,1630)(698,1629)(699,1628)(700,1627)(701,1626)(702,1625)(703,1624)(704,1623)(705,1622)(706,1621)(707,1620)(708,1619)(709,1618)(710,1617)(711,1616)(712,1615)(713,1614)(714,1613)(715,1612)(716,1611)(717,1610)(718,1609)(719,1608)(720,1607)(721,1606)(722,1605)(723,1604)(724,1603)(725,1602)(726,1601)(727,1600)(728,1599)(729,1598)(730,1597)(731,1596)(732,1595)(733,1594)(734,1593)(735,1592)(736,1591)(737,1590)(738,1589)(739,1588)(740,1587)(741,1586)(742,1585)(743,1584)(744,1583)(745,1582)(746,1581)(747,1580)(748,1579)(749,1578)(750,1577)(751,1576)(752,1575)(753,1574)(754,1573)(755,1572)(756,1571)(757,1570)(758,1569)(759,1568)(760,1567)(761,1566)(762,1565)(763,1564)(764,1563)(765,1562)(766,1561)(767,1560)(768,1559)(769,1558)(770,1557)(771,1556)(772,1555)(773,1554)(774,1553)(775,1552)(776,1551)(777,1550)(778,1549)(779,1548)(780,1547)(781,1546)(782,1545)(783,1544)(784,1543)(785,1542)(786,1541)(787,1540)(788,1539)(789,1538)(790,1537)(791,1536)(792,1535)(793,1534)(794,1533)(795,1532)(796,1531)(797,1530)(798,1529)(799,1528)(800,1527)(801,1526)(802,1525)(803,1524)(804,1523)(805,1522)(806,1521)(807,1520)(808,1519)(809,1518)(810,1517)(811,1516)(812,1515)(813,1514)(814,1513)(815,1512)(816,1511)(817,1510)(818,1509)(819,1508)(820,1507)(821,1506)(822,1505)(823,1504)(824,1503)(825,1502)(826,1501)(827,1500)(828,1499)(829,1498)(830,1497)(831,1496)(832,1495)(833,1494)(834,1493)(835,1492)(836,1491)(837,1490)(838,1489)(839,1488)(840,1487)(841,1486)(842,1485)(843,1484)(844,1483)(845,1482)(846,1481)(847,1480)(848,1479)(849,1478)(850,1477)(851,1476)(852,1475)(853,1474)(854,1473)(855,1472)(856,1471)(857,1470)(858,1469)(859,1468)(860,1467)(861,1466)(862,1465)(863,1464)(864,1463)(865,1462)(866,1461)(867,1460)(868,1459)(869,1458)(870,1457)(871,1456)(872,1455)(873,1454)(874,1453)(875,1452)(876,1451)(877,1450)(878,1449)(879,1448)(880,1447)(881,1446)(882,1445)(883,1444)(884,1443)(885,1442)(886,1441)(887,1440)(888,1439)(889,1438)(890,1437)(891,1436)(892,1435)(893,1434)(894,1433)(895,1432)(896,1431)(897,1430)(898,1429)(899,1428)(900,1427)(901,1426)(902,1425)(903,1424)(904,1423)(905,1422)(906,1421)(907,1420)(908,1419)(909,1418)(910,1417)(911,1416)(912,1415)(913,1414)(914,1413)(915,1412)(916,1411)(917,1410)(918,1409)(919,1408)(920,1407)(921,1406)(922,1405)(923,1404)(924,1403)(925,1402)(926,1401)(927,1400)(928,1399)(929,1398)(930,1397)(931,1396)(932,1395)(933,1394)(934,1393)(935,1392)(936,1391)(937,1390)(938,1389)(939,1388)(940,1387)(941,1386)(942,1385)(943,1384)(944,1383)(945,1382)(946,1381)(947,1380)(948,1379)(949,1378)(950,1377)(951,1376)(952,1375)(953,1374)(954,1373)(955,1372)(956,1371)(957,1370)(958,1369)(959,1368)(960,1367)(961,1366)(962,1365)(963,1364)(964,1363)(965,1362)(966,1361)(967,1360)(968,1359)(969,1358)(970,1357)(971,1356)(972,1355)(973,1354)(974,1353)(975,1352)(976,1351)(977,1350)(978,1349)(979,1348)(980,1347)(981,1346)(982,1345)(983,1344)(984,1343)(985,1342)(986,1341)(987,1340)(988,1339)(989,1338)(990,1337)(991,1336)(992,1335)(993,1334)(994,1333)(995,1332)(996,1331)(997,1330)(998,1329)(999,1328)(1000,1327)(1001,1326)(1002,1325)(1003,1324)(1004,1323)(1005,1322)(1006,1321)(1007,1320)(1008,1319)(1009,1318)(1010,1317)(1011,1316)(1012,1315)(1013,1314)(1014,1313)(1015,1312)(1016,1311)(1017,1310)(1018,1309)(1019,1308)(1020,1307)(1021,1306)(1022,1305)(1023,1304)(1024,1303)(1025,1302)(1026,1301)(1027,1300)(1028,1299)(1029,1298)(1030,1297)(1031,1296)(1032,1295)(1033,1294)(1034,1293)(1035,1292)(1036,1291)(1037,1290)(1038,1289)(1039,1288)(1040,1287)(1041,1286)(1042,1285)(1043,1284)(1044,1283)(1045,1282)(1046,1281)(1047,1280)(1048,1279)(1049,1278)(1050,1277)(1051,1276)(1052,1275)(1053,1274)(1054,1273)(1055,1272)(1056,1271)(1057,1270)(1058,1269)(1059,1268)(1060,1267)(1061,1266)(1062,1265)(1063,1264)(1064,1263)(1065,1262)(1066,1261)(1067,1260)(1068,1259)(1069,1258)(1070,1257)(1071,1256)(1072,1255)(1073,1254)(1074,1253)(1075,1252)(1076,1251)(1077,1250)(1078,1249)(1079,1248)(1080,1247)(1081,1246)(1082,1245)(1083,1244)(1084,1243)(1085,1242)(1086,1241)(1087,1240)(1088,1239)(1089,1238)(1090,1237)(1091,1236)(1092,1235)(1093,1234)(1094,1233)(1095,1232)(1096,1231)(1097,1230)(1098,1229)(1099,1228)(1100,1227)(1101,1226)(1102,1225)(1103,1224)(1104,1223)(1105,1222)(1106,1221)(1107,1220)(1108,1219)(1109,1218)(1110,1217)(1111,1216)(1112,1215)(1113,1214)(1114,1213)(1115,1212)(1116,1211)(1117,1210)(1118,1209)(1119,1208)(1120,1207)(1121,1206)(1122,1205)(1123,1204)(1124,1203)(1125,1202)(1126,1201)(1127,1200)(1128,1199)(1129,1198)(1130,1197)(1131,1196)(1132,1195)(1133,1194)(1134,1193)(1135,1192)(1136,1191)(1137,1190)(1138,1189)(1139,1188)(1140,1187)(1141,1186)(1142,1185)(1143,1184)(1144,1183)(1145,1182)(1146,1181)(1147,1180)(1148,1179)(1149,1178)(1150,1177)(1151,1176)(1152,1175)(1153,1174)(1154,1173)(1155,1172)(1156,1171)(1157,1170)(1158,1169)(1159,1168)(1160,1167)(1161,1166)(1162,1165)(1163,1164)

Polycyclic presentation:

2^3,2309|a^2=c,b^2=c,b^a=bc,d^b=d^2308

Conjugacy classes & character table

4621 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#49149187, #49149188, #49149189, …
maximal normal subgroup of	#49149187, #49149188, #49149189, …
maximal quotient of	#49149178, C₄⋊Dic₂₃₀₉, C₂×Dic₄₆₁₈, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18472, 11);

Dic4618 #32914792