D₇₁₇₉ #28385178

order	14358
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₇₁₇₉
unambiguous semidirect product	C₃⋊D₂₃₉₃
unambiguous semidirect product	C₂₃₉₃⋊D₃

Splittings

Fitting, socle, derived, Hall	C₃×C₂₃₉₃ ⋊ C₂
Sylow	C₂₃₉₃ ⋊ D₃
Sylow	C₃ ⋊ D₂₃₉₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₂₃₉₃	C₂
LCS	G ▷ C₃×C₂₃₉₃
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 2396
transitive degree	μ_t(G) = 7179

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

Polycyclic presentation:

2,3,2393|b^a=b^2,c^a=c^2392

Conjugacy classes & character table

3591 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×D₂₃₉₃, C₂×D₇₁₇₉
maximal normal subgroup of	D₃×D₂₃₉₃, C₂×D₇₁₇₉
maximal quotient of	Dic₇₁₇₉, C₂×D₇₁₇₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14358, 3);

D7179 #28385178