Dic₆₀₃₃ #37563254

order	24132
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₆₀₃₃
unambiguous semidirect product	C₃⋊Dic₂₀₁₁
unambiguous semidirect product	C₂₀₁₁⋊Dic₃

Splittings

derived, Hall	C₃×C₂₀₁₁ ⋊ C₄
Sylow	C₂₀₁₁ ⋊ Dic₃
Sylow	C₃ ⋊ Dic₂₀₁₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₀₃₃
commutator, hypocenter	C₃×C₂₀₁₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₂₀₁₁	C₂
LCS	G ▷ C₃×C₂₀₁₁
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 2018
transitive degree	μ_t(G) = 24132

A minimal faithful permutation representation — 2 generators on 2018 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);(1,3,2,4)(6,7)(9,2018)(10,2017)(11,2016)(12,2015)(13,2014)(14,2013)(15,2012)(16,2011)(17,2010)(18,2009)(19,2008)(20,2007)(21,2006)(22,2005)(23,2004)(24,2003)(25,2002)(26,2001)(27,2000)(28,1999)(29,1998)(30,1997)(31,1996)(32,1995)(33,1994)(34,1993)(35,1992)(36,1991)(37,1990)(38,1989)(39,1988)(40,1987)(41,1986)(42,1985)(43,1984)(44,1983)(45,1982)(46,1981)(47,1980)(48,1979)(49,1978)(50,1977)(51,1976)(52,1975)(53,1974)(54,1973)(55,1972)(56,1971)(57,1970)(58,1969)(59,1968)(60,1967)(61,1966)(62,1965)(63,1964)(64,1963)(65,1962)(66,1961)(67,1960)(68,1959)(69,1958)(70,1957)(71,1956)(72,1955)(73,1954)(74,1953)(75,1952)(76,1951)(77,1950)(78,1949)(79,1948)(80,1947)(81,1946)(82,1945)(83,1944)(84,1943)(85,1942)(86,1941)(87,1940)(88,1939)(89,1938)(90,1937)(91,1936)(92,1935)(93,1934)(94,1933)(95,1932)(96,1931)(97,1930)(98,1929)(99,1928)(100,1927)(101,1926)(102,1925)(103,1924)(104,1923)(105,1922)(106,1921)(107,1920)(108,1919)(109,1918)(110,1917)(111,1916)(112,1915)(113,1914)(114,1913)(115,1912)(116,1911)(117,1910)(118,1909)(119,1908)(120,1907)(121,1906)(122,1905)(123,1904)(124,1903)(125,1902)(126,1901)(127,1900)(128,1899)(129,1898)(130,1897)(131,1896)(132,1895)(133,1894)(134,1893)(135,1892)(136,1891)(137,1890)(138,1889)(139,1888)(140,1887)(141,1886)(142,1885)(143,1884)(144,1883)(145,1882)(146,1881)(147,1880)(148,1879)(149,1878)(150,1877)(151,1876)(152,1875)(153,1874)(154,1873)(155,1872)(156,1871)(157,1870)(158,1869)(159,1868)(160,1867)(161,1866)(162,1865)(163,1864)(164,1863)(165,1862)(166,1861)(167,1860)(168,1859)(169,1858)(170,1857)(171,1856)(172,1855)(173,1854)(174,1853)(175,1852)(176,1851)(177,1850)(178,1849)(179,1848)(180,1847)(181,1846)(182,1845)(183,1844)(184,1843)(185,1842)(186,1841)(187,1840)(188,1839)(189,1838)(190,1837)(191,1836)(192,1835)(193,1834)(194,1833)(195,1832)(196,1831)(197,1830)(198,1829)(199,1828)(200,1827)(201,1826)(202,1825)(203,1824)(204,1823)(205,1822)(206,1821)(207,1820)(208,1819)(209,1818)(210,1817)(211,1816)(212,1815)(213,1814)(214,1813)(215,1812)(216,1811)(217,1810)(218,1809)(219,1808)(220,1807)(221,1806)(222,1805)(223,1804)(224,1803)(225,1802)(226,1801)(227,1800)(228,1799)(229,1798)(230,1797)(231,1796)(232,1795)(233,1794)(234,1793)(235,1792)(236,1791)(237,1790)(238,1789)(239,1788)(240,1787)(241,1786)(242,1785)(243,1784)(244,1783)(245,1782)(246,1781)(247,1780)(248,1779)(249,1778)(250,1777)(251,1776)(252,1775)(253,1774)(254,1773)(255,1772)(256,1771)(257,1770)(258,1769)(259,1768)(260,1767)(261,1766)(262,1765)(263,1764)(264,1763)(265,1762)(266,1761)(267,1760)(268,1759)(269,1758)(270,1757)(271,1756)(272,1755)(273,1754)(274,1753)(275,1752)(276,1751)(277,1750)(278,1749)(279,1748)(280,1747)(281,1746)(282,1745)(283,1744)(284,1743)(285,1742)(286,1741)(287,1740)(288,1739)(289,1738)(290,1737)(291,1736)(292,1735)(293,1734)(294,1733)(295,1732)(296,1731)(297,1730)(298,1729)(299,1728)(300,1727)(301,1726)(302,1725)(303,1724)(304,1723)(305,1722)(306,1721)(307,1720)(308,1719)(309,1718)(310,1717)(311,1716)(312,1715)(313,1714)(314,1713)(315,1712)(316,1711)(317,1710)(318,1709)(319,1708)(320,1707)(321,1706)(322,1705)(323,1704)(324,1703)(325,1702)(326,1701)(327,1700)(328,1699)(329,1698)(330,1697)(331,1696)(332,1695)(333,1694)(334,1693)(335,1692)(336,1691)(337,1690)(338,1689)(339,1688)(340,1687)(341,1686)(342,1685)(343,1684)(344,1683)(345,1682)(346,1681)(347,1680)(348,1679)(349,1678)(350,1677)(351,1676)(352,1675)(353,1674)(354,1673)(355,1672)(356,1671)(357,1670)(358,1669)(359,1668)(360,1667)(361,1666)(362,1665)(363,1664)(364,1663)(365,1662)(366,1661)(367,1660)(368,1659)(369,1658)(370,1657)(371,1656)(372,1655)(373,1654)(374,1653)(375,1652)(376,1651)(377,1650)(378,1649)(379,1648)(380,1647)(381,1646)(382,1645)(383,1644)(384,1643)(385,1642)(386,1641)(387,1640)(388,1639)(389,1638)(390,1637)(391,1636)(392,1635)(393,1634)(394,1633)(395,1632)(396,1631)(397,1630)(398,1629)(399,1628)(400,1627)(401,1626)(402,1625)(403,1624)(404,1623)(405,1622)(406,1621)(407,1620)(408,1619)(409,1618)(410,1617)(411,1616)(412,1615)(413,1614)(414,1613)(415,1612)(416,1611)(417,1610)(418,1609)(419,1608)(420,1607)(421,1606)(422,1605)(423,1604)(424,1603)(425,1602)(426,1601)(427,1600)(428,1599)(429,1598)(430,1597)(431,1596)(432,1595)(433,1594)(434,1593)(435,1592)(436,1591)(437,1590)(438,1589)(439,1588)(440,1587)(441,1586)(442,1585)(443,1584)(444,1583)(445,1582)(446,1581)(447,1580)(448,1579)(449,1578)(450,1577)(451,1576)(452,1575)(453,1574)(454,1573)(455,1572)(456,1571)(457,1570)(458,1569)(459,1568)(460,1567)(461,1566)(462,1565)(463,1564)(464,1563)(465,1562)(466,1561)(467,1560)(468,1559)(469,1558)(470,1557)(471,1556)(472,1555)(473,1554)(474,1553)(475,1552)(476,1551)(477,1550)(478,1549)(479,1548)(480,1547)(481,1546)(482,1545)(483,1544)(484,1543)(485,1542)(486,1541)(487,1540)(488,1539)(489,1538)(490,1537)(491,1536)(492,1535)(493,1534)(494,1533)(495,1532)(496,1531)(497,1530)(498,1529)(499,1528)(500,1527)(501,1526)(502,1525)(503,1524)(504,1523)(505,1522)(506,1521)(507,1520)(508,1519)(509,1518)(510,1517)(511,1516)(512,1515)(513,1514)(514,1513)(515,1512)(516,1511)(517,1510)(518,1509)(519,1508)(520,1507)(521,1506)(522,1505)(523,1504)(524,1503)(525,1502)(526,1501)(527,1500)(528,1499)(529,1498)(530,1497)(531,1496)(532,1495)(533,1494)(534,1493)(535,1492)(536,1491)(537,1490)(538,1489)(539,1488)(540,1487)(541,1486)(542,1485)(543,1484)(544,1483)(545,1482)(546,1481)(547,1480)(548,1479)(549,1478)(550,1477)(551,1476)(552,1475)(553,1474)(554,1473)(555,1472)(556,1471)(557,1470)(558,1469)(559,1468)(560,1467)(561,1466)(562,1465)(563,1464)(564,1463)(565,1462)(566,1461)(567,1460)(568,1459)(569,1458)(570,1457)(571,1456)(572,1455)(573,1454)(574,1453)(575,1452)(576,1451)(577,1450)(578,1449)(579,1448)(580,1447)(581,1446)(582,1445)(583,1444)(584,1443)(585,1442)(586,1441)(587,1440)(588,1439)(589,1438)(590,1437)(591,1436)(592,1435)(593,1434)(594,1433)(595,1432)(596,1431)(597,1430)(598,1429)(599,1428)(600,1427)(601,1426)(602,1425)(603,1424)(604,1423)(605,1422)(606,1421)(607,1420)(608,1419)(609,1418)(610,1417)(611,1416)(612,1415)(613,1414)(614,1413)(615,1412)(616,1411)(617,1410)(618,1409)(619,1408)(620,1407)(621,1406)(622,1405)(623,1404)(624,1403)(625,1402)(626,1401)(627,1400)(628,1399)(629,1398)(630,1397)(631,1396)(632,1395)(633,1394)(634,1393)(635,1392)(636,1391)(637,1390)(638,1389)(639,1388)(640,1387)(641,1386)(642,1385)(643,1384)(644,1383)(645,1382)(646,1381)(647,1380)(648,1379)(649,1378)(650,1377)(651,1376)(652,1375)(653,1374)(654,1373)(655,1372)(656,1371)(657,1370)(658,1369)(659,1368)(660,1367)(661,1366)(662,1365)(663,1364)(664,1363)(665,1362)(666,1361)(667,1360)(668,1359)(669,1358)(670,1357)(671,1356)(672,1355)(673,1354)(674,1353)(675,1352)(676,1351)(677,1350)(678,1349)(679,1348)(680,1347)(681,1346)(682,1345)(683,1344)(684,1343)(685,1342)(686,1341)(687,1340)(688,1339)(689,1338)(690,1337)(691,1336)(692,1335)(693,1334)(694,1333)(695,1332)(696,1331)(697,1330)(698,1329)(699,1328)(700,1327)(701,1326)(702,1325)(703,1324)(704,1323)(705,1322)(706,1321)(707,1320)(708,1319)(709,1318)(710,1317)(711,1316)(712,1315)(713,1314)(714,1313)(715,1312)(716,1311)(717,1310)(718,1309)(719,1308)(720,1307)(721,1306)(722,1305)(723,1304)(724,1303)(725,1302)(726,1301)(727,1300)(728,1299)(729,1298)(730,1297)(731,1296)(732,1295)(733,1294)(734,1293)(735,1292)(736,1291)(737,1290)(738,1289)(739,1288)(740,1287)(741,1286)(742,1285)(743,1284)(744,1283)(745,1282)(746,1281)(747,1280)(748,1279)(749,1278)(750,1277)(751,1276)(752,1275)(753,1274)(754,1273)(755,1272)(756,1271)(757,1270)(758,1269)(759,1268)(760,1267)(761,1266)(762,1265)(763,1264)(764,1263)(765,1262)(766,1261)(767,1260)(768,1259)(769,1258)(770,1257)(771,1256)(772,1255)(773,1254)(774,1253)(775,1252)(776,1251)(777,1250)(778,1249)(779,1248)(780,1247)(781,1246)(782,1245)(783,1244)(784,1243)(785,1242)(786,1241)(787,1240)(788,1239)(789,1238)(790,1237)(791,1236)(792,1235)(793,1234)(794,1233)(795,1232)(796,1231)(797,1230)(798,1229)(799,1228)(800,1227)(801,1226)(802,1225)(803,1224)(804,1223)(805,1222)(806,1221)(807,1220)(808,1219)(809,1218)(810,1217)(811,1216)(812,1215)(813,1214)(814,1213)(815,1212)(816,1211)(817,1210)(818,1209)(819,1208)(820,1207)(821,1206)(822,1205)(823,1204)(824,1203)(825,1202)(826,1201)(827,1200)(828,1199)(829,1198)(830,1197)(831,1196)(832,1195)(833,1194)(834,1193)(835,1192)(836,1191)(837,1190)(838,1189)(839,1188)(840,1187)(841,1186)(842,1185)(843,1184)(844,1183)(845,1182)(846,1181)(847,1180)(848,1179)(849,1178)(850,1177)(851,1176)(852,1175)(853,1174)(854,1173)(855,1172)(856,1171)(857,1170)(858,1169)(859,1168)(860,1167)(861,1166)(862,1165)(863,1164)(864,1163)(865,1162)(866,1161)(867,1160)(868,1159)(869,1158)(870,1157)(871,1156)(872,1155)(873,1154)(874,1153)(875,1152)(876,1151)(877,1150)(878,1149)(879,1148)(880,1147)(881,1146)(882,1145)(883,1144)(884,1143)(885,1142)(886,1141)(887,1140)(888,1139)(889,1138)(890,1137)(891,1136)(892,1135)(893,1134)(894,1133)(895,1132)(896,1131)(897,1130)(898,1129)(899,1128)(900,1127)(901,1126)(902,1125)(903,1124)(904,1123)(905,1122)(906,1121)(907,1120)(908,1119)(909,1118)(910,1117)(911,1116)(912,1115)(913,1114)(914,1113)(915,1112)(916,1111)(917,1110)(918,1109)(919,1108)(920,1107)(921,1106)(922,1105)(923,1104)(924,1103)(925,1102)(926,1101)(927,1100)(928,1099)(929,1098)(930,1097)(931,1096)(932,1095)(933,1094)(934,1093)(935,1092)(936,1091)(937,1090)(938,1089)(939,1088)(940,1087)(941,1086)(942,1085)(943,1084)(944,1083)(945,1082)(946,1081)(947,1080)(948,1079)(949,1078)(950,1077)(951,1076)(952,1075)(953,1074)(954,1073)(955,1072)(956,1071)(957,1070)(958,1069)(959,1068)(960,1067)(961,1066)(962,1065)(963,1064)(964,1063)(965,1062)(966,1061)(967,1060)(968,1059)(969,1058)(970,1057)(971,1056)(972,1055)(973,1054)(974,1053)(975,1052)(976,1051)(977,1050)(978,1049)(979,1048)(980,1047)(981,1046)(982,1045)(983,1044)(984,1043)(985,1042)(986,1041)(987,1040)(988,1039)(989,1038)(990,1037)(991,1036)(992,1035)(993,1034)(994,1033)(995,1032)(996,1031)(997,1030)(998,1029)(999,1028)(1000,1027)(1001,1026)(1002,1025)(1003,1024)(1004,1023)(1005,1022)(1006,1021)(1007,1020)(1008,1019)(1009,1018)(1010,1017)(1011,1016)(1012,1015)(1013,1014)

Polycyclic presentation:

2,3,2011,2|a^2=d,b^a=b^2,c^a=c^2010

Conjugacy classes & character table

6036 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₂₀₆₆
maximal normal subgroup of	Dic₁₂₀₆₆

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24132, 6);

Dic6033 #37563254