Finite Group Databasebeta

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C₂×D₁₆₈₁⋊C₅ #46777374

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1683 points:

(4,13,15,88,103,6,7,33,38,235)(5,25,27,187,201,10,11,67,72,87)(8,48,50,358,369,18,19,133,138,846)(9,60,61,446,456,22,23,167,170,778)(12,82,84,194,195,30,31,227,69,517)(14,70,98,519,665,26,36,196,264,977)(16,113,115,116,276,41,42,305,310,313)(17,125,127,811,533,45,46,337,341,275)(20,148,150,911,771,53,54,397,402,1110)(21,160,161,956,963,57,58,427,430,1554)(24,180,181,1067,1071,64,65,485,488,1610)(28,210,212,1165,277,75,76,554,558,690)(29,222,224,226,86,79,80,584,81,32)(34,245,247,1191,1137,91,92,626,631,599)(35,256,258,1283,412,95,96,649,653,186)(37,183,273,1089,1331,83,101,495,684,1557)(39,285,287,278,279,106,107,288,104,311)(40,297,299,534,535,110,111,730,202,664)(43,319,44,330,331,118,119,122,123,798)(47,350,352,1473,516,130,131,837,839,1124)(49,199,366,168,996,71,136,528,449,450)(51,378,380,1506,688,141,142,883,885,592)(52,389,391,1514,1148,145,146,898,900,865)(55,410,169,1005,607,153,154,453,454,1238)(56,420,421,1541,1544,157,158,942,945,1406)(59,440,441,1268,451,164,165,982,843,1000)(62,465,467,1590,689,173,174,1026,1030,597)(63,477,479,1566,234,177,178,1054,984,102)(66,100,497,680,1383,184,185,271,1094,1328)(68,505,507,894,1136,190,191,385,1108,600)(73,539,490,282,283,204,205,1077,105,701)(74,549,551,189,538,208,209,553,203,504)(77,565,567,647,340,215,216,1184,255,639)(78,577,578,1306,1011,219,220,1201,740,1423)(85,422,595,993,691,231,232,947,1073,1336)(89,608,386,236,1227,238,239,896,601,602)(90,618,620,499,407,242,243,934,782,357)(93,596,433,434,351,250,233,162,967,630)(94,644,645,394,395,253,254,1275,147,907)(97,354,658,1475,557,261,262,842,1300,1125)(99,672,192,1114,1116,267,268,510,511,1335)(108,716,717,866,229,290,291,1359,370,137)(109,724,725,298,1012,294,295,1364,457,732)(112,741,743,514,515,302,303,1384,193,1122)(114,651,754,1577,1597,257,308,1287,1038,1562)(117,772,329,1433,944,316,317,795,796,1405)(120,786,315,1118,1109,323,324,770,512,508)(121,632,564,1289,1353,327,328,1079,711,1239)(124,806,807,912,1611,334,335,1445,1153,1524)(126,629,598,437,438,246,269,368,163,975)(128,824,799,670,693,344,345,1374,1172,635)(129,831,833,581,582,347,348,1466,221,263)(132,260,844,1304,590,355,356,660,1476,1107)(134,604,852,991,992,353,361,1234,447,1225)(135,854,856,1169,875,363,364,1062,1484,445)(139,871,214,694,695,372,373,487,280,614)(140,876,878,1149,968,375,376,1499,536,1488)(143,621,712,1250,800,383,384,1253,1166,939)(144,609,850,249,321,387,360,930,636,637)(149,531,917,889,1183,200,400,1144,1510,1511)(151,817,818,1579,591,405,339,1457,1226,228)(152,751,752,1032,1033,408,307,1320,468,1526)(155,935,919,502,292,413,414,1527,1101,719)(156,230,526,527,705,417,418,198,1133,284)(159,952,953,674,1128,424,425,1550,1316,524)(166,367,989,887,1656,443,444,863,1202,1508)(171,1015,1017,698,699,459,460,1254,281,1311)(172,1021,1023,540,927,463,464,1584,537,1152)(175,1037,1039,1537,801,470,471,1178,1599,938)(176,1047,1048,1605,322,474,475,1429,1543,784)(179,625,301,1380,586,482,483,738,739,1212)(182,1078,1080,1534,1334,491,492,1546,1600,1158)(188,768,747,237,1235,500,501,686,605,606)(197,793,1127,1616,1413,522,523,1430,1629,765)(206,990,985,868,869,543,544,1567,371,1495)(207,954,1096,813,1014,547,548,1552,458,1269)(211,1009,244,745,1259,518,455,623,624,1389)(213,1177,1179,1395,703,561,562,1648,759,573)(217,579,1192,1420,1416,570,571,1205,1652,1594)(218,568,1196,1623,929,574,575,1189,1106,1478)(223,1064,1065,1257,1337,506,484,1008,835,1157)(225,1214,349,669,704,587,588,682,836,572)(240,392,1104,847,266,611,612,503,948,671)(241,381,1245,827,748,615,616,888,1229,306)(248,332,401,314,1414,633,634,593,766,767)(251,1083,1084,1549,318,640,493,1211,1123,776)(252,1115,981,892,1520,643,585,1564,1360,1513)(259,1297,1298,1643,1243,656,657,1576,1350,1617)(265,1309,1059,702,1660,667,668,480,1228,1343)(270,1323,1324,365,909,677,678,1187,461,859)(272,304,622,1390,1171,580,683,746,1256,873)(274,1262,872,983,760,627,687,1497,569,1407)(286,1251,826,814,815,619,709,1230,338,1453)(289,1355,342,1246,1076,713,714,819,820,1615)(293,1363,1004,1270,1271,722,723,1575,638,1517)(296,1242,755,994,1612,728,613,1400,1072,1523)(300,1375,559,1645,325,735,736,1173,1174,789)(309,809,1403,1659,1653,662,757,1424,1542,1432)(312,1288,733,955,1082,762,763,426,541,1553)(320,903,769,1482,1399,652,780,1111,1129,998)(326,1333,1035,1041,1193,791,792,914,1498,1507)(333,1439,563,1628,1208,803,804,1181,1182,758)(336,756,1449,1630,1631,409,810,1401,1130,1276)(343,1241,1162,556,1091,822,823,1640,542,1170)(346,1461,1462,1249,1580,828,829,1682,1379,1664)(359,972,812,603,821,610,848,1451,1231,1232)(362,1020,1483,1013,1386,462,853,1582,742,1521)(374,915,469,1493,1308,874,399,1036,867,781)(377,1502,1504,1120,1121,880,881,1676,513,1560)(379,966,452,1573,1151,855,432,1002,1003,1154)(382,1282,628,932,429,890,891,1264,1265,961)(388,910,1263,1539,1625,396,858,1522,1492,1220)(390,1255,1515,1679,1410,841,899,1593,1655,1561)(393,1518,1001,1198,1199,904,905,1572,576,860)(398,1150,1006,404,1533,808,913,466,924,925)(403,1530,1377,1339,1260,921,922,1571,696,1393)(406,1321,1322,864,882,928,676,1040,1197,416)(411,1147,886,895,707,532,933,1203,521,1347)(415,435,1459,1452,1348,936,937,970,1421,838)(419,552,1540,560,995,734,941,1066,448,1176)(423,1448,849,473,1224,949,950,1477,1045,918)(428,1294,1344,1472,1455,845,959,1596,1674,861)(431,1100,1160,1056,1285,964,550,1145,697,666)(436,1454,1069,1070,783,973,862,486,787,1103)(439,1481,879,1677,1213,979,980,1500,1501,1657)(442,1568,1167,1168,1159,986,987,555,1512,546)(472,1325,1598,965,1618,1042,1043,1595,1422,1088)(476,1397,775,1602,1470,1051,1052,1419,1046,1219)(478,1570,1161,529,1408,997,1057,1622,1138,1139)(481,1307,1346,1209,1210,661,706,1237,583,1010)(489,1613,1614,1055,1341,1074,1075,1683,700,1273)(494,1085,646,1633,785,1086,1087,1277,1278,1102)(496,971,1025,1290,1105,1092,1093,1468,1538,940)(498,1551,1528,1438,1156,1097,1098,920,1603,545)(509,1068,1295,1296,1164,1112,1113,655,1587,1215)(520,1372,1373,692,1417,897,731,1646,1236,774)(525,1632,764,1447,1387,1131,1132,1411,931,779)(530,1639,870,1266,594,1142,1143,1315,1496,1221)(566,1060,851,1505,1398,1126,962,1479,1480,999)(589,974,906,1280,1281,1217,1218,1491,648,1267)(617,1556,960,1358,1369,1247,1248,1061,893,1675)(641,1090,1365,1027,1338,1272,988,1585,1591,1310)(642,1081,1621,1029,1396,1274,1099,1195,1525,753)(650,1366,773,659,1409,976,1286,1018,1302,761)(654,1666,737,1661,1204,1291,1292,1378,1240,1638)(663,1474,1636,715,1663,840,1279,1135,1356,1357)(673,1635,1654,884,1486,1134,1314,1200,1019,978)(675,1049,794,1620,777,1318,1319,1431,1207,1415)(679,1665,1163,1141,1188,1326,1327,1641,1565,958)(681,1471,1465,1312,1601,834,1329,830,1671,1044)(685,857,1563,1345,1427,744,1332,1223,1592,790)(708,1368,1007,877,720,1349,726,1284,1031,1361)(710,1244,1233,1619,1299,1258,1352,1404,1376,957)(718,1425,901,1261,1155,1252,902,1426,1516,1186)(721,1626,1485,1574,1555,1117,1194,1609,1545,1642)(727,1668,1058,1586,1063,1370,1371,1022,1569,1185)(729,1351,1669,1634,1662,1362,1301,1463,1531,1678)(749,750,816,969,908,1385,1392,1394,1456,1313)(788,1436,1437,916,1402,1412,802,1650,1034,1050)(797,1222,1608,1028,1649,1434,1435,1146,1180,1529)(805,1489,943,1658,1216,1443,1444,1450,1382,951)(825,1680,1354,1388,1446,1458,1460,1604,1644,1487)(832,1588,1016,1647,1670,1024,1469,1175,1548,1367)(923,946,1578,1519,1581,1381,1532,1547,1494,1340)(926,1442,1606,1627,1607,1535,1536,1206,1119,1053)(1095,1681,1667,1303,1673,1559,1467,1293,1342,1418)(1140,1305,1583,1589,1317,1624,1637,1440,1330,1503)(1190,1464,1672,1391,1441,1509,1651,1428,1558,1490);(1,2)(3,26,229,1224,653,142,820,1493,1323,1315,198,197,1099,1553,1667,959,745,744,747,729,511,721,720,273,1644,655,654,1369,492,1128,1131,1122,371,370,1127,616,890,1538,401,49,6,10,83,598,1033,1241,389,1519,1043,1495,673,70,498,1629,1397,1371,1393,303,821,304,296,293,292,988,1170,1578,258,727,726,1482,1630,1549,1214,138,1539,1510,1375,1360,934,149,18,22,30,234,1148,1222,612,904,1588,1439,1267,267,185,1207,1206,753,750,749,343,342,112,109,108,442,1245,1008,1007,666,295,852,1205,1633,951,948,935,1168,1287,1571,718,411,53,57,64,86,533,594,780,1380,1491,1490,1536,629,677,580,579,1406,307,306,1015,127,1013,40,39,165,1191,1190,454,816,264,1585,1683,1132,1542,423,422,1282,999,998,1273,291,153,157,164,184,201,230,1271,1658,1328,863,1569,1318,1321,1326,220,1507,759,113,773,1451,458,457,15,619,569,568,1298,339,338,1021,1680,1682,942,1288,158,664,648,450,642,641,413,417,424,443,412,84,1105,1213,1276,1237,987,1309,752,1573,887,886,952,310,316,1421,824,170,238,242,1258,216,864,825,125,832,1468,1467,1532,651,1450,1405,263,255,252,251,936,882,734,733,875,154,504,586,645,1119,606,1363,699,1546,1545,380,548,766,770,776,1230,1229,611,615,623,1063,1155,367,344,347,1330,831,1647,1400,810,1605,758,97,94,93,801,800,377,299,374,1265,871,224,516,513,512,1473,1184,1297,945,1514,1359,501,1111,1110,1415,602,1242,695,1247,483,1076,544,136,828,682,681,1257,1255,1254,1050,1049,309,35,34,340,331,1317,140,139,796,1497,1171,195,193,192,1211,1610,958,957,1429,1262,876,509,508,1594,767,1617,1352,844,1379,490,489,1138,1142,1465,271,1674,622,621,1666,475,781,114,13,126,369,674,1031,50,341,1041,1040,557,69,68,585,1524,1466,427,1556,792,1499,1500,191,1088,1030,1085,1357,1637,740,737,181,1624,1565,1560,1559,1552,1558,243,1358,1354,917,320,41,45,351,268,467,610,609,1587,471,1187,211,25,223,1220,1219,964,966,1521,1445,1665,1623,496,494,493,1537,1367,1366,301,300,1113,1204,981,974,972,971,1166,1067,715,712,711,118,122,130,843,1506,1477,239,1479,1023,1650,566,75,79,590,589,1422,1384,907,1487,1648,1266,1263,183,182,1183,926,725,923,111,1619,578,1135,439,436,435,554,994,993,289,288,323,327,334,355,930,929,1353,1661,980,1390,1182,215,219,226,225,1642,779,778,859,1453,1489,628,627,65,564,563,404,403,1372,1089,1679,527,1223,163,162,1173,448,447,1054,107,789,791,795,409,407,406,963,1449,1678,985,984,570,574,581,80,1164,1163,319,1423,862,861,925,245,1069,214,213,1600,150,799,853,1457,1531,595,650,58,1488,1016,167,1022,1347,1349,1427,523,1434,152,151,1520,1504,1420,1418,441,704,703,1198,1209,553,552,637,784,1226,366,1225,633,636,956,76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Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33620, 9);