Finite Group Databasebeta

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C₂×D₁₆₀₁⋊C₅ #44545019

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1603 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32020, 9);