Finite Group Databasebeta

?

← Prev (#44569770) Next (#44569772) →

C₂×D₁₆₂₁⋊C₅ #44569771

• 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 1623 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32420, 9);