Finite Group Databasebeta

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C₂×D₁₅₇₁⋊C₅ #44536162

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31420, 8);