C₂×D₁₄₈₁⋊C₅ #44444169

order	29620
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₁₄₈₁⋊C₅
unambiguous semidirect product	D₁₄₈₁⋊(C₂×C₅)
unambiguous semidirect product	(C₂×D₁₄₈₁)⋊C₅
unambiguous semidirect product	(C₁₄₈₁⋊C₅)⋊C₂²
unambiguous semidirect product	(C₂×C₁₄₈₁⋊C₅)⋊C₂

Splittings

Fitting, socle	C₂×C₁₄₈₁ ⋊ C₂×C₅
derived, Sylow	C₁₄₈₁ ⋊ C₂²×C₅
Hall	C₁₄₈₁⋊C₅ ⋊ C₂²
Hall	C₂×D₁₄₈₁ ⋊ C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₁₄₈₁⋊C₅
commutator, cosocle, hypocenter	C₁₄₈₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₁₄₈₁	C₂×C₅
LCS	G ▷ C₁₄₈₁
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1483
transitive degree	μ_t(G) = 2962

A minimal faithful permutation representation — 2 generators on 1483 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29620, 9);

C2×D1481⋊C5 #44444169