D₇₄₃₅ #28415586

order	14870
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₇₄₃₅
unambiguous semidirect product	C₅⋊D₁₄₈₇
unambiguous semidirect product	C₁₄₈₇⋊D₅

Splittings

Fitting, socle, derived, Hall	C₅×C₁₄₈₇ ⋊ C₂
Sylow	C₁₄₈₇ ⋊ D₅
Sylow	C₅ ⋊ D₁₄₈₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₄₈₇	C₂
LCS	G ▷ C₅×C₁₄₈₇
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1492
transitive degree	μ_t(G) = 7435

A minimal faithful permutation representation — 2 generators on 1492 points:

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

Polycyclic presentation:

2,5,1487|b^a=b^4,c^a=c^1486

Conjugacy classes & character table

3719 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₅×D₁₄₈₇, C₂×D₇₄₃₅
maximal normal subgroup of	D₅×D₁₄₈₇, C₂×D₇₄₃₅
maximal quotient of	Dic₇₄₃₅, C₂×D₇₄₃₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14870, 3);

D7435 #28415586