Finite Group DatabasebetaFinite Group Databasebeta| order | 36932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic9233 |
| unambiguous semidirect product | C7⋊Dic1319 |
| unambiguous semidirect product | C1319⋊Dic7 |
| derived, Hall | C7×C1319 ⋊ C4 |
| Sylow | C1319 ⋊ Dic7 |
| Sylow | C7 ⋊ Dic1319 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D9233 |
| commutator, hypocenter | C7×C1319 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C7×C1319 | C2 |
| LCS | G ▷ C7×C1319 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1330 |
| transitive degree | μt(G) = 36932 |
A minimal faithful permutation representation — 2 generators on 1330 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);(1,3,2,4)(6,11)(7,10)(8,9)(13,1330)(14,1329)(15,1328)(16,1327)(17,1326)(18,1325)(19,1324)(20,1323)(21,1322)(22,1321)(23,1320)(24,1319)(25,1318)(26,1317)(27,1316)(28,1315)(29,1314)(30,1313)(31,1312)(32,1311)(33,1310)(34,1309)(35,1308)(36,1307)(37,1306)(38,1305)(39,1304)(40,1303)(41,1302)(42,1301)(43,1300)(44,1299)(45,1298)(46,1297)(47,1296)(48,1295)(49,1294)(50,1293)(51,1292)(52,1291)(53,1290)(54,1289)(55,1288)(56,1287)(57,1286)(58,1285)(59,1284)(60,1283)(61,1282)(62,1281)(63,1280)(64,1279)(65,1278)(66,1277)(67,1276)(68,1275)(69,1274)(70,1273)(71,1272)(72,1271)(73,1270)(74,1269)(75,1268)(76,1267)(77,1266)(78,1265)(79,1264)(80,1263)(81,1262)(82,1261)(83,1260)(84,1259)(85,1258)(86,1257)(87,1256)(88,1255)(89,1254)(90,1253)(91,1252)(92,1251)(93,1250)(94,1249)(95,1248)(96,1247)(97,1246)(98,1245)(99,1244)(100,1243)(101,1242)(102,1241)(103,1240)(104,1239)(105,1238)(106,1237)(107,1236)(108,1235)(109,1234)(110,1233)(111,1232)(112,1231)(113,1230)(114,1229)(115,1228)(116,1227)(117,1226)(118,1225)(119,1224)(120,1223)(121,1222)(122,1221)(123,1220)(124,1219)(125,1218)(126,1217)(127,1216)(128,1215)(129,1214)(130,1213)(131,1212)(132,1211)(133,1210)(134,1209)(135,1208)(136,1207)(137,1206)(138,1205)(139,1204)(140,1203)(141,1202)(142,1201)(143,1200)(144,1199)(145,1198)(146,1197)(147,1196)(148,1195)(149,1194)(150,1193)(151,1192)(152,1191)(153,1190)(154,1189)(155,1188)(156,1187)(157,1186)(158,1185)(159,1184)(160,1183)(161,1182)(162,1181)(163,1180)(164,1179)(165,1178)(166,1177)(167,1176)(168,1175)(169,1174)(170,1173)(171,1172)(172,1171)(173,1170)(174,1169)(175,1168)(176,1167)(177,1166)(178,1165)(179,1164)(180,1163)(181,1162)(182,1161)(183,1160)(184,1159)(185,1158)(186,1157)(187,1156)(188,1155)(189,1154)(190,1153)(191,1152)(192,1151)(193,1150)(194,1149)(195,1148)(196,1147)(197,1146)(198,1145)(199,1144)(200,1143)(201,1142)(202,1141)(203,1140)(204,1139)(205,1138)(206,1137)(207,1136)(208,1135)(209,1134)(210,1133)(211,1132)(212,1131)(213,1130)(214,1129)(215,1128)(216,1127)(217,1126)(218,1125)(219,1124)(220,1123)(221,1122)(222,1121)(223,1120)(224,1119)(225,1118)(226,1117)(227,1116)(228,1115)(229,1114)(230,1113)(231,1112)(232,1111)(233,1110)(234,1109)(235,1108)(236,1107)(237,1106)(238,1105)(239,1104)(240,1103)(241,1102)(242,1101)(243,1100)(244,1099)(245,1098)(246,1097)(247,1096)(248,1095)(249,1094)(250,1093)(251,1092)(252,1091)(253,1090)(254,1089)(255,1088)(256,1087)(257,1086)(258,1085)(259,1084)(260,1083)(261,1082)(262,1081)(263,1080)(264,1079)(265,1078)(266,1077)(267,1076)(268,1075)(269,1074)(270,1073)(271,1072)(272,1071)(273,1070)(274,1069)(275,1068)(276,1067)(277,1066)(278,1065)(279,1064)(280,1063)(281,1062)(282,1061)(283,1060)(284,1059)(285,1058)(286,1057)(287,1056)(288,1055)(289,1054)(290,1053)(291,1052)(292,1051)(293,1050)(294,1049)(295,1048)(296,1047)(297,1046)(298,1045)(299,1044)(300,1043)(301,1042)(302,1041)(303,1040)(304,1039)(305,1038)(306,1037)(307,1036)(308,1035)(309,1034)(310,1033)(311,1032)(312,1031)(313,1030)(314,1029)(315,1028)(316,1027)(317,1026)(318,1025)(319,1024)(320,1023)(321,1022)(322,1021)(323,1020)(324,1019)(325,1018)(326,1017)(327,1016)(328,1015)(329,1014)(330,1013)(331,1012)(332,1011)(333,1010)(334,1009)(335,1008)(336,1007)(337,1006)(338,1005)(339,1004)(340,1003)(341,1002)(342,1001)(343,1000)(344,999)(345,998)(346,997)(347,996)(348,995)(349,994)(350,993)(351,992)(352,991)(353,990)(354,989)(355,988)(356,987)(357,986)(358,985)(359,984)(360,983)(361,982)(362,981)(363,980)(364,979)(365,978)(366,977)(367,976)(368,975)(369,974)(370,973)(371,972)(372,971)(373,970)(374,969)(375,968)(376,967)(377,966)(378,965)(379,964)(380,963)(381,962)(382,961)(383,960)(384,959)(385,958)(386,957)(387,956)(388,955)(389,954)(390,953)(391,952)(392,951)(393,950)(394,949)(395,948)(396,947)(397,946)(398,945)(399,944)(400,943)(401,942)(402,941)(403,940)(404,939)(405,938)(406,937)(407,936)(408,935)(409,934)(410,933)(411,932)(412,931)(413,930)(414,929)(415,928)(416,927)(417,926)(418,925)(419,924)(420,923)(421,922)(422,921)(423,920)(424,919)(425,918)(426,917)(427,916)(428,915)(429,914)(430,913)(431,912)(432,911)(433,910)(434,909)(435,908)(436,907)(437,906)(438,905)(439,904)(440,903)(441,902)(442,901)(443,900)(444,899)(445,898)(446,897)(447,896)(448,895)(449,894)(450,893)(451,892)(452,891)(453,890)(454,889)(455,888)(456,887)(457,886)(458,885)(459,884)(460,883)(461,882)(462,881)(463,880)(464,879)(465,878)(466,877)(467,876)(468,875)(469,874)(470,873)(471,872)(472,871)(473,870)(474,869)(475,868)(476,867)(477,866)(478,865)(479,864)(480,863)(481,862)(482,861)(483,860)(484,859)(485,858)(486,857)(487,856)(488,855)(489,854)(490,853)(491,852)(492,851)(493,850)(494,849)(495,848)(496,847)(497,846)(498,845)(499,844)(500,843)(501,842)(502,841)(503,840)(504,839)(505,838)(506,837)(507,836)(508,835)(509,834)(510,833)(511,832)(512,831)(513,830)(514,829)(515,828)(516,827)(517,826)(518,825)(519,824)(520,823)(521,822)(522,821)(523,820)(524,819)(525,818)(526,817)(527,816)(528,815)(529,814)(530,813)(531,812)(532,811)(533,810)(534,809)(535,808)(536,807)(537,806)(538,805)(539,804)(540,803)(541,802)(542,801)(543,800)(544,799)(545,798)(546,797)(547,796)(548,795)(549,794)(550,793)(551,792)(552,791)(553,790)(554,789)(555,788)(556,787)(557,786)(558,785)(559,784)(560,783)(561,782)(562,781)(563,780)(564,779)(565,778)(566,777)(567,776)(568,775)(569,774)(570,773)(571,772)(572,771)(573,770)(574,769)(575,768)(576,767)(577,766)(578,765)(579,764)(580,763)(581,762)(582,761)(583,760)(584,759)(585,758)(586,757)(587,756)(588,755)(589,754)(590,753)(591,752)(592,751)(593,750)(594,749)(595,748)(596,747)(597,746)(598,745)(599,744)(600,743)(601,742)(602,741)(603,740)(604,739)(605,738)(606,737)(607,736)(608,735)(609,734)(610,733)(611,732)(612,731)(613,730)(614,729)(615,728)(616,727)(617,726)(618,725)(619,724)(620,723)(621,722)(622,721)(623,720)(624,719)(625,718)(626,717)(627,716)(628,715)(629,714)(630,713)(631,712)(632,711)(633,710)(634,709)(635,708)(636,707)(637,706)(638,705)(639,704)(640,703)(641,702)(642,701)(643,700)(644,699)(645,698)(646,697)(647,696)(648,695)(649,694)(650,693)(651,692)(652,691)(653,690)(654,689)(655,688)(656,687)(657,686)(658,685)(659,684)(660,683)(661,682)(662,681)(663,680)(664,679)(665,678)(666,677)(667,676)(668,675)(669,674)(670,673)(671,672)Polycyclic presentation:
2,7,1319,2|a^2=d,b^a=b^6,c^a=c^13189236 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36932, 4);