Finite Group DatabasebetaFinite Group Databasebeta| order | 36148 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic9037 |
| unambiguous semidirect product | C7⋊Dic1291 |
| unambiguous semidirect product | C1291⋊Dic7 |
| derived, Hall | C7×C1291 ⋊ C4 |
| Sylow | C1291 ⋊ Dic7 |
| Sylow | C7 ⋊ Dic1291 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D9037 |
| commutator, hypocenter | C7×C1291 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C7×C1291 | C2 |
| LCS | G ▷ C7×C1291 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1302 |
| transitive degree | μt(G) = 36148 |
A minimal faithful permutation representation — 2 generators on 1302 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);(1,3,2,4)(6,11)(7,10)(8,9)(13,1302)(14,1301)(15,1300)(16,1299)(17,1298)(18,1297)(19,1296)(20,1295)(21,1294)(22,1293)(23,1292)(24,1291)(25,1290)(26,1289)(27,1288)(28,1287)(29,1286)(30,1285)(31,1284)(32,1283)(33,1282)(34,1281)(35,1280)(36,1279)(37,1278)(38,1277)(39,1276)(40,1275)(41,1274)(42,1273)(43,1272)(44,1271)(45,1270)(46,1269)(47,1268)(48,1267)(49,1266)(50,1265)(51,1264)(52,1263)(53,1262)(54,1261)(55,1260)(56,1259)(57,1258)(58,1257)(59,1256)(60,1255)(61,1254)(62,1253)(63,1252)(64,1251)(65,1250)(66,1249)(67,1248)(68,1247)(69,1246)(70,1245)(71,1244)(72,1243)(73,1242)(74,1241)(75,1240)(76,1239)(77,1238)(78,1237)(79,1236)(80,1235)(81,1234)(82,1233)(83,1232)(84,1231)(85,1230)(86,1229)(87,1228)(88,1227)(89,1226)(90,1225)(91,1224)(92,1223)(93,1222)(94,1221)(95,1220)(96,1219)(97,1218)(98,1217)(99,1216)(100,1215)(101,1214)(102,1213)(103,1212)(104,1211)(105,1210)(106,1209)(107,1208)(108,1207)(109,1206)(110,1205)(111,1204)(112,1203)(113,1202)(114,1201)(115,1200)(116,1199)(117,1198)(118,1197)(119,1196)(120,1195)(121,1194)(122,1193)(123,1192)(124,1191)(125,1190)(126,1189)(127,1188)(128,1187)(129,1186)(130,1185)(131,1184)(132,1183)(133,1182)(134,1181)(135,1180)(136,1179)(137,1178)(138,1177)(139,1176)(140,1175)(141,1174)(142,1173)(143,1172)(144,1171)(145,1170)(146,1169)(147,1168)(148,1167)(149,1166)(150,1165)(151,1164)(152,1163)(153,1162)(154,1161)(155,1160)(156,1159)(157,1158)(158,1157)(159,1156)(160,1155)(161,1154)(162,1153)(163,1152)(164,1151)(165,1150)(166,1149)(167,1148)(168,1147)(169,1146)(170,1145)(171,1144)(172,1143)(173,1142)(174,1141)(175,1140)(176,1139)(177,1138)(178,1137)(179,1136)(180,1135)(181,1134)(182,1133)(183,1132)(184,1131)(185,1130)(186,1129)(187,1128)(188,1127)(189,1126)(190,1125)(191,1124)(192,1123)(193,1122)(194,1121)(195,1120)(196,1119)(197,1118)(198,1117)(199,1116)(200,1115)(201,1114)(202,1113)(203,1112)(204,1111)(205,1110)(206,1109)(207,1108)(208,1107)(209,1106)(210,1105)(211,1104)(212,1103)(213,1102)(214,1101)(215,1100)(216,1099)(217,1098)(218,1097)(219,1096)(220,1095)(221,1094)(222,1093)(223,1092)(224,1091)(225,1090)(226,1089)(227,1088)(228,1087)(229,1086)(230,1085)(231,1084)(232,1083)(233,1082)(234,1081)(235,1080)(236,1079)(237,1078)(238,1077)(239,1076)(240,1075)(241,1074)(242,1073)(243,1072)(244,1071)(245,1070)(246,1069)(247,1068)(248,1067)(249,1066)(250,1065)(251,1064)(252,1063)(253,1062)(254,1061)(255,1060)(256,1059)(257,1058)(258,1057)(259,1056)(260,1055)(261,1054)(262,1053)(263,1052)(264,1051)(265,1050)(266,1049)(267,1048)(268,1047)(269,1046)(270,1045)(271,1044)(272,1043)(273,1042)(274,1041)(275,1040)(276,1039)(277,1038)(278,1037)(279,1036)(280,1035)(281,1034)(282,1033)(283,1032)(284,1031)(285,1030)(286,1029)(287,1028)(288,1027)(289,1026)(290,1025)(291,1024)(292,1023)(293,1022)(294,1021)(295,1020)(296,1019)(297,1018)(298,1017)(299,1016)(300,1015)(301,1014)(302,1013)(303,1012)(304,1011)(305,1010)(306,1009)(307,1008)(308,1007)(309,1006)(310,1005)(311,1004)(312,1003)(313,1002)(314,1001)(315,1000)(316,999)(317,998)(318,997)(319,996)(320,995)(321,994)(322,993)(323,992)(324,991)(325,990)(326,989)(327,988)(328,987)(329,986)(330,985)(331,984)(332,983)(333,982)(334,981)(335,980)(336,979)(337,978)(338,977)(339,976)(340,975)(341,974)(342,973)(343,972)(344,971)(345,970)(346,969)(347,968)(348,967)(349,966)(350,965)(351,964)(352,963)(353,962)(354,961)(355,960)(356,959)(357,958)(358,957)(359,956)(360,955)(361,954)(362,953)(363,952)(364,951)(365,950)(366,949)(367,948)(368,947)(369,946)(370,945)(371,944)(372,943)(373,942)(374,941)(375,940)(376,939)(377,938)(378,937)(379,936)(380,935)(381,934)(382,933)(383,932)(384,931)(385,930)(386,929)(387,928)(388,927)(389,926)(390,925)(391,924)(392,923)(393,922)(394,921)(395,920)(396,919)(397,918)(398,917)(399,916)(400,915)(401,914)(402,913)(403,912)(404,911)(405,910)(406,909)(407,908)(408,907)(409,906)(410,905)(411,904)(412,903)(413,902)(414,901)(415,900)(416,899)(417,898)(418,897)(419,896)(420,895)(421,894)(422,893)(423,892)(424,891)(425,890)(426,889)(427,888)(428,887)(429,886)(430,885)(431,884)(432,883)(433,882)(434,881)(435,880)(436,879)(437,878)(438,877)(439,876)(440,875)(441,874)(442,873)(443,872)(444,871)(445,870)(446,869)(447,868)(448,867)(449,866)(450,865)(451,864)(452,863)(453,862)(454,861)(455,860)(456,859)(457,858)(458,857)(459,856)(460,855)(461,854)(462,853)(463,852)(464,851)(465,850)(466,849)(467,848)(468,847)(469,846)(470,845)(471,844)(472,843)(473,842)(474,841)(475,840)(476,839)(477,838)(478,837)(479,836)(480,835)(481,834)(482,833)(483,832)(484,831)(485,830)(486,829)(487,828)(488,827)(489,826)(490,825)(491,824)(492,823)(493,822)(494,821)(495,820)(496,819)(497,818)(498,817)(499,816)(500,815)(501,814)(502,813)(503,812)(504,811)(505,810)(506,809)(507,808)(508,807)(509,806)(510,805)(511,804)(512,803)(513,802)(514,801)(515,800)(516,799)(517,798)(518,797)(519,796)(520,795)(521,794)(522,793)(523,792)(524,791)(525,790)(526,789)(527,788)(528,787)(529,786)(530,785)(531,784)(532,783)(533,782)(534,781)(535,780)(536,779)(537,778)(538,777)(539,776)(540,775)(541,774)(542,773)(543,772)(544,771)(545,770)(546,769)(547,768)(548,767)(549,766)(550,765)(551,764)(552,763)(553,762)(554,761)(555,760)(556,759)(557,758)(558,757)(559,756)(560,755)(561,754)(562,753)(563,752)(564,751)(565,750)(566,749)(567,748)(568,747)(569,746)(570,745)(571,744)(572,743)(573,742)(574,741)(575,740)(576,739)(577,738)(578,737)(579,736)(580,735)(581,734)(582,733)(583,732)(584,731)(585,730)(586,729)(587,728)(588,727)(589,726)(590,725)(591,724)(592,723)(593,722)(594,721)(595,720)(596,719)(597,718)(598,717)(599,716)(600,715)(601,714)(602,713)(603,712)(604,711)(605,710)(606,709)(607,708)(608,707)(609,706)(610,705)(611,704)(612,703)(613,702)(614,701)(615,700)(616,699)(617,698)(618,697)(619,696)(620,695)(621,694)(622,693)(623,692)(624,691)(625,690)(626,689)(627,688)(628,687)(629,686)(630,685)(631,684)(632,683)(633,682)(634,681)(635,680)(636,679)(637,678)(638,677)(639,676)(640,675)(641,674)(642,673)(643,672)(644,671)(645,670)(646,669)(647,668)(648,667)(649,666)(650,665)(651,664)(652,663)(653,662)(654,661)(655,660)(656,659)(657,658)Polycyclic presentation:
2,7,1291,2|a^2=d,b^a=b^6,c^a=c^12909040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36148, 4);