Finite Group DatabasebetaFinite Group Databasebeta| order | 33628 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8407 |
| unambiguous semidirect product | C7⋊Dic1201 |
| derived, Hall | C7×C1201 ⋊ C4 |
| Sylow | C1201 ⋊ Dic7 |
| Sylow | C7 ⋊ Dic1201 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8407 |
| commutator, hypocenter | C7×C1201 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C7×C1201 | C2 |
| LCS | G ▷ C7×C1201 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1212 |
| transitive degree | μt(G) = 33628 |
A minimal faithful permutation representation — 2 generators on 1212 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);(1,3,2,4)(6,11)(7,10)(8,9)(13,1212)(14,1211)(15,1210)(16,1209)(17,1208)(18,1207)(19,1206)(20,1205)(21,1204)(22,1203)(23,1202)(24,1201)(25,1200)(26,1199)(27,1198)(28,1197)(29,1196)(30,1195)(31,1194)(32,1193)(33,1192)(34,1191)(35,1190)(36,1189)(37,1188)(38,1187)(39,1186)(40,1185)(41,1184)(42,1183)(43,1182)(44,1181)(45,1180)(46,1179)(47,1178)(48,1177)(49,1176)(50,1175)(51,1174)(52,1173)(53,1172)(54,1171)(55,1170)(56,1169)(57,1168)(58,1167)(59,1166)(60,1165)(61,1164)(62,1163)(63,1162)(64,1161)(65,1160)(66,1159)(67,1158)(68,1157)(69,1156)(70,1155)(71,1154)(72,1153)(73,1152)(74,1151)(75,1150)(76,1149)(77,1148)(78,1147)(79,1146)(80,1145)(81,1144)(82,1143)(83,1142)(84,1141)(85,1140)(86,1139)(87,1138)(88,1137)(89,1136)(90,1135)(91,1134)(92,1133)(93,1132)(94,1131)(95,1130)(96,1129)(97,1128)(98,1127)(99,1126)(100,1125)(101,1124)(102,1123)(103,1122)(104,1121)(105,1120)(106,1119)(107,1118)(108,1117)(109,1116)(110,1115)(111,1114)(112,1113)(113,1112)(114,1111)(115,1110)(116,1109)(117,1108)(118,1107)(119,1106)(120,1105)(121,1104)(122,1103)(123,1102)(124,1101)(125,1100)(126,1099)(127,1098)(128,1097)(129,1096)(130,1095)(131,1094)(132,1093)(133,1092)(134,1091)(135,1090)(136,1089)(137,1088)(138,1087)(139,1086)(140,1085)(141,1084)(142,1083)(143,1082)(144,1081)(145,1080)(146,1079)(147,1078)(148,1077)(149,1076)(150,1075)(151,1074)(152,1073)(153,1072)(154,1071)(155,1070)(156,1069)(157,1068)(158,1067)(159,1066)(160,1065)(161,1064)(162,1063)(163,1062)(164,1061)(165,1060)(166,1059)(167,1058)(168,1057)(169,1056)(170,1055)(171,1054)(172,1053)(173,1052)(174,1051)(175,1050)(176,1049)(177,1048)(178,1047)(179,1046)(180,1045)(181,1044)(182,1043)(183,1042)(184,1041)(185,1040)(186,1039)(187,1038)(188,1037)(189,1036)(190,1035)(191,1034)(192,1033)(193,1032)(194,1031)(195,1030)(196,1029)(197,1028)(198,1027)(199,1026)(200,1025)(201,1024)(202,1023)(203,1022)(204,1021)(205,1020)(206,1019)(207,1018)(208,1017)(209,1016)(210,1015)(211,1014)(212,1013)(213,1012)(214,1011)(215,1010)(216,1009)(217,1008)(218,1007)(219,1006)(220,1005)(221,1004)(222,1003)(223,1002)(224,1001)(225,1000)(226,999)(227,998)(228,997)(229,996)(230,995)(231,994)(232,993)(233,992)(234,991)(235,990)(236,989)(237,988)(238,987)(239,986)(240,985)(241,984)(242,983)(243,982)(244,981)(245,980)(246,979)(247,978)(248,977)(249,976)(250,975)(251,974)(252,973)(253,972)(254,971)(255,970)(256,969)(257,968)(258,967)(259,966)(260,965)(261,964)(262,963)(263,962)(264,961)(265,960)(266,959)(267,958)(268,957)(269,956)(270,955)(271,954)(272,953)(273,952)(274,951)(275,950)(276,949)(277,948)(278,947)(279,946)(280,945)(281,944)(282,943)(283,942)(284,941)(285,940)(286,939)(287,938)(288,937)(289,936)(290,935)(291,934)(292,933)(293,932)(294,931)(295,930)(296,929)(297,928)(298,927)(299,926)(300,925)(301,924)(302,923)(303,922)(304,921)(305,920)(306,919)(307,918)(308,917)(309,916)(310,915)(311,914)(312,913)(313,912)(314,911)(315,910)(316,909)(317,908)(318,907)(319,906)(320,905)(321,904)(322,903)(323,902)(324,901)(325,900)(326,899)(327,898)(328,897)(329,896)(330,895)(331,894)(332,893)(333,892)(334,891)(335,890)(336,889)(337,888)(338,887)(339,886)(340,885)(341,884)(342,883)(343,882)(344,881)(345,880)(346,879)(347,878)(348,877)(349,876)(350,875)(351,874)(352,873)(353,872)(354,871)(355,870)(356,869)(357,868)(358,867)(359,866)(360,865)(361,864)(362,863)(363,862)(364,861)(365,860)(366,859)(367,858)(368,857)(369,856)(370,855)(371,854)(372,853)(373,852)(374,851)(375,850)(376,849)(377,848)(378,847)(379,846)(380,845)(381,844)(382,843)(383,842)(384,841)(385,840)(386,839)(387,838)(388,837)(389,836)(390,835)(391,834)(392,833)(393,832)(394,831)(395,830)(396,829)(397,828)(398,827)(399,826)(400,825)(401,824)(402,823)(403,822)(404,821)(405,820)(406,819)(407,818)(408,817)(409,816)(410,815)(411,814)(412,813)(413,812)(414,811)(415,810)(416,809)(417,808)(418,807)(419,806)(420,805)(421,804)(422,803)(423,802)(424,801)(425,800)(426,799)(427,798)(428,797)(429,796)(430,795)(431,794)(432,793)(433,792)(434,791)(435,790)(436,789)(437,788)(438,787)(439,786)(440,785)(441,784)(442,783)(443,782)(444,781)(445,780)(446,779)(447,778)(448,777)(449,776)(450,775)(451,774)(452,773)(453,772)(454,771)(455,770)(456,769)(457,768)(458,767)(459,766)(460,765)(461,764)(462,763)(463,762)(464,761)(465,760)(466,759)(467,758)(468,757)(469,756)(470,755)(471,754)(472,753)(473,752)(474,751)(475,750)(476,749)(477,748)(478,747)(479,746)(480,745)(481,744)(482,743)(483,742)(484,741)(485,740)(486,739)(487,738)(488,737)(489,736)(490,735)(491,734)(492,733)(493,732)(494,731)(495,730)(496,729)(497,728)(498,727)(499,726)(500,725)(501,724)(502,723)(503,722)(504,721)(505,720)(506,719)(507,718)(508,717)(509,716)(510,715)(511,714)(512,713)(513,712)(514,711)(515,710)(516,709)(517,708)(518,707)(519,706)(520,705)(521,704)(522,703)(523,702)(524,701)(525,700)(526,699)(527,698)(528,697)(529,696)(530,695)(531,694)(532,693)(533,692)(534,691)(535,690)(536,689)(537,688)(538,687)(539,686)(540,685)(541,684)(542,683)(543,682)(544,681)(545,680)(546,679)(547,678)(548,677)(549,676)(550,675)(551,674)(552,673)(553,672)(554,671)(555,670)(556,669)(557,668)(558,667)(559,666)(560,665)(561,664)(562,663)(563,662)(564,661)(565,660)(566,659)(567,658)(568,657)(569,656)(570,655)(571,654)(572,653)(573,652)(574,651)(575,650)(576,649)(577,648)(578,647)(579,646)(580,645)(581,644)(582,643)(583,642)(584,641)(585,640)(586,639)(587,638)(588,637)(589,636)(590,635)(591,634)(592,633)(593,632)(594,631)(595,630)(596,629)(597,628)(598,627)(599,626)(600,625)(601,624)(602,623)(603,622)(604,621)(605,620)(606,619)(607,618)(608,617)(609,616)(610,615)(611,614)(612,613)Polycyclic presentation:
2,7,1201,2|a^2=d,b^a=b^6,c^a=c^12008410 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33628, 4);