Finite Group Databasebeta

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Dic₈₇₄₄ #46854054

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1125 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18)(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);(1,17,9,25)(2,18,10,26)(3,19,11,27)(4,20,12,28)(5,21,13,29)(6,22,14,30)(7,23,15,31)(8,24,16,32)(34,1125)(35,1124)(36,1123)(37,1122)(38,1121)(39,1120)(40,1119)(41,1118)(42,1117)(43,1116)(44,1115)(45,1114)(46,1113)(47,1112)(48,1111)(49,1110)(50,1109)(51,1108)(52,1107)(53,1106)(54,1105)(55,1104)(56,1103)(57,1102)(58,1101)(59,1100)(60,1099)(61,1098)(62,1097)(63,1096)(64,1095)(65,1094)(66,1093)(67,1092)(68,1091)(69,1090)(70,1089)(71,1088)(72,1087)(73,1086)(74,1085)(75,1084)(76,1083)(77,1082)(78,1081)(79,1080)(80,1079)(81,1078)(82,1077)(83,1076)(84,1075)(85,1074)(86,1073)(87,1072)(88,1071)(89,1070)(90,1069)(91,1068)(92,1067)(93,1066)(94,1065)(95,1064)(96,1063)(97,1062)(98,1061)(99,1060)(100,1059)(101,1058)(102,1057)(103,1056)(104,1055)(105,1054)(106,1053)(107,1052)(108,1051)(109,1050)(110,1049)(111,1048)(112,1047)(113,1046)(114,1045)(115,1044)(116,1043)(117,1042)(118,1041)(119,1040)(120,1039)(121,1038)(122,1037)(123,1036)(124,1035)(125,1034)(126,1033)(127,1032)(128,1031)(129,1030)(130,1029)(131,1028)(132,1027)(133,1026)(134,1025)(135,1024)(136,1023)(137,1022)(138,1021)(139,1020)(140,1019)(141,1018)(142,1017)(143,1016)(144,1015)(145,1014)(146,1013)(147,1012)(148,1011)(149,1010)(150,1009)(151,1008)(152,1007)(153,1006)(154,1005)(155,1004)(156,1003)(157,1002)(158,1001)(159,1000)(160,999)(161,998)(162,997)(163,996)(164,995)(165,994)(166,993)(167,992)(168,991)(169,990)(170,989)(171,988)(172,987)(173,986)(174,985)(175,984)(176,983)(177,982)(178,981)(179,980)(180,979)(181,978)(182,977)(183,976)(184,975)(185,974)(186,973)(187,972)(188,971)(189,970)(190,969)(191,968)(192,967)(193,966)(194,965)(195,964)(196,963)(197,962)(198,961)(199,960)(200,959)(201,958)(202,957)(203,956)(204,955)(205,954)(206,953)(207,952)(208,951)(209,950)(210,949)(211,948)(212,947)(213,946)(214,945)(215,944)(216,943)(217,942)(218,941)(219,940)(220,939)(221,938)(222,937)(223,936)(224,935)(225,934)(226,933)(227,932)(228,931)(229,930)(230,929)(231,928)(232,927)(233,926)(234,925)(235,924)(236,923)(237,922)(238,921)(239,920)(240,919)(241,918)(242,917)(243,916)(244,915)(245,914)(246,913)(247,912)(248,911)(249,910)(250,909)(251,908)(252,907)(253,906)(254,905)(255,904)(256,903)(257,902)(258,901)(259,900)(260,899)(261,898)(262,897)(263,896)(264,895)(265,894)(266,893)(267,892)(268,891)(269,890)(270,889)(271,888)(272,887)(273,886)(274,885)(275,884)(276,883)(277,882)(278,881)(279,880)(280,879)(281,878)(282,877)(283,876)(284,875)(285,874)(286,873)(287,872)(288,871)(289,870)(290,869)(291,868)(292,867)(293,866)(294,865)(295,864)(296,863)(297,862)(298,861)(299,860)(300,859)(301,858)(302,857)(303,856)(304,855)(305,854)(306,853)(307,852)(308,851)(309,850)(310,849)(311,848)(312,847)(313,846)(314,845)(315,844)(316,843)(317,842)(318,841)(319,840)(320,839)(321,838)(322,837)(323,836)(324,835)(325,834)(326,833)(327,832)(328,831)(329,830)(330,829)(331,828)(332,827)(333,826)(334,825)(335,824)(336,823)(337,822)(338,821)(339,820)(340,819)(341,818)(342,817)(343,816)(344,815)(345,814)(346,813)(347,812)(348,811)(349,810)(350,809)(351,808)(352,807)(353,806)(354,805)(355,804)(356,803)(357,802)(358,801)(359,800)(360,799)(361,798)(362,797)(363,796)(364,795)(365,794)(366,793)(367,792)(368,791)(369,790)(370,789)(371,788)(372,787)(373,786)(374,785)(375,784)(376,783)(377,782)(378,781)(379,780)(380,779)(381,778)(382,777)(383,776)(384,775)(385,774)(386,773)(387,772)(388,771)(389,770)(390,769)(391,768)(392,767)(393,766)(394,765)(395,764)(396,763)(397,762)(398,761)(399,760)(400,759)(401,758)(402,757)(403,756)(404,755)(405,754)(406,753)(407,752)(408,751)(409,750)(410,749)(411,748)(412,747)(413,746)(414,745)(415,744)(416,743)(417,742)(418,741)(419,740)(420,739)(421,738)(422,737)(423,736)(424,735)(425,734)(426,733)(427,732)(428,731)(429,730)(430,729)(431,728)(432,727)(433,726)(434,725)(435,724)(436,723)(437,722)(438,721)(439,720)(440,719)(441,718)(442,717)(443,716)(444,715)(445,714)(446,713)(447,712)(448,711)(449,710)(450,709)(451,708)(452,707)(453,706)(454,705)(455,704)(456,703)(457,702)(458,701)(459,700)(460,699)(461,698)(462,697)(463,696)(464,695)(465,694)(466,693)(467,692)(468,691)(469,690)(470,689)(471,688)(472,687)(473,686)(474,685)(475,684)(476,683)(477,682)(478,681)(479,680)(480,679)(481,678)(482,677)(483,676)(484,675)(485,674)(486,673)(487,672)(488,671)(489,670)(490,669)(491,668)(492,667)(493,666)(494,665)(495,664)(496,663)(497,662)(498,661)(499,660)(500,659)(501,658)(502,657)(503,656)(504,655)(505,654)(506,653)(507,652)(508,651)(509,650)(510,649)(511,648)(512,647)(513,646)(514,645)(515,644)(516,643)(517,642)(518,641)(519,640)(520,639)(521,638)(522,637)(523,636)(524,635)(525,634)(526,633)(527,632)(528,631)(529,630)(530,629)(531,628)(532,627)(533,626)(534,625)(535,624)(536,623)(537,622)(538,621)(539,620)(540,619)(541,618)(542,617)(543,616)(544,615)(545,614)(546,613)(547,612)(548,611)(549,610)(550,609)(551,608)(552,607)(553,606)(554,605)(555,604)(556,603)(557,602)(558,601)(559,600)(560,599)(561,598)(562,597)(563,596)(564,595)(565,594)(566,593)(567,592)(568,591)(569,590)(570,589)(571,588)(572,587)(573,586)(574,585)(575,584)(576,583)(577,582)(578,581)(579,580)

Polycyclic presentation:

2^5,1093|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^1092,c^b=cd,d^b=de,f^b=f^1092

Conjugacy classes & character table

8747 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34976, 93);