Finite Group Databasebeta

?

← Prev (#45683076) Next (#45683078) →

Dic₈₂₆₄ #45683077

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

Polycyclic presentation:

2^5,1033|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^1032,c^b=cd,d^b=de,f^b=f^1032

Conjugacy classes & character table

8267 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33056, 93);