Finite Group Databasebeta

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#27210683

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

Aliases

No aliases for this group.

Splittings

Subgroups

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 837 points:

(1,2)(3,11)(4,5)(6,7)(8,24)(9,10)(12,20)(13,14)(15,16)(17,41)(18,19)(21,37)(22,23)(25,33)(26,27)(28,29)(30,62)(31,32)(34,58)(35,36)(38,54)(39,40)(42,50)(43,44)(45,46)(47,87)(48,49)(51,83)(52,53)(55,79)(56,57)(59,75)(60,61)(63,71)(64,65)(66,67)(68,116)(69,70)(72,112)(73,74)(76,108)(77,78)(80,104)(81,82)(84,100)(85,86)(88,96)(89,90)(91,92)(93,149)(94,95)(97,145)(98,99)(101,141)(102,103)(105,137)(106,107)(109,133)(110,111)(113,129)(114,115)(117,125)(118,119)(120,121)(122,186)(123,124)(126,182)(127,128)(130,178)(131,132)(134,174)(135,136)(138,170)(139,140)(142,166)(143,144)(146,162)(147,148)(150,158)(151,152)(153,154)(155,227)(156,157)(159,223)(160,161)(163,219)(164,165)(167,215)(168,169)(171,211)(172,173)(175,207)(176,177)(179,203)(180,181)(183,199)(184,185)(187,195)(188,189)(190,191)(192,272)(193,194)(196,268)(197,198)(200,264)(201,202)(204,260)(205,206)(208,256)(209,210)(212,252)(213,214)(216,248)(217,218)(220,244)(221,222)(224,240)(225,226)(228,236)(229,230)(231,232)(233,321)(234,235)(237,317)(238,239)(241,313)(242,243)(245,309)(246,247)(249,305)(250,251)(253,301)(254,255)(257,297)(258,259)(261,293)(262,263)(265,289)(266,267)(269,285)(270,271)(273,281)(274,275)(276,277)(278,374)(279,280)(282,370)(283,284)(286,366)(287,288)(290,362)(291,292)(294,358)(295,296)(298,354)(299,300)(302,350)(303,304)(306,346)(307,308)(310,342)(311,312)(314,338)(315,316)(318,334)(319,320)(322,330)(323,324)(325,326)(327,431)(328,329)(331,427)(332,333)(335,423)(336,337)(339,419)(340,341)(343,415)(344,345)(347,411)(348,349)(351,407)(352,353)(355,403)(356,357)(359,399)(360,361)(363,395)(364,365)(367,391)(368,369)(371,387)(372,373)(375,383)(376,377)(378,379)(380,492)(381,382)(384,488)(385,386)(388,484)(389,390)(392,480)(393,394)(396,476)(397,398)(400,472)(401,402)(404,468)(405,406)(408,464)(409,410)(412,460)(413,414)(416,456)(417,418)(420,452)(421,422)(424,448)(425,426)(428,444)(429,430)(432,440)(433,434)(435,436)(437,557)(438,439)(441,553)(442,443)(445,549)(446,447)(449,545)(450,451)(453,541)(454,455)(457,537)(458,459)(461,533)(462,463)(465,529)(466,467)(469,525)(470,471)(473,521)(474,475)(477,517)(478,479)(481,513)(482,483)(485,509)(486,487)(489,505)(490,491)(493,501)(494,495)(496,497)(498,626)(499,500)(502,622)(503,504)(506,618)(507,508)(510,614)(511,512)(514,610)(515,516)(518,606)(519,520)(522,602)(523,524)(526,598)(527,528)(530,594)(531,532)(534,590)(535,536)(538,586)(539,540)(542,582)(543,544)(546,578)(547,548)(550,574)(551,552)(554,570)(555,556)(558,566)(559,560)(561,562)(563,692)(564,565)(567,690)(568,569)(571,688)(572,573)(575,686)(576,577)(579,682)(580,581)(583,678)(584,585)(587,674)(588,589)(591,670)(592,593)(595,666)(596,597)(599,663)(600,601)(603,659)(604,605)(607,655)(608,609)(611,651)(612,613)(615,647)(616,617)(619,643)(620,621)(623,639)(624,625)(627,635)(628,629)(630,631)(632,717)(633,634)(636,724)(637,638)(640,723)(641,642)(644,722)(645,646)(648,721)(649,650)(652,720)(653,654)(656,719)(657,658)(660,718)(661,662)(664,665)(667,693)(668,669)(671,691)(672,673)(675,689)(676,677)(679,687)(680,681)(684,685)(694,745)(695,696)(697,751)(698,699)(700,750)(701,702)(703,749)(704,705)(706,748)(707,708)(709,747)(710,711)(712,746)(713,714)(715,716)(725,769)(726,727)(728,774)(729,730)(731,773)(732,733)(734,772)(735,736)(737,771)(738,739)(740,770)(741,742)(743,744)(752,789)(753,754)(755,793)(756,757)(758,792)(759,760)(761,791)(762,763)(764,790)(765,766)(767,768)(775,805)(776,777)(778,808)(779,780)(781,807)(782,783)(784,806)(785,786)(787,788)(794,817)(795,796)(797,819)(798,799)(800,818)(801,802)(803,804)(809,825)(810,811)(812,826)(813,814)(815,816)(820,829)(821,822)(823,824)(827,828)(831,834)(835,837);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,153)(99,126,127,149)(103,130,131,145)(107,134,135,141)(111,138,139,137)(115,142,143,133)(119,146,147,129)(121,150,151,125)(124,155,156,190)(128,159,160,186)(132,163,164,182)(136,167,168,178)(140,171,172,174)(144,175,176,170)(148,179,180,166)(152,183,184,162)(154,187,188,158)(157,192,193,231)(161,196,197,227)(165,200,201,223)(169,204,205,219)(173,208,209,215)(177,212,213,211)(181,216,217,207)(185,220,221,203)(189,224,225,199)(191,228,229,195)(194,233,234,276)(198,237,238,272)(202,241,242,268)(206,245,246,264)(210,249,250,260)(214,253,254,256)(218,257,258,252)(222,261,262,248)(226,265,266,244)(230,269,270,240)(232,273,274,236)(235,278,279,325)(239,282,283,321)(243,286,287,317)(247,290,291,313)(251,294,295,309)(255,298,299,305)(259,302,303,301)(263,306,307,297)(267,310,311,293)(271,314,315,289)(275,318,319,285)(277,322,323,281)(280,327,328,378)(284,331,332,374)(288,335,336,370)(292,339,340,366)(296,343,344,362)(300,347,348,358)(304,351,352,354)(308,355,356,350)(312,359,360,346)(316,363,364,342)(320,367,368,338)(324,371,372,334)(326,375,376,330)(329,380,381,435)(333,384,385,431)(337,388,389,427)(341,392,393,423)(345,396,397,419)(349,400,401,415)(353,404,405,411)(357,408,409,407)(361,412,413,403)(365,416,417,399)(369,420,421,395)(373,424,425,391)(377,428,429,387)(379,432,433,383)(382,437,438,496)(386,441,442,492)(390,445,446,488)(394,449,450,484)(398,453,454,480)(402,457,458,476)(406,461,462,472)(410,465,466,468)(414,469,470,464)(418,473,474,460)(422,477,478,456)(426,481,482,452)(430,485,486,448)(434,489,490,444)(436,493,494,440)(439,498,499,561)(443,502,503,557)(447,506,507,553)(451,510,511,549)(455,514,515,545)(459,518,519,541)(463,522,523,537)(467,526,527,533)(471,530,531,529)(475,534,535,525)(479,538,539,521)(483,542,543,517)(487,546,547,513)(491,550,551,509)(495,554,555,505)(497,558,559,501)(500,563,564,630)(504,567,568,626)(508,571,572,622)(512,575,576,618)(516,579,580,614)(520,583,584,610)(524,587,588,606)(528,591,592,602)(532,595,596,598)(536,599,600,594)(540,603,604,590)(544,607,608,586)(548,611,612,582)(552,615,616,578)(556,619,620,574)(560,623,624,570)(562,627,628,566)(565,632,633,669)(569,636,637,692)(573,640,641,690)(577,644,645,688)(581,648,649,686)(585,652,653,682)(589,656,657,678)(593,660,661,674)(597,634,664,670)(601,667,668,666)(605,671,672,663)(609,675,676,659)(613,679,680,655)(617,683,684,651)(621,687,685,647)(625,689,681,643)(629,691,677,639)(631,693,673,635)(638,694,695,717)(642,697,698,724)(646,700,701,723)(650,703,704,722)(654,706,707,721)(658,709,710,720)(662,712,713,719)(665,696,715,718)(699,725,726,745)(702,728,729,751)(705,731,732,750)(708,734,735,749)(711,737,738,748)(714,740,741,747)(716,727,743,746)(730,752,753,769)(733,755,756,774)(736,758,759,773)(739,761,762,772)(742,764,765,771)(744,754,767,770)(757,775,776,789)(760,778,779,793)(763,781,782,792)(766,784,785,791)(768,777,787,790)(780,794,795,805)(783,797,798,808)(786,800,801,807)(788,796,803,806)(799,809,810,817)(802,812,813,819)(804,811,815,818)(814,820,821,825)(816,822,823,826)(824,827,828,829)(830,831,832,835,833,834,836,837)

Polycyclic presentation:

2^4,829|a^2=c,c^2=d,b^a=bd,e^a=e^583,e^b=e^828,e^c=e^828

Conjugacy classes & character table

838 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13264, 50);