Finite Group Databasebeta

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#27165834

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

Aliases

No aliases for this group.

Splittings

Subgroups

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 417 points:

(1,2)(3,17)(4,6)(5,23)(7,9)(8,37)(10,11)(12,64)(13,15)(14,70)(16,18)(19,97)(20,22)(21,102)(24,119)(25,27)(26,55)(28,30)(29,132)(31,32)(33,155)(34,36)(35,161)(38,92)(39,41)(40,175)(42,44)(43,85)(45,47)(46,84)(48,49)(50,203)(51,53)(52,208)(54,120)(56,58)(57,116)(59,234)(60,62)(61,148)(63,65)(66,251)(67,69)(68,256)(71,271)(72,74)(73,118)(75,77)(76,277)(78,79)(80,284)(81,83)(82,183)(86,87)(88,247)(89,91)(90,130)(93,134)(94,96)(95,171)(98,313)(99,101)(100,197)(103,226)(104,106)(105,174)(107,109)(108,243)(110,111)(112,332)(113,115)(114,333)(117,272)(121,190)(122,124)(123,311)(125,127)(126,269)(128,353)(129,131)(133,305)(135,137)(136,178)(138,140)(139,172)(141,142)(143,365)(144,146)(145,367)(147,235)(149,151)(150,223)(152,254)(153,270)(154,156)(157,380)(158,160)(159,245)(162,273)(163,165)(164,225)(166,168)(167,371)(169,170)(173,321)(176,177)(179,180)(181,276)(182,337)(184,244)(185,280)(186,188)(187,377)(189,230)(191,193)(192,222)(194,262)(195,196)(198,296)(199,206)(200,202)(201,294)(204,364)(205,207)(209,314)(210,212)(211,274)(213,215)(214,231)(216,217)(218,360)(219,221)(220,358)(224,370)(227,229)(228,304)(232,233)(236,362)(237,239)(238,400)(240,242)(241,347)(246,319)(248,250)(249,326)(252,257)(253,255)(258,260)(259,301)(261,263)(264,265)(266,357)(267,268)(275,281)(278,291)(279,389)(282,295)(283,369)(285,342)(286,288)(287,335)(289,381)(290,292)(293,366)(297,382)(298,299)(300,324)(302,303)(306,378)(307,336)(308,310)(309,388)(312,372)(315,316)(317,398)(318,320)(322,383)(323,325)(327,401)(328,330)(329,355)(331,363)(338,340)(339,354)(341,343)(344,394)(345,346)(348,349)(350,399)(351,352)(356,359)(361,384)(368,375)(373,385)(374,376)(379,390)(386,387)(391,392)(393,395)(396,397)(403,407)(408,413)(409,414)(415,417);(2,3,5,8,4,7,10,16)(6,12,14,29,13,28,31,63)(9,19,21,46,20,45,48,37)(11,24,26,57,25,56,23,54)(15,33,35,76,34,75,78,154)(17,38,40,18,39,43,86,42)(22,50,52,108,51,107,110,132)(27,59,61,126,60,125,70,147)(30,66,68,139,67,138,141,84)(32,71,73,150,72,149,55,117)(36,80,82,167,81,166,169,272)(41,88,90,65,89,136,179,135)(44,93,95,184,94,64,83,133)(47,98,100,192,99,191,102,116)(49,103,105,198,104,119,85,173)(53,112,114,214,113,213,216,277)(58,121,123,176,122,97,189,87)(62,128,130,241,129,240,161,235)(69,143,145,262,144,261,264,243)(74,152,153,275,91,181,148,156)(77,157,159,282,158,281,255,172)(79,162,164,270,163,165,118,224)(92,182,183,120,131,228,175,227)(96,185,187,306,186,155,278,279)(101,194,160,283,195,315,208,269)(106,199,201,263,200,234,171,293)(109,204,206,326,205,260,256,222)(111,209,211,331,210,271,174,297)(115,218,220,335,219,334,336,371)(124,231,146,266,232,203,267,244)(127,236,238,298,237,251,348,177)(134,221,246,137,245,249,215,248)(140,252,254,294,253,212,197,223)(142,257,259,363,258,226,178,300)(151,273,274,302,217,190,312,180)(168,285,287,268,286,368,382,295)(170,289,291,385,290,370,225,292)(188,307,309,390,308,284,381,372)(193,314,301,386,265,313,311,296)(196,317,319,394,318,393,333,347)(202,322,324,396,323,353,377,349)(207,327,329,398,328,397,367,369)(229,320,339,305,338,247,310,358)(230,325,342,321,341,337,304,388)(233,344,330,399,345,332,376,378)(239,350,352,401,351,365,392,357)(242,354,356,343,355,380,366,299)(250,359,361,395,360,280,379,346)(276,373,375,340,374,362,389,303)(288,383,384,391,364,400,387,316)(402,403,404,408,405,409,410,415,406,407,411,413,412,414,416,417)

Polycyclic presentation:

2^5,401|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^45,f^b=f^400,f^c=f^20,f^d=f^400

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12832, 243);