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#27189812

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 425 points:

(1,2)(3,17)(4,6)(5,23)(7,9)(8,37)(10,11)(12,64)(13,15)(14,70)(16,18)(19,93)(20,22)(21,98)(24,112)(25,27)(26,55)(28,30)(29,121)(31,32)(33,66)(34,36)(35,147)(38,90)(39,41)(40,160)(42,44)(43,83)(45,47)(46,82)(48,49)(51,53)(52,192)(54,113)(56,58)(57,109)(59,81)(60,62)(61,133)(63,65)(67,69)(68,225)(71,231)(72,74)(73,111)(75,77)(76,161)(78,79)(80,207)(84,85)(86,217)(87,89)(88,209)(91,124)(92,153)(94,287)(95,97)(96,183)(99,202)(100,102)(101,159)(103,105)(104,173)(106,107)(108,206)(110,232)(114,175)(115,197)(116,152)(117,273)(118,120)(119,253)(122,174)(123,282)(125,127)(126,162)(128,130)(129,157)(131,132)(134,136)(135,199)(137,335)(138,140)(139,230)(141,142)(143,165)(144,146)(145,274)(148,354)(149,151)(150,201)(154,156)(155,366)(158,290)(163,164)(166,168)(167,377)(169,305)(170,172)(171,272)(176,178)(177,198)(179,270)(180,182)(181,296)(184,269)(185,187)(186,263)(188,200)(189,191)(190,317)(193,264)(194,196)(195,271)(203,205)(204,278)(208,308)(210,212)(211,310)(213,322)(214,216)(215,338)(218,220)(219,265)(221,399)(222,224)(223,292)(226,304)(227,228)(229,318)(233,286)(234,236)(235,385)(237,239)(238,331)(240,267)(241,243)(242,353)(244,246)(245,275)(247,248)(249,250)(251,378)(252,311)(254,256)(255,303)(257,404)(258,260)(259,332)(261,262)(266,268)(276,277)(279,281)(280,312)(283,284)(285,334)(288,386)(289,302)(291,309)(293,374)(294,295)(297,373)(298,390)(299,301)(300,365)(306,321)(307,313)(314,316)(315,405)(319,384)(320,358)(323,324)(325,364)(326,328)(327,389)(329,330)(333,356)(336,337)(339,341)(340,392)(342,344)(343,369)(345,401)(346,348)(347,387)(349,351)(350,376)(352,396)(355,379)(357,362)(359,398)(360,400)(361,363)(367,368)(370,372)(371,407)(375,380)(381,383)(382,406)(388,391)(393,397)(394,395)(402,403)(408,409);(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)(15,33,35,76,34,75,78,141)(17,38,40,18,39,43,84,42)(22,50,52,104,51,103,106,121)(27,59,61,116,60,36,70,80)(30,66,68,129,67,128,131,82)(32,71,73,135,72,134,55,110)(41,86,88,65,87,126,163,125)(44,91,92,173,69,64,122,123)(47,94,96,177,95,176,98,109)(49,99,101,184,100,112,83,158)(53,93,108,85,58,114,115,161)(62,117,119,208,118,168,147,252)(74,137,139,238,138,237,133,229)(77,143,145,239,144,247,249,157)(79,148,150,255,149,254,111,200)(81,153,155,102,154,186,264,185)(89,165,167,142,166,245,276,244)(90,169,171,113,170,204,160,203)(97,179,181,261,180,201,192,152)(105,188,190,236,189,294,225,198)(107,193,195,297,194,231,159,270)(120,209,211,172,210,280,207,279)(124,213,215,127,214,219,317,218)(130,221,223,220,222,323,183,199)(132,226,187,293,227,202,162,273)(136,233,235,274,234,175,285,164)(140,240,242,316,241,336,253,352)(146,217,251,320,205,306,307,282)(151,257,259,359,258,358,230,322)(156,265,267,228,266,301,367,329)(174,262,191,232,283,333,272,332)(178,288,289,354,271,287,197,269)(182,290,291,305,278,379,206,308)(196,298,300,390,299,335,263,364)(212,313,315,309,314,328,366,376)(216,318,319,246,312,343,284,342)(224,325,327,344,326,387,296,331)(243,338,340,321,339,372,310,393)(248,345,347,392,346,363,292,303)(250,337,350,402,349,304,275,375)(256,355,357,378,356,286,334,277)(260,360,362,403,361,405,353,341)(268,369,371,351,370,389,398,348)(281,380,382,311,381,383,377,394)(295,368,388,404,365,399,302,373)(324,400,330,401,391,386,385,374)(384,407,397,396,408,395,406,409)(410,411,412,415,413,416,418,421,414,417,419,422,420,423,424,425)

Polycyclic presentation:

2^5,409|a^2=c,c^2=d,d^2=e,f^a=f^31,f^b=f^408,f^c=f^143,f^d=f^408

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13088, 241);