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#27189784

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 421 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)(192,271)(193,194)(196,267)(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)(233,303)(234,235)(237,304)(238,239)(241,302)(242,243)(245,299)(246,247)(249,295)(250,251)(253,291)(254,255)(257,287)(258,259)(261,283)(262,263)(265,266)(268,272)(269,270)(274,330)(275,276)(277,331)(278,279)(280,329)(281,282)(284,326)(285,286)(288,322)(289,290)(292,318)(293,294)(296,314)(297,298)(300,301)(305,353)(306,307)(308,354)(309,310)(311,352)(312,313)(315,349)(316,317)(319,345)(320,321)(323,341)(324,325)(327,328)(332,372)(333,334)(335,373)(336,337)(338,371)(339,340)(342,368)(343,344)(346,364)(347,348)(350,351)(355,387)(356,357)(358,388)(359,360)(361,386)(362,363)(365,383)(366,367)(369,370)(374,398)(375,376)(377,399)(378,379)(380,397)(381,382)(384,385)(389,405)(390,391)(392,406)(393,394)(395,396)(400,409)(401,402)(403,404)(407,408)(410,411,412,413);(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)(194,233,234,270)(198,237,238,271)(202,241,242,267)(206,245,246,264)(210,249,250,260)(214,253,254,256)(218,257,258,252)(222,261,262,248)(226,235,265,244)(230,268,269,240)(232,272,273,236)(239,274,275,303)(243,277,278,304)(247,280,281,302)(251,284,285,299)(255,288,289,295)(259,292,293,291)(263,296,297,287)(266,276,300,283)(279,305,306,330)(282,308,309,331)(286,311,312,329)(290,315,316,326)(294,319,320,322)(298,323,324,318)(301,307,327,314)(310,332,333,353)(313,335,336,354)(317,338,339,352)(321,342,343,349)(325,346,347,345)(328,334,350,341)(337,355,356,372)(340,358,359,373)(344,361,362,371)(348,365,366,368)(351,357,369,364)(360,374,375,387)(363,377,378,388)(367,380,381,386)(370,376,384,383)(379,389,390,398)(382,392,393,399)(385,391,395,397)(394,400,401,405)(396,402,403,406)(404,407,408,409)(411,413)(414,415,416,418,417,419,420,421)

Polycyclic presentation:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13088, 213);