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#27163153

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 409 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)(233,318)(234,235)(237,316)(238,239)(241,312)(242,243)(245,308)(246,247)(249,304)(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)(278,338)(279,280)(282,342)(283,284)(286,341)(287,288)(290,340)(291,292)(294,339)(295,296)(298,337)(299,300)(302,303)(305,319)(306,307)(309,317)(310,311)(314,315)(320,357)(321,322)(323,361)(324,325)(326,360)(327,328)(329,359)(330,331)(332,358)(333,334)(335,336)(343,373)(344,345)(346,376)(347,348)(349,375)(350,351)(352,374)(353,354)(355,356)(362,385)(363,364)(365,387)(366,367)(368,386)(369,370)(371,372)(377,393)(378,379)(380,394)(381,382)(383,384)(388,397)(389,390)(391,392)(395,396)(399,401);(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)(235,278,279,307)(239,282,283,318)(243,286,287,316)(247,290,291,312)(251,294,295,308)(255,298,299,304)(259,280,302,301)(263,305,306,297)(267,309,310,293)(271,313,314,289)(275,317,315,285)(277,319,311,281)(284,320,321,338)(288,323,324,342)(292,326,327,341)(296,329,330,340)(300,332,333,339)(303,322,335,337)(325,343,344,357)(328,346,347,361)(331,349,350,360)(334,352,353,359)(336,345,355,358)(348,362,363,373)(351,365,366,376)(354,368,369,375)(356,364,371,374)(367,377,378,385)(370,380,381,387)(372,379,383,386)(382,388,389,393)(384,390,391,394)(392,395,396,397)(398,399)(400,401)(402,403,404,406,405,407,408,409)

Polycyclic presentation:

2^5,397|a^2=d,d^2=e,b^a=bc,f^a=f^334,f^b=f^396,f^d=f^396

Conjugacy classes & character table

812 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12704, 203);