Finite Group Databasebeta

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#27165812

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

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)(3,11)(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)(192,265)(193,194)(196,262)(197,198)(200,258)(201,202)(204,254)(205,206)(208,250)(209,210)(212,246)(213,214)(216,242)(217,218)(220,238)(221,222)(224,234)(225,226)(228,229)(231,296)(232,233)(235,293)(236,237)(239,289)(240,241)(243,285)(244,245)(247,281)(248,249)(251,277)(252,253)(255,273)(256,257)(259,269)(260,261)(263,264)(266,323)(267,268)(270,320)(271,272)(274,316)(275,276)(278,312)(279,280)(282,308)(283,284)(286,304)(287,288)(290,300)(291,292)(294,295)(297,346)(298,299)(301,343)(302,303)(305,339)(306,307)(309,335)(310,311)(313,331)(314,315)(317,327)(318,319)(321,322)(324,365)(325,326)(328,362)(329,330)(332,358)(333,334)(336,354)(337,338)(340,350)(341,342)(344,345)(347,380)(348,349)(351,377)(352,353)(355,373)(356,357)(359,369)(360,361)(363,364)(366,391)(367,368)(370,388)(371,372)(374,384)(375,376)(378,379)(381,398)(382,383)(385,395)(386,387)(389,390)(392,401)(393,394)(396,397)(399,400)(403,407)(408,413)(409,414)(415,417);(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)(157,192,193,230)(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)(191,194,228,195)(198,231,232,265)(202,235,236,262)(206,239,240,258)(210,243,244,254)(214,247,248,250)(218,251,252,246)(222,255,256,242)(226,259,260,238)(229,233,263,234)(237,266,267,296)(241,270,271,293)(245,274,275,289)(249,278,279,285)(253,282,283,281)(257,286,287,277)(261,290,291,273)(264,268,294,269)(272,297,298,323)(276,301,302,320)(280,305,306,316)(284,309,310,312)(288,313,314,308)(292,317,318,304)(295,299,321,300)(303,324,325,346)(307,328,329,343)(311,332,333,339)(315,336,337,335)(319,340,341,331)(322,326,344,327)(330,347,348,365)(334,351,352,362)(338,355,356,358)(342,359,360,354)(345,349,363,350)(353,366,367,380)(357,370,371,377)(361,374,375,373)(364,368,378,369)(372,381,382,391)(376,385,386,388)(379,383,389,384)(387,392,393,398)(390,394,396,395)(397,399,400,401)(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^20,f^b=f^400,f^c=f^400

Conjugacy classes & character table

820 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12832, 221);