Finite Group Databasebeta

?

← Prev (#153592) Next (#153594) →

#153593

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Subgroups

114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 132 points:

(1,2,4,3)(5,6)(7,19)(8,25)(9,32)(10,37)(11,41)(12,14)(13,20)(15,28)(16,27)(17,34)(18,39)(21,65)(22,69)(23,72)(24,58)(26,53)(29,85)(30,89)(31,57)(33,50)(35,97)(36,91)(38,59)(40,99)(42,60)(43,64)(44,77)(45,76)(46,102)(47,61)(48,66)(49,70)(51,111)(52,113)(54,117)(55,62)(56,63)(67,128)(68,127)(71,129)(73,80)(74,83)(75,87)(78,118)(79,108)(81,93)(82,92)(84,101)(86,115)(88,122)(90,116)(94,112)(95,114)(96,106)(98,110)(100,121)(103,131)(104,130)(105,132)(107,125)(109,126)(119,124)(120,123);(5,7,12,24)(6,13,14,43)(8,26,31,79)(9,33,36,96)(10,38,40,100)(11,42,39,23)(15,50,47,106)(16,53,48,108)(17,55,49,109)(18,56,41,46)(19,57,58,25)(20,61,64,28)(21,66,68,27)(22,70,71,34)(29,86,88,132)(30,90,87,78)(32,44,91,103)(35,98,81,95)(37,45,99,104)(51,112,107,128)(52,114,101,110)(54,118,92,116)(59,122,121,85)(60,75,72,89)(62,125,126,111)(63,84,102,113)(65,119,127,73)(67,82,94,117)(69,120,129,74)(76,124,130,80)(77,123,131,83)(93,115,97,105);(1,3,4,2)(6,14)(13,43)(15,47)(16,48)(17,49)(18,41)(19,58)(25,57)(32,91)(37,99)(44,103)(45,104)(46,56)(50,106)(51,107)(52,101)(53,108)(54,92)(55,109)(59,121)(60,72)(65,127)(69,129)(73,119)(74,120)(75,89)(85,122)(93,97)(105,115)(110,114)(112,128)(116,118)

Polycyclic presentation:

2^9|a^2=e,b^2=i,c^2=e,d^2=fg,f^2=gh,g^2=hi,h^2=i,b^a=bd,c^a=ci,d^a=df,f^a=fg,g^a=gh,h^a=hi,d^b=df,f^b=fg,g^b=gh,h^b=hi

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 60789);