Finite Group Databasebeta

?

← Prev (#7623438) Next (#7623440) →

#7623439

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

Aliases

No aliases for this group.

Subgroups

1198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 80 points:

(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18,23,29)(19,24,30,45)(20,26,34,50)(21,25,39,49)(22,40,38,28)(27,53,48,37)(31,42,54,67)(32,46,55,41)(33,61,56,44)(35,47,62,72)(36,65,63,52)(43,59,70,60)(51,74,73,64)(57,71,75,66)(58,79,76,69)(68,77,80,78);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14)(17,19)(18,24)(20,31)(21,32)(22,33)(23,30)(25,46)(26,42)(27,43)(28,44)(29,45)(34,54)(35,57)(36,58)(37,60)(38,56)(39,55)(40,61)(41,49)(47,71)(48,70)(50,67)(51,68)(52,69)(53,59)(62,75)(63,76)(64,78)(65,79)(66,72)(73,80)(74,77);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(18,25)(19,30)(21,37)(22,38)(24,41)(26,47)(27,28)(29,49)(31,54)(32,59)(35,64)(36,63)(39,53)(40,48)(42,66)(43,61)(44,70)(45,46)(50,72)(51,52)(55,60)(57,77)(62,74)(65,73)(67,71)(68,79)(69,80)(75,78);(2,8)(6,9)(7,16)(14,15)(17,20)(18,26)(19,31)(21,35)(22,36)(23,34)(24,42)(25,47)(27,51)(28,52)(29,50)(30,54)(32,57)(33,58)(37,64)(38,63)(39,62)(40,65)(41,66)(43,68)(44,69)(45,67)(46,71)(48,73)(49,72)(53,74)(55,75)(56,76)(59,77)(60,78)(61,79)(70,80);(20,34)(26,50)(31,54)(35,62)(36,63)(42,67)(47,72)(51,73)(52,65)(57,75)(58,76)(64,74)(66,71)(68,80)(69,79)(77,78)

Polycyclic presentation:

2^9|a^2=i,b^2=f,c^2=f,g^2=hi,h^2=i,b^a=bf,c^a=cg,d^a=df,g^a=gh,h^a=hi,c^b=cfi,g^c=gh,h^c=hi,e^d=ei

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530635);