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#7624331

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

Aliases

No aliases for this group.

Subgroups

1222 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)(19,25)(20,27)(21,28)(22,41)(23,45)(24,30)(26,36)(29,43)(31,47)(32,48)(33,64)(34,51)(35,55)(37,57)(38,50)(39,56)(40,58)(42,52)(44,70)(46,60)(49,63)(53,69)(54,67)(59,73)(61,76)(62,75)(65,74)(66,77)(68,78)(71,79)(72,80);(1,3)(2,6)(4,10)(5,11)(7,13)(8,9)(12,16)(14,15)(17,19,24,34)(18,25,30,51)(20,31,37,62)(21,38,23,32)(22,33,44,66)(26,46,54,72)(27,47,57,75)(28,50,45,48)(29,49,58,78)(35,61,39,59)(36,60,67,80)(40,68,43,63)(41,64,70,77)(42,65,69,79)(52,74,53,71)(55,76,56,73);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)(17,20)(18,26)(19,31)(21,35)(22,42)(23,39)(24,37)(25,46)(27,41)(28,52)(29,56)(30,54)(32,59)(33,65)(34,62)(36,43)(38,61)(40,67)(44,69)(45,53)(47,64)(48,71)(49,73)(50,74)(51,72)(55,58)(57,70)(60,63)(66,79)(68,80)(75,77)(76,78);(3,11)(6,9)(10,16)(13,15)(17,20)(18,27)(19,31)(21,39)(22,36)(23,35)(24,37)(25,47)(26,41)(28,56)(29,52)(30,57)(32,61)(33,60)(34,62)(38,59)(40,69)(42,43)(44,67)(45,55)(46,64)(48,76)(49,74)(50,73)(51,75)(53,58)(54,70)(63,65)(66,80)(68,79)(71,78)(72,77);(2,8)(6,9)(7,14)(13,15)(17,21,24,23)(18,28,30,45)(19,32,34,38)(20,35,37,39)(22,40,44,43)(25,48,51,50)(26,52,54,53)(27,55,57,56)(29,41,58,70)(31,59,62,61)(33,63,66,68)(36,42,67,69)(46,71,72,74)(47,73,75,76)(49,77,78,64)(60,79,80,65)

Polycyclic presentation:

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

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7531527);