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#7624414

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

Aliases

No aliases for this group.

Subgroups

1165 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)(20,34)(21,27)(22,40)(23,44)(24,29)(26,36)(28,42)(30,56)(31,47)(32,48)(33,63)(35,65)(37,66)(38,50)(39,55)(41,51)(43,69)(45,54)(46,59)(49,62)(52,70)(53,67)(57,77)(58,75)(60,80)(61,74)(64,76)(68,73)(71,78)(72,79);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14)(17,19)(18,25)(20,30)(21,38)(22,33)(23,32)(24,31)(26,46)(27,50)(28,49)(29,47)(34,56)(35,60)(36,59)(37,57)(39,68)(40,63)(41,64)(42,62)(43,61)(44,48)(45,58)(51,76)(52,72)(53,71)(54,75)(55,73)(65,80)(66,77)(67,78)(69,74)(70,79);(17,20)(18,26)(19,30)(21,35)(22,41)(23,45)(24,37)(25,46)(27,51)(28,54)(29,53)(31,57)(32,58)(33,64)(34,40)(36,42)(38,60)(39,67)(43,70)(44,52)(47,71)(48,72)(49,75)(50,76)(55,65)(56,63)(59,62)(61,79)(66,69)(68,78)(73,80)(74,77);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(19,31)(25,47)(30,57)(32,38)(33,61)(46,71)(48,50)(49,73)(56,77)(58,60)(59,78)(62,68)(63,74)(64,79)(72,76)(75,80);(2,8)(6,9)(7,16)(14,15)(17,21,24,23)(18,27,29,44)(19,32,31,38)(20,35,37,45)(22,39,43,42)(25,48,47,50)(26,51,53,52)(28,40,55,69)(30,58,57,60)(33,62,61,68)(34,65,66,54)(36,41,67,70)(46,72,71,76)(49,74,73,63)(56,75,77,80)(59,79,78,64)

Polycyclic presentation:

2^9|b^2=f,d^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=dfi,e^b=ei,g^c=gh,h^c=hi

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, 7531610);