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#7624757

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

Aliases

No aliases for this group.

Subgroups

1181 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

71 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7531953);