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#7624799

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

Aliases

No aliases for this group.

Subgroups

1174 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)(20,37)(21,30)(22,28)(23,43)(24,27)(25,34)(26,40)(29,45)(32,59)(33,48)(35,65)(36,50)(38,71)(39,70)(41,54)(42,53)(44,56)(46,55)(47,75)(49,63)(51,73)(52,72)(57,62)(58,67)(60,77)(61,69)(64,74)(66,76)(68,79)(78,80);(1,3)(2,6)(4,11)(5,10)(7,14)(8,9)(12,15)(13,16)(17,19)(18,25)(20,32)(21,33)(22,34)(23,35)(24,36)(26,47)(27,48)(28,31)(29,49)(30,50)(37,69)(38,60)(39,61)(40,62)(41,63)(42,64)(43,74)(44,66)(45,67)(46,68)(51,76)(52,57)(53,65)(54,58)(55,77)(56,78)(59,70)(71,79)(72,75)(73,80);(17,20,22,39)(18,26,28,52)(19,32,34,61)(21,38,24,46)(23,44,42,73)(25,47,31,57)(27,51,30,56)(29,55,54,71)(33,60,36,68)(35,66,64,80)(37,53,70,43)(40,41,72,45)(48,76,50,78)(49,77,58,79)(59,74,69,65)(62,63,75,67);(3,10)(6,9)(11,16)(14,15)(17,21,22,24)(18,27,28,30)(19,33,34,36)(20,38,39,46)(23,41,42,45)(25,48,31,50)(26,51,52,56)(29,53,54,43)(32,60,61,68)(35,63,64,67)(37,55,70,71)(40,44,72,73)(47,76,57,78)(49,65,58,74)(59,79,69,77)(62,66,75,80);(1,4,5,13)(2,7,8,12)(3,11,10,16)(6,14,9,15)(18,28)(19,34)(26,52)(27,30)(29,54)(32,61)(33,36)(35,64)(37,70)(43,53)(51,56)(55,71)(60,68)(62,75)(63,67)(66,80)

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=dfi,e^b=ei,g^c=gh,h^c=hi

Conjugacy classes & character table

65 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7531995);