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#7186738

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

Aliases

No aliases for this group.

Subgroups

1572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=fi,b^2=h,c^2=gi,d^2=f,e^2=h,f^2=i,g^2=i,b^a=bf,c^a=cg,e^a=eh,g^a=gi,c^b=ch,d^b=df,e^b=eh,f^b=fi,d^c=dh,e^d=ei

Conjugacy classes & character table

62 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7093934);