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#6498685

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

Aliases

No aliases for this group.

Subgroups

1602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=fi,c^2=ghi,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=dh,f^b=fi,e^d=ei

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6405881);