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#6687809

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

Aliases

No aliases for this group.

Subgroups

1609 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=f,c^2=fg,d^2=fi,e^2=fi,g^2=i,h^2=i,b^a=bf,c^a=cg,d^a=df,g^a=gi,c^b=ch,e^b=efh,h^b=hi,d^c=di,h^c=hi,e^d=ei,h^e=hi

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, 6595005);