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#6481907

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

Aliases

No aliases for this group.

Subgroups

1636 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=i,b^2=fi,d^2=h,e^2=i,f^2=i,g^2=i,b^a=bf,c^a=cg,e^a=eh,f^a=fi,g^a=gi,c^b=ch,d^b=dh,g^c=gi,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, 6389103);