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#7167153

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

Aliases

No aliases for this group.

Subgroups

1634 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

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, 7074349);