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#7125200

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

Aliases

No aliases for this group.

Subgroups

1622 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)(9,11)(10,14)(12,15)(13,16)(17,18,24,30)(19,31,36,48)(20,37,40,56)(21,27,44,55)(22,29,23,28)(25,35,49,34)(26,45,51,39)(32,59,62,46)(33,58,64,52)(38,66,70,75)(41,71,63,47)(42,54,43,53)(50,69,76,68)(57,65,73,61)(60,78,80,72)(67,74,79,77);(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,19,23,35,24,36,22,34)(18,25,29,48,30,49,28,31)(20,32,45,65,40,62,39,61)(21,41,42,33,44,63,43,64)(26,46,56,73,51,59,37,57)(27,52,53,47,55,58,54,71)(38,67,68,60,70,79,69,80)(50,74,66,72,76,77,75,78);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14)(17,20)(18,26)(19,32)(21,38)(22,39)(23,45)(24,40)(25,46)(27,50)(28,37)(29,56)(30,51)(31,57)(33,60)(34,61)(35,65)(36,62)(41,67)(42,68)(43,69)(44,70)(47,72)(48,73)(49,59)(52,74)(53,66)(54,75)(55,76)(58,77)(63,79)(64,80)(71,78);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(17,21)(18,27)(19,33)(20,38)(22,42)(23,43)(24,44)(25,47)(26,50)(28,53)(29,54)(30,55)(31,58)(32,60)(34,63)(35,41)(36,64)(37,66)(39,68)(40,70)(45,69)(46,72)(48,52)(49,71)(51,76)(56,75)(57,77)(59,78)(61,79)(62,80)(65,67)(73,74);(2,8)(6,9)(7,16)(14,15)(17,22,24,23)(18,28,30,29)(19,34,36,35)(20,39,40,45)(21,42,44,43)(25,31,49,48)(26,37,51,56)(27,53,55,54)(32,61,62,65)(33,63,64,41)(38,68,70,69)(46,57,59,73)(47,58,71,52)(50,66,76,75)(60,79,80,67)(72,77,78,74)

Polycyclic presentation:

2^9|a^2=i,b^2=fi,c^2=h,d^2=h,e^2=i,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, 7032396);