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#488795

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

Aliases

No aliases for this group.

Subgroups

675 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 80 points:

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

Polycyclic presentation:

2^9|a^2=h,d^2=ghi,e^2=gi,f^2=i,g^2=i,b^a=be,c^a=cf,d^a=dghi,e^a=eg,f^a=fi,g^a=gi,d^b=dg,e^b=eg,f^b=fh,g^b=gi,d^c=di,e^c=eh,f^c=fi

Conjugacy classes & character table

59 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 395991);