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#488631

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

Aliases

No aliases for this group.

Subgroups

692 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|b^2=i,d^2=hi,e^2=gi,f^2=i,g^2=i,b^a=be,c^a=cf,d^a=dh,e^a=eg,f^a=fi,g^a=gi,e^b=eg,f^b=fh,g^b=gi,d^c=di,e^c=eh,f^c=fi

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 395827);