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#488633

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

Aliases

No aliases for this group.

Subgroups

706 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)(20,36)(21,40)(22,30)(23,29)(24,27)(25,33)(26,39)(28,43)(32,59)(34,65)(35,58)(37,55)(38,69)(41,56)(42,52)(44,54)(45,51)(46,53)(47,74)(48,64)(49,72)(50,68)(57,62)(60,77)(61,66)(63,79)(67,71)(70,76)(73,78)(75,80);(1,2)(3,6)(4,7)(5,8)(9,13)(10,12)(11,14)(15,16)(17,19)(18,25)(20,32)(21,41)(22,34)(23,46)(24,35)(26,47)(27,48)(28,53)(29,49)(30,56)(31,40)(33,43)(36,66)(37,60)(38,70)(39,62)(42,64)(44,72)(45,63)(50,77)(51,76)(52,65)(54,58)(55,75)(57,67)(59,69)(61,71)(68,74)(73,80)(78,79);(1,3)(2,6)(4,9)(5,10)(7,13)(8,12)(11,15)(14,16)(17,20)(18,26)(19,32)(21,38)(22,45)(23,39)(24,37)(25,47)(27,51)(28,50)(29,55)(30,36)(31,57)(33,61)(34,63)(35,60)(40,67)(41,70)(42,73)(43,71)(44,68)(46,62)(48,76)(49,75)(52,69)(53,77)(54,78)(56,66)(58,79)(59,65)(64,80)(72,74);(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,13,12,16)(18,27)(20,37)(25,48)(28,52)(29,30)(31,58)(32,60)(38,68)(39,45)(40,54)(49,56)(53,65)(61,80)(62,63)(70,74)(71,73)

Polycyclic presentation:

2^9|d^2=h,e^2=gi,f^2=i,g^2=i,b^a=be,c^a=cf,d^a=dhi,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

56 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 395829);