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#6815760

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

Aliases

No aliases for this group.

Subgroups

1630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=i,c^2=fgh,d^2=fi,e^2=hi,g^2=i,h^2=i,b^a=bf,c^a=cg,d^a=df,g^a=gi,c^b=ch,e^b=efh,h^b=hi,d^c=di,e^d=ei

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, 6722956);