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#6687800

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

Aliases

No aliases for this group.

Subgroups

1609 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=fi,c^2=fg,d^2=f,e^2=f,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,h^c=hi,h^e=hi

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, 6594996);