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#7623575

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

Aliases

No aliases for this group.

Subgroups

1237 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=i,d^2=i,e^2=f,g^2=hi,h^2=i,b^a=bf,c^a=cg,d^a=df,g^a=gh,h^a=hi,c^b=cfi,d^b=di,g^c=gh,h^c=hi,e^d=ei

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530771);