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#7625133

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

Aliases

No aliases for this group.

Subgroups

1209 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)(7,12)(11,16)(13,15)(17,18)(19,30)(20,36)(21,26)(22,27)(23,44)(24,33)(25,40)(28,37)(29,42)(31,56)(32,50)(34,64)(35,46)(38,66)(39,67)(41,72)(43,52)(45,74)(47,62)(48,70)(49,71)(51,68)(53,69)(54,60)(55,57)(58,77)(59,65)(61,78)(63,73)(75,80)(76,79);(1,3)(2,7)(4,11)(5,13)(6,12)(8,15)(9,10)(14,16)(17,19)(18,24)(20,31)(21,35)(22,33)(23,34)(25,45)(26,50)(27,30)(28,47)(29,46)(32,42)(36,65)(37,57)(38,61)(39,59)(40,60)(41,58)(43,63)(44,73)(48,76)(49,54)(51,75)(52,64)(53,55)(56,67)(62,69)(66,77)(68,79)(70,80)(71,74)(72,78);(1,4,6,5)(2,8,9,14)(3,11,12,13)(7,15,10,16)(17,20,37,68,21,41,43,71,22,39,69,70,42,38,23,40)(18,25,44,66,29,48,53,67,27,49,52,72,26,51,28,36)(19,31,57,79,35,58,63,74,33,59,62,80,32,61,34,60)(24,45,73,77,46,76,55,56,30,54,64,78,50,75,47,65);(3,12)(7,10)(11,13)(15,16)(17,21,22,42)(18,26,27,29)(19,32,33,35)(20,38,39,41)(23,37,43,69)(24,46,30,50)(25,48,49,51)(28,52,53,44)(31,58,59,61)(34,62,63,57)(36,66,67,72)(40,70,71,68)(45,75,54,76)(47,73,55,64)(56,77,65,78)(60,79,74,80);(1,5,6,4)(2,8,9,14)(3,13,12,11)(7,15,10,16)(18,27)(19,33)(25,49)(26,29)(28,53)(31,59)(32,35)(34,63)(36,67)(44,52)(48,51)(57,62)(58,61)(60,74)(66,72)(79,80)

Polycyclic presentation:

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

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, 7532329);