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#7624320

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

Aliases

No aliases for this group.

Subgroups

1208 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

65 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7531516);