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#7624347

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

Aliases

No aliases for this group.

Subgroups

1203 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)(17,18,21,27)(19,30,32,24)(20,26,35,49)(22,25,38,47)(23,41,39,29)(28,52,48,40)(31,54,57,43)(33,53,60,42)(34,45,61,56)(36,46,63,70)(37,66,64,51)(44,62,55,73)(50,72,71,65)(58,74,77,67)(59,69,78,76)(68,79,75,80);(1,3)(2,6)(4,10)(5,11)(7,13)(8,9)(12,16)(14,15)(17,19,21,32)(18,24,27,30)(20,31,35,57)(22,33,38,60)(23,34,39,61)(25,42,47,53)(26,43,49,54)(28,44,48,55)(29,45,41,56)(36,58,63,77)(37,59,64,78)(40,62,52,73)(46,67,70,74)(50,68,71,75)(51,69,66,76)(65,79,72,80);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)(18,25)(22,40)(23,39)(24,42)(26,46)(27,47)(28,29)(30,53)(33,62)(34,61)(36,65)(37,64)(38,52)(41,48)(43,67)(44,45)(49,70)(50,51)(54,74)(55,56)(58,79)(59,78)(60,73)(63,72)(66,71)(68,69)(75,76)(77,80);(3,11)(6,9)(10,16)(13,15)(17,20)(18,26)(19,31)(21,35)(22,36)(23,37)(24,43)(25,46)(27,49)(28,50)(29,51)(30,54)(32,57)(33,58)(34,59)(38,63)(39,64)(40,65)(41,66)(42,67)(44,68)(45,69)(47,70)(48,71)(52,72)(53,74)(55,75)(56,76)(60,77)(61,78)(62,79)(73,80);(2,8)(6,9)(7,14)(13,15)(18,27)(19,32)(20,35)(25,47)(28,48)(29,41)(33,60)(34,61)(36,63)(37,64)(43,54)(62,73)(65,72)(67,74)(68,75)(69,76)

Polycyclic presentation:

2^9|a^2=i,b^2=i,c^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=dfi,e^b=ei,g^c=gh,h^c=hi,e^d=ei

Conjugacy classes & character table

71 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7531543);