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#7624289

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

Aliases

No aliases for this group.

Subgroups

1215 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)(19,25)(20,35)(21,27)(22,40)(23,44)(24,29)(26,37)(28,42)(30,55)(31,47)(32,48)(33,61)(34,64)(36,66)(38,67)(39,54)(41,50)(43,69)(45,53)(46,58)(49,63)(51,70)(52,68)(56,76)(57,77)(59,74)(60,79)(62,71)(65,75)(72,78)(73,80);(1,3)(2,6)(4,10)(5,11)(7,13)(8,9)(12,16)(14,15)(17,19)(18,25)(20,30)(21,31)(22,33)(23,34)(24,32)(26,46)(27,47)(28,49)(29,48)(35,55)(36,56)(37,58)(38,57)(39,59)(40,61)(41,62)(42,63)(43,60)(44,64)(45,65)(50,71)(51,73)(52,72)(53,75)(54,74)(66,76)(67,77)(68,78)(69,79)(70,80);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)(17,20)(18,26)(19,30)(21,36)(22,41)(23,45)(24,38)(25,46)(27,50)(28,53)(29,52)(31,56)(32,57)(33,62)(34,65)(35,40)(37,42)(39,68)(43,70)(44,51)(47,71)(48,72)(49,75)(54,66)(55,61)(58,63)(59,78)(60,80)(64,73)(67,69)(74,76)(77,79);(3,11)(6,9)(10,16)(13,15)(17,21,24,23)(18,27,29,44)(19,31,32,34)(20,36,38,45)(22,39,43,42)(25,47,48,64)(26,50,52,51)(28,40,54,69)(30,56,57,65)(33,59,60,63)(35,66,67,53)(37,41,68,70)(46,71,72,73)(49,61,74,79)(55,76,77,75)(58,62,78,80);(2,8)(6,9)(7,14)(13,15)(19,32)(25,48)(30,57)(31,34)(33,60)(46,72)(47,64)(49,74)(55,77)(56,65)(58,78)(59,63)(61,79)(62,80)(71,73)(75,76)

Polycyclic presentation:

2^9|c^2=f,d^2=i,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,g^c=gh,h^c=hi

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, 7531485);