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#7624342

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

Polycyclic presentation:

2^9|c^2=f,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, 7531538);