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#7625113

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

Aliases

No aliases for this group.

Subgroups

1225 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)(19,24)(20,34)(21,26)(22,40)(23,29)(25,37)(27,35)(28,39)(30,52)(31,43)(32,44)(33,59)(36,60)(38,62)(41,50)(42,56)(45,53)(46,57)(47,63)(48,72)(49,66)(51,64)(54,73)(55,74)(58,70)(61,65)(67,76)(68,79)(69,80)(71,77)(75,78);(1,3)(2,7)(4,11)(5,13)(6,12)(8,15)(9,10)(14,16)(17,19)(18,24)(20,30)(21,31)(22,33)(23,32)(25,42)(26,43)(27,45)(28,46)(29,44)(34,52)(35,53)(36,54)(37,56)(38,55)(39,57)(40,59)(41,58)(47,67)(48,69)(49,68)(50,70)(51,71)(60,73)(61,75)(62,74)(63,76)(64,77)(65,78)(66,79)(72,80);(1,4,6,5)(2,8,9,14)(3,11,12,13)(7,15,10,16)(17,20,35,63,21,36,41,66,23,38,64,72,39,65,22,37)(18,25,40,61,28,48,51,62,29,49,50,60,26,47,27,34)(19,30,53,76,31,54,58,79,32,55,77,80,57,78,33,56)(24,42,59,75,46,69,71,74,44,68,70,73,43,67,45,52);(3,12)(7,10)(11,13)(15,16)(17,21,23,39)(18,26,29,28)(19,31,32,57)(20,36,38,65)(22,35,41,64)(24,43,44,46)(25,47,49,48)(27,50,51,40)(30,54,55,78)(33,53,58,77)(34,60,62,61)(37,63,66,72)(42,67,68,69)(45,70,71,59)(52,73,74,75)(56,76,79,80);(1,5,6,4)(2,8,9,14)(3,13,12,11)(7,15,10,16)(19,32)(24,44)(30,55)(31,57)(33,58)(42,68)(43,46)(45,71)(52,74)(53,77)(54,78)(56,79)(59,70)(67,69)(73,75)(76,80)

Polycyclic presentation:

2^9|c^2=fgh,d^2=i,e^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=df,e^b=ei

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532309);