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#7625114

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

Polycyclic presentation:

2^9|c^2=fghi,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, 7532310);