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#7625172

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

Aliases

No aliases for this group.

Subgroups

1218 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)(17,18,23,29)(19,24,32,45)(20,34,37,65)(21,26,40,28)(22,41,42,52)(25,48,50,38)(27,53,54,35)(30,55,60,77)(31,44,61,47)(33,63,62,73)(36,64,39,68)(43,69,71,58)(46,75,74,56)(49,66,51,67)(57,76,59,80)(70,78,72,79);(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)(34,55)(35,56)(36,57)(37,60)(38,58)(39,59)(40,61)(41,63)(42,62)(48,69)(49,70)(50,71)(51,72)(52,73)(53,75)(54,74)(64,76)(65,77)(66,78)(67,79)(68,80);(1,4,6,5)(2,8,9,14)(3,11,12,13)(7,15,10,16)(17,20,35,66,21,39,42,48,23,37,53,67,40,36,22,38)(18,25,41,64,28,49,54,65,29,50,52,68,26,51,27,34)(19,30,56,78,31,59,62,69,32,60,75,79,61,57,33,58)(24,43,63,76,47,70,74,77,45,71,73,80,44,72,46,55);(3,12)(7,10)(11,13)(15,16)(17,21,23,40)(18,26,29,28)(19,31,32,61)(20,36,37,39)(22,35,42,53)(24,44,45,47)(25,49,50,51)(27,52,54,41)(30,57,60,59)(33,56,62,75)(34,64,65,68)(38,67,48,66)(43,70,71,72)(46,73,74,63)(55,76,77,80)(58,79,69,78);(1,5,6,4)(2,8,9,14)(3,13,12,11)(7,15,10,16)(19,32)(20,37)(24,45)(25,50)(31,61)(33,62)(34,65)(36,39)(38,48)(44,47)(46,74)(49,51)(56,75)(63,73)(64,68)(66,67)

Polycyclic presentation:

2^9|a^2=i,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,d^c=di,e^c=ei

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532368);