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#7625160

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

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,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, 7532356);