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#7625165

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

Aliases

No aliases for this group.

Subgroups

1216 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)(19,30)(20,36)(21,26)(22,27)(23,44)(24,33)(25,40)(28,42)(29,41)(31,56)(32,52)(34,63)(35,46)(37,53)(38,66)(39,67)(43,48)(45,74)(47,57)(49,71)(50,72)(51,69)(54,60)(55,64)(58,77)(59,65)(61,80)(62,73)(68,70)(75,79)(76,78);(1,3)(2,7)(4,11)(5,13)(6,12)(8,15)(9,10)(14,16)(17,19)(18,24)(20,31)(21,35)(22,33)(23,34)(25,45)(26,52)(27,30)(28,47)(29,46)(32,41)(36,65)(37,57)(38,61)(39,59)(40,60)(42,64)(43,62)(44,73)(48,63)(49,76)(50,54)(51,75)(53,55)(56,67)(58,70)(66,77)(68,80)(69,78)(71,79)(72,74);(1,4,6,5)(2,8,9,14)(3,11,12,13)(7,15,10,16)(17,20,37,69,21,38,23,40,22,39,42,71,41,70,43,72)(18,25,48,66,29,51,28,36,27,50,44,68,26,49,53,67)(19,31,57,78,35,61,34,60,33,59,64,79,32,58,62,74)(24,45,63,77,46,75,47,65,30,54,73,80,52,76,55,56);(3,12)(7,10)(11,13)(15,16)(17,21,22,41)(18,26,27,29)(19,32,33,35)(20,38,39,70)(23,42,43,37)(24,46,30,52)(25,49,50,51)(28,48,53,44)(31,58,59,61)(34,57,62,64)(36,66,67,68)(40,71,72,69)(45,75,54,76)(47,73,55,63)(56,77,65,80)(60,78,74,79);(1,5,6,4)(2,8,9,14)(3,13,12,11)(7,15,10,16)(18,27)(19,33)(20,39)(26,29)(28,53)(32,35)(34,62)(38,70)(40,72)(44,48)(45,54)(56,65)(57,64)(69,71)(75,76)(77,80)

Polycyclic presentation:

2^9|c^2=fgh,d^2=i,e^2=fi,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, 7532361);