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#7625121

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

Aliases

No aliases for this group.

Subgroups

1213 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)(23,43)(24,33)(25,40)(28,37)(29,41)(31,55)(32,50)(34,63)(35,45)(38,65)(39,66)(42,51)(44,73)(46,61)(47,68)(48,71)(49,76)(52,69)(53,59)(54,56)(57,77)(58,64)(60,80)(62,72)(67,70)(74,78)(75,79);(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)(25,44)(26,50)(27,30)(28,46)(29,45)(32,41)(36,64)(37,56)(38,60)(39,58)(40,59)(42,62)(43,72)(47,75)(48,53)(49,74)(51,63)(52,54)(55,66)(57,70)(61,69)(65,77)(67,80)(68,78)(71,73)(76,79);(1,4,6,5)(2,8,9,14)(3,11,12,13)(7,15,10,16)(17,20,37,68,21,38,42,71,22,39,69,76,41,70,23,40)(18,25,43,67,29,49,52,66,27,48,51,65,26,47,28,36)(19,31,56,78,35,60,62,73,33,58,61,79,32,57,34,59)(24,44,72,80,45,74,54,55,30,53,63,77,50,75,46,64);(3,12)(7,10)(11,13)(15,16)(17,21,22,41)(18,26,27,29)(19,32,33,35)(20,38,39,70)(23,37,42,69)(24,45,30,50)(25,47,48,49)(28,51,52,43)(31,57,58,60)(34,61,62,56)(36,65,66,67)(40,68,71,76)(44,74,53,75)(46,72,54,63)(55,77,64,80)(59,79,73,78);(1,5,6,4)(2,8,9,14)(3,13,12,11)(7,15,10,16)(18,27)(19,33)(25,48)(26,29)(28,52)(31,58)(32,35)(34,62)(36,66)(43,51)(47,49)(56,61)(57,60)(59,73)(65,67)(78,79)

Polycyclic presentation:

2^9|c^2=fghi,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

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, 7532317);