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#7624731

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

Aliases

No aliases for this group.

Subgroups

1184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 80 points:

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

Polycyclic presentation:

2^9|a^2=fi,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,g^c=gh,h^c=hi

Conjugacy classes & character table

71 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7531927);