Finite Group Databasebeta

?

← Prev (#7624778) Next (#7624780) →

#7624779

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

Aliases

No aliases for this group.

Subgroups

1178 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)(20,36)(21,27)(22,28)(23,42)(24,45)(25,33)(26,39)(29,44)(31,58)(32,56)(34,64)(35,48)(37,70)(38,71)(40,53)(41,69)(43,50)(46,54)(47,75)(49,62)(51,72)(52,73)(55,61)(57,66)(59,78)(60,68)(63,74)(65,77)(67,79)(76,80);(1,3)(2,6)(4,11)(5,10)(7,14)(8,9)(12,15)(13,16)(17,19)(18,25)(20,31)(21,32)(22,33)(23,34)(24,35)(26,47)(27,48)(28,30)(29,49)(36,68)(37,59)(38,60)(39,61)(40,62)(41,63)(42,74)(43,65)(44,66)(45,56)(46,67)(50,76)(51,55)(52,77)(53,57)(54,78)(58,71)(64,69)(70,79)(72,75)(73,80);(17,20,22,38)(18,26,28,51)(19,31,33,60)(21,37,24,46)(23,43,41,73)(25,47,30,55)(27,50,45,52)(29,54,53,70)(32,59,35,67)(34,65,63,80)(36,69,71,42)(39,40,72,44)(48,76,56,77)(49,78,57,79)(58,74,68,64)(61,62,75,66);(3,10)(6,9)(11,16)(14,15)(17,21,22,24)(18,27,28,45)(19,32,33,35)(20,37,38,46)(23,40,41,44)(25,48,30,56)(26,50,51,52)(29,42,53,69)(31,59,60,67)(34,62,63,66)(36,70,71,54)(39,43,72,73)(47,76,55,77)(49,74,57,64)(58,78,68,79)(61,65,75,80);(1,4,5,13)(2,7,8,12)(3,11,10,16)(6,14,9,15)(18,28)(19,33)(26,51)(27,45)(29,53)(31,60)(32,35)(34,63)(36,71)(42,69)(50,52)(54,70)(59,67)(61,75)(62,66)(65,80)

Polycyclic presentation:

2^9|a^2=fi,c^2=i,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=dfi,e^b=ei,g^c=gh,h^c=hi

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7531975);