Finite Group Databasebeta

?

← Prev (#6585816) Next (#6585818) →

#6585817

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

Aliases

No aliases for this group.

Subgroups

1852 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 72 points:

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

Polycyclic presentation:

2^9|a^2=fi,c^2=fg,d^2=f,e^2=f,g^2=i,h^2=i,b^a=bf,c^a=cg,g^a=gi,c^b=ch,e^b=eh,h^b=hi,d^c=dh,h^c=hi,e^d=eh,h^d=hi,h^e=hi

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, 6493013);