Finite Group Databasebeta

?

← Prev (#9481944) Next (#9481946) →

#9481945

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

Aliases

No aliases for this group.

Subgroups

3865 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 72 points:

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

Polycyclic presentation:

2^9|a^2=h,b^2=ghi,c^2=h,d^2=gi,e^2=gi,f^2=h,b^a=bg,c^a=ch,d^a=di,f^a=fh,c^b=ci,e^b=eghi,d^c=dh,f^c=fgi,e^d=egi

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, 9389141);