Finite Group Databasebeta

?

← Prev (#7625181) Next (#7625183) →

C₂×#33974 #7625182

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

Aliases

Subgroups

1344 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 66 points:

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

Conjugacy classes & character table

272 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532378);