Finite Group Databasebeta

?

← Prev (#512708) Next (#512710) →

C₂×#13630 #512709

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

Aliases

Subgroups

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 66 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 419905);