Finite Group Databasebeta

?

← Prev (#493130) Next (#493132) →

C₂×#12667 #493131

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

Aliases

Subgroups

708 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,8,13,9,14,23,29,7,12,20,28,22,6,11,21)(5,10,16,25,17,26,31,34,18,15,24,30,32,19,27,33);(3,5)(4,10,12,15)(6,19,14,26)(7,18)(8,16)(9,17)(11,27)(13,25,28,30)(20,24)(21,33,29,34)(22,32)(23,31);(3,6,20,29,9,4,11,28,7,14,8,21,22,12,23,13)(5,15,16,30,17,19,31,33,18,10,24,25,32,26,27,34)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400327);