Finite Group Databasebeta

?

← Prev (#6382916) Next (#6382918) →

C₂×#23235 #6382917

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

Aliases

Subgroups

2028 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(4,8)(9,10)(11,12,15,20,16,21,25,19)(13,17,14,23,22,18,24,26);(3,4)(5,9)(6,10)(7,8)(11,13,15,14,16,22,25,24)(12,17,20,23,21,18,19,26);(3,5,7,6)(4,9,8,10)(11,14,15,22,16,24,25,13)(12,18,19,23,21,17,20,26);(3,6,7,5)(4,9,8,10)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6290113);