Finite Group Databasebeta

?

← Prev (#7636671) Next (#7636673) →

C₂×#39438 #7636672

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

Aliases

Subgroups

9456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 7543868);