Finite Group Databasebeta

?

← Prev (#7636669) Next (#7636671) →

C₂×#39419 #7636670

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

Aliases

Subgroups

9820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7543866);