Finite Group Databasebeta

?

← Prev (#607667) Next (#607669) →

C₂×#14736 #607668

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

Aliases

Subgroups

6662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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, 514864);