Finite Group Databasebeta

?

← Prev (#6373153) Next (#6373155) →

C₂×#21617 #6373154

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

Aliases

Subgroups

2770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6280350);