Finite Group Databasebeta

?

← Prev (#6369863) Next (#6369865) →

C₂×#20421 #6369864

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

Aliases

Subgroups

5142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277060);