Finite Group Databasebeta

?

← Prev (#6443431) Next (#6443433) →

C₂×#26068 #6443432

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

Aliases

Subgroups

2446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6350628);