Finite Group Databasebeta

?

← Prev (#72286775) Next (#72286777) →

C₂×#612626 #72286776

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

Aliases

Subgroups

164931 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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