Finite Group Databasebeta

?

← Prev (#72286814) Next (#72286816) →

C₂×#612426 #72286815

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

Aliases

Subgroups

193533 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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