Finite Group Databasebeta

?

← Prev (#72302510) Next (#72302512) →

C₂×#1393449 #72302511

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

Aliases

Subgroups

67559 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

172 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((1,2)(3,4)(5,6)(7,8)(9,10)(11,12,14,13)(15,16)(17,20)(18,21)(19,22), (5,6)(8,10)(12,13)(15,17,19,21)(16,20,22,18), (3,5,4,6)(15,18,19,20)(16,21,22,17), (5,6)(7,8)(9,10)(11,13,14,12)(17,21)(18,20), (5,6)(7,8)(9,10)(15,18)(16,17)(19,20)(21,22), (3,5)(4,6)(15,17)(16,20)(18,22)(19,21));