Finite Group Databasebeta

?

← Prev (#72278101) Next (#72278103) →

C₂×#648595 #72278102

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

Aliases

Subgroups

70871 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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((3,4)(5,6)(15,16,19,17)(18,20,22,21), (3,4,5,6)(7,8,9,10), (12,14)(15,16,19,17)(18,21,22,20), (7,8)(9,10)(11,12)(13,14)(15,17,19,16)(18,21,22,20), (3,4)(5,6)(7,8)(9,10)(15,18)(16,20)(17,21)(19,22), (1,2));