Finite Group Databasebeta

?

← Prev (#72286860) Next (#72286862) →

C₂×#517252 #72286861

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

Aliases

Subgroups

166241 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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)(7,8,9,10)(15,16,18,20)(17,21,22,19), (11,12,13,14)(15,16)(17,19)(18,20)(21,22), (1,2), (4,6)(8,10)(15,16)(17,21)(18,20)(19,22), (3,4)(5,6)(7,8)(9,10), (15,17)(16,19)(18,22)(20,21));