Finite Group Databasebeta

?

← Prev (#72278135) Next (#72278137) →

C₂×#686982 #72278136

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

Aliases

Subgroups

69345 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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((8,9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22), (7,8,10,9)(12,14)(16,20)(18,22), (4,6)(8,9)(11,12)(13,14)(17,21)(18,22), (3,4)(5,6)(7,9,10,8)(15,17)(16,18)(19,21)(20,22), (15,18)(16,21)(17,20)(19,22), (1,2));