Finite Group Databasebeta

?

← Prev (#72334679) Next (#72334681) →

C₂×#1418386 #72334680

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

Aliases

Subgroups

73053 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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