Finite Group Databasebeta

?

← Prev (#72334444) Next (#72334446) →

C₂×#612833 #72334445

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

Aliases

Subgroups

75477 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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)(7,8,9,10)(11,12)(13,14)(15,16,18,20)(17,21,22,19), (4,6)(7,8,9,10)(12,14)(15,17,18,22)(16,19,20,21), (12,14)(15,16)(17,21)(18,20)(19,22), (11,12)(13,14)(15,16)(17,21)(18,20)(19,22), (1,2), (3,4)(5,6)(7,8)(9,10)(15,16)(17,21)(18,20)(19,22));