Finite Group Databasebeta

?

← Prev (#72233735) Next (#72233737) →

C₂×#359509 #72233736

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

Aliases

Subgroups

45125 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

160 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((1,2), (10,18)(12,19)(13,20)(16,22), (3,4)(5,6), (4,6)(7,8)(9,15,17,21)(10,13)(11,14)(12,16,19,22)(18,20), (7,9)(8,12,14,19)(10,16)(11,17)(13,15,20,21)(18,22));