Finite Group Databasebeta

?

← Prev (#72227621) Next (#72227623) →

C₂×#13106267 #72227622

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

5570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

266 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2,4,5,3)(6,7,9,10,8)(17,18,19,20), (2,3)(4,5)(7,8)(9,10)(13,14,15,16), (11,12), (14,16)(18,20), (7,8)(9,10)(14,16));