Finite Group Databasebeta

?

← Prev (#72293710) Next (#72293712) →

C₂²×#35000 #72293711

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

Aliases

Subgroups

154429 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 20 points:

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

Conjugacy classes & character table

256 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((6,8)(10,12)(13,14,17,18)(15,16,19,20), (6,8)(9,10,11,12)(14,18)(15,19), (13,14)(15,16)(17,18)(19,20), (5,6,7,8)(13,15)(14,16)(17,19)(18,20), (13,16)(14,15)(17,20)(18,19), (3,4), (1,2)(3,4));