Finite Group Databasebeta

?

← Prev (#72286599) Next (#72286601) →

C₂⁴×C₄×D₈ #72286600

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

Aliases

Subgroups

158389 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

448 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), (3,4), (14,17)(15,18)(19,20), (5,6), (1,2)(3,4)(5,6)(7,8)(13,14,18,20,16,19,15,17), (7,8), (1,2)(3,4)(5,6)(7,8)(9,10,11,12));