Finite Group Databasebeta

?

← Prev (#72291059) Next (#72291061) →

C₂⁴×#385 #72291060

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

Aliases

Subgroups

553749 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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