Finite Group Databasebeta

?

← Prev (#72291064) Next (#72291066) →

C₂⁴×#2410 #72291065

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

Aliases

Subgroups

10319576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 20 points:

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

Conjugacy classes & character table

608 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((9,10,11,12)(14,16)(18,20), (3,4), (17,18)(19,20), (9,10,11,12)(13,14)(15,16)(17,18)(19,20), (9,10)(11,12), (5,6), (7,8), (1,2)(3,4)(5,6)(7,8));