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C₂⁴×#2403 #72289144

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

Aliases

Subgroups

15617864 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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