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C₂⁴×#2847 #72291066

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

Aliases

Subgroups

10199784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

704 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((17,18,19,20), (3,4), (10,12)(14,16), (14,16)(17,18,19,20), (9,10)(11,12)(13,14)(15,16)(17,18)(19,20), (5,6), (7,8), (1,2)(3,4)(5,6)(7,8));