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C₂⁴×#2668 #72325203

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

Aliases

Subgroups

4369896 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 24 points:

(3,4);(9,10,12,11)(14,16)(18,21)(22,24);(5,6);(7,8);(10,11)(13,14)(15,16)(19,23)(22,24);(1,2)(3,4)(5,6)(7,8);(10,11)(17,18)(19,22)(20,21)(23,24);(9,11,12,10)(17,19)(18,22)(20,23)(21,24)

Conjugacy classes & character table

512 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((3,4), (9,10,12,11)(14,16)(18,21)(22,24), (5,6), (7,8), (10,11)(13,14)(15,16)(19,23)(22,24), (1,2)(3,4)(5,6)(7,8), (10,11)(17,18)(19,22)(20,21)(23,24), (9,11,12,10)(17,19)(18,22)(20,23)(21,24));