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C₂⁴×#397 #72325084

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

Aliases

Subgroups

268885 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 24 points:

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

Conjugacy classes & character table

352 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), (9,10,11,12)(14,16)(19,23)(21,24), (5,6), (7,8), (10,12)(13,14)(15,16)(17,18,20,22)(19,21,23,24), (1,2)(3,4)(5,6)(7,8), (9,10)(11,12)(17,19)(18,21)(20,23)(22,24));