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C₂²×#13153 #72310252

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

Aliases

Subgroups

5329 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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