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C₂²×#13155 #72313497

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

Aliases

Subgroups

5909 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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