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C₂²×#10742 #72317018

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

Aliases

Subgroups

39629 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((5,6,7,8)(10,14)(12,19)(13,20)(15,18)(16,23)(17,22), (9,10,13,16,11,18,20,17)(12,14,21,22,19,15,24,23), (1,2), (6,8)(10,15,18,14)(13,20)(16,22,17,23)(21,24), (3,4)(5,7)(6,8)(9,11)(12,19)(13,20)(21,24));