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C₂²×#15673 #72337027

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

Aliases

Subgroups

95149 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

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