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C₂²×#15215 #72337026

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

Aliases

Subgroups

108229 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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((17,18,21,20)(19,22,23,24), (10,12)(13,14,16,15)(18,20)(19,23), (6,8)(10,12)(14,15)(17,19)(18,22)(20,24)(21,23), (5,6)(7,8)(9,10,11,12)(13,15,16,14)(17,20,21,18)(19,24,23,22), (3,4), (1,2)(3,4));