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C₂²×#15259 #72293259

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

Aliases

Subgroups

184549 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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