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C₂²×#686216 #72321330

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

Aliases

Subgroups

1005712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 24 points:

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

Conjugacy classes & character table

368 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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