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C₂²×#43094 #72324596

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

Aliases

Subgroups

111653 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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