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C₂²×#35713 #72299841

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

Aliases

Subgroups

119961 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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