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C₂²×#43887 #72320577

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

Aliases

Subgroups

117721 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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