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C₂²×#37662 #72299798

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

Aliases

Subgroups

115993 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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