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C₂²×#34983 #72325819

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

Aliases

Subgroups

118469 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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