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C₂²×#34988 #72296002

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

Aliases

Subgroups

204893 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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