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C₂²×#47946 #72295939

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

Aliases

Subgroups

111185 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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)(11,15)(14,16)(17,18)(19,23)(20,22)(21,24), (5,6,7,8)(11,15)(14,16)(17,18,20,22)(19,21,24,23), (10,13)(11,15)(17,19)(18,21)(20,24)(22,23), (9,10,12,13)(11,16,15,14)(17,18)(19,21)(20,22)(23,24), (5,6)(7,8)(9,11)(10,14)(12,15)(13,16)(17,19)(18,21)(20,24)(22,23), (1,2)(3,4));