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C₂²×#49562 #72301158

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

Aliases

Subgroups

101177 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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