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C₂²×#47829 #72295879

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

Aliases

Subgroups

111345 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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