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C₂²×#16810 #72320829

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

Aliases

Subgroups

85125 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

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