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C₂²×#50864 #72236684

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

Aliases

Subgroups

106161 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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