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C₂²×#13088 #72291671

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

Aliases

Subgroups

30041 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 16 points:

(1,2)(3,4)(5,6)(7,8)(11,16)(13,14);(9,10)(11,14,16,13)(12,15);(5,7,8,6)(10,13,15,14);(1,2);(3,4)

Conjugacy classes & character table

148 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((1,2)(3,4)(5,6)(7,8)(11,16)(13,14), (9,10)(11,14,16,13)(12,15), (5,7,8,6)(10,13,15,14), (1,2), (3,4));