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C₂²×#13971 #72296083

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

Aliases

Subgroups

175141 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

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

Conjugacy classes & character table

304 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((13,14,16,15)(18,20), (9,10)(11,12)(17,18)(19,20), (6,8)(9,10,11,12)(13,15,16,14), (5,6)(7,8)(9,10)(11,12), (3,4), (1,2)(3,4));