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C₂²×#8375 #72317191

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

Aliases

Subgroups

57453 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

172 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((13,14)(15,17)(16,19)(18,20), (5,6)(7,9)(8,10)(11,12), (1,2), (6,9,10,12)(7,11)(13,15,16,20,18,19,17,14), (3,4));