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C₂²×#35728 #72278992

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

Aliases

Subgroups

145829 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 20 points:

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

Conjugacy classes & character table

256 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)(15,19)(16,18)(17,20), (9,10,11,12)(15,20)(17,19), (6,8)(13,14,16,18)(15,17,20,19), (5,6)(7,8)(9,10)(11,12)(13,14)(15,19)(16,18)(17,20), (13,15)(14,17)(16,20)(18,19), (3,4), (1,2)(3,4));