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C₂²×#35223 #72320604

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

Aliases

Subgroups

143637 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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