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C₂²×#35168 #72324159

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

Aliases

Subgroups

144781 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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