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C₂²×#7630939 #72268544

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

Aliases

Subgroups

9327144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 20 points:

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

Conjugacy classes & character table

512 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((14,17)(18,20), (15,19)(18,20), (6,8)(10,12), (3,4), (1,2)(3,4), (10,12), (13,14,16,17)(15,18,19,20), (5,6)(7,8)(9,10)(11,12)(13,15)(14,18)(16,19)(17,20));