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C₂²×#7670203 #72267367

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

Aliases

Subgroups

4134720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

464 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((6,8)(15,19)(18,20), (10,12), (3,4)(14,17)(18,20), (1,2)(3,4)(14,17)(18,20), (15,19)(18,20), (14,17)(18,20), (9,10)(11,12)(13,14)(15,18)(16,17)(19,20), (5,6,7,8)(13,15,16,19)(14,18,17,20));