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C₂²×D₄×#518 #72324185

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

Aliases

Subgroups

2101200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

680 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((10,11), (9,10,12,11), (10,11)(13,14)(15,18)(16,19)(17,20), (9,11,12,10)(13,15)(14,17)(16,20)(18,19), (3,4), (1,2)(3,4), (13,15)(14,18)(16,20)(17,19), (5,6,7,8)(13,14)(15,17)(16,19)(18,20));