Graphical Representations of Groups

Cayley diagram for A4

Permutation diagram for A4

Monochrome diagram for A4

Dessin d'enfant for A4
There are many ways that the structure of a finite group can be represented by a diagram. This page describes four of these, with an example of each shown to the right:

and discusses the relationships between them. They all show permutation groups, with the set permuted being of vertices, vertices, half-edges and edges respectively.

Two other graphical representations of groups are shown below. This page does not discuss Coxeter or Coxeter-Dynkin diagrams.

Coxeter diagram
for BC3

Coxeter-Dynkin diagram
for BC3 as full symmetry
group of the truncated

Cayley diagrams: show

Permutation diagrams: show

Monochrome diagrams: show

Dessins d'enfants: show

Comparison of these four types of diagram: show

Index for pages on groups