Supercharacter theories for symmetric group:S3

This page discusses the various possible supercharacter theories for symmetric group:S3. Thus, it builds on a thorough understanding of the element structure of symmetric group:S3, subgroup structure of symmetric group:S3, and linear representation theory of symmetric group:S3.

We describe the group $$S_3$$ as the symmetric group on $$\{ 1,2,3\}$$, and elements of the group are described by means of their cycle decompositions.

Character table
Below, the character table of $$S_4$$ is given. This table is crucial for understanding the possible supercharacter theories.

Summary
There are only two supercharacter theories possible for symmetric group:S3, namely the two extreme cases:

There are no other possibilities to consider because the group has only three conjugacy classes.