Supercharacter theories for alternating group:A4

This page discusses the various possible supercharacter theories for alternating group:A4. Thus, it builds on a thorough understanding of the element structure of alternating group:A4, subgroup structure of alternating group:A4, and linear representation theory of alternating group:A4.

We describe the group $$A_4$$ as the alternating group on $$\{ 1,2,3,4 \}$$, and elements of the group are described by means of their cycle decompositions.

Character table
Below, the character table of $$A_4$$ is given. This table is crucial for understanding the possible supercharacter theories.

Supercharacter theories
Note that for each of the supercharacter tables presented, the supercharacter is the smallest positive integer linear combination of the characters in the block that takes constant values on each superconjugacy class.