Department of Mathematics

We classify and construct all supercharacter theories for the groups $C_p \times C_2 \times C_2$ where $p$ is an odd prime. It is known that every nontrivial supercharacter theory of a cyclic group can be constructed as a wedge product, a direct product, or is generated by automorphisms. We show that these constructions are also sufficient to construct every nontrivial supercharacter theory of $C_p \times C_2 \times C_2$. We give a precise count of the distinct supercharacter theories of $C_p\times C_2\times C_2$ and describe when a supercharacter theory can be constructed by more than one method.