Supercharacter theories for groups of prime order

Let $$p$$ be a prime number. This page describes the possible supercharacter theories for a group of prime order.

The supercharacter theories are parametrized by positive divisors of $$p - 1$$. The number of supercharacter theories equals the divisor count function of $$p - 1$$. The theories can be described as follows:


 * For a given divisor $$d$$ of order $$p - 1$$, the corresponding supercharacter theory is the one obtained by considering the orbits (both for conjugacy classes and irreducible characters) under the unique subgroup of the automorphism group that has order $$d$$. Note that the automorphism group is cyclic of order $$p - 1$$.
 * For a given divisor $$d$$ of order $$p - 1$$, the corresponding supercharacter theory is the one obtained by considering the orbits (both for conjugacy classes and irreducible characters) under the unique subgroup of the Galois group that has order $$d$$. Note that the Galois group is cyclic of order $$p - 1$$.