Supercharacter theories for quaternion group

This page lists the various possible supercharacter theories for the quaternion group of order eight. It builds on a thorough understanding of element structure of quaternion group, subgroup structure of quaternion group, and linear representation theory of quaternion group.

We use the standard notation for the elements of the quaternion group: the identity element is denoted 1, the non-identity element of the center is denoted -1, and the other elements are $$i,-i,j,-j,k,-k$$.

Character table
Below is the character table of the quaternion group.