This is more a request to find out if there is any work in the literature discussing certain things.
Is there a naturally defined partial ordering on the set of conjugacy classes of a finite group G? Or a graph with the classes as vertices?
Definitely the class of the identity element will be an extremal element in the partial ordering, or an isolated vertex in case a graph is defined.
Ideally a relation with some bearing on the representation of the group would be interesting.
Suppose Z is the centralizer of an element, then a relation might make sense when defined in terms of the inner products between of Ind$_Z^G 1_Z$ for two such centrlizers of non-conjugate elements.
Perhaps this has been studied. Can someone point me out to any such work?
