What is a good reference for learning about representations/characters of central products of groups?
By central product, I mean the following. If $G$ and $H$ are groups, containing isomorphic central subgroups $G_1$ and $H_1$ given by an isomorphism $\theta$, then $ G*H = (G \times H)/\langle (g,\theta(g)^{-1}) \rangle $ is what I'm calling the central product, which obviously depends on $G_1$, $H_1$, and $\theta$.
Update: I've found some basic information about central products in the book by Gorenstein, but I'm still wondering if anywhere else has more discussion of this.