Given two groups of the same order $G_1$ and $G_2$, how do I find the number of homomorphisms between these two groups?
Is it possible for any groups $G_1$ and $G_2$ of the same order or only for some specific type of groups like cyclic groups?
In my specific case, $G_1$ is $S_5$ and $G_2$ is $D_{120}$ but I would like to know how to solve this kind of questions for general groups, if possible.
EDIT: I'm not looking for anything more advanced than an introductory course on group theory