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Let $G=< g_1,\ldots ,g_n| r_1,\ldots r_k>$ be a finite presentation of a group and let $S$ be a finite group, let's say for concreteness the symmetric group on 4 elements.

We want to create all homomorphisms $G\rightarrow S$.

One could just do the brute force search by looking at all maps from the set of generators $g_1,\ldots, g_n$ to $S$ and check which ones are homomorphisms.

Is this (or a more clever way of doing this) already implemented?

Let $G=< g_1,\ldots ,g_n| r_1,\ldots r_k>$ be a finite presentation of a group and let $S$ be a finite group, let's say for concreteness the symmetric group on 4 elements.

We want to create all homomorphisms $G\rightarrow S$.

One could just do the brute force search by looking at all maps from the set of generators $g_1,\ldots, g_n$ to $S$ and check which ones are homomorphisms.

Is this (or a more clever way of doing this) already implemented?