Presentation of a group to generators in A(S)

[TylerH]

Is there a general algorithm for taking the presentation of a group and get the permutation generators for the subgroup of A(S) to which the group is isomorphic?

For example, given x^5=y^4=e, xy=f(c^2) how do I find (12345) and (1243), the permutations corresponding to x and y? BTW, the example is the Frobenious group of order 20, but I'm asking about a general method.

 

[spamiam]

I think the usual method is the Todd-Coxeter algorithm. It's covered quite extensively in Artin's Algebra.