Finitely presented groups are groups and so all operations for groups should be applicable to them (though not necessarily efficient methods are available.) Most methods for finitely presented groups rely on coset enumeration. See Coset Tables and Coset Enumeration for details.
The command IsomorphismPermGroup can be used to obtain a faithful
permutation representation.
gap> f := FreeGroup( "a", "b" ); <free group on the generators [ a, b ]> gap> g := f / [ f.1^2, f.2^3, (f.1*f.2)^5 ]; <fp group on the generators [ a, b ]> gap> h := IsomorphismPermGroup( g ); [ a, b ] -> [ (1,2)(4,5), (2,3,4) ]
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GAP 4 manual