I'm glad to see the recent articles on going from a finitely presented
group to a permutation group in GAP. I have been having trouble with
just this. I would find it helpful if someone would post a complete
example of how this is done. Specifically:

Let's say I define G as a finitely presented group and H as a subgroup:

a:=AbstractGenerator("a");
b:=AbstractGenerator("b");

G:=Group(a,b);
G.relators:=[a^2,b^3,(a*b)^5]

H:=Subgroup(G,[a,(b*a)^2*b^-1];

OperationCosetsFpGroup(G,H);

So far, I am following the example of 21.5 of the GAP manual. According
to that example, GAP now returns:

Group( (2,3)(4,5), (1,2,4) );

Can someone now post the code that (with this example) lets one take
any word w in a,b and returns the corresponding permutation, along with
a transcript showing that the code works?

Allan Adler
ara@altdorf.ai.mit.edu