Find a relation in GAP

Question

I have a finitely presented group $G$ and a finitely generated subgroup $H<G$. GAP computed that $H$ has finite index in $G$. However, PresentationSubgroupMtc(G,H) cannot compute the presentation ($[G:H]$ is a few thousands). I am wondering if its possible to find at least a few relations in $H$ using GAP.

Answer 1

First, the caveat that MTC usually provides far worse presentations that RRS. Are you sure you need MTC?

With this, if you look at the code for PresentationSubgroupMtc (in your gapdirectory/lib/sgpres,gi) you see that there is a rather brief function that computes an augmented coset table and then calls the function NEWTC_PresentationMTC which rewrites the presentation relator-by-relator. You could duplicate this code (renaming the functions) to have it return a partial set of relators.