Alternative to PresentationViaCosetTable in GAP

Question

I generate abstract tilings of surfaces, which are represented as graphs and use GAP to calculate the permutation group and based on that the finite group presentation using the following commands:

gap> di:=ReadDigraphs("/data/graph.ds6",1);
<immutable digraph with 450 vertices, 1500 edges>

gap> dg:=DigraphGroup(di);
<permutation group of size 5033164800 with 28 generators>

gap> pr:=PresentationViaCosetTable(dg);

Unfortunately, not even a server with 480GB of memory manages to find the finite presentation of the group.

In the GAP Documentation an alternative is described, which proposes to give a subgroup of the group in terms of words and generators to PresentationViaCosetTable. Unfortunately, my knowledge of groups is quite limited and I do not know how to approach this solution starting from my permutation group. Can anyone point me in the right direction?

Answer 1

PresentationViaCosetTable is an older function that will be inefficien for all but small examples. I suggest you try IsomorphismFpGroup (chooses generators itself to get a nicer presentation) or IsomorphismFpGroupByGenerators (takes your given generators).

When hom is such an isomorphism, let F:=Range(hom), then FreeGeneratorsOfFpGroup(F) are the free generators and RelatorsOfFpGroup(F) the relators.

You also first could call hom:=hom*IsomorphismSimplifiedFpGroup(Range(hom)); to try to simplyfy the presentation, but that can be a question of luck.