[GAP Forum] Questions about representations in Sn and Tz Transformations

[Nikos Apostolakis]

Dear Forum,

I am looking for representations of some fp groups in to symmetric
groups.  Searching the documentation and the archives I came up with
the following code:

sncolorings := function( gp, n )
    local   ls;

    ls := ShallowCopy(LowIndexSubgroupsFpGroup(gp, TrivialSubgroup(gp), n));
    ls := List(ls, g -> CosetTable(gp, g));
    ls := List(ls, ct -> List(ct, PermList));

    return List(ls, x -> x{[2,4..Length(x)]});
end;


My first question is: Is there a way to specify *a priory* that the
generators will be mapped within a given conjugacy class?  For
example I would like all the generators to be mapped to
transpositions.  (I work with Wirtinger presentations of knot and
link groups where the generators are in relatively few conjugacy
classes.)

The second question has to do with Tietze transformations.  The
above process seems to be faster if I first apply the function TzGo
to the presentation.  Also checking if the resulting representation
maps in the desired conjugacy cass is easier since there are fewer
generators.  However, I need to know the images of the original
generators.  So the question is, after I apply TzGo how can I get 
the old generators expressed in terms of the new ones?  I mean, 
by setting "printLevel=2" I can have this information printed out
but how can I use it in a program?

TIA