Dear GAP Forum:
 Following Joachim Neubueser's very interesting email reply I played
around some more with GAP. I've stumbled upon the following facts:
 Let 
     x:=(24,21,20,13,19,5,23,3,18,16,6,9,22,14,4,2,17,8,15,12,7,11,10)
and
      y:=(4,8,9,12,10)(7,6,3,5,11)(15,19,20,23,21)(18,17,14,16,22).
Then M23 is generated by x, y and 
                    (x*y)^6=1, (x^5*y^7)^4=1.
This suggests M23 might be Free(a,b)/[(a*b)^6,(a^5*y^7)^4]. 

Could someone tell me how GAP could be used to see if this is correct?
I tried Size(...) with the maxlimit=0 option but GASMAN kicked me out
again.

                                                                  -
David Joyner