Thanks Marek,
   
  Things work now. It looks like your method  of checking whether a 
  vector is in a subspace is better than what I was using.
  
> bb:=MutableBasis(F, V); # MM
> M:=List(vD4,x->List(V,y->IsContainedInSpan(bb,x*y))); #MM
   
  It would be good to have what I was using also works (in principle
  there's no reason for it to fail) since that gives a matrix for the action;
  maybe it's a simple fix in GAP.
   
  Regards,
  R.N.
  


 


       
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