diff --git a/lib/grpcompl.gi b/lib/grpcompl.gi
index d5bbface82..bba9f2afdd 100644
--- a/lib/grpcompl.gi
+++ b/lib/grpcompl.gi
@@ -99,9 +99,8 @@ local G,N,K,s, h, q, fpi, factorpres, com, comgens, cen, ocrels, fpcgs, ncom,
        Length(MappingGeneratorsImages(fpi)[2])," generators");
   factorpres:=[FreeGeneratorsOfFpGroup(Range(fpi)),
                RelatorsOfFpGroup(Range(fpi)),
-	       List(MappingGeneratorsImages(fpi)[2],
+	       List(GeneratorsOfGroup(Range(fpi)),
 	            i->PreImagesRepresentative(fpi,i))];
-
   Assert(1,ForAll(factorpres[3],i->Image(h,PreImagesRepresentative(h,i))=i));
   # initialize
   com:=[G];
diff --git a/lib/grppcfp.gi b/lib/grppcfp.gi
index 1dc3ef8498..b71abcfbb0 100644
--- a/lib/grppcfp.gi
+++ b/lib/grppcfp.gi
@@ -878,6 +878,9 @@ local g, sq, hom;
   g:=arg[1];
   sq:=CallFuncList(SQ,arg);
   hom:=GroupHomomorphismByImages(g,sq.image,GeneratorsOfGroup(g),sq.imgs);
+  if HasSize(g) and Size(g)=Size(sq.image) then
+    SetIsInjective(hom,true);
+  fi;
   return hom;
 end);
 
diff --git a/tst/testbugfix/2019-04-09-Lattice.tst b/tst/testbugfix/2019-04-09-Lattice.tst
index 13537a39da..77d8b6c664 100644
--- a/tst/testbugfix/2019-04-09-Lattice.tst
+++ b/tst/testbugfix/2019-04-09-Lattice.tst
@@ -1,3 +1,10 @@
 # see https://github.com/gap-system/gap/pull/3397
+# and https://github.com/gap-system/gap/issues/3496
 gap> l:=AllSmallGroups(960,IsSolvableGroup,false);;g:=l[5];;
+gap> nat:=NaturalHomomorphismByNormalSubgroup(g,RadicalGroup(g));;
+gap> fpi:=IsomorphismFpGroup(Group(GeneratorsOfGroup(Range(nat))));;
+gap> fpi:=GroupHomomorphismByImages(Range(nat),Range(fpi),
+> GeneratorsOfGroup(Range(nat)),List(GeneratorsOfGroup(Range(nat)),
+> x->ImagesRepresentative(fpi,x)));;
+gap> SetIsomorphismFpGroup(ImagesSource(nat),fpi);;
 gap> StructureDescription(g);;t:=TableOfMarks(g);;