diff --git a/lib/memory.gi b/lib/memory.gi
index d8e85b5367..31f267f516 100644
--- a/lib/memory.gi
+++ b/lib/memory.gi
@@ -123,13 +123,14 @@ InstallGlobalFunction( CopyMemory,
 
 InstallGlobalFunction( GroupWithMemory,
   function(gens)
-    # gens a list of generators
+    # gens a list of generators or a group
     local g,memgens;
-    if IsGroup(gens) then
-        memgens := GeneratorsWithMemory(GeneratorsOfGroup(gens));
-    else
-        memgens := GeneratorsWithMemory(gens);
+    if not IsGroup(gens) then
+        # trick: ensure all transformations that GroupWithGenerators applies
+        # to the generators are applied here, too
+        gens := GroupWithGenerators(gens);
     fi;
+    memgens := GeneratorsWithMemory(GeneratorsOfGroup(gens));
     g := GroupWithGenerators(memgens);
     return g;
   end);
diff --git a/tst/testinstall/memory.tst b/tst/testinstall/memory.tst
index dea81b2c32..dfa6a1116f 100644
--- a/tst/testinstall/memory.tst
+++ b/tst/testinstall/memory.tst
@@ -1,5 +1,5 @@
 #@local G, H, g, h, tmp, stabChain, s1, s2
-gap> G := GroupWithMemory(GroupByGenerators([ (1,2,3,4,5), (1,2) ]));;
+gap> G := GroupWithMemory([ (1,2,3,4,5), (1,2) ]);;
 gap> H := GroupWithMemory(GL(IsMatrixGroup, 3, 3));;
 gap> g := H.1 ^ 2;; h := H.2 ^ 2;;
 gap> StripMemory(g);