diff --git a/gap/bytable.gi b/gap/bytable.gi
index c4c47bc..1ae2223 100644
--- a/gap/bytable.gi
+++ b/gap/bytable.gi
@@ -39,13 +39,32 @@ end);
       
 ## And now create them from multiplication tables
 
-#First a helper function
+# First a helper function
+MagmaNumber@ := 1;
+MagmaLetters@ := "ABCDEFGHJKMNPSTUV";
+MagmaBase@ := Length(magmaLetters@);
+NextMagmaString@ := function(filts)
+  local str, n;
+  str := "l";
+  if filts <> (filts and IsLeftQuotientElement) then
+    str := "r";
+  fi;
+  n := MagmaNumber@;
+  MagmaNumber@ := MagmaNumber@ + 1;
+  while n > 0 do
+    Add(str, MagmaLetters[RemInt(n, MagmaBase@) + 1]);
+    n := QuoInt(n, MagmaBase@);
+  od;
+  return str;
+end;
+
 FiniteMagmaCreator@ := function(tbl, cnstr, filts)
   local M;
   M := MagmaByMultiplicationTableCreatorNC(
          tbl, cnstr, filts and IsMagmaByMultiplicationTableObj);
   # Is there such a thing as a non-finite table in GAP? Anyhow...
   SetIsFinite(ElementsFamily(FamilyObj(M)), IsFinite(tbl));
+  SpecifyElmNamePrefix(M, NextMagmaString@(filts));
   return M;
 end;