diff --git a/lib/newgeneratingtuples.gi b/lib/newgeneratingtuples.gi
index 64a4bcf..d408005 100644
--- a/lib/newgeneratingtuples.gi
+++ b/lib/newgeneratingtuples.gi
@@ -18,10 +18,12 @@ InstallGlobalFunction(NumberGeneratingTuples,function(group,p,t,g)
   
   full:=[];
   sz:=Size(group);
-  cc:=ConjugacyClasses(group);
+  # class positions are passed to TotalNumberOfTuples, so they must refer to
+  # the classes of the character table, whose order may differ from the group's
+  ct:=CharacterTable(group);
+  cc:=ConjugacyClasses(ct);
   oc:=List(t,s->Filtered([1..Length(cc)],i->s in cc[i]));
    
-  ct:=CharacterTable(group);     
   str:=TotalNumberOfTuples(ct,g,List(oc,c->c[1]));
  
   Add(full,rec(gp:=group,sz:=sz,cc:=cc,oc:=oc,str:=str,pr:=0,nx:=0));
@@ -55,11 +57,11 @@ InstallGlobalFunction(NumberGeneratingTuples,function(group,p,t,g)
         fi;
       od;
       if not fl then 
-        mcc:=ConjugacyClasses(m);
+        ct:=CharacterTable(m);
+        mcc:=ConjugacyClasses(ct);
         moc:=List(oc,s-> Union(List(s, n-> Filtered([1..Length(mcc)],i ->
               Representative(mcc[i]) in cc[n]))));
         if not ([] in moc) then
-          ct:=CharacterTable(m);     
           str:=0;
           t:=List(tp,c->1);
           repeat
diff --git a/tst/ClassOrder.tst b/tst/ClassOrder.tst
new file mode 100644
index 0000000..febb81e
--- /dev/null
+++ b/tst/ClassOrder.tst
@@ -0,0 +1,38 @@
+gap> START_TEST("MapClass package: ClassOrder.tst");
+
+# A character table may list the conjugacy classes in another order than
+# its group does. Here the group and each subgroup returned by
+# MaximalSubgroupClassReps store the identity class last, whereas a character
+# table has it first.
+gap> IdLast:=function(G)
+>   local reps,H;
+>   reps:=List(ConjugacyClasses(G),Representative);
+>   reps:=Concatenation(reps{[2..Length(reps)]},reps{[1]});
+>   H:=GroupWithGenerators(GeneratorsOfGroup(G),One(G));
+>   SetConjugacyClasses(H,List(reps,x->ConjugacyClass(H,x)));
+>   SetMaximalSubgroupClassReps(H,List(MaximalSubgroupClassReps(G),IdLast));
+>   return H;
+> end;;
+gap> G:=IdLast(SymmetricGroup(4));;
+gap> ForAll(Concatenation([G],MaximalSubgroupClassReps(G)),
+>      H->IdentificationOfConjugacyClasses(CharacterTable(H))
+>         <>[1..NrConjugacyClasses(H)]);
+true
+gap> t7:=ListWithIdenticalEntries(7,(1,2));;
+gap> t8:=ListWithIdenticalEntries(8,(1,2));;
+gap> NumberGeneratingTuples(G,[7],t7,0);
+0
+gap> NumberGeneratingTuples(G,[8],t8,0);
+131040
+gap> NumberGeneratingTuples(G,[2,2],[(1,2),(1,2),(1,2,3),(1,2,3)],0);
+144
+gap> NumberGeneratingTuples(G,[1],[(1,2,3)],1);
+216
+gap> orbs:=GeneratingMCOrbits(G,0,t7:OutputStyle:="silent");;
+gap> Length(orbs);
+0
+gap> orbs:=GeneratingMCOrbits(G,0,[(1,2),(1,2),(1,2,3),(1,2,3)]:
+>      OutputStyle:="silent");;
+gap> List(orbs,o->Length(o.TupleTable));
+[ 6 ]
+gap> STOP_TEST( "ClassOrder.tst" );