diff --git a/lib/grpreps.gi b/lib/grpreps.gi
index 5259acfe57..4a317738e9 100644
--- a/lib/grpreps.gi
+++ b/lib/grpreps.gi
@@ -55,20 +55,39 @@ local modu, modus,gens,v,subs,sub,ser,i,j,a,si,dims,cf,mats,clos,bas,rad;
     a:=DerivedSubgroup(G);
     if Size(a)=Size(G) then
       return [gens,[TrivialModule(Length(gens),F)]];
-    else
-      a:=MaximalAbelianQuotient(G);
-      si:=List(gens,x->ImagesRepresentative(a,x));
-      sub:=IrreducibleModules(Group(si),F,1);
-      if sub[1]=si then
-        return [gens,sub[2]];
+    elif IsAbelian(G) then
+      if IsPrimeField(F) then
+        if CanEasilyComputePcgs(G) then
+          # call `IrreducibleMethods` again;
+          # we assume that now another method is applicable
+          return IrreducibleModules(G, F, 1);
+        else
+          # delegate to a pc group,
+          # for which another method is available
+          a:= IsomorphismPcGroup(G);
+        fi;
       else
-        modu:=[];
-        for i in sub[2] do
+        a:= IsomorphismPermGroup(G);
+      fi;
+    else
+      # delegate to a proper factor group
+      a:= MaximalAbelianQuotient(G);
+    fi;
+    si:=List(gens,x->ImagesRepresentative(a,x));
+    sub:= Group(si);
+    SetIsAbelian(sub, true);
+    sub:= IrreducibleModules(sub,F,0);
+    if sub[1]=si then
+      return [gens, Filtered( sub[2], x -> x.dimension = 1 )];
+    else
+      modu:=[];
+      for i in sub[2] do
+        if i.dimension = 1 then
           v:=GroupHomomorphismByImages(Image(a),Group(i.generators),sub[1],i.generators);
           Add(modu,GModuleByMats(List(si,x->ImagesRepresentative(v,x)),F));
-        od;
-        return [gens,modu];
-      fi;
+        fi;
+      od;
+      return [gens,modu];
     fi;
 
   fi;
diff --git a/tst/testinstall/grpreps.tst b/tst/testinstall/grpreps.tst
index 859e2d15f6..427c94bc4b 100644
--- a/tst/testinstall/grpreps.tst
+++ b/tst/testinstall/grpreps.tst
@@ -16,5 +16,21 @@ gap> res2:= AbsolutelyIrreducibleModules( G2, F, 10 );;
 gap> List( res2[2], r -> [ r.field, r.dimension ] );
 [ [ GF(2), 1 ] ]
 
+# Test that the delegation between methods for 'IrreducibleModules' works.
+gap> Length( IrreducibleModules( AlternatingGroup(5), GF(3), 1 )[2] ) = 1;
+true
+gap> Length( IrreducibleModules( Group( (1,2), (1,2) ), GF(3), 1 )[2] ) = 2;
+true
+gap> Length( IrreducibleModules( Group( (1,2), (1,2) ), GF(4), 1 )[2] ) = 1;
+true
+gap> Length( IrreducibleModules( Group( (1,2,3,4,5) ), GF(4), 1 )[2] ) = 1;
+true
+gap> Length( IrreducibleModules( CyclicGroup( IsFpGroup, 2 ), GF(3), 1 )[2] ) = 2;
+true
+gap> Length( IrreducibleModules( CyclicGroup( IsFpGroup, 2 ), GF(4), 1 )[2] ) = 1;
+true
+gap> Length( IrreducibleModules( SymmetricGroup(5), GF(3), 1 )[2] ) = 2;
+true
+
 #
 gap> STOP_TEST( "grpreps.tst" );