diff --git a/src/sage/groups/perm_gps/partn_ref2/refinement_generic.pxd b/src/sage/groups/perm_gps/partn_ref2/refinement_generic.pxd
index e9c99789df1..b3081e0b506 100644
--- a/src/sage/groups/perm_gps/partn_ref2/refinement_generic.pxd
+++ b/src/sage/groups/perm_gps/partn_ref2/refinement_generic.pxd
@@ -9,6 +9,7 @@
 
 from sage.groups.perm_gps.partn_ref.data_structures cimport OrbitPartition, PartitionStack
 from sage.libs.gap.element cimport GapElement, GapElement_Permutation
+from sage.structure.parent cimport Parent
 
 cdef extern from "refinement_generic.h":
     cdef long *global_refine_vals_array
@@ -35,6 +36,7 @@ cdef class LabelledBranching:
     cdef int *father
     cdef int *act_perm
     cpdef GapElement group, ClosureGroup
+    cdef Parent sym_gp
     cdef bint has_empty_intersection(self, PartitionStack * part)
     cpdef add_gen(self, GapElement_Permutation gen)
 
diff --git a/src/sage/groups/perm_gps/partn_ref2/refinement_generic.pyx b/src/sage/groups/perm_gps/partn_ref2/refinement_generic.pyx
index 998febe0839..f46cbfdda6b 100644
--- a/src/sage/groups/perm_gps/partn_ref2/refinement_generic.pyx
+++ b/src/sage/groups/perm_gps/partn_ref2/refinement_generic.pyx
@@ -334,11 +334,13 @@ cdef class LabelledBranching:
             sage: L = LabelledBranching(3)
         """
         from sage.libs.gap.libgap import libgap
+        from sage.groups.perm_gps.permgroup_named import SymmetricGroup
 
         self.n = n
         self.group = libgap.eval("Group(())")
         self.ClosureGroup = libgap.eval("ClosureGroup")
         self.father = < int *> sig_malloc(n * sizeof(int))
+        self.sym_gp = SymmetricGroup(self.n)
         if self.father is NULL:
             raise MemoryError('allocating LabelledBranching')
         self.act_perm = < int *> sig_malloc(n * sizeof(int))
@@ -433,8 +435,7 @@ cdef class LabelledBranching:
             [(1,2,3)]
         """
         from sage.libs.gap.libgap import libgap
-
-        return libgap.SmallGeneratingSet(self.group).sage()
+        return libgap.SmallGeneratingSet(self.group).sage(parent=self.sym_gp)
 
     def get_order(self):
         r"""
diff --git a/src/sage/libs/gap/libgap.pyx b/src/sage/libs/gap/libgap.pyx
index 63e3cab4391..8d2fc467aad 100644
--- a/src/sage/libs/gap/libgap.pyx
+++ b/src/sage/libs/gap/libgap.pyx
@@ -49,14 +49,24 @@ equivalent::
     sage: libgap.eval('5/3 + 7*E(3)').sage()
     7*zeta3 + 5/3
 
-    sage: generators = libgap.AlternatingGroup(4).GeneratorsOfGroup().sage()
+    sage: gens_of_group = libgap.AlternatingGroup(4).GeneratorsOfGroup()
+    sage: generators = gens_of_group.sage()
     sage: generators   # a Sage list of Sage permutations!
-    [(1,2,3), (2,3,4)]
+    [[2, 3, 1], [1, 3, 4, 2]]
     sage: PermutationGroup(generators).cardinality()   # computed in Sage
     12
     sage: libgap.AlternatingGroup(4).Size()            # computed in GAP
     12
 
+We can also specify which group in Sage the permutations should
+consider themselves as elements of when converted to Sage::
+
+    sage: A4 = groups.permutation.Alternating(4)
+    sage: generators = gens_of_group.sage(parent=A4); generators
+    [(1,2,3), (2,3,4)]
+    sage: all(gen.parent() is A4 for gen in generators)
+    True
+
 So far, the following GAP data types can be directly converted to the
 corresponding Sage datatype: