diff --git a/OrbitDecomposition.jl b/OrbitDecomposition.jl
index 33702e4..4ceef3a 100644
--- a/OrbitDecomposition.jl
+++ b/OrbitDecomposition.jl
@@ -57,8 +57,8 @@ function elements(F::Nemo.FqNmodFiniteField)
 end
 
 function AutFG_emb(A::AutGroup, g::WreathProductElem)
-    isa(A.objectGroup, FreeGroup) || throw("Not an Aut(FN)")
-    parent(g).P.n == length(A.objectGroup.gens) || throw("No natural action of $(parent(g)) on $A")
+    isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
+    parent(g).P.n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
     powers = [(elt == parent(elt)() ? 0: 1) for elt in g.n.elts]
     elt = reduce(*, [A(Groups.flip_autsymbol(i))^pow for (i,pow) in enumerate(powers)])
     Groups.r_multiply!(elt, [Groups.perm_autsymbol(g.p)])