diff --git a/AutFN_orbit.jl b/AutFN_orbit.jl
index 071847b..b396fac 100644
--- a/AutFN_orbit.jl
+++ b/AutFN_orbit.jl
@@ -15,11 +15,22 @@ function AutFG_emb(A::AutGroup, g::WreathProductElem)
     return elt
 end
 
+function AutFG_emb(A::AutGroup, p::perm)
+    isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
+    parent(p).n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
+    return A(Groups.perm_autsymbol(p))
+end
+
 function (g::WreathProductElem)(a::AutGroupElem)
     g = AutFG_emb(parent(a),g)
     return g*a*g^-1
 end
 
+function (p::perm)(a::AutGroupElem)
+    g = AutFG_emb(parent(a),p)
+    return g*a*g^-1
+end
+
 ###############################################################################
 #
 #  Generating set
@@ -103,6 +114,7 @@ function main()
    info(logger, "Symmetric generating set of size $(length(S))")
    info(logger, S)
    AutS = WreathProduct(Nemo.FiniteField(2,1, "a")[1], PermutationGroup(N))
+   # AutS = PermutationGroup(N)
 
    solver = SCS.SCSSolver(eps=tol, max_iters=iterations, verbose=true, linearsolver=SCS.Indirect)