diff --git a/Orb_AutFN.jl b/Orb_AutFN.jl
index 121a5bd..91ed676 100644
--- a/Orb_AutFN.jl
+++ b/Orb_AutFN.jl
@@ -194,14 +194,14 @@ function SOutFN_generating_set(logger, name::String, N::Int)
 end
 
 function init_orbit_data{T<:Nemo.GroupElem}(logger, name::String, G::Nemo.Group,
-   S::Vector{T}; radius=2)
+   S::Vector{T}, AutS::Nemo.Group; radius=2)
 
    ex(fname) = isfile(joinpath(name, fname))
 
    files_exists = ex.(["delta.jld", "pm.jld", "U_pis.jld", "orbits.jld"])
 
    if !all(files_exists)
-      compute_orbit_data(logger, name, SOutFN, S, radius=radius)
+      compute_orbit_data(logger, name, SOutFN, S, AutS, radius=radius)
    end
 
    return 0
diff --git a/OrbitDecomposition.jl b/OrbitDecomposition.jl
index 8694dbb..6a43211 100644
--- a/OrbitDecomposition.jl
+++ b/OrbitDecomposition.jl
@@ -157,7 +157,8 @@ function Uπ_matrices(P_matrices; orth=orthSVD)
     return U_p_matrices
 end
 
-function compute_orbit_data{T<:GroupElem}(logger, name::String, G::Group, S::Vector{T}; radius=2)
+
+function compute_orbit_data{T<:GroupElem}(logger, name::String, G::Group, S::Vector{T}, AutS; radius=2)
    isdir(name) || mkdir(name)
 
    info(logger, "Generating ball of radius 4")
@@ -173,30 +174,26 @@ function compute_orbit_data{T<:GroupElem}(logger, name::String, G::Group, S::Vec
    save(joinpath(name, "delta.jld"), "Δ", Δ.coeffs)
    save(joinpath(name, "pm.jld"), "pm", pm)
 
-   N = length(G.objectGroup.gens)
-   info(logger, "WreathProduct")
-   @time BN = WreathProduct(Nemo.FiniteField(2,1, "a")[1], PermutationGroup(N))
-
-   info(logger, "Decomposing E into orbits of B$(N)")
-   @time orbs = orbit_decomposition(BN, E4, E_dict)
+   info(logger, "Decomposing E into orbits of $(Aut_S)")
+   @time orbs = orbit_decomposition(AutS, E4, E_dict)
    @assert sum(length(o) for o in orbs) == length(E4)
    save(joinpath(name, "orbits.jld"), "orbits", orbs)
 
    info(logger, "Action matrices")
    E2 = E4[1:sizes[radius]]
-   @time BNactionE_mreps = [matrix_repr(g, E2, E_dict) for g in elements(BN)]
+   @time AutS_matrixreps = [matrix_repr(g, E2, E_dict) for g in elements(AutS)]
 
    info(logger, "Projections")
-   @time BN_mps = rankOne_projections(BN);
+   @time AutS_mps = rankOne_projections(AutS);
 
-   @time π_E_projections = [Cstar_repr(p, BNactionE_mreps) for p in BN_mps]
+   @time π_E_projections = [Cstar_repr(p, AutS_matrixreps) for p in AutS_mps]
 
    info(logger, "Uπs...")
    @time Uπs = Uπ_matrices(π_E_projections);
 
    multiplicities = [size(U,2) for U in Uπs];
    info(logger, "multiplicities = $multiplicities")
-   dimensions = [Int(p[BN()]*Int(order(BN))) for p in BN_mps];
+   dimensions = [Int(p[AutS()]*Int(order(AutS))) for p in AutS_mps];
    info(logger, "dimensions = $dimensions")
    @assert dot(multiplicities, dimensions) == sizes[radius]