diff --git a/.travis.yml b/.travis.yml
index edc5a30..4c7dc0b 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -14,6 +14,10 @@ matrix:
   allow_failures:
     - julia: nightly
     - os: osx
+addons:
+  apt:
+    packages:
+    - hdf5-tools
 
 ## uncomment the following lines to override the default test
 # script:
diff --git a/Manifest.toml b/Manifest.toml
index caf452f..0f5e58b 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -2,9 +2,9 @@
 
 [[AbstractAlgebra]]
 deps = ["InteractiveUtils", "LinearAlgebra", "Markdown", "Random", "SparseArrays", "Test"]
-git-tree-sha1 = "56bdd9e9bb2cfdf0876d0846b337c8f395d9a4b7"
+git-tree-sha1 = "c0d57a3f0618bfbb214005860b9b5e5bceafa61c"
 uuid = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
-version = "0.4.6"
+version = "0.5.0"
 
 [[Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
@@ -16,10 +16,10 @@ uuid = "9e28174c-4ba2-5203-b857-d8d62c4213ee"
 version = "0.8.10"
 
 [[BinaryProvider]]
-deps = ["Libdl", "Pkg", "SHA", "Test"]
-git-tree-sha1 = "055eb2690182ebc31087859c3dd8598371d3ef9e"
+deps = ["Libdl", "SHA"]
+git-tree-sha1 = "c7361ce8a2129f20b0e05a89f7070820cfed6648"
 uuid = "b99e7846-7c00-51b0-8f62-c81ae34c0232"
-version = "0.5.3"
+version = "0.5.4"
 
 [[Blosc]]
 deps = ["BinaryProvider", "CMakeWrapper", "Compat", "Libdl"]
@@ -34,19 +34,16 @@ uuid = "e1450e63-4bb3-523b-b2a4-4ffa8c0fd77d"
 version = "1.0.0"
 
 [[CMake]]
-deps = ["BinDeps", "Libdl", "Test"]
-git-tree-sha1 = "6e39bef3cbb8321e8a464b18a5c20d7cef813938"
+deps = ["BinDeps"]
+git-tree-sha1 = "c67a8689dc5444adc5eb2be7d837100340ecba11"
 uuid = "631607c0-34d2-5d66-819e-eb0f9aa2061a"
-version = "1.1.1"
+version = "1.1.2"
 
 [[CMakeWrapper]]
 deps = ["BinDeps", "CMake", "Libdl", "Parameters", "Test"]
-git-tree-sha1 = "2b43d451639984e3571951cc687b8509b0a86c6d"
+git-tree-sha1 = "16d4acb3d37dc05b714977ffefa8890843dc8985"
 uuid = "d5fb7624-851a-54ee-a528-d3f3bac0b4a0"
-version = "0.2.2"
-
-[[CRC32c]]
-uuid = "8bf52ea8-c179-5cab-976a-9e18b702a9bc"
+version = "0.2.3"
 
 [[CRlibm]]
 deps = ["Libdl", "Test"]
@@ -103,10 +100,9 @@ deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
 [[ErrorfreeArithmetic]]
-deps = ["Test"]
-git-tree-sha1 = "e38834f24946eb8c7dcf2bb00580e087faa60c44"
+git-tree-sha1 = "a2b7d5a7962e5bfaab0e2e87c9cde7d3087f4e2c"
 uuid = "90fa49ef-747e-5e6f-a989-263ba693cf1a"
-version = "0.3.2"
+version = "0.4.0"
 
 [[FastRounding]]
 deps = ["ErrorfreeArithmetic", "Test"]
@@ -115,10 +111,10 @@ uuid = "fa42c844-2597-5d31-933b-ebd51ab2693f"
 version = "0.2.0"
 
 [[FileIO]]
-deps = ["Pkg", "Random", "Test"]
-git-tree-sha1 = "da32159d4a2e526338506685e280e39ed2f18961"
+deps = ["Pkg"]
+git-tree-sha1 = "351f001a78aa1b7ad2696e386e110b5abd071c71"
 uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
-version = "1.0.6"
+version = "1.0.7"
 
 [[ForwardDiff]]
 deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "InteractiveUtils", "LinearAlgebra", "NaNMath", "Random", "SparseArrays", "SpecialFunctions", "StaticArrays", "Test"]
@@ -128,25 +124,25 @@ version = "0.10.3"
 
 [[GroupRings]]
 deps = ["AbstractAlgebra", "LinearAlgebra", "Markdown", "SparseArrays"]
-git-tree-sha1 = "0d259b2e2254cc22c526938f37936618784fd03d"
-repo-rev = "enh/julia-v0.7"
+git-tree-sha1 = "30ed912be2eb74523699bfdaaefd5d5426c43afa"
+repo-rev = "master"
 repo-url = "https://github.com/kalmarek/GroupRings.jl"
 uuid = "0befed6a-bd73-11e8-1e41-a1190947c2f5"
 version = "0.2.0"
 
 [[Groups]]
 deps = ["AbstractAlgebra", "LinearAlgebra", "Markdown"]
-git-tree-sha1 = "35b712a91e9910bbf150ef1d20d78393e244deaf"
-repo-rev = "enh/julia-v0.7"
+git-tree-sha1 = "64dcaa46affb4568501d35e6fae36a71a7ae5cbb"
+repo-rev = "master"
 repo-url = "https://github.com/kalmarek/Groups.jl"
 uuid = "5d8bd718-bd84-11e8-3b40-ad14f4a32557"
-version = "0.2.0"
+version = "0.2.1"
 
 [[HDF5]]
-deps = ["BinDeps", "Blosc", "CRC32c", "Distributed", "Homebrew", "Libdl", "LinearAlgebra", "Mmap", "Pkg", "Test", "WinRPM"]
-git-tree-sha1 = "dd83e1e9c72e44e3a156438b552cf75dbdda722f"
+deps = ["BinDeps", "Blosc", "Homebrew", "Libdl", "Mmap", "WinRPM"]
+git-tree-sha1 = "e6f0c154d01faef0d0831d075aa8f279f95946da"
 uuid = "f67ccb44-e63f-5c2f-98bd-6dc0ccc4ba2f"
-version = "0.11.0"
+version = "0.11.1"
 
 [[HTTPClient]]
 deps = ["Compat", "LibCURL"]
@@ -183,10 +179,10 @@ uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 version = "0.20.0"
 
 [[JuMP]]
-deps = ["Calculus", "DataStructures", "ForwardDiff", "LinearAlgebra", "MathOptInterface", "NaNMath", "Random", "SparseArrays", "Statistics", "Test"]
-git-tree-sha1 = "db9f08540c1a23269acbae5d520c79f4722899f4"
+deps = ["Calculus", "DataStructures", "ForwardDiff", "LinearAlgebra", "MathOptInterface", "NaNMath", "Random", "SparseArrays", "Statistics"]
+git-tree-sha1 = "a37fdb14ee3a04b4df44c20a73da89c57035bdf2"
 uuid = "4076af6c-e467-56ae-b986-b466b2749572"
-version = "0.19.0"
+version = "0.19.2"
 
 [[LegacyStrings]]
 deps = ["Compat"]
@@ -195,10 +191,10 @@ uuid = "1b4a561d-cfcb-5daf-8433-43fcf8b4bea3"
 version = "0.4.1"
 
 [[LibCURL]]
-deps = ["BinaryProvider", "Libdl", "Printf", "Test"]
-git-tree-sha1 = "d051c8057512ca38a273aaa514145a0b25f24d46"
+deps = ["BinaryProvider", "Libdl"]
+git-tree-sha1 = "5ee138c679fa202ebe211b2683d1eee2a87b3dbe"
 uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
-version = "0.5.0"
+version = "0.5.1"
 
 [[LibExpat]]
 deps = ["Compat"]
@@ -252,15 +248,15 @@ version = "0.3.2"
 
 [[Nemo]]
 deps = ["AbstractAlgebra", "BinaryProvider", "InteractiveUtils", "Libdl", "LinearAlgebra", "Markdown", "Test"]
-git-tree-sha1 = "a152b26c888fbe3c191424938243552935ca2f51"
+git-tree-sha1 = "b359c25b708c3edcc2f17345d59da7169c207385"
 uuid = "2edaba10-b0f1-5616-af89-8c11ac63239a"
-version = "0.13.1"
+version = "0.14.0"
 
 [[OrderedCollections]]
 deps = ["Random", "Serialization", "Test"]
-git-tree-sha1 = "85619a3f3e17bb4761fe1b1fd47f0e979f964d5b"
+git-tree-sha1 = "c4c13474d23c60d20a67b217f1d7f22a40edf8f1"
 uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
-version = "1.0.2"
+version = "1.1.0"
 
 [[Parameters]]
 deps = ["Markdown", "OrderedCollections", "REPL", "Test"]
@@ -289,10 +285,9 @@ deps = ["Serialization"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
 [[RecipesBase]]
-deps = ["Random", "Test"]
-git-tree-sha1 = "0b3cb370ee4dc00f47f1193101600949f3dcf884"
+git-tree-sha1 = "7bdce29bc9b2f5660a6e5e64d64d91ec941f6aa2"
 uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
-version = "0.6.0"
+version = "0.7.0"
 
 [[SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
@@ -324,10 +319,10 @@ uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
 version = "0.7.2"
 
 [[StaticArrays]]
-deps = ["InteractiveUtils", "LinearAlgebra", "Random", "Statistics", "Test"]
-git-tree-sha1 = "3841b39ed5f047db1162627bf5f80a9cd3e39ae2"
+deps = ["LinearAlgebra", "Random", "Statistics"]
+git-tree-sha1 = "db23bbf50064c582b6f2b9b043c8e7e98ea8c0c6"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "0.10.3"
+version = "0.11.0"
 
 [[Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
diff --git a/Project.toml b/Project.toml
index 55b843e..21135bd 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "PropertyT"
 uuid = "03b72c93-0167-51e2-8a1e-eb4ff1fb940d"
 authors = ["Marek Kaluba <kalmar@amu.edu.pl>"]
-version = "0.2.0"
+version = "0.2.1"
 
 [deps]
 AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
@@ -20,7 +20,7 @@ SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [compat]
 GroupRings = "^0.2.0"
-Groups = "^0.2.0"
+Groups = "^0.2.1"
 JuMP = "^0.19.0"
 
 [extras]
diff --git a/src/checksolution.jl b/src/checksolution.jl
index c102191..8a4a166 100644
--- a/src/checksolution.jl
+++ b/src/checksolution.jl
@@ -37,7 +37,7 @@ function compute_SOS(RG::GroupRing, Q::AbstractMatrix{<:Real})
     return GroupRingElem(result, RG)
 end
 
-function compute_SOS_square(pm::AbstractMatrix{<:Integer}, Q::AbstractMatrix{<:Real})
+function compute_SOS_square(pm::AbstractMatrix{<:Integer}, Q::AbstractMatrix)
     result = zeros(eltype(Q), maximum(pm));
 
     for i in 1:size(Q,2)
@@ -47,12 +47,12 @@ function compute_SOS_square(pm::AbstractMatrix{<:Integer}, Q::AbstractMatrix{<:R
     return result
 end
 
-function compute_SOS_square(RG::GroupRing, Q::AbstractMatrix{<:Real})
+function compute_SOS_square(RG::GroupRing, Q::AbstractMatrix)
     return GroupRingElem(compute_SOS_square(RG.pm, Q), RG)
 end
 
-function augIdproj(Q::AbstractMatrix{T}) where {T<:Real}
-    result = zeros(size(Q))
+function augIdproj(Q::AbstractMatrix{T}) where T
+    result = zeros(T, size(Q))
     l = size(Q, 2)
     Threads.@threads for j in 1:l
         col = sum(view(Q, :,j))/l
diff --git a/src/orbitdata.jl b/src/orbitdata.jl
index 4a8b61f..13fe2da 100644
--- a/src/orbitdata.jl
+++ b/src/orbitdata.jl
@@ -58,9 +58,9 @@ function orthSVD(M::AbstractMatrix{T}) where {T<:AbstractFloat}
     return fact.U[:,1:M_rank]
 end
 
-function orbit_decomposition(G::Group, E::Vector, rdict=GroupRings.reverse_dict(E))
+orbit_decomposition(G::Group, E::AbstractVector, rdict=GroupRings.reverse_dict(E)) = orbit_decomposition(collect(G), E, rdict)
 
-    elts = collect(G)
+function orbit_decomposition(elts::AbstractVector{<:GroupElem}, E::AbstractVector, rdict=GroupRings.reverse_dict(E))
 
     tovisit = trues(size(E));
     orbits = Vector{Vector{Int}}()
@@ -178,13 +178,47 @@ end
 #
 ###############################################################################
 
-function (p::perm)(A::GroupRingElem)
-    RG = parent(A)
-    result = zero(RG, eltype(A.coeffs))
+function (g::GroupRingElem)(y::GroupRingElem)
+    res = parent(y)()
+    for elt in GroupRings.supp(g)
+        res += g[elt]*elt(y)
+    end
+    return res
+end
 
-    for (idx, c) in enumerate(A.coeffs)
-        if c!= zero(eltype(A.coeffs))
-            result[p(RG.basis[idx])] = c
+###############################################################################
+#
+#  perm actions
+#
+###############################################################################
+
+function (g::perm)(y::GroupRingElem)
+    RG = parent(y)
+    result = zero(RG, eltype(y.coeffs))
+
+    for (idx, c) in enumerate(y.coeffs)
+        if c!= zero(eltype(y.coeffs))
+            result[g(RG.basis[idx])] = c
+        end
+    end
+    return result
+end
+
+function (g::perm)(y::GroupRingElem{T, <:SparseVector}) where T
+    RG = parent(y)
+    index = [RG.basis_dict[g(RG.basis[idx])] for idx in y.coeffs.nzind]
+
+    result = GroupRingElem(sparsevec(index, y.coeffs.nzval, y.coeffs.n), RG)
+
+    return result
+end
+
+function (p::perm)(A::MatElem)
+    length(p.d) == size(A, 1) == size(A,2) || throw("Can't act via $p on matrix of size $(size(A))")
+    result = similar(A)
+    @inbounds for i in 1:size(A, 1)
+        for j in 1:size(A, 2)
+            result[i, j] = A[p[i], p[j]] # action by permuting rows and colums/conjugation
         end
     end
     return result
@@ -192,45 +226,35 @@ end
 
 ###############################################################################
 #
-#  Action of WreathProductElems on Nemo.MatElem
+#  WreathProductElems action on Nemo.MatElem
 #
 ###############################################################################
 
-function matrix_emb(n::DirectPowerGroupElem, p::perm)
-    Id = parent(n.elts[1])()
-    elt = Diagonal([(-1)^(el == Id ? 0 : 1) for el in n.elts])
-    return elt[:, p.d]
+function (g::WreathProductElem)(y::GroupRingElem)
+    RG = parent(y)
+    result = zero(RG, eltype(y.coeffs))
+
+    for (idx, c) in enumerate(y.coeffs)
+        if c!= zero(eltype(y.coeffs))
+            result[g(RG.basis[idx])] = c
+        end
+    end
+    return result
 end
 
-function (g::WreathProductElem)(A::MatElem)
-    g_inv = inv(g)
-    G = matrix_emb(g.n, g_inv.p)
-    G_inv = matrix_emb(g_inv.n, g.p)
-    M = parent(A)
-    return M(G)*A*M(G_inv)
-end
-
-import Base.*
-
-@doc doc"""
-    *(x::AbstractAlgebra.MatElem, P::Generic.perm)
-> Apply the pemutation $P$ to the rows of the matrix $x$ and return the result.
-"""
-function *(x::AbstractAlgebra.MatElem, P::Generic.perm)
-   z = similar(x)
-   m = nrows(x)
-   n = ncols(x)
-   for i = 1:m
-      for j = 1:n
-         z[i, j] = x[i,P[j]]
-      end
-   end
-   return z
-end
-
-function (p::perm)(A::MatElem)
-    length(p.d) == A.r == A.c || throw("Can't act via $p on matrix of size ($(A.r), $(A.c))")
-    return p*A*inv(p)
+function (g::WreathProductElem{N})(A::MatElem) where N
+    # @assert N == size(A,1) == size(A,2)
+    flips = ntuple(i->(g.n[i].d[1]==1 && g.n[i].d[2]==2 ? 1 : -1), N)
+    result = similar(A)
+    @inbounds for i = 1:size(A,1)
+        for j = 1:size(A,2)
+            x = A[g.p[i], g.p[j]]
+            result[i, j] = x*(flips[i]*flips[j])
+            # result[i, j] = AbstractAlgebra.mul!(x, x, flips[i]*flips[j])
+            # this mul! needs to be separately defined, but is 2x faster
+        end
+    end
+    return result
 end
 
 ###############################################################################
@@ -250,23 +274,18 @@ 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(p)) into $A")
-    return A(Groups.perm_autsymbol(p))
-end
-
 function (g::WreathProductElem)(a::Groups.Automorphism)
     A = parent(a)
-    g = AutFG_emb(A,g)
-    res = A()
-    Groups.r_multiply!(res, g.symbols, reduced=false)
-    Groups.r_multiply!(res, a.symbols, reduced=false)
-    Groups.r_multiply!(res, [inv(s) for s in reverse!(g.symbols)])
+    g_emb = AutFG_emb(A,g)
+    res = deepcopy(g_emb)
+    res = Groups.r_multiply!(res, a.symbols, reduced=false)
+    res = Groups.r_multiply!(res, [inv(s) for s in reverse!(g_emb.symbols)])
     return res
 end
 
 function (p::perm)(a::Groups.Automorphism)
-    g = AutFG_emb(parent(a),p)
-    return g*a*inv(g)
+    res = parent(a)(Groups.perm_autsymbol(p))
+    res = Groups.r_multiply!(res, a.symbols, reduced=false)
+    res = Groups.r_multiply!(res, [Groups.perm_autsymbol(inv(p))])
+    return res
 end