diff --git a/src/CondensedMatterSOS.jl b/src/CondensedMatterSOS.jl
index 16b5efd..6adfce3 100644
--- a/src/CondensedMatterSOS.jl
+++ b/src/CondensedMatterSOS.jl
@@ -41,6 +41,8 @@ include("monom-set.jl")
 include("ising.jl")
 
 include("symmetry.jl")
+export Lattice1Group
+
 include("action.jl")
 include("sos.jl")
 
diff --git a/src/action.jl b/src/action.jl
index 17aa3f6..9985317 100644
--- a/src/action.jl
+++ b/src/action.jl
@@ -1,3 +1,4 @@
+import SumOfSquares.Symmetry
 export Action
 
 struct Action <: Symmetry.OnMonomials
@@ -11,7 +12,7 @@ function Symmetry.SymbolicWedderburn.action(a::Action, el::DirectSum, mono::Cond
         rel_id = var.id - a.σ[1][1].id
         rel_index = var.index + 1
         @assert a.σ[rel_index][rel_id + 1] == var
-        id = ((rel_id + el.c.id) % el.c.n) + a.σ[1][1].id
+        id = ((rel_id + el.h.id) % el.h.n) + a.σ[1][1].id
         index = (rel_index^el.k.p) - 1
         new_var = CondensedMatterSOS.SpinVariable(id, index)
         if el.k.k.id != 0 && el.k.k.id != index + 1
diff --git a/src/symmetry.jl b/src/symmetry.jl
index 75717d4..5cd2fdd 100644
--- a/src/symmetry.jl
+++ b/src/symmetry.jl
@@ -1,4 +1,3 @@
-using SumOfSquares
 import Random
 using GroupsCore
 
@@ -8,8 +7,6 @@ function __symmetric_grp_gens(n::Integer)
 end
 symmetric_group(n::Integer) = PermGroup(__symmetric_grp_gens(n)...)
 
-export Lattice1Group
-
 ## Klein C₂⊕C₂ group
 struct KleinGroup <: Group end
 """
@@ -130,12 +127,11 @@ function Base.rand(rng::Random.AbstractRNG, ::Random.SamplerTrivial{KleinPermGro
 end
 
 function Base.deepcopy_internal(g::KleinPermElement, dict::IdDict)
-    p = if haskey(dict, objectid(g.p))
-        dict[objectid(g.p)]
-    else
-        Base.deepcopy_internal(g.p, dict)
-    end
-    return KleinPermElement(p, g.k)
+    haskey(dict, g) && return dict[g]
+
+    h = KleinPermElement(Base.deepcopy_internal(g.p, dict), g.k)
+    dict[g] = h
+    return h
 end
 
 # CyclicGroup
@@ -233,22 +229,24 @@ function Base.rand(rng::Random.AbstractRNG, st::Random.SamplerTrivial{<:DirectSu
 end
 
 function Base.deepcopy_internal(g::DirectSumElem, dict::IdDict)
+    haskey(dict, g) && return g
     h = if isbits(g.h)
         g.h
-    elseif haskey(dict, objectid(g.h))
-        dict[objectid(g.h)]
+    elseif haskey(dict, g.h)
+        dict[g.h]
     else
         Base.deepcopy_internal(g.h, dict)
     end
-
     k = if isbits(g.k)
         g.k
-    elseif haskey(dict, objectid(g.k))
-        dict[objectid(g.k)]
+    elseif haskey(dict, g.k)
+        dict[g.k]
     else
         Base.deepcopy_internal(g.k, dict)
     end
-    return DirectSumElem(h, k)
+    new_g = DirectSumElem(h, k)
+    dict[g] = new_g
+    return new_g
 end
 
 # two aliases