diff --git a/src/groups/special_euclidean.jl b/src/groups/special_euclidean.jl
index 12756f209d..a6c32ec4a9 100644
--- a/src/groups/special_euclidean.jl
+++ b/src/groups/special_euclidean.jl
@@ -725,7 +725,7 @@ function get_coordinates(
         get_coordinates(M2.manifold, p.x[2], X.x[2], basis),
     )
 end
-function hat(M::SpecialEuclidean{2}, p::ArrayPartition, c)
+function hat(M::SpecialEuclidean{2}, p::ArrayPartition, c::AbstractVector)
     M1, M2 = M.manifold.manifolds
     return ArrayPartition(
         get_vector_orthogonal(M1.manifold, p.x[1], c[SOneTo(2)], ℝ),
@@ -744,7 +744,7 @@ function get_vector(
     )
 end
 
-function hat(M::SpecialEuclidean{3}, p::ArrayPartition, c)
+function hat(M::SpecialEuclidean{3}, p::ArrayPartition, c::AbstractVector)
     M1, M2 = M.manifold.manifolds
     return ArrayPartition(
         get_vector_orthogonal(M1.manifold, p.x[1], c[SOneTo(3)], ℝ),
diff --git a/test/groups/special_euclidean.jl b/test/groups/special_euclidean.jl
index d19c6df846..2200de7c6b 100644
--- a/test/groups/special_euclidean.jl
+++ b/test/groups/special_euclidean.jl
@@ -382,15 +382,29 @@ Random.seed!(10)
             @test isapprox(SEn, log(SEn, pts[1], pts[1]), 0 .* Xs[1]; atol=1e-16)
             @test isapprox(SEn, exp(SEn, pts[1], 0 .* Xs[1]), pts[1])
             vee(SEn, pts[1], Xs[2])
+            get_coordinates(SEn, pts[1], Xs[2], DefaultOrthogonalBasis())
             csen = n == 2 ? SA[1.0, 2.0, 3.0] : SA[1.0, 0.0, 2.0, 2.0, -1.0, 1.0]
             hat(SEn, pts[1], csen)
+            get_vector(SEn, pts[1], csen, DefaultOrthogonalBasis())
             # @btime shows 0 but `@allocations` is inaccurate
             @static if VERSION >= v"1.9-DEV"
                 @test (@allocations exp(SEn, pts[1], Xs[1])) <= 4
                 @test (@allocations compose(SEn, pts[1], pts[2])) <= 4
                 @test (@allocations log(SEn, pts[1], pts[2])) <= 28
                 @test (@allocations vee(SEn, pts[1], Xs[2])) <= 13
+                @test (@allocations get_coordinates(
+                    SEn,
+                    pts[1],
+                    Xs[2],
+                    DefaultOrthogonalBasis(),
+                )) <= 13
                 @test (@allocations hat(SEn, pts[1], csen)) <= 13
+                @test (@allocations get_vector(
+                    SEn,
+                    pts[1],
+                    csen,
+                    DefaultOrthogonalBasis(),
+                )) <= 13
             end
         end
     end