diff --git a/Project.toml b/Project.toml
index 3829cf4838..c751d96dc4 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "Manifolds"
 uuid = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e"
 authors = ["Seth Axen <seth.axen@gmail.com>", "Mateusz Baran <mateuszbaran89@gmail.com>", "Ronny Bergmann <manopt@ronnybergmann.net>", "Antoine Levitt <antoine.levitt@gmail.com>"]
-version = "0.8.71"
+version = "0.8.72"
 
 [deps]
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
diff --git a/src/manifolds/GeneralUnitaryMatrices.jl b/src/manifolds/GeneralUnitaryMatrices.jl
index 1428ff9a63..494f3a485a 100644
--- a/src/manifolds/GeneralUnitaryMatrices.jl
+++ b/src/manifolds/GeneralUnitaryMatrices.jl
@@ -342,17 +342,22 @@ function get_coordinates_orthogonal(M::GeneralUnitaryMatrices{n,ℝ}, p, X, N) w
     return get_coordinates_orthogonal!(M, Y, p, X, N)
 end
 
+function get_coordinates_orthogonal!(::GeneralUnitaryMatrices{1,ℝ}, Xⁱ, p, X, ::RealNumbers)
+    return Xⁱ
+end
 function get_coordinates_orthogonal!(::GeneralUnitaryMatrices{2,ℝ}, Xⁱ, p, X, ::RealNumbers)
     Xⁱ[1] = X[2]
     return Xⁱ
 end
 function get_coordinates_orthogonal!(
-    ::GeneralUnitaryMatrices{n,ℝ},
+    M::GeneralUnitaryMatrices{n,ℝ},
     Xⁱ,
     p,
     X,
     ::RealNumbers,
 ) where {n}
+    @assert length(Xⁱ) == manifold_dimension(M)
+    @assert size(X) == (n, n)
     @inbounds begin
         Xⁱ[1] = X[3, 2]
         Xⁱ[2] = X[1, 3]
@@ -414,6 +419,9 @@ function get_vector_orthogonal(::GeneralUnitaryMatrices{2,ℝ}, p::SMatrix, Xⁱ
     return @SMatrix [0 -Xⁱ[]; Xⁱ[] 0]
 end
 
+function get_vector_orthogonal!(::GeneralUnitaryMatrices{1,ℝ}, X, p, Xⁱ, N::RealNumbers)
+    return X .= 0
+end
 function get_vector_orthogonal!(M::GeneralUnitaryMatrices{2,ℝ}, X, p, Xⁱ, N::RealNumbers)
     return get_vector_orthogonal!(M, X, p, Xⁱ[1], N)
 end
@@ -526,6 +534,7 @@ Return the radius of injectivity on the [`Rotations`](@ref) manifold `M`, which
     > For a derivation of the injectivity radius, see [sethaxen.com/blog/2023/02/the-injectivity-radii-of-the-unitary-groups/](https://sethaxen.com/blog/2023/02/the-injectivity-radii-of-the-unitary-groups/).
 """
 injectivity_radius(::GeneralUnitaryMatrices{n,ℝ}) where {n} = π * sqrt(2.0)
+injectivity_radius(::GeneralUnitaryMatrices{1,ℝ}) = 0.0
 
 # Resolve ambiguity on Rotations and Orthogonal
 function _injectivity_radius(
@@ -537,6 +546,12 @@ end
 function _injectivity_radius(::GeneralUnitaryMatrices{n,ℝ}, ::PolarRetraction) where {n}
     return π / sqrt(2.0)
 end
+function _injectivity_radius(::GeneralUnitaryMatrices{1,ℝ}, ::ExponentialRetraction)
+    return 0.0
+end
+function _injectivity_radius(::GeneralUnitaryMatrices{1,ℝ}, ::PolarRetraction)
+    return 0.0
+end
 
 inner(::GeneralUnitaryMatrices, p, X, Y) = dot(X, Y)
 
diff --git a/test/manifolds/rotations.jl b/test/manifolds/rotations.jl
index 5c3ff11a88..25c0f62264 100644
--- a/test/manifolds/rotations.jl
+++ b/test/manifolds/rotations.jl
@@ -218,4 +218,22 @@ include("../utils.jl")
             PolarInverseRetraction(),
         )
     end
+
+    @testset "Rotations(1)" begin
+        M = Rotations(1)
+        p = fill(1.0, 1, 1)
+        X = get_vector(M, p, Float64[], DefaultOrthonormalBasis())
+        @test X isa Matrix{Float64}
+        @test X == fill(0.0, 1, 1)
+        Xc = get_coordinates(M, p, X, DefaultOrthonormalBasis())
+        @test length(Xc) == 0
+        @test Xc isa Vector{Float64}
+
+        @test injectivity_radius(M) == 0.0
+        @test injectivity_radius(M, p) == 0.0
+        @test injectivity_radius(M, ExponentialRetraction()) == 0.0
+        @test injectivity_radius(M, p, ExponentialRetraction()) == 0.0
+        @test injectivity_radius(M, PolarRetraction()) == 0.0
+        @test injectivity_radius(M, p, PolarRetraction()) == 0.0
+    end
 end