diff --git a/docs/src/Groups/group_characters.md b/docs/src/Groups/group_characters.md
index b9f59f84be44..1fd15c209833 100644
--- a/docs/src/Groups/group_characters.md
+++ b/docs/src/Groups/group_characters.md
@@ -209,7 +209,8 @@ arithmetic operations:
   where the group of `chi` is a subgroup of the group of `tbl`.
 
 ```@docs
-scalar_product
+scalar_product(chi::GAPGroupClassFunction, psi::GAPGroupClassFunction)
+tensor_product(chi::GAPGroupClassFunction, psi::GAPGroupClassFunction)
 coordinates(chi::GAPGroupClassFunction)
 multiplicities_eigenvalues
 induce(chi::GAPGroupClassFunction, tbl::GAPGroupCharacterTable)
diff --git a/src/Groups/group_characters.jl b/src/Groups/group_characters.jl
index 42280273a14a..2c08fb765e62 100644
--- a/src/Groups/group_characters.jl
+++ b/src/Groups/group_characters.jl
@@ -2405,6 +2405,17 @@ function Base.:*(chi::GAPGroupClassFunction, psi::GAPGroupClassFunction)
     return GAPGroupClassFunction(parent(chi), GapObj(chi) * GapObj(psi))
 end
 
+"""
+    tensor_product(chi::GAPGroupClassFunction, psi::GAPGroupClassFunction)
+
+Return the pointwise product of `chi` and `psi`.
+The resulting character is afforded by the tensor product of representations
+corresponding to `chi` and `psi`, hence the name.
+
+Alias for `chi * psi`.
+"""
+tensor_product(chi::GAPGroupClassFunction, psi::GAPGroupClassFunction) = chi * psi
+
 function Base.zero(chi::GAPGroupClassFunction)
     val = QQAbFieldElem(0)
     return class_function(parent(chi), [val for i in 1:length(chi)])
diff --git a/test/Groups/group_characters.jl b/test/Groups/group_characters.jl
index 3c2698066302..dfa29cf5e2b5 100644
--- a/test/Groups/group_characters.jl
+++ b/test/Groups/group_characters.jl
@@ -858,6 +858,8 @@ end
   @test sort!([order(center(chi)[1]) for chi in t]) == [1, 1, 4, 24, 24]
   @test all(i -> findfirst(==(t[i]), t) == i, 1:nrows(t))
 
+  @test all(chi -> chi * chi == tensor_product(chi, chi), t)
+
   scp = scalar_product(t[1], t[1])
   @test scp == 1
   @test scp isa QQFieldElem
@@ -1232,6 +1234,8 @@ end
     @test all(chi -> order(center(chi)[1]) == n, tbl1)
     @test all(chi -> is_subgroup(kernel(chi)[1], G1)[1], tbl1)
 
+    @test all(chi -> chi * chi == tensor_product(chi, chi), tbl1)
+
     scp = scalar_product(tbl1[1], tbl1[1])
     @test scp == 1
     @test scp isa QQFieldElem