diff --git a/test/DirectProd-tests.jl b/test/DirectProd-tests.jl
new file mode 100644
index 0000000..ae7b9fc
--- /dev/null
+++ b/test/DirectProd-tests.jl
@@ -0,0 +1,84 @@
+@testset "DirectProducts" begin
+   using Nemo
+
+   G = PermutationGroup(3)
+   g = G([2,3,1])
+   F, a = FiniteField(2,3,"a")
+
+   @testset "Constructors" begin
+      @test isa(Groups.DirectProductGroup(G,2), Nemo.Group)
+      @test isa(G×G, Nemo.Group)
+      @test isa(Groups.DirectProductGroup(G,2), Groups.DirectProductGroup{Nemo.PermGroup})
+
+      GG = Groups.DirectProductGroup(G,2)
+
+      @test GG == Groups.DirectProductGroup(G,2)
+
+      @test Groups.DirectProductGroupElem([G(), G()]) == GG()
+      @test GG(G(), G()) == GG()
+
+      @test isa(GG([g, g^2]), GroupElem)
+      @test isa(GG([g, g^2]), Groups.DirectProductGroupElem{Nemo.perm})
+
+      h = GG([g,g^2])
+
+      @test h == GG(h)
+
+      @test isa(GG(g, g^2), GroupElem)
+      @test isa(GG(g, g^2), Groups.DirectProductGroupElem)
+
+      @test_throws String GG(g,g,g)
+      @test GG(g,g^2) == h
+
+      @test size(h) == (2,)
+      @test h[1] == g
+      @test h[2] == g^2
+      h[2] = G()
+      @test h == GG(g, G())
+   end
+
+   @testset "Types" begin
+      GG = Groups.DirectProductGroup(G,2)
+      FF = Groups.DirectProductGroup(F,2)
+
+      @test elem_type(GG) == Groups.DirectProductGroupElem{elem_type(G)}
+      @test elem_type(FF) == Groups.DirectProductGroupElem{elem_type(F)}
+      @test parent_type(typeof(GG(g,g^2))) == Groups.DirectProductGroup{typeof(G)}
+      @test parent_type(typeof(FF(a,a^2))) == Groups.DirectProductGroup{typeof(F)}
+
+      @test isa(FF([0,1]), GroupElem)
+      @test isa(FF([0,1]), Groups.DirectProductGroupElem)
+      @test isa(FF([0,1]), Groups.DirectProductGroupElem{elem_type(F)})
+      @test_throws MethodError FF(1,0)
+   end
+
+   @testset "Basis arithmetic" begin
+      g = G([2,3,1])
+      h = GG([g,g^2])
+
+      @test h^2 == GG(g^2,g)
+      @test h^6 == GG()
+
+      @test h*h == h^2
+
+      @test h*inv(h) == GG()
+
+      @test FF([0,a])*FF([a,1]) == FF(a,1+a)
+      x, y = FF([1,a]), FF([a^2,1])
+      @test x*y == FF([a^2+1, a+1])
+      @test inv(x) == FF([1,a])
+   end
+
+   @testset "Misc" begin
+      @test order(GG) == 36
+      @test order(FF) == 64
+
+
+      @test isa([elements(GG)...], Vector{Groups.DirectProductGroupElem{elem_type(G)}})
+      elts = [elements(GG)...]
+
+      @test length(elts) == 36
+      @test all([g*inv(g) for g in elts] .== GG())
+      @test all(inv(g*h) == inv(h)*inv(g) for g in elts for h in elts)
+   end
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 336260f..86cc369 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -6,4 +6,5 @@ using Base.Test
 @testset "Groups" begin
    include("FreeGroup-tests.jl")
    include("AutGroup-tests.jl")
+   include("DirectProd-tests.jl")
 end