diff --git a/gtsam/base/tests/testGroup.cpp b/gtsam/base/tests/testGroup.cpp
new file mode 100644
index 000000000..2cee30070
--- /dev/null
+++ b/gtsam/base/tests/testGroup.cpp
@@ -0,0 +1,78 @@
+/* ----------------------------------------------------------------------------
+
+ * GTSAM Copyright 2010, Georgia Tech Research Corporation, 
+ * Atlanta, Georgia 30332-0415
+ * All Rights Reserved
+ * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
+
+ * See LICENSE for the license information
+
+ * -------------------------------------------------------------------------- */
+
+/**
+ * @file   testGroup.cpp
+ * @brief  Unit tests for groups
+ * @author Frank Dellaert
+ **/
+
+#include <gtsam/base/Group.h>
+#include <Eigen/Core>
+#include <iostream>
+
+namespace gtsam {
+
+template<int N>
+class Permutation: public Eigen::PermutationMatrix<N> {
+public:
+  Permutation() {
+    Eigen::PermutationMatrix<N>::setIdentity();
+  }
+  Permutation(const Eigen::PermutationMatrix<N>& P) :
+      Eigen::PermutationMatrix<N>(P) {
+  }
+  Permutation inverse() const {
+    return Eigen::PermutationMatrix<N>(Eigen::PermutationMatrix<N>::inverse());
+  }
+};
+
+/// Define permutation group traits to be a model of the Multiplicative Group concept
+template<int N>
+struct traits<Permutation<N> > : internal::MultiplicativeGroupTraits<
+    Permutation<N> > {
+  static void Print(const Permutation<N>& m, const std::string& str = "") {
+    std::cout << m << std::endl;
+  }
+  static bool Equals(const Permutation<N>& m1, const Permutation<N>& m2,
+      double tol = 1e-8) {
+    return m1.indices() == m2.indices();
+  }
+};
+
+} // namespace gtsam
+
+#include <gtsam/base/Testable.h>
+#include <CppUnitLite/TestHarness.h>
+
+using namespace std;
+using namespace gtsam;
+
+typedef Permutation<3> G; // Let's use the permutation group of order 3
+
+//******************************************************************************
+TEST(Group, Concept) {
+  BOOST_CONCEPT_ASSERT((IsGroup<G>));
+}
+
+//******************************************************************************
+TEST(Group , Invariants) {
+  G g, h;
+  EXPECT(check_group_invariants(g, h));
+}
+
+//******************************************************************************
+int main() {
+  TestResult tr;
+  return TestRegistry::runAllTests(tr);
+}
+//******************************************************************************
+