diff --git a/gtsam/base/concepts.h b/gtsam/base/concepts.h
index 0ffb2fbd2..39e707a95 100644
--- a/gtsam/base/concepts.h
+++ b/gtsam/base/concepts.h
@@ -149,6 +149,17 @@ check_invariants(const T& a, const T& b, double tol = 1e-9) {
 }
 } // \ namespace group
 
+#define GTSAM_MULTIPLICATIVE_GROUP2(T1,A1,T2,A2,GROUP) \
+namespace group { \
+template<T1 A1, T2 A2> GROUP<A1,A2> compose(const GROUP<A1,A2> &g, const GROUP<A1,A2> & h) { return g * h;} \
+template<T1 A1, T2 A2> GROUP<A1,A2> between(const GROUP<A1,A2> &g, const GROUP<A1,A2> & h) { return g.inverse() * h;} \
+template<T1 A1, T2 A2> GROUP<A1,A2> inverse(const GROUP<A1,A2> &g) { return g.inverse();} \
+namespace traits { \
+template<T1 A1, T2 A2> struct identity<GROUP<A1,A2> > { static const GROUP<A1,A2> value; typedef GROUP<A1,A2> value_type;};\
+template<T1 A1, T2 A2> const GROUP<A1,A2> identity<GROUP<A1,A2> >::value = GROUP<A1,A2>::Identity();\
+template<T1 A1, T2 A2> struct flavor<GROUP<A1,A2> > { typedef multiplicative_tag type;};\
+}}
+
 /**
  * Group Concept
  */
diff --git a/gtsam/geometry/tests/testQuaternion.cpp b/gtsam/geometry/tests/testQuaternion.cpp
index 89dcd3024..eaef53230 100644
--- a/gtsam/geometry/tests/testQuaternion.cpp
+++ b/gtsam/geometry/tests/testQuaternion.cpp
@@ -111,47 +111,8 @@ struct DefaultChart<Eigen::Quaternion<S, O> > {
 } // \namespace gtsam::manifold::traits
 } // \namespace gtsam::manifold
 
-namespace group {
+GTSAM_MULTIPLICATIVE_GROUP2(typename,_Scalar, int,_Options ,Eigen::Quaternion)
 
-template<typename S, int O>
-Eigen::Quaternion<S, O> compose(const Eigen::Quaternion<S, O> &g,
-    const Eigen::Quaternion<S, O> & h) {
-  return g * h;
-}
-
-template<typename S, int O>
-Eigen::Quaternion<S, O> between(const Eigen::Quaternion<S, O> &g,
-    const Eigen::Quaternion<S, O> & h) {
-  return g.inverse() * h;
-}
-
-template<typename S, int O>
-Eigen::Quaternion<S, O> inverse(const Eigen::Quaternion<S, O> &g) {
-  return g.inverse();
-}
-
-namespace traits {
-
-/// Declare the trait that specifies a quaternion's identity element
-template<typename S, int O>
-struct identity<Eigen::Quaternion<S, O> > {
-  static const Eigen::Quaternion<S, O> value;
-  typedef Eigen::Quaternion<S, O> value_type;
-};
-
-/// Out of line definition of identity
-template<typename S, int O>
-const Eigen::Quaternion<S, O> identity<Eigen::Quaternion<S, O> >::value =
-    Eigen::Quaternion<S, O>::Identity();
-
-/// Define the trait that asserts quaternions are a multiplicative group
-template<typename S, int O>
-struct flavor<Eigen::Quaternion<S, O> > {
-  typedef multiplicative_tag type;
-};
-
-} // \namespace gtsam::group::traits
-} // \namespace gtsam::group
 } // \namespace gtsam
 
 /**