diff --git a/escnn/group/groups/cyclicgroup.py b/escnn/group/groups/cyclicgroup.py
index 57afff79..f6772ba7 100644
--- a/escnn/group/groups/cyclicgroup.py
+++ b/escnn/group/groups/cyclicgroup.py
@@ -46,7 +46,10 @@ def __init__(self, N: int):
         
         Args:
             N (int): order of the group
-            
+
+        Attributes:
+            ~.rotation_order (int): the number of rotations, i.e. the order of the group
+
         """
         
         assert (isinstance(N, int) and N > 0), N
@@ -54,7 +57,10 @@ def __init__(self, N: int):
         super(CyclicGroup, self).__init__("C%d" % N, False, True)
         
         self.N = N
-        
+
+        # int: for consistency with the DihedralGroup, store the number of rotations also in this attribute
+        self.rotation_order = N
+
         self._elements = [self.element(i) for i in range(N)]
         # self._elements_names = ['e'] + ['r%d' % i for i in range(1, N)]
 
diff --git a/escnn/group/groups/o2group.py b/escnn/group/groups/o2group.py
index bdf381c3..1f607721 100644
--- a/escnn/group/groups/o2group.py
+++ b/escnn/group/groups/o2group.py
@@ -84,6 +84,7 @@ def __init__(self, maximum_frequency: int = 6):
         Attributes:
             
             ~.reflection: the reflection element :math:`(j, \theta) = (1, 0.)`
+            ~.rotation_order (int): this is equal to ``-1``, which means the group contains an infinite number of rotations
 
         """
         
diff --git a/escnn/group/groups/so2group.py b/escnn/group/groups/so2group.py
index a550b22e..4f68e3b0 100644
--- a/escnn/group/groups/so2group.py
+++ b/escnn/group/groups/so2group.py
@@ -52,6 +52,9 @@ def __init__(self, maximum_frequency: int = 6):
         Args:
             maximum_frequency (int, optional): the maximum frequency to consider when building the irreps of the group
         
+        Attributes:
+            ~.rotation_order (int): this is equal to ``-1``, which means the group contains an infinite number of rotations
+
         """
         
         assert (isinstance(maximum_frequency, int) and maximum_frequency >= 0)
@@ -59,7 +62,8 @@ def __init__(self, maximum_frequency: int = 6):
         super(SO2, self).__init__("SO(2)", True, True)
         
         self._maximum_frequency = maximum_frequency
-        
+        self.rotation_order = -1
+
         self._identity = self.element(0.)
         
         self._build_representations()