diff --git a/moto/iam/models.py b/moto/iam/models.py
index 9eefc9c70..4952f2335 100644
--- a/moto/iam/models.py
+++ b/moto/iam/models.py
@@ -1225,7 +1225,9 @@ class IAMBackend(BaseBackend):
         try:
             del self.groups[group_name]
         except KeyError:
-            raise IAMNotFoundException("Group {0} not found".format(group_name))
+            raise IAMNotFoundException(
+                "The group with name {0} cannot be found.".format(group_name)
+            )
 
     def create_user(self, user_name, path="/"):
         if user_name in self.users:
diff --git a/moto/iam/responses.py b/moto/iam/responses.py
index ac6332080..4bd1aa80c 100644
--- a/moto/iam/responses.py
+++ b/moto/iam/responses.py
@@ -429,10 +429,10 @@ class IamResponse(BaseResponse):
         return template.render(name="GetGroupPolicyResponse", **policy_result)
 
     def delete_group(self):
-        group_name = self._get_param('GroupName')
+        group_name = self._get_param("GroupName")
         iam_backend.delete_group(group_name)
         template = self.response_template(GENERIC_EMPTY_TEMPLATE)
-        return template.render(name='DeleteGroup')
+        return template.render(name="DeleteGroup")
 
     def create_user(self):
         user_name = self._get_param("UserName")
diff --git a/tests/test_iam/test_iam_groups.py b/tests/test_iam/test_iam_groups.py
index bb54761a2..7b73e89ea 100644
--- a/tests/test_iam/test_iam_groups.py
+++ b/tests/test_iam/test_iam_groups.py
@@ -8,6 +8,7 @@ import sure  # noqa
 
 from nose.tools import assert_raises
 from boto.exception import BotoServerError
+from botocore.exceptions import ClientError
 from moto import mock_iam, mock_iam_deprecated
 
 MOCK_POLICY = """
@@ -186,10 +187,21 @@ def test_list_group_policies():
 
 @mock_iam
 def test_delete_group():
-    conn = boto3.client('iam', region_name='us-east-1')
-    conn.create_group(GroupName='my-group')
+    conn = boto3.client("iam", region_name="us-east-1")
+    conn.create_group(GroupName="my-group")
     groups = conn.list_groups()
-    assert groups['Groups'][0]['GroupName'] == 'my-group'
-    assert len(groups['Groups']) == 1
-    conn.delete_group(GroupName='my-group')
-    conn.list_groups()['Groups'].should.be.empty
+    assert groups["Groups"][0]["GroupName"] == "my-group"
+    assert len(groups["Groups"]) == 1
+    conn.delete_group(GroupName="my-group")
+    conn.list_groups()["Groups"].should.be.empty
+
+
+@mock_iam
+def test_delete_unknown_group():
+    conn = boto3.client("iam", region_name="us-east-1")
+    with assert_raises(ClientError) as err:
+        conn.delete_group(GroupName="unknown-group")
+    err.exception.response["Error"]["Code"].should.equal("NoSuchEntity")
+    err.exception.response["Error"]["Message"].should.equal(
+        "The group with name unknown-group cannot be found."
+    )