REGR: Fix TypeError in groupby min / max of period column

doc/source/whatsnew/v1.1.0.rst

@@ -179,6 +179,7 @@ Groupby/resample/rolling
 
 - Bug in :meth:`GroupBy.apply` raises ``ValueError`` when the ``by`` axis is not sorted and has duplicates and the applied ``func`` does not mutate passed in objects (:issue:`30667`)
 - Bug in :meth:`DataFrameGroupby.transform` produces incorrect result with transformation functions (:issue:`30918`)
+- Bug in :meth:`DataFrame.groupby` whereby taking the minimum or maximum of a column with period dtype would raise a ``TypeError``. (:issue:`31471`)
 
 Reshaping
 ^^^^^^^^^

pandas/core/groupby/ops.py

@@ -31,6 +31,7 @@
     is_extension_array_dtype,
     is_integer_dtype,
     is_numeric_dtype,
+    is_period_dtype,
     is_sparse,
     is_timedelta64_dtype,
     needs_i8_conversion,
@@ -567,7 +568,9 @@ def _cython_operation(
         if swapped:
             result = result.swapaxes(0, axis)
 
-        if is_datetime64tz_dtype(orig_values.dtype):
+        if is_datetime64tz_dtype(orig_values.dtype) or is_period_dtype(
+            orig_values.dtype
+        ):
             result = type(orig_values)(result.astype(np.int64), dtype=orig_values.dtype)
         elif is_datetimelike and kind == "aggregate":
             result = result.astype(orig_values.dtype)

pandas/tests/groupby/test_groupby.py

@@ -2037,3 +2037,19 @@ def test_groupby_list_level():
     expected = pd.DataFrame(np.arange(0, 9).reshape(3, 3))
     result = expected.groupby(level=[0]).mean()
     tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize("func", ["min", "max"])
+def test_groupby_aggregate_period(func):
+    # GH 31471
+    groups = [1, 2]
+    periods = pd.period_range("2020", periods=2, freq="Y")
+
+    df = pd.DataFrame({"a": groups, "b": periods})
+
+    result = getattr(df.groupby("a")["b"], func)()
+
+    idx = pd.Int64Index([1, 2], name="a")
+    expected = pd.Series(periods, index=idx, name="b")
+
+    tm.assert_series_equal(result, expected)