diff --git a/xarray/core/groupby.py b/xarray/core/groupby.py
index 54806988205..b718eed1b31 100644
--- a/xarray/core/groupby.py
+++ b/xarray/core/groupby.py
@@ -287,7 +287,7 @@ def codes(self) -> DataArray:
         return self.encoded.codes
 
     @property
-    def unique_coord(self) -> DataArray:
+    def unique_coord(self) -> Variable | _DummyGroup:
         return self.encoded.unique_coord
 
     def __post_init__(self) -> None:
@@ -300,13 +300,13 @@ def __post_init__(self) -> None:
 
         self.group = _resolve_group(self.obj, self.group)
 
-        self.encoded = self.factorize()
+        self.encoded = self.grouper.factorize(self.group)
 
     @property
     def name(self) -> Hashable:
         """Name for the grouped coordinate after reduction."""
         # the name has to come from unique_coord because we need `_bins` suffix for BinGrouper
-        (name,) = self.unique_coord.dims
+        (name,) = self.encoded.unique_coord.dims
         return name
 
     @property
@@ -318,28 +318,6 @@ def __len__(self) -> int:
         """Number of groups."""
         return len(self.encoded.full_index)
 
-    @property
-    def dims(self):
-        return self.group1d.dims
-
-    def factorize(self) -> EncodedGroups:
-        encoded = self.grouper.factorize(self.group)
-
-        if encoded.group_indices is None:
-            encoded.group_indices = tuple(
-                g
-                for g in _codes_to_group_indices(
-                    encoded.codes.data.ravel(), len(encoded.full_index)
-                )
-                if g
-            )
-        if encoded.unique_coord is None:
-            unique_values = encoded.full_index[np.unique(encoded.codes)]
-            encoded.unique_coord = Variable(
-                dims=encoded.codes.name, data=unique_values, attrs=self.group.attrs
-            )
-        return encoded
-
 
 def _validate_groupby_squeeze(squeeze: Literal[False]) -> None:
     # While we don't generally check the type of every arg, passing
@@ -446,7 +424,7 @@ def factorize(self) -> EncodedGroups:
             (grouper.full_index.values for grouper in groupers),
             names=tuple(grouper.name for grouper in groupers),
         )
-        dim_name = "stacked_" + "_".join(grouper.name for grouper in groupers)
+        dim_name = "stacked_" + "_".join(str(grouper.name) for grouper in groupers)
 
         return EncodedGroups(
             codes=first_codes.copy(data=_flatcodes),
diff --git a/xarray/groupers.py b/xarray/groupers.py
index 45bca540c35..d30d0eeea74 100644
--- a/xarray/groupers.py
+++ b/xarray/groupers.py
@@ -45,7 +45,7 @@ def _coordinates_from_variable(variable: Variable) -> Coordinates:
     return Coordinates(new_vars, indexes)
 
 
-@dataclass
+@dataclass(init=False)
 class EncodedGroups:
     """
     Dataclass for storing intermediate values for GroupBy operation.
@@ -67,19 +67,45 @@ class EncodedGroups:
 
     codes: DataArray
     full_index: pd.Index
-    group_indices: GroupIndices | None = field(default=None)
-    unique_coord: Variable | _DummyGroup | None = field(default=None)
-    coords: Coordinates = field(default_factory=Coordinates)
-
-    def __post_init__(self):
-        assert isinstance(self.codes, DataArray)
-        if self.codes.name is None:
+    group_indices: GroupIndices
+    unique_coord: Variable | _DummyGroup
+    coords: Coordinates
+
+    def __init__(
+        self,
+        codes: DataArray,
+        full_index: pd.Index,
+        group_indices: GroupIndices | None = None,
+        unique_coord: Variable | _DummyGroup | None = None,
+        coords: Coordinates | None = None,
+    ):
+        from xarray.core.groupby import _codes_to_group_indices
+
+        assert isinstance(codes, DataArray)
+        if codes.name is None:
             raise ValueError("Please set a name on the array you are grouping by.")
-        assert isinstance(self.full_index, pd.Index)
-        assert (
-            isinstance(self.unique_coord, Variable | _DummyGroup)
-            or self.unique_coord is None
-        )
+        self.codes = codes
+        assert isinstance(full_index, pd.Index)
+        self.full_index = full_index
+
+        if group_indices is None:
+            self.group_indices = tuple(
+                g
+                for g in _codes_to_group_indices(codes.data.ravel(), len(full_index))
+                if g
+            )
+        else:
+            self.group_indices = group_indices
+
+        if unique_coord is None:
+            unique_values = full_index[np.unique(codes)]
+            self.unique_coord = Variable(
+                dims=codes.name, data=unique_values, attrs=codes.attrs
+            )
+        else:
+            self.unique_coord = unique_coord
+
+        self.coords = coords or Coordinates()
 
 
 class Grouper(ABC):