diff --git a/Framework/PythonInterface/plugins/algorithms/SaveINS.py b/Framework/PythonInterface/plugins/algorithms/SaveINS.py
index 99e79fed41e8..ccd690ef4b69 100644
--- a/Framework/PythonInterface/plugins/algorithms/SaveINS.py
+++ b/Framework/PythonInterface/plugins/algorithms/SaveINS.py
@@ -5,14 +5,47 @@
 #   Institut Laue - Langevin & CSNS, Institute of High Energy Physics, CAS
 # SPDX - License - Identifier: GPL - 3.0 +
 from mantid.api import AlgorithmFactory, FileProperty, FileAction, WorkspaceProperty, PythonAlgorithm
-from mantid.kernel import Direction
+from mantid.kernel import Direction, V3D
 from mantid.geometry import SymmetryOperationFactory, SpaceGroupFactory
 from os import path, makedirs
+import numpy as np
 
 
 class SaveINS(PythonAlgorithm):
     LATT_TYPE_MAP = {type: itype + 1 for itype, type in enumerate(["P", "I", "R", "F", "A", "B", "C"])}
+    IDENTIY_OP = SymmetryOperationFactory.createSymOp("x,y,z")
     INVERSION_OP = SymmetryOperationFactory.createSymOp("-x,-y,-z")
+    ROTATION_OPS = {1: [IDENTIY_OP, INVERSION_OP], -1: [IDENTIY_OP]}
+    A_CENTERING_OP = SymmetryOperationFactory.createSymOp("x,y+1/2,z+1/2")
+    B_CENTERING_OP = (SymmetryOperationFactory.createSymOp("x+1/2,y,z+1/2"),)
+    C_CENTERING_OP = SymmetryOperationFactory.createSymOp("x+1/2,y+1/2,z")
+    CENTERING_OPS = {
+        1: [IDENTIY_OP],
+        2: [
+            IDENTIY_OP,
+            SymmetryOperationFactory.createSymOp("x+1/2,y+1/2,z+1/2"),
+        ],
+        3: [
+            IDENTIY_OP,
+            SymmetryOperationFactory.createSymOp("x+1/3,y+2/3,z+2/3"),
+            SymmetryOperationFactory.createSymOp("x+2/3,y+1/3,z+1/3"),
+        ],
+        4: [
+            IDENTIY_OP,
+            A_CENTERING_OP,
+            B_CENTERING_OP,
+            C_CENTERING_OP,
+        ],
+        5: [
+            IDENTIY_OP,
+            A_CENTERING_OP,
+        ],
+        6: [IDENTIY_OP, B_CENTERING_OP],
+        7: [
+            IDENTIY_OP,
+            C_CENTERING_OP,
+        ],
+    }
     DUMMY_WAVELENGTH = 1.0
 
     def category(self):
@@ -113,7 +146,7 @@ def PyExec(self):
             f_handle.write(f"LATT {latt_type}\n")
 
             # print sym operations
-            for sym_str in spgr.getSymmetryOperationStrings():
+            for sym_str in self._get_shelx_symmetry_operators(spgr, latt_type):
                 f_handle.write(f"SYMM {sym_str}\n")
 
             # print atom info
@@ -140,5 +173,84 @@ def PyExec(self):
             f_handle.write("HKLF 2\n")  # tells SHELX the columns saved in the reflection file
             f_handle.write("END")
 
+    def _symmetry_operation_key(self, W1_mat, w1_vec, W2_mat=np.eye(3), w2_vec=np.zeros(3)):
+        """
+        Generate a key for symmetry operation comparison.
+        Combines rotation and translation into a unique tuple representation.
+        Ex: "x,y,z+1/2" is equivalent to "x,y,z+0.5"
+        """
+        W_mat = W1_mat @ W2_mat
+        w_vec = W1_mat @ w2_vec + w1_vec
+        w_vec = np.mod(w_vec, 1)  # Ensure w_vec is within [0, 1)
+        return tuple(np.round(W_mat, 0).astype(int).flatten().tolist() + np.round(w_vec, 3).tolist())
+
+    def _symmetry_matrix_vector(self, symop):
+        """
+        Extract the rotation matrix (W_mat) and translation vector (w_vec) from a symmetry element.
+        This symmetry operation transform any point via a matrix/translation pair.
+        """
+        W_mat = np.linalg.inv(np.vstack([symop.transformHKL(V3D(*vec)) for vec in np.eye(3)]))
+        w_vec = np.array(symop.transformCoordinates(V3D(0, 0, 0)))
+        return W_mat, w_vec
+
+    def _generate_equivalent_operators(self, rotation_ops, centering_ops):
+        """
+        Generate all equivalent symmetry operators for the given lattice rotation and centering operations.
+        """
+        equivalent_ops = set()
+        for rot in rotation_ops:
+            W2_mat, _ = self._symmetry_matrix_vector(rot)
+            for cent in centering_ops:
+                _, w2_vec = self._symmetry_matrix_vector(cent)
+                key = self._symmetry_operation_key(np.eye(3), np.zeros(3), W2_mat, w2_vec)
+                equivalent_ops.add(key)
+        return equivalent_ops
+
+    def _update_symmetry_dict(self, W1_mat, w1_vec, S3, sym_key, sym_ops_dict, W_mat_dict, w_vec_dict):
+        """
+        Update the symmetry operations dictionary with priority for closeness to identity/origin.
+        This bias improves readability.
+        # Ex: lattice type 3; "-x+y,-x,z" is simpler than "-x+y+1/3,-x+2/3,z+2/3"
+        """
+        if S3 not in sym_ops_dict or (
+            np.linalg.det(W1_mat) > np.linalg.det(W_mat_dict[S3])  # identity preferred
+            or np.linalg.norm(w1_vec) < np.linalg.norm(w_vec_dict[S3])  # origin preferred
+        ):
+            sym_ops_dict[S3] = sym_key
+            W_mat_dict[S3] = W1_mat
+            w_vec_dict[S3] = w1_vec
+
+    def _get_shelx_symmetry_operators(self, spgr, latt_type):
+        """
+        Get SHELX symmetry operators for the given space group and lattice type.
+        Returns symmetry set.
+        """
+        latt_numb = abs(latt_type)
+        latt_sign = 1 if latt_type > 0 else -1
+
+        # Generate equivalent lattice type operators common to lattice type.
+        latt_type_ops_set = self._generate_equivalent_operators(self.ROTATION_OPS[latt_sign], self.CENTERING_OPS[latt_numb])
+
+        sym_ops = spgr.getSymmetryOperations()
+        sym_ops_dict = {}
+        W_mat_dict = {}
+        w_vec_dict = {}
+
+        for sym_op in sym_ops:
+            W1_mat, w1_vec = self._symmetry_matrix_vector(sym_op)
+            sym_key = sym_op.getIdentifier()
+            S1 = self._symmetry_operation_key(W1_mat, w1_vec)
+
+            if S1 not in latt_type_ops_set:
+                # re-iterate over lattice operators to map equivalently generated
+                for rot in self.ROTATION_OPS[latt_sign]:
+                    W2_mat, _ = self._symmetry_matrix_vector(rot)
+                    for cent in self.CENTERING_OPS[latt_numb]:
+                        _, w2_vec = self._symmetry_matrix_vector(cent)
+                        S3 = self._symmetry_operation_key(W1_mat, w1_vec, W2_mat, w2_vec)
+                        self._update_symmetry_dict(W1_mat, w1_vec, S3, sym_key, sym_ops_dict, W_mat_dict, w_vec_dict)
+
+        return set(sym_ops_dict.values())
+
 
 AlgorithmFactory.subscribe(SaveINS)
diff --git a/Framework/PythonInterface/test/python/plugins/algorithms/SaveINSTest.py b/Framework/PythonInterface/test/python/plugins/algorithms/SaveINSTest.py
index faa356458667..8e53f49db6aa 100644
--- a/Framework/PythonInterface/test/python/plugins/algorithms/SaveINSTest.py
+++ b/Framework/PythonInterface/test/python/plugins/algorithms/SaveINSTest.py
@@ -25,9 +25,6 @@ def setUpClass(cls):
             "ZERR 4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
             "LATT 1\n",
             "SYMM -x+1/2,y+1/2,-z+1/2\n",
-            "SYMM -x,-y,-z\n",
-            "SYMM x+1/2,-y+1/2,z+1/2\n",
-            "SYMM x,y,z\n",
             "NEUT\n",
         ]
         cls.file_end = ["UNIT 48 36 12 8 4\n", "MERG 0\n", "HKLF 2\n", "END"]
@@ -143,6 +140,87 @@ def test_save_ins_constant_wavelength(self):
 
         self._assert_file_contents(output_file, expected_lines)
 
+    def test_save_ins_symmetry_Rbar3(self):
+        output_file = path.join(self._tmp_directory, "test5.ins")
+
+        SaveINS(InputWorkspace=self.ws, Filename=output_file, Spacegroup="R -3")
+
+        self.file_start = [
+            "TITL ws\n",
+            "REM This file was produced by mantid using SaveINS\n",
+            "CELL 1.0 7.6508 13.2431 11.6243 90.0000 104.1183 90.0000\n",
+            "ZERR 4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
+            "LATT 3\n",
+            "SYMM -x+y,-x,z\n",
+            "SYMM -y,x-y,z\n",
+            "NEUT\n",
+        ]
+
+        expected_lines = [*self.file_start, "SFAC C H N O S\n", *self.file_end]
+
+        self._assert_line_in_file_contents(output_file, expected_lines)
+
+    def test_save_ins_symmetry_R3(self):
+        output_file = path.join(self._tmp_directory, "test6.ins")
+
+        SaveINS(InputWorkspace=self.ws, Filename=output_file, Spacegroup="R 3")
+
+        self.file_start = [
+            "TITL ws\n",
+            "REM This file was produced by mantid using SaveINS\n",
+            "CELL 1.0 7.6508 13.2431 11.6243 90.0000 104.1183 90.0000\n",
+            "ZERR 4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
+            "LATT -3\n",
+            "SYMM -x+y,-x,z\n",
+            "SYMM -y,x-y,z\n",
+            "NEUT\n",
+        ]
+
+        expected_lines = [*self.file_start, "SFAC C H N O S\n", *self.file_end]
+
+        self._assert_line_in_file_contents(output_file, expected_lines)
+
+    def test_save_ins_symmetry_Iabar3d(self):
+        output_file = path.join(self._tmp_directory, "test7.ins")
+
+        SaveINS(InputWorkspace=self.ws, Filename=output_file, Spacegroup="I a -3 d")
+
+        self.file_start = [
+            "TITL ws\n",
+            "REM This file was produced by mantid using SaveINS\n",
+            "CELL 1.0 7.6508 13.2431 11.6243 90.0000 104.1183 90.0000\n",
+            "ZERR 4 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
+            "LATT 2\n",
+            "SYMM -x+1/4,-z+1/4,-y+1/4\n",
+            "SYMM -x,-y+1/2,z\n",
+            "SYMM x+3/4,z+1/4,-y+1/4\n",
+            "SYMM -z+1/4,y+3/4,x+1/4\n",
+            "SYMM z,x,y\n",
+            "SYMM -x+1/2,y,-z\n",
+            "SYMM x,-y,-z+1/2\n",
+            "SYMM -y+1/4,-x+1/4,-z+1/4\n",
+            "SYMM -z+1/4,-y+1/4,-x+1/4\n",
+            "SYMM y,-z,-x+1/2\n",
+            "SYMM y+3/4,x+1/4,-z+1/4\n",
+            "SYMM -z,-x+1/2,y\n",
+            "SYMM y+1/4,-x+1/4,z+3/4\n",
+            "SYMM -x+1/4,z+3/4,y+1/4\n",
+            "SYMM -y+1/2,z,-x\n",
+            "SYMM -y,-z+1/2,x\n",
+            "SYMM y,z,x\n",
+            "SYMM z+3/4,y+1/4,-x+1/4\n",
+            "SYMM x+1/4,-z+1/4,y+3/4\n",
+            "SYMM z,-x,-y+1/2\n",
+            "SYMM -y+1/4,x+3/4,z+1/4\n",
+            "SYMM z+1/4,-y+1/4,x+3/4\n",
+            "SYMM -z+1/2,x,-y\n",
+            "NEUT\n",
+        ]
+
+        expected_lines = [*self.file_start, "SFAC C H N O S\n", *self.file_end]
+
+        self._assert_line_in_file_contents(output_file, expected_lines)
+
     def _assert_file_contents(self, filepath, expected_lines):
         with open(filepath, "r") as f:
             lines = f.readlines()
@@ -150,6 +228,13 @@ def _assert_file_contents(self, filepath, expected_lines):
         for iline, line in enumerate(lines):
             self.assertEqual(line, expected_lines[iline])
 
+    def _assert_line_in_file_contents(self, filepath, expected_lines):
+        with open(filepath, "r") as f:
+            lines = f.readlines()
+        self.assertEqual(len(lines), len(expected_lines))
+        for line in lines:
+            self.assertTrue(line in lines)
+
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/docs/source/release/6.12.0/Diffraction/Single_Crystal/Bugfixes/38605.rst b/docs/source/release/6.12.0/Diffraction/Single_Crystal/Bugfixes/38605.rst
new file mode 100644
index 000000000000..39db9482bee9
--- /dev/null
+++ b/docs/source/release/6.12.0/Diffraction/Single_Crystal/Bugfixes/38605.rst
@@ -0,0 +1 @@
+- Fix :ref:`SaveINS<algm-SaveINS-v1>` that saved all symmetry records to file. Only the minimum are needed that can be generated by translation/rotation corresponding to the lattice type.