diff --git a/clifford.py b/clifford.py
index 4765438..25623ba 100644
--- a/clifford.py
+++ b/clifford.py
@@ -12,6 +12,7 @@ Following the prescription of Anders (thesis pg. 26):
 """
 
 from numpy import *
+from tqdm import tqdm
 
 def find_up_to_phase(u):
     """ Find the index of a given u within a list of unitaries, up to a global phase  """
@@ -22,27 +23,21 @@ def find_up_to_phase(u):
                 return i, phase
     raise IndexError
 
+def construct_tables():
+    """ Constructs multiplication and conjugation tables """
+    permutations = (id, ha, ph, ha*ph, ha*ph*ha, ha*ph*ha*ph)
+    signs = (id, px, py, pz)
+    unitaries = [p*s for p in permutations for s in signs]
+    conjugation_table = [find_up_to_phase(u.H)[0] for i, u in enumerate(unitaries)]
+    times_table = [[find_up_to_phase(u*v)[0] for v in unitaries] 
+            for u in tqdm(unitaries, "Building times-table")]
+
 id = matrix(eye(2, dtype=complex))
 px = matrix([[0, 1], [1, 0]], dtype=complex)
 py = matrix([[0, -1j], [1j, 0]], dtype=complex)
 pz = matrix([[1, 0], [0, -1]], dtype=complex)
 ha = matrix([[1, 1], [1, -1]], dtype=complex) / sqrt(2)
-ph= matrix([[1, 0], [0, 1j]], dtype=complex)
-
-permutations = (id, ha, ph, ha*ph, ha*ph*ha, ha*ph*ha*ph)
-signs = (id, px, py, pz)
-unitaries = [p*s for p in permutations for s in signs]
-
-conjugation_table = []
-
-for i, u in enumerate(unitaries):
-    i, phase = find_up_to_phase(u.H)
-    conjugation_table.append(i)
+ph = matrix([[1, 0], [0, 1j]], dtype=complex)
 
 
-# TODO:
-# - check that we re-generate the table
-# - do conjugation
-# - do times table
-# - write tests
 
diff --git a/ct.txt b/ct.txt
new file mode 100644
index 0000000..e976c4e
--- /dev/null
+++ b/ct.txt
@@ -0,0 +1 @@
+[0, 1, 2, 3, 4, 7, 6, 5, 11, 9, 10, 8, 20, 22, 23, 21, 17, 16, 18, 19, 12, 15, 13, 14]
diff --git a/tests/test_clifford.py b/tests/test_clifford.py
index 5a7aefa..45bc4cc 100644
--- a/tests/test_clifford.py
+++ b/tests/test_clifford.py
@@ -61,3 +61,6 @@ def test_conjugation_table():
     """ Check that the table of Hermitian conjugates is okay """
     assert len(set(lc.conjugation_table))==24
 
+def test_times_table():
+    """ Check the times table """
+    assert lc.times_table[0][4]==4
diff --git a/tt.txt b/tt.txt
new file mode 100644
index 0000000..430daff
--- /dev/null
+++ b/tt.txt
@@ -0,0 +1 @@
+[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [1, 0, 3, 2, 7, 6, 5, 4, 10, 11, 8, 9, 15, 14, 13, 12, 17, 16, 19, 18, 22, 23, 20, 21], [2, 3, 0, 1, 6, 7, 4, 5, 9, 8, 11, 10, 13, 12, 15, 14, 19, 18, 17, 16, 23, 22, 21, 20], [3, 2, 1, 0, 5, 4, 7, 6, 11, 10, 9, 8, 14, 15, 12, 13, 18, 19, 16, 17, 21, 20, 23, 22], [4, 5, 6, 7, 0, 1, 2, 3, 12, 13, 14, 15, 8, 9, 10, 11, 21, 20, 23, 22, 17, 16, 19, 18], [5, 4, 7, 6, 3, 2, 1, 0, 14, 15, 12, 13, 11, 10, 9, 8, 20, 21, 22, 23, 19, 18, 17, 16], [6, 7, 4, 5, 2, 3, 0, 1, 13, 12, 15, 14, 9, 8, 11, 10, 22, 23, 20, 21, 18, 19, 16, 17], [7, 6, 5, 4, 1, 0, 3, 2, 15, 14, 13, 12, 10, 11, 8, 9, 23, 22, 21, 20, 16, 17, 18, 19], [8, 9, 10, 11, 21, 20, 23, 22, 3, 2, 1, 0, 17, 16, 19, 18, 15, 14, 13, 12, 4, 5, 6, 7], [9, 8, 11, 10, 22, 23, 20, 21, 1, 0, 3, 2, 18, 19, 16, 17, 14, 15, 12, 13, 6, 7, 4, 5], [10, 11, 8, 9, 23, 22, 21, 20, 2, 3, 0, 1, 16, 17, 18, 19, 12, 13, 14, 15, 7, 6, 5, 4], [11, 10, 9, 8, 20, 21, 22, 23, 0, 1, 2, 3, 19, 18, 17, 16, 13, 12, 15, 14, 5, 4, 7, 6], [12, 13, 14, 15, 16, 17, 18, 19, 7, 6, 5, 4, 20, 21, 22, 23, 11, 10, 9, 8, 0, 1, 2, 3], [13, 12, 15, 14, 19, 18, 17, 16, 5, 4, 7, 6, 23, 22, 21, 20, 10, 11, 8, 9, 2, 3, 0, 1], [14, 15, 12, 13, 18, 19, 16, 17, 6, 7, 4, 5, 21, 20, 23, 22, 8, 9, 10, 11, 3, 2, 1, 0], [15, 14, 13, 12, 17, 16, 19, 18, 4, 5, 6, 7, 22, 23, 20, 21, 9, 8, 11, 10, 1, 0, 3, 2], [16, 17, 18, 19, 12, 13, 14, 15, 20, 21, 22, 23, 7, 6, 5, 4, 1, 0, 3, 2, 10, 11, 8, 9], [17, 16, 19, 18, 15, 14, 13, 12, 22, 23, 20, 21, 4, 5, 6, 7, 0, 1, 2, 3, 8, 9, 10, 11], [18, 19, 16, 17, 14, 15, 12, 13, 21, 20, 23, 22, 6, 7, 4, 5, 2, 3, 0, 1, 9, 8, 11, 10], [19, 18, 17, 16, 13, 12, 15, 14, 23, 22, 21, 20, 5, 4, 7, 6, 3, 2, 1, 0, 11, 10, 9, 8], [20, 21, 22, 23, 11, 10, 9, 8, 19, 18, 17, 16, 0, 1, 2, 3, 4, 5, 6, 7, 12, 13, 14, 15], [21, 20, 23, 22, 8, 9, 10, 11, 17, 16, 19, 18, 3, 2, 1, 0, 5, 4, 7, 6, 14, 15, 12, 13], [22, 23, 20, 21, 9, 8, 11, 10, 18, 19, 16, 17, 1, 0, 3, 2, 7, 6, 5, 4, 15, 14, 13, 12], [23, 22, 21, 20, 10, 11, 8, 9, 16, 17, 18, 19, 2, 3, 0, 1, 6, 7, 4, 5, 13, 12, 15, 14]]