The precise structure of the sudoku symmetry group can be expressed succinctly using the wreath product (≀). The possible row (or column) permutations form a group isomorphic to "S"3 ≀ "S"3 of order 3!4 = 1,296. The whole rearrangement group is formed by letting the transposition operation (isomorphic to "C"2) act on two copies of that group, one for the row permutations and one for the column permutations. This is "S"3 ≀ "S"3 ≀ "C"2, a group of order 1,2962 × 2 = 3,359,232. Finally, the relabelling operations commute with the rearrangement operations, so the full sudoku (VPT) group is ("S"3 ≀ "S"3 ≀ "C"2) × "S"9 of order 1,218,998,108,160.