[xjm]

I counted one trillion or 9! * 3!^8 * 2 : the 8 because you have can choose 3 independent permutations of columns inside column blocks + 1 permutation of column blocks, plus same for rows. Then only one rotation should be counted, because flips are included in col/row permutations.

I think wreath products relate to the second sentence; see this page, which mentions the same result: https://en.wikipedia.org/wiki/Mathematics_of_Sudoku#The_sudo...

[lifebeyondfife]

You're correct, the horizontal and vertical flips for the square, are already accounted for in the wreath product. And I miscounted the products themselves. Up to 1.2*10^12 symmetries.