The Structure of Reduced Sudoku Grids and the Sudoku Symmetry Group

Table 1

Permutation operations generating 𝔖.

Permutation operation	Order
Permutation of the values (for example replacing all the values 1 in the entire grid with the value 2 and vice versa)	𝑛!
Permutation of bands	𝑦!
Permutation of stacks	𝑥!
Permutation of the columns within the stacks	𝑦!^𝑥
Permutation of the rows within the bands	𝑥!^𝑦