The Structure of Reduced Sudoku Grids and the Sudoku Symmetry Group

Table 2

Permutation operations used to form isomorphic Sudoku grids.

Permutation operation	Order
Permutation of values 1,…,𝑛 (equivalent to rearranging the values in 𝑆^𝑥,𝑦1,1)	𝑛!
Permutation of rows in bands 2,…,𝑥	(𝑦!)^(𝑥−1)
Permutation of columns in stacks 2,…,𝑦	(𝑥!)^(𝑦−1)
Permutation of bands 2,…,𝑥	(𝑥−1)!
Permutation of stacks 2,…,𝑦	(𝑦−1)!