# Operation Table for Permutation Group

I cannot seem to figure out how the operation table for this permutation is formed. Is it multiplying each index and doing modulus? I can't seem to figure out.

This is a Table 4.2 found in "Cryptography and Network Security" by Forouzan

For example, the permutation listed as [3, 1, 2] is the permutation that maps the element 1 to 3, the element 2 to 1, and the element 3 to 2.
And, the permutation listed as [1, 3, 2] is the permutation that maps the element 1 to 1, the element 2 to 3 and the element 3 to 2.
So, if we combine these two permutations, applying [3, 1, 2] first, we can compute this by tracking what the permutations do to the specific elements. For example, it maps the element 1 to 3 (which is what the first permutation does), and then mapping the resulting 3 to 2 (which is what the second permutation does). Similarly, 2 is mapped to 1 (again, the first permutation), and then the second permutation maps the resulting 1 to 1. And, the element 3 is mapped to 2 by the first permutation, and that is then mapped to 3 by the second.
Hence, the resulting permutation is [2, 1, 3], which is what is listed in the [3, 1 2] row and the [1, 3, 2] column.