Looking for a simple way to generate some permutation-like numbers!

Given a few set of positive integers, I am trying to generate some numbers using some sort of programming .

Lets say we have three sets of integers of the same size. I would like to pick a permutation f on the first set and form a number by putting the values of f at i next to each other. Then apply the same permutation to the next set and then the last set and finally get an integer by putting these 3 numbers one after another.

For example lets say we have three sets of integers of size three, say {1, 2, 3}, {4,5,6} and {7,8,9} I would like to generate the following numbers:

123456789 (corresponding to the permutation that fixes all numbers)

132465798 (corresponding to the permutation that fixes 1 and switche 2 and 3)

321654987 (corresponding to the permutation that fixes 2 and switches 1 and 3)

213546879 (corresponding to the permutation that fixes 3 and switches 1 and 2)

231564897 (corresponding to the permutation that sends 1 to 2, 2 to 3 and 3 to 1)

312645978 (corresponding to the permutation that sends 1 to 3, 3 to 2 and 2 to 1)

How can I go about generating such numbers either online or with an accessible program?