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EXAMPLE
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For n = 3 there are the following 14 orbits of 4-tuples for the group D6 = S3:
1) [[1,1,1,1], [2,2,2,2], [3,3,3,3]],
2) [[1,1,1,2], [2,2,2,3], [1,1,1,3], [3,3,3,1], [3,3,3,2], [2,2,2,1]],
3) [[1,1,2,1], [2,2,3,2], [1,1,3,1], [3,3,1,3], [3,3,2,3], [2,2,1,2]],
4) [[1,1,2,2], [2,2,3,3], [1,1,3,3], [3,3,1,1], [3,3,2,2], [2,2,1,1]],
5) [[1,1,2,3], [2,2,3,1], [1,1,3,2], [3,3,1,2], [3,3,2,1], [2,2,1,3]],
6) [[1,2,1,1], [2,3,2,2], [1,3,1,1], [3,1,3,3], [3,2,3,3], [2,1,2,2]],
7) [[1,2,1,2], [2,3,2,3], [1,3,1,3], [3,1,3,1], [3,2,3,2], [2,1,2,1]],
8) [[1,2,1,3], [2,3,2,1], [1,3,1,2], [3,1,3,2], [3,2,3,1], [2,1,2,3]],
9) [[1,2,2,1], [2,3,3,2], [1,3,3,1], [3,1,1,3], [3,2,2,3], [2,1,1,2]],
10) [[1,2,2,2], [2,3,3,3], [1,3,3,3], [3,1,1,1], [3,2,2,2], [2,1,1,1]],
11) [[1,2,2,3], [2,3,3,1], [1,3,3,2], [3,1,1,2], [3,2,2,1], [2,1,1,3]],
12) [[1,2,3,1], [2,3,1,2], [1,3,2,1], [3,1,2,3], [3,2,1,3], [2,1,3,2]],
13) [[1,2,3,2], [2,3,1,3], [1,3,2,3], [3,1,2,1], [3,2,1,2], [2,1,3,1]],
14) [[1,2,3,3], [2,3,1,1], [1,3,2,2], [3,1,2,2], [3,2,1,1], [2,1,3,3]].
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