S4S_4S4 the symmetric group of all permutations of 4 elements.
It has 4!=24 elements. For example,
(12341234),(12344321)=(1,4)(2,3)or1→4,2→3,3→2,4→1\begin{pmatrix} 1 & 2&3&4 \\ 1&2&3&4 \end{pmatrix}, \begin{pmatrix} 1 & 2&3&4 \\ 4&3&2&1 \end{pmatrix}=(1,4)(2,3)\\ or \\ 1\to4, 2\to3,3\to2,4\to1(11223344),(14233241)=(1,4)(2,3)or1→4,2→3,3→2,4→1
In our case
1→3,2→1,3→2(12343124)=(1,3,2)(4)=(1,3,2)1\to3, 2\to1, 3\to2\\ \begin{pmatrix} 1 & 2&3&4 \\ 3&1&2&4 \end{pmatrix}=(1,3,2)(4) =(1,3,2)1→3,2→1,3→2(13213244)=(1,3,2)(4)=(1,3,2)
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