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For groups represented as permutations. Group transitivity, rank 3 groups, orbits and suborbits, stablizers, permutation characters, primitivity are all on-topic.

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A permutation with reflection property

Consider permutations $\pi$ of the set $\{1,\dots,n\}$ having the symmetry property $\pi \pi^* \pi = \pi^*$, where $\pi^*$ is the "reflection" $k \mapsto n+1-k$. Are there references or other informa …