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The transitive subgroups of $S_n$ have been classified, up to conjugation, for small values of $n$, including all $n\leq 47$. The ordering is weakly increasing by the order of the group. The $T$-number of a subgroup is its index in this classification.

An algorithm for generating the classification is given in [10.1016/j.jsc.2004.08.002, MR:2168238], and the results can be accessed from the computer algebra systems SageMath, GAP, and Magma.

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• Last edited by John Jones on 2019-09-12 13:01:08
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