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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**Knowl status:**

- Review status: reviewed
- Last edited by John Jones on 2019-09-12 13:01:08

**Referred to by:**

- artin.label
- artin.permutation_container
- gg.label
- gg.resolvents
- nf.galois_group.name
- rcs.cande.nf
- lmfdb/galois_groups/templates/gg-index.html (line 117)
- lmfdb/galois_groups/templates/gg-search.html (line 61)
- lmfdb/galois_groups/templates/gg-show-group.html (line 16)
- lmfdb/number_fields/templates/galois_groups.html (line 8)
- lmfdb/number_fields/templates/nf-statistics.html (line 61)

**History:**(expand/hide all)

- 2019-09-12 13:01:08 by John Jones (Reviewed)
- 2019-09-12 13:00:40 by John Jones
- 2018-07-07 23:42:57 by John Jones (Reviewed)

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