The Saxl hypergraph, whose hyperedges are bases of minimum size, is complete exactly for Frobenius groups, alternating and symmetric natural actions, certain projective line actions, Suzuki groups, and five exceptional actions.
Local representation theory and simple groups
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The Saxl hypergraph of a permutation group
The Saxl hypergraph, whose hyperedges are bases of minimum size, is complete exactly for Frobenius groups, alternating and symmetric natural actions, certain projective line actions, Suzuki groups, and five exceptional actions.