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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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Mclaughlin Graph

Here is some code for generating these graphs in SAGE gap('LoadPackage("design")') McL = graphs.McLaughlinGraph() D = designs.projective_plane(4) flags = [(x,B) for x in D.points() for B in D.blocks …
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