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Symmetric (36, 15, 6) design having U(3, 3) as an automorphism group

Up to isomorphism there are four symmetric (36, 15, 6) designs with automorphisms of order 7. Full automorphism group of one of them is the Chevalley group G(2, 2) isomorphic to U(3, 3) : Z2 of order 12096. Unitary group U(3, 3) acts transitively on that design.

symmetric design; automorphism group; orbit structure

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