Glasnik Matematicki, Vol. 38, No.1 (2003), 1-9.
SOME SYMMETRIC (47,23,11) DESIGNS
Dean Crnković and Sanja Rukavina
Department of Mathematics, Faculty of Philosophy,
Omladinska 14,51000 Rijeka, Croatia
Abstract. Up to isomorphism there are precisely
fifty-four symmetric designs with parameters
(47,23,11) admitting a faithful action of a Frobenius group of order
55. From these fifty-four designs one can construct 179 pairwise
nonisomorphic 2-(23,11,10) designs as derived and 191 pairwise
nonisomorphic 2-(24,12,11) designs as residual designs. We have
determined full automorphism groups of all constructed designs.
One of 2-(24,12,11) designs has full automorphism group of order
15840, isomorphic to the group M11 ×
transitively on the set of points.
2000 Mathematics Subject Classification.
Key words and phrases. Symmetric design, Hadamard design, orbit structure,
automorphism group, Mathieu group.
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