Glasnik Matematicki, Vol. 38, No.1 (2003), 1-9.

SOME SYMMETRIC (47,23,11) DESIGNS

Dean Crnković and Sanja Rukavina

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 × Z₂, acting transitively on the set of points.

2000 Mathematics Subject Classification.   05B05, 05E20.

Key words and phrases.   Symmetric design, Hadamard design, orbit structure, automorphism group, Mathieu group.