Glasnik Matematicki, Vol. 34, No.2 (1999), 105-108.

ON SYMMETRIC (36,15,6) DESIGNS

Dean Crnković

Abstract.   Up to isomorphism there are 4 symmetric (36,15,6) designs with automorphisms of order 7 and 38 symmetric (36,15,6) designs with automorphisms of order 5. For those designs full automorphism groups are determined. Also, all symmetric (36,15,6) designs having automorphisms of order 3 acting with 9 and 6 fixed points, or cyclic automorphism groups of order 4 acting standardly are constructed and orders of their full automorphism groups are determined.

1991 Mathematics Subject Classification.   05B05.

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