Abstract. Up to isomorphism there are three symmetric (66,26,10) designs with automorphism group isomorphic to Frob55. Among them there is one self-dual and one pair of dual designs. Full automorphism groups of dual designs are isomorphic to Frob55, and full automorphism group of the self-dual design is isomorphic to Frob55 × D10. For those three designs corresponding derived and residual designs with respect to a block are constructed.
1991 Mathematics Subject Classification. 05B05.
Key words and phrases. Symmetric design, automorphism group, orbit structure.