In the paper

G. B. Khosrovshahi, M. Mohammad-Noori, and B. Tayfeh-Rezaie, Classification of 6-(14,7,4) designs with nontrivial
automorphism groups, J. Combin. Des., 10 (2002), 180-194 (ps, pdf),

all 6-(14,7,4) designs having the full automorphism group isomorphic to Z_2 or Z_7 have been  found.
The block and orbit representations of these designs are presented here. The point set is V={1,2,...9,A,B,C,D,E}.
We only give the blocks and orbits which contain 1. If 1 does not appear in an orbit, then it lies in the design if and only if its
complement does not lie in the design.
Design #1 has the full automorphism group G=<(1 2 3 4 5 6 7)(8 9 A B C D E)> and is non-isomorphic to its supplement
(not presented here). Designs #2 to #5 have the full automorphism group G=<(2 3)(5 6)(7 8)(9 A)(B C)(D E)> and are
isomorphic to their supplements.

Orbit representation:  Design #1, Design #2, Design #3, Design #4, Design #5.

Block representation: Design #1, Design #2, Design #3, Design #4, Design #5.

Page last updated: April 13, 2003