Some Hadamard designs with parameters (71,35,17)

Up to isomorphisms there are precisely eight symmetric designs with parameters (71, 35, 17) admitting a faithful action of a Frobenius group of order 21 in such a way that an element of order 3 fixes precisely 11 points. Five of these designs have 84 and three have 420 as the order of the full automorphism group G. If | G | = 420, then the structure of G is unique and we have G  = (Frob 21  ×  Z 5): Z 4. In this case Z ( G ) = 〈1〉, G′ has order 35, and G induces an automorphism group of order 6 of Z 7. If | G | = 84, then Z ( G ) is of order 2, and in precisely one case a Sylow 2‐subgroup is elementary abelian. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 144–149, 2002; DOI 10.1002/jcd.996