Hadamard matrices of order 28 with automorphisms of order 7 (Q1063032)

A \((-1,+1)\) square matrix H of order n is called a Hadamard matrix of order n if \(HH^ T=nI_ n\). An automorphism of a Hadamard matrix H is a signed permutation of its rows and columns transforming H to itself. The set of all automorphisms from a group under composition called the automorphism group of H. It is well-known that Hadamard matrices of order 28 have automorphism groups of orders 13, 7, 3, and 2. It has been proved that there are four equivalence classes of Hadamard matrices of order 28 with automorphisms of order 13. In this paper the author proves that there are exactly 12 equivalence classes of Hadamard matrices of order 28 with automorphisms of order 7. Tables containing representatives of all equivalence classes are given as well.