Construction of the outer automorphism of \(\mathcal {S}_{6}\) via a complex Hadamard matrix. (English) Zbl 1444.20003
Summary: We give a new construction of the outer automorphism of the symmetric group on six points. Our construction features a complex Hadamard matrix of order six containing third roots of unity and the algebra of split quaternions over the real numbers.
MSC:
| 20B25 | Finite automorphism groups of algebraic, geometric, or combinatorial structures |
| 05B20 | Combinatorial aspects of matrices (incidence, Hadamard, etc.) |
| 20B20 | Multiply transitive finite groups |
| 20B30 | Symmetric groups |
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