A non-solvable Galois extension of $\Q$ ramified at 2 only

Abstract

In this paper, we show the existence of a non-solvable Galois extension of $\Q$ which is unramified outside 2. The extension $K$ we construct has degree $2251731094732800=2^{19}(3\cdot 5\cdot 17\cdot 257{)}^2$ and has root discriminant ${\delta }_K<2^{47/8}=\mathrm{58.68...}$, and is totally complex.