The determination of the astrophysical properties of stars remains challenging and frequently relies on the application of stellar models. Stellar sequences in nearby open clusters provide some of the best means to test and calibrate stellar evolutionary models and isochrones and to use these models to assign astrophysical properties consistently to a large sample of stars. We aim at updating the single-star sequence of the members of the Hyades cluster, identifying the best-fitting isochrones, and determining the astrophysical properties of the stars. The Gaia Catalog of Nearby Stars provides a comprehensive sample of high-probability members of the Hyades cluster. We apply a multistep method to flag photometric outliers and to identify bona fide single stars and likely binary and multiple systems. The single stars define a tight sequence, which in the mass range 0.12-2.2M{sun} is well fitted by PARSEC isochrones for a supersolar metallicity of [M/H]=+0.18{+/-}0.03 and an age of 775{+/-}25Myr. The isochrones enable us to assign mass, effective temperature, luminosity, and surface gravity to each of the 600 bona fide single main-sequence stars. The observed sequence validates the PARSEC isochrones. The derived stellar properties can serve as benchmarks for atmospheric and evolutionary models and for all-sky catalogs of stellar astrophysical properties. The stellar properties are also relevant for studies of exoplanet properties among Hyades exoplanet hosts.