  Space asteroseismology reveals that stellar structure and evolution models of
intermediate- and high-mass stars are in need of improvement in terms of
angular momentum and chemical element transport. We aim to probe the interior
structure of a hot massive star in the core-hydrogen burning phase of its
evolution. We analyse CoRoT space photometry, Gaia DR2 space astrometry, and
high-resolution high signal-to-noise HERMES and HARPS time-series spectroscopy
of the slowly rotating B2V star HD 170580. From the time-series spectroscopy we
derive $vsini=4\pm 2\,$km\,s$^{-1}$, where the uncertainty results from the
complex pulsational line-profile variability. We detect 42 frequencies with
amplitude above 5$\sigma$. Among these we identify 5 rotationally split
triplets and 1 quintuplet. Asteroseismic modelling based on CoRoT, Gaia DR2 and
spectroscopic data leads to a star of 8M$_\odot$ near core-hydrogen exhaustion
and an extended overshoot zone. The detected low-order pressure-mode
frequencies cannot be fit within the uncertainties of the CoRoT data by models
without atomic diffusion.
  Irrespective of this limitation, the low-order gravity modes reveal HD 170580
to be a slow rotator with an average rotation period between 73 and 98 d and a
hint of small differential rotation. Future Gaia DR3 data taking into account
the multiplicity of the star, along with long-term TESS photometry would allow
to put better observational constraints on the asteroseismic models of this
blue evolved massive star. Improved modelling with atomic diffusion, including
radiative levitation, is needed to achieve compliance with the low helium
surface abundance of the star. This poses immense computational challenges but
is required to derive the interior rotation and mixing profiles of this star.
