  A hadron resonance gas model including all known particles and resonances
with masses $m<2$ GeV and an exponentially rising density of Hagedorn states
for $m>2$ GeV is used to obtain an upper bound on the shear viscosity to
entropy density ratio, $\eta/s\approx1/(4\pi)$, of hadronic matter near $T_c$.
We found a large trace anomaly and small speed of sound near $T_c$, which agree
well with recent lattice calculations. We comment on the bulk viscosity to
entropy density ratio close to $T_c$.
