  The open cluster NGC 7419 is known to contain five red supergiants and a very
high number of Be stars. However, there are conflicting reports about its age
and distance that prevent a useful comparison with other clusters. We intend to
obtain more accurate parameters for NGC 7419, using techniques different from
those of previous authors, so that it may be used as a calibrator for more
obscured clusters. We obtained Str\"omgren photometry of the open cluster NGC
7419, as well as classification spectroscopy of ~20 stars in the area. We then
applied standard analysis and classification techniques. We find a distance of
4+-0.4 kpc and an age of 14+-2 Myr for NGC 7419. The main-sequence turn-off is
found at spectral type B1, in excellent agreement. We identify 179 B-type
members, implying that there are more than 1200 $M_{\sun}$ in B stars at
present. Extrapolating this to lower masses indicates an initial cluster mass
of between 7000 and 10000 Msolar, depending on the shape of the Initial Mass
Function. We find a very high fraction (~40%) of Be stars around the turn-off,
but very few Be stars at lower masses. We also report for the first time a
strong variability in the emission characteristics of Be stars. We verified
that the parameters of the red supergiant members can be used to obtain
accurate cluster parameters. NGC 7419 is sufficiently massive to serve as a
testbed for theoretical predictions and as a template to compare more obscured
clusters. The distribution of stars above the main-sequence turn-off is
difficult to accommodate with current evolutionary tracks. Though the presence
of five red supergiants is marginally consistent with theoretical expectations,
the high number of Be stars and very low number of luminous evolved B stars
hint at some unknown physical factor that is not considered in current
synthesis models.
