  NGC 3105 is a young open cluster hosting blue, yellow and red supergiants.
This rare combination makes it an excellent laboratory to constrain
evolutionary models of high-mass stars. It is poorly studied and fundamental
parameters such as its age or distance are not well defined. We intend to
characterize in an accurate way the cluster as well as its evolved stars, for
which we derive for the first time atmospheric parameters and chemical
abundances. We identify 126 B-type likely members within a radius of
2.7$\pm$0.6 arcmin, which implies an initial mass, $M_{cl}\approx$4100
M$_{\odot}$. We find a distance of 7.2$\pm$0.7 kpc for NGC 3105, placing it at
$R_{GC}$=10.0$\pm$1.2 kpc. Isochrone fitting supports an age of 28$\pm$6 Ma,
implying masses around 9.5 M$_{\odot}$ for the supergiants. A high fraction of
Be stars ($\approx$25 %) is found at the top of the main sequence down to
spectral type b3. From the spectral analysis we estimate for the cluster a
$v_{rad}$=+46.9$\pm$0.9 km s$^{-1}$ and a low metallicity,
[Fe/H]=-0.29$\pm$0.22. We also have determined, for the first time, chemical
abundances for Li, O, Na, Mg, Si, Ca, Ti, Ni, Rb, Y, and Ba for the evolved
stars. The chemical composition of the cluster is consistent with that of the
Galactic thin disc. An overabundance of Ba is found, supporting the enhanced
$s$-process. NGC 3105 has a low metallicity for its Galactocentric distance,
comparable to typical LMC stars. It is a valuable spiral tracer in a very
distant region of the Carina-Sagittarius spiral arm, a poorly known part of the
Galaxy. As one of the few Galactic clusters containing blue, yellow and red
supergiants, it is massive enough to serve as a testbed for theoretical
evolutionary models close to the boundary between intermediate and high-mass
stars.
