  Alhena A ($\gamma$ Gem A) is a bright Am star, with the strongest
disc-integrated magnetic field strength reported so far for an Am star. Its
spectrum exhibits standard circularly polarized Zeeman signatures, contrary to
all previously studied Am stars that display abnormal signatures dominated by a
single-signed lobe.
  We present here the result of follow-up observations of Alhena, using very
high signal-to-noise spectropolarimetric data obtained over 25 observing nights
with NARVAL at T\'elescope Bernard Lyot, in the frame of the BRITE (BRIght
Target Explorer) spectropolarimetric survey.
  We confirm that Alhena A is magnetic and we determine its surface magnetic
properties using different methods. Inclined dipole models are used to
reproduce the longitudinal field measurements, as well as the Stokes V line
profiles themselves. In both cases, the model is consistent with a polar field
strength of $\sim$ 30 G. This is confirmed by a Zeeman-Doppler Imaging (ZDI)
model, which also unveils smaller scale magnetic structures. A rotational
period of 8.975 days was identified using intensity line profile variations.
The ZDI inversion suggests that the surface magnetic field is sheared by
differential rotation, with a difference in rotation rate between high and low
latitudes at about 15\% of the solar value. This result challenges theories of
the development of surface differential rotation in intermediate mass main
sequence stars.
