  We utilize the galaxy shape catalogue from the first-year data release of the
Subaru Hyper Suprime-cam Survey (HSC) to study the dark matter content of
galaxy groups in the Universe using weak lensing. We use galaxy groups from the
Galaxy Mass and Assembly galaxy survey in approximately $100$ sq. degrees of
the sky that overlap with the HSC survey as lenses. We restrict our analysis to
the $1587$ groups with at least five members. We divide these groups into six
bins each of group luminosity and group member velocity dispersion and measure
the lensing signal with a signal-to-noise ratio of $55$ and $51$ for these two
different selections, respectively. We use a Bayesian halo model framework to
infer the halo mass distribution of our groups binned in the two different
observable properties and constrain the power-law scaling relation, and the
scatter between mean halo masses and the two group observable properties. We
obtain a 5 percent constraint on the amplitude of the scaling relation between
halo mass and group luminosity with $\avg{M} = (0.81\pm
0.04)\times10^{14}\hinvMsun$ for $L_{\rm grp}=10^{11.5}\hinvsqLsun$, and a
power-law index of $\alpha=1.01\pm 0.07$. We constrain the amplitude of the
scaling relation between halo mass and velocity dispersion to be
$\avg{M}=(0.93\pm 0.05)\times10^{14}\hinvMsun$ for $\sigma=500 \kms$ and a
power-law index to be $\alpha=1.52\pm0.10$. However, these scaling relations
are sensitive to the exact cuts applied to the number of group members.
Comparisons with similar scaling relations from the literature show that our
results are consistent and have significantly reduced errors.
