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 gravitational lensing. As our lens sample, we use galaxy groups that have been spectroscopically selected from the Galaxy Mass and Assembly galaxy survey in approximately 100 sq. degrees of the sky that overlap with the HSC survey. We restrict our analysis to the 1587 groups with at least five group members. We divide these galaxy groups into six bins each of galaxy group luminosity and group member velocity dispersion and measure the coherent tangential ellipticity pattern on background HSC galaxies imprinted by weak gravitational lensing. We measure the weak 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 galaxy groups binned in the two different observable properties and obtain constraints on the power-law scaling relation 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 $langle Mrangle = (0.81pm0.04)times10^{14}h^{-1}M_odot$ for $L_{rm grp}=10^{11.5}h^{-2}L_odot$, and a power-law index of $alpha=1.01pm0.07$. We also obtain a 5-percent constraint on the amplitude of the scaling relation between halo mass and velocity dispersion with $langle Mrangle=(0.93pm0.05)times10^{14}h^{-1}M_odot$ for $sigma=500{,rm kms}^{-1}$ and a power-law index $alpha=1.52pm0.10$, although these scaling relations are sensitive to the exact cuts applied to the number of group members. Comparisons with similar scaling relations from the literature indicate that our results are consistent, but have significantly reduced errors.
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