  The detailed study of the selected thermodynamic properties of the
superconducting phase in the molecular hydrogen under the pressure at 428 GPa
has been presented. For the increasing value of the Coulomb pseudopotential,
$\mu^{*}\in<0.08,0.15>$, the following results have been obtained: (i) the
critical temperature decreases from 179 K to 141 K, (ii) the ratio
$R_{1}\equiv\Delta(0)/k_{B}T_{C}$ differs noticeably from the BCS value:
$R_{1}\in<4.71,3.60>$; (iii) the electron effective mass is large and grows
slightly together with the temperature ($[m^{*}_{e}/m_{e}]_{{\rm max}} = 2.2$
for $T = T_{C}$).
