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The detailed study of the selected thermodynamic properties of thesuperconducting phase in the molecular hydrogen under the pressure at 428 GPahas been presented. For the increasing value of the Coulomb pseudopotential,$\mu^{*}\in<0.08,0.15>$, the following results have been obtained: (i) thecritical 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 growsslightly together with the temperature ($[m^{*}_{e}/m_{e}]_{{\rm max}} = 2.2$for $T = T_{C}$).

Strong-coupling description of the high-temperature superconductivity in the molecular hydrogen