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The superconducting state in Carbonaceous Sulfur Hydride (C-S-H) system ischaracterized by the record-high critical temperature of $288$~K experimentallyobserved at $\sim$267 GPa. Herein, we determined the properties of the\mbox{C-S-H} superconducting phase within the scope of both classicalEliashberg equations (CEE) and the Eliashberg equations with vertex corrections(VCEE). We took into account the scenarios pertinent to either the intermediateor the high value of electron-phonon coupling constant ($\lambda\sim 0.75$ or$\lambda\sim 3.3$, respectively). The scenario for the intermediate value,however, cannot be actually realized due to the anomally high value oflogarithmic phonon frequency ($\omega_{\rm ln}/k_{B}=7150$~K) it would require.On the other hand, we found it possible to reproduce correctly the value of$T_{C}$ and other thermodynamic quantities in the case of strong coupling.However, the vertex corrections lower the order parameter values within therange from $\sim 50$~K to $\sim275$~K. For the upper critical field $H_{C2}\sim27$~T, the Ginzburg-Landau parameter $\kappa$ is of the order of $1.7$. Thiscorrelates well with the sharp drop of resistance observed by Hirsch andMarsiglio at the critical temperature. The strong-coupling scenario for C-S-Hsystem is also suggested by the high values of $\lambda$ estimated for ${\rmH_{3}S}$ ($\lambda\sim 2.1$, $\kappa\sim 1.5$), ${\rm LaH_{10}}$ ($\lambda\sim2.8$-$3.9$, $\kappa\sim 1.6$), and ${\rm YH_{6}}$ ($\lambda\sim 1.7$,$\kappa\sim 1.3$) compounds.

Carbonaceous sulfur hydride system: the strong-coupled room-temperature superconductor with a low value of Ginzburg-Landau parameter