It was recently demonstrated on high-quality single crystal that Ce${}_{3}$Pt${}_{23}$Si${}_{11}$ orders ferromagnetically at ${T}_{c}$ $=$ 440 mK. Extensive studies of the physical properties of this compound are reported. In the paramagnetic phase, heat capacity and electrical resistivity measurements on a single crystal confirm a good metal behavior with a residual resistivity of ${\ensuremath{\rho}}_{0}$ $=$ 12.17 $\ensuremath{\mu}\ensuremath{\Omega}$ cm, no Kondo-type anomaly, and a Debye temperature of 280 K, similar to the one of the the isostructural nonmagnetic compound La${}_{3}$Pt${}_{23}$Si${}_{11}$. In the ferromagnetic phase, the easy magnetization axis is the threefold one with a spontaneous magnetization of 0.91 ${\ensuremath{\mu}}_{B}$/Ce at 100 mK. This value differs from the expectations within a cubic crystalline electric field (CEF) model. More surprisingly, the inelastic neutron scattering shows two CEF peaks, while neutron diffraction experiments reveal that the structure remains cubic down to 800 mK. These results are very reminiscent of those of CeAl${}_{2}$. Using the CEF formalism, the fits of the magnetic susceptibility lead to a quadruplet ground state, which is not consistent with the anisotropy found in the ferromagnetic state. This strongly suggests a splitting of the ground state by a dynamical Jahn-Teller effect, which retains the apparent cubic symmetry for static measurements.